Search for a correlation between HiSPARC cosmic-ray data and weather measurements

Transcription

1 MASTER S THESIS PHYSICS COMMUNICATION AND EDUCATION VARIANT Search for a correlation between HiSPARC cosmic-ray data and weather measurements Author: Loran de Vries Supervisor: Prof. dr. Ing. Bob van Eijk, University of Twente Second reviewer: Dr. Els. de Wolf, University of Amsterdam, Institute of Physics National institute for subatomic physics, Amsterdam August 7, 2012

2 Contents 1 Introduction 1 2 Cosmic rays Appetizer: history of cosmic rays Composition of primary cosmic rays Energy spectrum Sources of UHECRs The Hillas plot The GZK energy limit Air shower development Particle flux and composition at sea level Cosmic-ray detection Energy loss in a scintillator Mass per unit area Bethe Bloch formula Photomultiplier Electronics and trigger conditions Trigger conditions HiSPARC data flow Shower data acquisition Pulse heights Event rate Poisson statistics Research question Atmospheric conditions 27 Weather station: Davis Vantage Pro HiSPARC weather software Initialization Connect to weather station Select sensors Measure and send to database Weather variables Temperature Data logger

3 5 Cosmic-ray and weather data analysis Acquiring shower and weather data Number of events per hour MPV of the pulse heights histogram Uncertainty in the MPV of the pulse heights Correlation analysis Correlation coefficient Coefficient of determination Models for the number of events per hour A conventional model using the barometric coefficient An extended linear model Uncertainty in the model parameters Model for the MPV of the pulse heights Correlation between the event rate and weather variables Number of events and weather variables Atmospheric pressure Outside relative humidity Outside air temperature Solar radiation Independence between variables Building the model Selection of model variables A linear model for detection station A linear model using the barometric coefficient for detection station A linear model for detection station A linear model using the barometric coefficient for detection station A linear model for detection station A linear model using the barometric coefficient for detection station A linear model for detection station A linear model using the barometric coefficient for detection station Using temperature as a model variable A linear model for detection station A linear model using the barometric coefficient for detection station Correlation between the MPV of the pulse heights and weather variables Correlation between the MPV of the pulse heights and individual weather variables Correlation between the MPV of the pulse heights and the ambient temperature of the detector Extending the linear model with more weather variables Conclusions 90 Bibliography 92 Samenvatting 95 Acknowledgements 97

4 A Cosmic-ray and weather data analysis software (in English) 99 A.1 Downloading data A.2 Plotting data A.2.1 Event rates A.2.2 Pulse heights A.2.3 Pulse integrals A.3 Correlation analysis A.3.1 Interpolation A.3.2 Least squares fit A.3.3 Correlation coefficient A.3.4 Coefficient of determination A.4 Use at high school B Weather station software - Installation manual (in Dutch) 115 C Data correlation software - getting started guide for high school students (in Dutch) 116

5 Abstract The number of events per hour and the most probable value (MPV) of the PMT pulse heights registered by HiSPARC cosmic-ray detectors fluctuate over time. I have developed linear models that attribute these fluctuations to atmospheric variables. I found a strong negative correlation between the number of events per hour and the atmospheric pressure and a weak negative correlation between the number of events per hour and the outside air temperature. No correlation was found between the number of events per hour and the outside relative humidity or the solar radiation. I have developed a model that describes the fluctuations in the number of events per hour using atmospheric pressure and outside air temperature at sea level. The model resulted in χ 2 r in the range I found a medium correlation between the most probable value of the pulse heights for a three hour period and the temperature of the photomultiplier tube (PMT). The PMT temperature can be described with a linear model that incorporates the outside air temperature and the solar radiation at sea level. I have developed a model that describes the MPV fluctuations using outside air temperature and solar radiation. The model resulted in correlation coefficients in the ranger = 0.54 tor = To acquire weather data I developed LabVIEW software that reads data from a Vantage Pro weather station and sends this to the HiSPARC local database. Moreover, I developed correlation software for high school students using Python. The software requires no prior knowledge of Python itself. High school students can download, plot and analyze HiSPARC cosmic-ray and weather data in the classroom.

6 Chapter 1 Introduction The Earth is constantly bombarded with subatomic particles called cosmic rays. If a cosmic-ray particle (most probably a proton) collides with an air nucleus (probably a nitrogen or oxygen nucleus) they will interact strongly and create new secondary particles (mostly pions). These secondary particles will collide with other air nuclei and create even more particles. In this way, a shower of particles develops in the atmosphere. Most secondaries are not stable particles and will therefore decay. If the energy of the incoming cosmic-ray particle is large enough the shower will reach sea level. More information about cosmic rays is found in chapter 2. At sea level the HiSPARC detectors measure the secondaries and their decay products using scintillation detectors. These detectors are positioned at the rooftops of high schools and universities. They are build by high school students using the resources of HiSPARC (High School Project on Astrophysics Research with Cosmics). The detectors are described in chapter 3. The high school students get the opportunity to be a part of real scientific research. High school students build cosmic-ray detectors under supervision of university staff. Once the detectors are installed on the roofs of high schools or universities, the high school students can analyze shower data for their research projects. HiSPARC focuses on the detection of Ultra High Energy Cosmic Rays (UHECRs). If a shower produced by a UHECR reaches ground level the surface area of the shower can be around 1 km 2. This is approximately the average distance between high schools in a large city. If we determine the density of secondary particles in a shower at several points we can determine the properties of the incoming cosmic ray Figure 1.1: HiSPARC logo [1] using computer simulations. This is the reason that detection stations are grouped in clusters at relatively short distances. Currently we have seven clusters: 1. Amsterdam (NIKHEF) 2. Utrecht (Utrecht university and Utrecht university college) 3. Nijmegen (Radboud university) 4. Leiden (Leiden university) 5. Groningen (Groningen university) 6. Enschede (University of Technology Twente) 7. Eindhoven (University of Technology Eindhoven). These clusters include in total more than 100 HiSPARC stations. From these around 75 are operational [2]. 1

7 The data rate measured by HiSPARC cosmic ray detectors fluctuate over time. We assume that these fluctuations are due to variations in environmental variables such as pressure and air temperature at sea level. This is formulated more precisely in my research question (section 3.5). In this thesis I report on the development of a model that describes the fluctuations observed by detection stations located at Science Park Amsterdam. In order to investigate the influence of weather conditions on HiSPARC cosmic-ray measurements some HiS- PARC detection stations are equipped with a commercial weather station. Such a weather station is installed next to HiSPARC detection station 501 at Science Park. It is described in section 4. Shower data from our cosmic-ray detectors is automatically send to the HiSPARC database using a LabVIEW software interface. At the start of my research project this was not the case for weather data. Although a rudimentary version of the weather software was available my first task was to make weather data acquisition possible using LabVIEW software. Currently, eight HiSPARC high schools 1 send their weather data to the local HiSPARC database using this software: 1. Het Amsterdams Lyceum (station 3) 2. Zaanlands Lyceum (station 102) 3. Nikhef (station 501) 4. Leiden University (station 3001) 5. CSG Prins Maurits Middelharnis (station 3201) 6. Eindhoven University (station 8001) 7. Pius X College Bladel (station 8005) 8. Stedelijk College Eindhoven (station 8006) [3]. The weather station in HiSPARC station 501 located at Science Park Amsterdam became operational at 23 May, 2011 and has been collecting weather data since. In the analysis described in this thesis these data are used. The development of the weather station software is described in section 4.1. The second part of my project was formed by data analysis. In order to do that I had to learn the programming language Python. My principal goal was to search for correlations between shower and weather measurements and with these correlations explain the observed fluctuations in the shower measurements. The methods I used for my shower and weather data analysis are described in chapter 5. The models I developed to describe the observed fluctuations of shower data are outlined in chapters 6 and 7. A secondary goal was the development of analysis software for use by high school students. Currently, the students can access shower measurements for every hour via the HiSPARC website. Data analysis can be done with Excel. I developed additional analysis software that enables high school students to download shower and weather data, plot the data and perform a correlation analysis between variables. Python runs in the background. Apart from knowledge of basic commands high school students do not have to master the Python language in order to use the software. Now this barrier has been removed, it has become possible to perform data analysis in the classroom. The software is described in appendix A. 1 Last check at July 1,

8 Chapter 2 Cosmic rays 2.1 Appetizer: history of cosmic rays Around 1900 a theoretical problem in physics was identified: electroscopes discharged faster than expected. An electroscope is an device for detecting electrical charge (figure 2.1). Figure 2.1: An electroscope [4] When you charge the electroscope, the charge is conducted through the metal onto the leaves at the bottom. The leaves will possess charge of the same sign and therefore they will repel each other. Eventually, the charge will leak off and the leaves will come together again. At the end of the nineteenth century, the knowledge that material consists of atoms was established well enough to explain the spontaneous leak of charge. In 1897 J.J. Thomson discovered the electron in his cathode ray experiments and Millikan indicated the electron in 1909 as the unit of electric charge. The discharge of the electroscope was explained by the idea that the molecules of a gas could be ionized. If the leaves were negatively charged, they would attract positive ions. The ions balance the charge of the leaves and in this way the leaves come together (vice versa for positively charged leaves). This still left the question unanswered of how this ionization of the air around the leaves took place. By discoveries of Röntgen in 1895 (X-rays), Becquerel in 1896 (radioactivity), and the Curies in 1898 (radium) it became clear that radioactive materials produced ionizing radiation and therefore in fact could cause the discharge of the electroscopes. This could partly explain the rapid discharge. The materials of the electroscope could be slightly radio-active and therefore be responsible. This effect could be minimized by shielding the leaves with water and lead. It appeared that the shielding had no effect, therefore, some radiation had to come from an external source. It became the dominant view that the rapid discharge was caused by radiation from radioactive materials in the outer layer of the Earth. This idea could be tested by setting up electroscope experiments at different altitudes and measure the time it would take to discharge from the same amount of charge. The radiation should become weaker, when the experiment is 3

9 carried out farther from the surface of the earth. These experiments were conducted by Theodor Wulf who took his electroscope to the top of the Eiffel tower in 1910 and by Gockel who took his electroscope in a hot air balloon. They concluded from their results that the rate at which their electroscopes discharged did not decrease with altitude, or not as fast as they expected. Figure 2.2: Victor Hess in his balloon [5] In 1912, Hess made several balloon flights and measured the discharge of his electroscope at various altitudes. He noticed, as Gockel had done earlier, that up to a height of 1100 meters no essential variation in the discharge time could be observed. On the morning of August 7, he took off from Außig in Germany to land 200 kilometers farther close to Berlin. During this flight, he measured the discharge at a height of 5350 m. After he had collected data from more than thirty flights he noticed something unexpected. Not only did the radiation not decrease as expected, at heights above the 2000 meters he even measured an increase in the radiation. From this he drew the conclusion that The discoveries revealed by the observations here given are best explained by assuming that radiation of great penetrating power enters our atmosphere from the outside. [6]. This conclusion was not shared by everyone in the physics community. Robbert Millikan was the most critical. He carried out a series of experiments and convinced himself and anyone else who had any doubts about the claim made by Hess. Moreover he coined the name cosmic rays [7] (p. 1 25). 2.2 Composition of primary cosmic rays The Earth s atmosphere is continuously bombarded by cosmic rays. The composition of these so called primary cosmic rays is estimated to consist of 89% protons, 10% alpha particles and 1% heavier nuclei and electrons. The tiny fraction of heavier nuclei consists of mainly lithium, beryllium and boron nuclei [8] (p. 278). 2.3 Energy spectrum The energy spectrum of the primary cosmic rays is displayed in figure 2.3. The flux Φ (in m 2 s 1 sr 1 GeV 1 ) is plotted against the energy E (in ev) per cosmic-ray particle. The energy spectrum above 10 9 ev as displayed in 4

10 figure 2.3 can be described by a power law. More explicitly the flux densityφhas the form: Φ = ae b (2.1) with E the energy of the cosmic rays (in ev) a and b are numerical constants. In figure 2.3, b has has a value of 2.7 in the range 10 9 ev < E < ev. At E the spectrum steepens. This point is called the knee. b has the value of 3.1 for the range ev < E < ev, where the spectrum flattens. This point is called the ankle. Note that the cosmic-ray energy spectrum ranges over more than thirteen orders of magnitude. Moreover, the flux ranges over thirty orders of magnitude. When the energy increases with a factor ten, the flux drops roughly a factor This is huge. It means that we detect a particle with an energy of ev once per second per square meter. However, we detect a particle with an energy of ev once per year per square kilometer! [9] Figure 2.3: The cosmic-ray energy spectrum [9]. The unit of flux needs some clarification. Usually, flux is the number of particles passing through a surface area per second (s 1 m 2 ). The cosmic-ray flux is also given per space angle. This space angle in steradian (sr 1 ) is defined analogous to the way the radian is defined. In a circle the radian is defined as the angle where the arc length is equal to the radius of that circle (figure 2.4 left). A circle has circumference 2πr. One turn around a circle from the center is therefore equal to an angle of 2π radians. For a sphere the steradian is the space angle where the 5

11 Figure 2.4: The definition of the radian and the steradian [10]. surface area of that sphere is equal to the radius of the sphere squared (figure 2.4 right). The surface area of a sphere is given by 4πr 2. The space angle of a sphere is therefore equal to 4π steradians [10]. Finally, the flux is also given per energy bin (GeV 1 ). Cosmic rays with energies ranging from ev mostly originate in the Sun and are therefore called Solar Cosmic Rays. Cosmic rays with energy smaller than 10 7 ev are stopped by interactions in the Van-Allen belts of the Earth. Therefore, most of them do not reach the Earth. This is why a flattening in the energy spectrum towards lower energies is visible. Particles with energies above ev are called Galactic Cosmic Rays and are thought to originate in our own galaxy. Above ev (the knee in the energy spectrum) is the regime of the Ultra- High Energy Cosmic Rays (UHECRs). In theoretical models these cosmic ray particles are accelerated in pulsars or shockwaves in supernova remnants [11] (p. 1-12) The most energetic particle ever detected has an energy of ev [12]. Before the development of particle accelerators in the 1930s cosmic rays were the only source of energetic particles available. Our most powerful accelerator, the LHC, has an energy limit that lies at ev. This is much lower than the highest energy cosmic rays we have observed. Therefore, to understand the highest energy particles, cosmic ray research is indispensable. 2.4 Sources of UHECRs Current models describing possible sources for UHECRs can be divided into three categories. The first category consists of the so called bottom up models. In these models low energy particles are accelerated up to high energies by energetic astrophysical objects. The acceleration takes place either in shockwaves by a process called first order Fermi acceleration, or the particles are accelerated by varying electromagnetic fields. The second category consists of the so called top down models. In top down models cosmic-ray particles originate from the decay of supermassive particles (often called X particles), with energies > ev, that originated in very high energy processes in the early Universe. Finally, the third category consists of so called hybrid models, which are combinations of the first two categories The Hillas plot Figure 2.5 contains the so-called Hillas plot which shows the distribution of possible cosmic ray sources as function of both the magnetic field strength and the size of the accelerator. The relation between these quantities can be derived as follows. One can make rough estimates for the possible energies an accelerator can achieve. A charged particle that moves in a magnetic field will rotate in a circle with radiusr given by: r = m 0γv ZeB with m 0 the particles rest mass, γ the relativistic Lorentz factor, v the velocity of the particle perpendicular to the magnetic field, Z its atomic number, e the elementary charge, and B the magnetic field strength [8] (p ). The maximum attainable energy for a particle accelerated by Fermi acceleration can be estimated. As long as a particle remains in the acceleration zone, it can acquire more energy. When the particle leaves this zone, i.e. if the particle (2.2) 6

12 takes a path with a radius larger than the Larmor radius, the particle will have the maximum energy that can be acquired in this accelerator. In the following calculation we will let the Larmor radius of the particle approach the size of the acceleration zone to get an expression for the maximum energy acquired by a particle, traveling in a medium with magnetic fieldb. We start with formula (2.2) of the Larmor radius. The energy of the particle is: E = γmc 2 (2.3) whereγ is the Lorentz factor,γ = (1 v v c ) 1 2 2,mis the mass of the particle, andcis the speed of light. With formula (2.3) andβ = v c we can rewrite the Larmor radius (2.2) and solve for the energye: E = ZeBrc β (2.4) The acceleration zone will have length of order 2r; substituting this in formula (2.4) and using the fact that β 1, we obtain E max 2ZeBrc (2.5) This expression for E max is only an estimate of the maximum energy for a particle traveling in a medium with magnetic fieldb. It is sometimes called the Hillas criterion, after A.M. Hillas who first made this analysis in The maximum attainable energy for a particle accelerated through the magnetic field generated by a pulsar can also be estimated. One of Maxwell s equations in free space reads (in Gaussian units): E = 1 c d B dt (2.6) where B is the magnetic field of the pulsar, E the generated electric field andcthe velocity of light. From a dimensional analysis we can write formula (2.6) as: E R B cp E = BR cp with P the period of the pulsar and R its radius. We want to formulate an expression for the maximum energy E max to which a particle can be accelerated by a pulsar. EnergyE is chargeze multiplied by an potential difference V : (2.7) E = ZeV (2.8) We can write a potential difference in terms of the electric field. The electric field can be described in units of [ V m ]. The radius of the pulsar has units of length. Thus the electric field multiplied by the radius of the pulsar will have units of a potential difference. Therefore the expression for the maximum energy E max, to which a particle can be accelerated, will be of the form: E max = ZeRE (2.9) If we substitute formula (2.7) into the expression for the maximum energy, formula (2.9) usingp = 2π ω we obtain: E max ZeR2 Bω c (2.10) where we indicate with that this is only an estimate for the maximum attainable energy of a particle accelerated by the magnetic field of a pulsar. From equations (2.5), (2.10) and equations based on similar reasoning, we can 7

13 Figure 2.5: In the Hillas diagram the magnetic field strength of possible acceleration sites is plotted against the accelerator size [13], (see text) make the plot in figure 2.5. In this figure, the logarithm of the magnetic field strength (in Gauss) is plotted against the logarithm of the accelerator size (in kilometers). The line labeled protons (1 ZeV) indicates that in the area above this line protons can not be accelerated to an energy larger than ev. Similarly, the line labeled protons (100 EeV) indicates that in the area above this line protons cannot be accelerated to an energy larger than ev. The line 100 Fe EeV indicates that in the area above this line iron nuclei cannot be accelerated to an energy larger than ev. The diagram shows that if you want to accelerate particles to a high energy you need an enormous acceleration zone, or a very large magnetic field, and ideally both. The higher the energy of the cosmic ray, the more energetic the source must be (or the primary is accelerated even more along its way towards us). For the highest observed cosmic-ray energy ( ev) an accelerator is needed that reaches energies of at least ev. As these accelerators stand at a larger distance from Earth the sources need to be even more energetic because the particles loose energy while traveling towards the Earth in interactions with interstellar matter. Moreover, charged particles will be deflected in interstellar magnetic fields. The traveled distance therefore becomes even larger, and the accelerator must be of an even higher energy, or must be at a closer distance. This forms a big problem. Radio galaxies and active galactic nuclei can only produce particles with energies a factor 100 smaller than the observed UHECRs. Looking at our options we need to bring up more energetic candidates that can account for these high energies [14] (p ), [15] (p.19-21), [16], [17], and [18]. 8

14 2.4.2 The GZK energy limit Greisen, Kuzmin and Zatsepin showed that an upper limit should exist on the energy of the UHECRs, because UHECRs with energies above ev will interact with the microwave background radiation (MBR). Around years after the Big Bang, the Universe was cool enough for recombination to occur: hydrogen and helium nuclei captured electrons to form neutral atoms. From this point in tim, the Universe has become transparent because the photons practically stopped interacting with charged matter. These photons are known as the microwave background radiation. The photons are cooled due to the expansion of the Universe and are present everywhere in the Cosmos with a characteristic black body spectrum that corresponds to a temperature of 2.7 K [19]. In the rest frame of the cosmic rays these MBR photons seem to be high energetic gamma photons. For UHECRs these gamma rays can have enough energy for pion production: γ MBR +p + n+π + (2.11) γ MBR +p + p+π 0 (2.12) These interactions 1 take place until the UHECR do no longer have enough energy for pion production ( 140MeV ). UHECR-photons can lose energy through pair production 2 : γ MBR +γ e +e +. (2.13) The energy spectrum for UHECRs is shown in figure 2.6 measured by HiRes and AGASA. In this figure the flux is multiplied by E 3 to make the changes more apparent. Not many cosmic rays have been detected above the GZKlimit (in figure 2.6 we can see a few events above the GZK-limit). If the GZK limit exist the sources where UHECRs (with energies above the GZK limit) originate must be relatively close by. A proton with an energy of ev has a mean free path around 10 Mpc. After 50 MPc the energies of UHECRs should have dropped below the GZK-limit. This limits the location of the sources of these UHECRs to our Virgo Supercluster [20] (p.294). Figure 2.6: The UHECRs energy spectrum [21] (p. 14) 1 The cross section for these processes is around 250 microbarns [8] (p.340). 2 The cross section for this process is around 0.01 barn. This is larger than the cross section for pion production. However, the pion process consumes more energy because the rest mass of the pion is so much larger than the rest mass of the electron [8] (p.341). 9

15 2.5 Air shower development Figure 2.7: Schematic diagram of the development of a shower in the atmosphere [22]. As mentioned in section 2.2 the incoming primary cosmic rays consist for 89% out of protons, 10% alpha particles and 1% heavier nuclei and electrons. If these charged particles enter the upper atmosphere, the primary cosmic rays collide inelastically with an individual nucleon in an air-particle nucleus (probably from an oxygen or nitrogen atom) and they will interact. The point of first interaction for a proton is on average around 15 km above sea level (figure 2.9). In this strong interaction between the quarks of the particles new particles are produced (mostly pions and also kaons because they are the lightest particles made out of quarks). These are called secondary particles. If these secondary particles still have enough energy they will generate new particles through collisions. In this way an air shower will form and will produce more particles with every interaction, which is displayed schematically in figure 2.7. This process continues until the energy per secondary particle drops below the pion s rest mass ( 140MeV ). At a certain depth X max the number of particles in the shower will be at a maximum. After this maximum the number of particles decreases. This is displayed in the longitudinal shower profile (from the point of first interaction to sea level) of figure 2.8b. The lateral shower profile (away from the shower core) for sea level is displayed in figure 2.8a. If many of the secondaries reach ground level this is called an Extensive Air Shower (EAS) of particles [23]. Mesons are not stable particles and will decay via the decay modes listed in table 2.1. Only the most probable modes are shown along with the branching ratio. Many pions and kaons decay during their flight since they have mean lifetimes of the order 10 8 s, whereas the muon has a lifetime of s. With γ > 20 a muon will reach the earth s surface. From the decay modes in table 2.1 it therefore follows that at sea level, we are mainly left with electrons, muons and photons [26] Particle flux and composition at sea level The particle fluxes measured at sea level altitude are listed in table 2.2. Of the electron flux, % are positrons, above 0.1 GeV (but only 5% at 1 MeV) For the photon flux, these values are theoretical values as measurements are inadequate [27]. 10

16 Decay Mode Branching ratio π + µ + +ν µ ± % π µ +ν µ ± % π 0 γ +γ ±0.034 % π 0 e + +e +γ 1.174±0.035 % K + µ + +ν µ 63.55±0.11 % K + π + +π ±0.08 % K + π + +π + +π 5.59±0.04 % K + π 0 +e + +ν e 5.07±0.04 % K + π 0 +µ + +ν µ ± % K + π + +π 0 +π ± % K modes are charge conjugates of the decay modes above. µ + e + +ν e +ν µ 100 % µ e +ν e +ν µ 100 % Table 2.1: Decay modes of secondary particles in a shower [26] 11

17 Figure 2.8: (a) Lateral and (b) Longitudinal shower profile for an incoming proton with energy of10 19 ev [24]. Figure 2.9: Schematic diagram of the development of a shower in the atmosphere. [8] (p.149), [25]. 12

18 E (GeV 1 ) I muon I electron I photons I protons Table 2.2: The secondary particle flux detected at sea level (inm 2 s 1 sr 1 ) 13

19 Chapter 3 Cosmic-ray detection A HiSPARC detector station consists of two or four individual cosmic ray detectors. A single detector consists of a scintillation plate, a light guide and a photomultiplier tube (figure 3.1). Figure 3.1: Schematic diagram of the HiSPARC detection setup. [28]. The scintillation material is a plastic doped with fluor. If a charged particle (e.g. a muon or an electron) with sufficient energy traverses the scintillation plate it brings fluor atoms in an excited state. The energy is re-emitted in the form of photons. These photons travel through the scintillator plate and the light guide until they reach the photomultiplier tube (PMT). The PMT converts the photon signal into an electric signal [29] (p.174). In a two detector setup, the detectors are placed 6 8 meters apart (figures 3.2 and 3.3). The four detector setup is placed in an equilateral triangle (figures 3.2 right and 3.4). Along with the detectors a GPS antenna is placed to acquire an accurate timestamp for every event. 3.1 Energy loss in a scintillator When a charged particle traverses the scintillation plate a fraction of its total energy is transferred by ionizing the material. For a muon the energy loss is in the order of 1. Charged particles loose their energy by ionizing the medium. The energy loss is expressed by the so called stopping power de dx of the medium. This is the energy a particle has lost after traversing 1 cm of material. By convention the stopping power is expressed not in terms of 14

20 Figure 3.2: Schematic diagram of a set of two (left) and a set of four (right) HiSPARC detectors on a rooftop. [30] (p.9 10). Figure 3.3: A set of two HiSPARC detectors on a rooftop. [30] (p.7). Figure 3.4: A set of four HiSPARC detectors (station 501) on a rooftop. length x, but in terms of traversed mass per unit of cross sectional area (X). This way of describing length needs some clarification [8] (p.51). Mass per unit area A centimeter of air will absorb less radiation than a centimeter of water, because the densities of the materials differ (ρ water /ρ air 800). However, if the particle travels through 8 meter of air the energy loss becomes comparable with the loss in 1 cm water. Hence, for the energy loss we have to take both the density ρ of the material and its thickness h into account. As a consequence it is customary to describe the energy loss in a 15

21 radiation absorber in a way independent of the density of the material. Figure 3.5: Definition of mass per unit area [7] (p.234), (see text). Consider a prism with 1 cm 2 of cross sectional area that is cut from a radiation absorber with thicknessh(figure 3.5). The mass of this prism is the mass per unit area ( g / cm 2 ). For constant density this mass is the volume (1 h = h) times its density ρ. More formally the so called interaction depth X is defined as the traversed mass per unit cross sectional area. X = ρ(h) dh (3.1) This definition is independent of the traversed material and allows for a comparison of the absorbing effects of a passage through lightyears of interstellar medium, to a passage through a few centimeters of scintillation material [7] (p ), [31] (p.18-19) [32]. MeV has unit g and is de- cm 2 Bethe Bloch formula Using the mass per unit area the stopping power of material de dx scribed by the Bethe Bloch formula: de dx = K z2z 1 A β 2 [ 1 2 ln ( 2me c 2 β 2 γ 2 T max I 2 ) β 2 δ(βγ) ] 2 withz the charge number of the incident particle,z the target charge number,athe target mass number,β = v c the relative velocity parameter, γ = 1 1 β 2,T max the maximum kinetic energy transfer in one collision with an electron, I the average ionization energy of the target andδ the so called density correction. The constantk is given by: (3.2) K = 4πN A r e 2 m e c 2 (3.3) with N A avogadro s number, r e the classical electron radius, m e c 2 the electron rest energy. The minus sign in de dx makes the stopping power a positive number. Moreover, the minus sign indicates that a particle loses kinetic energy. In figure 3.6 the stopping power de dx of electrons and muons in a polyvinyltoluene scintillator is shown. The stopping power in units of MeV g is plotted against βγ. βγ is used to make the plot independent of the type of cm 2 particle 1. The minimum stopping power lies around βγ 3.5. For electrons this corresponds to 1 MeV and for muons this corresponds to 325 MeV. These are called minimum ionizing particles (MIPs). The Bethe Bloch formula describes the average energy loss, but not the energy loss for an individual particle. Not every charged particle that traverses a scintillation plate will lose the same amount of energy. If the particle comes in close encounter with the atoms in the material it will lose more energy and vice versa. This results in statistical fluctuations of the mean energy loss. The fluctuations are described by a so called Landau distribution. An example of such a distribution is shown in figure 3.7 [33] (p ), [23]. 1 The momentumpof a particle is given by: p = γm 0 βc hence βγ = p m oc with m 0 the rest mass of the particle. 16

22 Figure 3.6: Stopping power of electrons and muons in a polyvinyltoluene scintillator. [23]. Figure 3.7: Landau distributed energy loss. Figure adapted from [34] (p. 9). 3.2 Photomultiplier A photomultiplier tube (PMT) converts a photon signal into an electric signal. A PMT consist of a photocathode, several electrodes called dynodes and an anode (figure 3.8). If a photon strikes the photocathode an electron will be emitted by means of the photoelectric effect. Due to an applied high voltage the electron is accelerated towards the first dynode. When the electron hits the dynode with its increased kinetic energy it transfers some of its energy to the electrons of the dynode. This results in secondary emission of several electrons. To every following dynode a higher voltage is applied than the previous one. This causes the electrons to be accelerated towards every next dynode. This acceleration and emission of electrons continues until sufficient charge hits the anode to give a current of several millivolts that can be measured. 2 The signal is send via the readout electronics to a computer [35] (p.169). The performance of the photomultiplier is influenced by its ambient temperature. The dark current (a small current caused by electrons emitted by the photocathode unrelated to the photon signal) increases with temperature. This background is suppressed in the HiSPARC detector by measuring only coincidences. The photocathode is sensitive to temperature too. Leo [35] claims that this is explained by the fact that the Fermi level and resistance of the cathode will change with temperature. The specifications of the photomultiplier mention a temperature coefficient of 0.5% C 1 of the PMT gain (amplification factor). A higher temperature will mean less photons that are emitted at the cathode, less charge will reach the anode and we will measure a lower signal [35] (p.196), [37], [38]. name. 2 The name photomultiplier is not well chosen, since the device multiplies electrons, not photons. An electronmuliplier might be a better 17

23 Figure 3.8: Schematic diagram of a photomultiplier tube. [36]. 3.3 Electronics and trigger conditions The analog pulses coming from the PMTs have to be digitized to allow for signal analysis using a computer. To analyze the signal with a computer. This is done by connecting each PMT with a HiSPARC electronics box. Each box has two inputs that contain four 12-bit ADCs (each channel has two ADCs). The ADCs measure voltages in the range 0 to 2 V. In figure 3.9 the electronic boxes are shown for a four detector setup. The two boxes act as a master-slave unit. A single box communicates with two cosmic-ray detectors (PMT 1 and PMT 2). The data is received (input) and the high voltage at the PMT-base can be adjusted (control).the master box also has an input for the signal from the GPS antenna (this input is situated on the back of the master box and is therefore not shown in figure 3.9). Figure 3.9: HiSPARC II version of the electronics. [28]. If the incoming signal meets certain trigger conditions (section 3.3) the ADC is read, along with a GPS time stamp and send to the HiSPARC computer through USB. An electronics box is equipped with a FPGA circuit (Field- Programmable Gate Array ). With this FPGA a user can control parameters such as the trigger levels, the high voltages of the individual PMTs and the coincidence time window. An electronics box has an internal memory that can only store the data of a few events. The computer can store events locally and sends data to the HiSPARC server. This means that if the computer is turned off or restarted, data is lost [39] (p.5). 18

24 Trigger conditions Secondary particles that are produced in the same shower arrive approximately at the same time at the detector. To make sure we only measure those particles, we use another scintillation detector (or more) in coincidence mode. This means that the electronics only registers an event if one (or more) detectors give a signal within a time window of 1.5 µs. We also want to make sure that a signal from the PMT corresponds to a real particle and not to some coincidental emission of electrons. Therefore, the electronics registers an event only if the amplitude of the pulse is above 70 mv. With this trigger condition a single scintillation detector has a detection rate of about120hz (this includes signals from particles that do not come from showers). For two detectors placed 6 8 m apart we measure an event rate around 0.3 Hz. This means that two signals were registered above 70 mv, within a time window of 1.5 µs. For a four detector station we require two signals above this high threshold of 70mV or three signals above30mv. This results in a trigger rate of about0.7hz. With these trigger conditions the probability that these coincidences are not due to particles that originate from the same shower is close to zero [23]. Figure 3.10: HiSPARC data flow [40]. HiSPARC data flow Shower data and weather data is send from the HiSPARC computer to the HiSPARC database. Three different detector types can be stored, each with its own table format:: shower detector (see section 3.4) weather station (see section 4) lightning detector It is speculated that there is a correlation between lightning strikes and the amount of secondary cosmic-ray particles. With the HiSPARC detectors, it might be possible to measure the correlation. Currently a lightning detector from the company Boltek is made operational at Nikhef. This detector registers the angle and the distance from the lightning strike. There are plans to place lightning detectors in Groningen and Eindhoven too. With these detectors operational, it will become possible to triangulate the position of the lightning strike 19

25 (the distance to the strike, from a single detector, has a relative large uncertainty, in this way the uncertainty of this measurements can be greatly reduced). 3.4 Shower data acquisition On the HiSPARC computer the software HiSPARC II DAQ 3 is used to control the electronics boxes. The graphical user interface (GUI) is written using LabVIEW. HiSPARC DAQ (figure 3.11) enables you to read the electronics boxes and to control the FPGAs. Via the GUI, the user can change settings such as the thresholds and the high voltages of the individual PMTs. One can also look at the detector response. An example is shown in figure Here two pulses are visible. These pulses are the result of photons generated in the scintillation plate that are converted into an electronic signal by the PMT and send through the electronics where it is finally digitized by the ADC. Along the way the pulse width broadens. We can see in both signals a second dip after the large dip which indicates that probably more than one particle traversed the scintillation plate. The minimum value of the signal is the pulse height of an event (figure 3.12). The pulse height has a negative value because of the negative charge that reaches the anode of the PMT. The pulse is registered in ADC counts. Raw ADC units can be converted to millivolts units by V = 0.57x+113. This unit is used on the vertical axis of figure The shower data that is processed by LabVIEW and send to the HiSPARC database is listed in table 3.1. Figure 3.11: Screenshot of HiSPARC II DAQ 3.04 the Data acquisition software. Figure 3.12: Detector response. Two PMTs produced a signal Pulse heights The minimum value of the pulse registered by the ADC is the pulse height of an event (figure 3.12). If we gather enough data a pulse height histogram can be plotted. On data.hisparc.nl the pulse height histogram for a day is displayed (figure 3.13). For a four-detector station it is important to realize that the trigger condition is satisfied for every event (two pulse heights above 70 mv or three pulse heights above 30 mv within an interval of 1.5 µs) and not for every registered pulse height. If the trigger condition is met all four PMTs are read. If two pulse heights were above 70 3 This software was developed by Jeroen van Leerdam et al. 20

26 Variable (s) Description Unit timestamp Unix timestamp in GPS time. seconds extended timestamp Unix timestamp in GPS time. nanoseconds nanoseconds part of the timestamp data reduction trigger pattern baseline nanoseconds = extended timestamp minus (timestamp 10 9 ) True or False if LabVIEW erased some of the data of the trace. Binary number representing the trigger conditions. Reference point for the trace of every plate ( 200 ADC counts). nanoseconds - - ADC counts standard deviation of baseline - ADC counts number of peaks pulse heights The number of peaks in the trace determined by LabVIEW Maximum pulse height of the trace minus the baseline. - ADC counts integrals Integrated trace. ADC counts nanoseconds event rate Triggered events per second averaged over the last 90 seconds Table 3.1: Variables stored in the events table of the HiSPARC database. [1]. Hz Figure 3.13: Pulse height histogram of station 501 January 12, [41]. mv than the pulse heights measured by the other two PMTs do not have to be above 70 mv. This is how pulse heights below the lower trigger level get registered. Not all photons that are generated in the scintillation plate will reach the photomultiplier. The position of impact will determine the distance traveled by the photons through the scintillation plate to the PMT as can be seen in figure If the traversed distance and/or the number of reflections increase, less photons will reach the PMT. This can be due to absorption or because the photons do not arrive within the coincidence interval of 1.5µs [42] (p ). 21

27 The electrons and muons that traverse a scintillation plate are minimum ionizing particles (MIPs). The energy loss of these MIPs in the scintillator are therefore Landau distributed (look back at figure 3.7). If a MIP loses more energy in the scintillation plate more photons will be produced and we will observe a higher pulse height. Therefore the pulse height will be proportional to the energy loss of the MIP and we expect the pulse heights of the MIPs to be Landau distributed too. The peak visible in figure 3.13 is called the Most Probable Value or (MPV) of the pulse heights. It does not look exactly like a part of the Landau distribution shown in figure 3.7. This is because we have to take other factors into account. More on this is described in section 5.3 [1]. Figure 3.14: Three possible photon paths through a HiSPARC detector. Despite of multiple reflections the left photon signal will not reach the PMT, whereas the other two will reach the PMT. [42] (p. 83) Event rate If the trigger conditions are met we have an event, the PMT registrations are saved and HiSPARC DAQ automatically calculates the event rate (in Hz) as a running average for the last 90 seconds. Sometimes the HiSPARC detector computer is rebooted. If this happens no data can be send to the database. If the computer was turned off the event rate becomes zero and then slowly increases to the actual value for the event rate. On data.hisparc.nl the number of events per hour is plotted for every day. Figure 3.15: Event rate of station 501 January 12, [41]. 22

28 Poisson statistics Cosmic-ray events occur at random times at a constant rate. Moreover, we assume that the signals produced by different cosmic rays are independent of each other. This makes sense since the time between events (around a second for a 4-plate station) is much larger than the duration of the signal (around 6 µs). Since these requirements are met the probabilityp k of observing exactlyk events in a given time interval is given by Poisson statistics: P k = λk k! e λ (3.4) with λ the expected number of events in the chosen time interval and e Euler s number ( ). k has to be an integer or zero (we cannot measure 1.2 events). The mean value is equal to λ and the variance is also equal to λ. So if we observe N events we expect the Poisson distributed events to fluctuate around N with standard deviation σ = N [43], [44]. If the number of events increases the Poisson distribution starts to look like a normal distribution, as can be seen from figure We can use a normal distribution as an approximation of the Poisson distribution to fit our data. Figure 3.16: For increasing occurencesk the poisson distribution begins to resemble a normal distribution. As a rule of thumb this approximation can be used if the number of events k is larger than 20 [45]. In figure 3.17 the number of events in a time interval of 90 seconds for a whole day (July 21, 2011, station 501) is plotted in a histogram. On the y-axis the normalized number of eventsn norm is shown: N norm = N bin N total d bin (3.5) with N bin the number of events in a bin, N total the total number of events and d bin the bin width. If this normalization is used the integral under the histogram is equal to 1 [46]. Now a normal probability density can be fitted to the histogram (dashed red line of the data in the histogram in figure 3.17). We see that the standard deviation is approximately given by N: σ measured = (3.6) σ theory = N = = (3.7) 23

29 Figure 3.17: Histogram of the number of events per 90 seconds for station 501 on July 21, 2011 (green bars) along with a Gaussian fit (red dashed line). 3.5 Research question Figure 3.18: Event rate fluctuations (for one hour intervals) of detection station 501 at Science Park Amsterdam. In figure 3.18 the fluctuating number of events per hour for detection station 501 is shown. The most probable value (MPV) of the pulse heights registered by HiSPARC cosmic-ray detectors fluctuates too. In figure 3.19 the fluctuating MPV-value for plate 1 of detection station 501 is shown (calculated for three hour intervals). Ideally we want our detection setup not to be sensitive to large fluctuations. The Earth is bombarded with cosmic rays at a constant rate, so ideally large fluctuations or a periodic pattern in the event rate should not exist. In figure 3.18 the event rate is clearly not constant. Moreover, most secondaries that traverse our detector have approximately the same mean energy therefore the energy loss in a scintillation plate for these ionizing particles 24

30 Figure 3.19: MPV fluctuations of the pulse heights (for three hour intervals) registered by scintillation plate 1 of detection station 501. (e.g. an electron or muon) should also be nearly constant. Therefore the MPV of the pulse heights should not fluctuate this much. However, this is not the case. Since we do not expect that these fluctuations are due to the secondary particles themselves we can look at environmental factors such as weather conditions. To investigate the influence of weather conditions on HiSPARC cosmic ray measurements some HiSPARC detection stations are equipped with a professional Vantage Pro or Vantage Pro 2 weather station. This device is described in section 4. Shower data is automatically send to the HiSPARC local database through a LabVIEW interface. For weather measurements this was not the case. Therefore the first part of my research project was formed by the development of such a LabVIEW interface (the software is described in section 4.1). The weather station software is now operational and since 23th of May, 2011 data is collected at Science Park Amsterdam, connected to detection station 501. In the second part of my thesis research project I developed linear models that describes the fluctuations of the number of events per hour and the MPV of the pulse heights (calculated for three hour intervals). In my models the observed fluctuations are described using atmospheric variables. In order to conduct this analysis I had to learn the programming language Python. My goal was to search for a correlation between shower and weather variables and with this correlation explain the observed fluctuations in the shower measurements. Research question To what extent do weather circumstances influence cosmic-ray data measured with HiSPARC cosmic-ray detectors? Subquestions Is there a correlation between the event rate measured per hour by HiSPARC cosmic-ray detectors and weather variables? Is there a correlation between the most probable value of the pulse heights (for three hour intervals) measured by HiSPARC cosmic-ray detectors and weather variables? 25

31 A secondary goal was the development of analysis software intended for use by high school students. Currently, students can access shower measurements for every hour via the HiSPARC website and data analysis can be done with Excel. I developed analysis software that enables high students to download shower and weather data, plot this data and perform a correlation analysis between variables. Python runs in the background. Apart from knowledge of basic commands high school students do not have to master the Python language in order to use the software. Now this barrier has been removed, it has become possible to perform data analysis in the classroom. The basic structure of the correlation analysis software is described in appendix A. The software can be downloaded from [47] or from Github [48]. The software consists of several Python scripts that can be modified if the user wishes to do so. They can also serve as examples for the analysis high school students can conduct on their own. For high school students I wrote a quick start guide which is included as appendix C. 26

32 Chapter 4 Atmospheric conditions Very soon after the discovery of cosmic rays it became clear that atmospheric conditions influence the number of secondary particles we detect at sea level. In 1926 Myssowsky and Tuwin [49] discovered time fluctuations that were attributed to pressure variations. This is called the barometric effect. These findings were confirmed with higher precision by Steinke in 1929 [50]. The barometric effect can be understood as an absorption effect. The atmospheric pressure is a measure for the air mass above the detector. The higher the pressure, the more material to stop the development of the shower and consequently, less particles are measured at sea level. This effect is enhanced by the higher altitude of the first collision of the primary cosmic ray particle in the atmosphere. Consequently, there is an anticorrelation between the event rate and the atmospheric pressure. The anticorrelation between the number of events per hour and the atmospheric pressure is shown in figure 4.1. Figure 4.1: The number of events per hour and the atmospheric pressure measured by detection station 501 in July, The temperature effect on the event rate was discovered about 10 years later. It is a much smaller effect than the barometric effect. Dorman [51] (p.10, 288) and James [21] (p.39, 42) offer the following explanation. If the 27

33 temperature of the atmosphere becomes higher, the atmosphere will expand 1. Consequently, it was expected that less particles would reach sea level. However, a positive temperature effect was measured. This is because if the temperature rises, the upper atmosphere expands and its density will become less. Hence the amount of pions that are captured by air nuclei becomes less and more pions will decay into muons, leading to more events at sea level: a positive effect. Hence the temperature effect is rather complicated. In addition to the temperature profile for the whole atmosphere, one has to know the distribution of pions, whereas HiSPARC only measure the temperature at sea level. If we want to make corrections on the measured event rate we need to monitor atmospheric conditions by installing a weather station near our cosmic-ray detection station. For this, the weather station Vantage pro and its successor Vantage pro 2 from Davis [52] were selected, which were installed at about twenty high schools and universities in the Netherlands six years ago. Shower data is send to the HiSPARC database with the use of LabVIEW software and python scripts. Davis developed its own software WeatherLink that enables you to display and store data on your computer. However, WeatherLink does not automatically enable us to do the same as the LabVIEW software. Therefore, it was decided to develop our own weather station software with LabVIEW by using a library with functions (dll) that was made available by Davis. Floor Terra, a student at NIKHEF designed the first rudimentary version of the weather station data. In January 2010 I was assigned to complete his work. Moreover I developed a software installation manual that is included as Appendix B. The basic structure of the software is described in section 4.1. The software itself along with its documentation can be found at [47]. The LabVIEW source code can be downloaded from [53]. Weather station: Davis Vantage Pro 2 The Vantage Pro system consists of two parts: an Integrated Sensor Suite (ISS) that is installed on the roof (figure 4.2 below and figure 4.3) and a console (figure 4.2 above) that collects the data and sends it to the HiSPARC computer. There are wireless and cabled versions of the sensor suite. The wireless model is equipped with a solar panel. Unfortunately, it appeared that after six years some of the solar panels could no longer recharge the 3 volt battery in periods during which there was not much sunlight. Therefore it is recommended that the new purchased weather stations have to be cabled. At Nikhef, the Amsterdams Lyceum and the Zaanlands Lyceum we installed our own adapter with the non cabled systems. This solved solved the problem of recharging the battery. The standard sensor suite has sensors for rain, air temperature, wind (speed and direction) and relative humidity. The temperature and humidity sensors are shielded from sunlight. The plus version of the sensor suite also has sensors that measure the solar radiation and the ultra-violet (UV) radiation. All HiSPARC weather stations are plus versions. The console of the system has its own sensors for the measurement of the internal local temperature and relative humidity and atmospheric pressure. Apart from these direct measurements the console calculates from these measurements the evapotranspiration rate, heat index, dew point and wind chill. More information about these variables is listed in section 4.1. In addition, the console displays time, moment of sunrise and sunset, moon phase and weather reports [54]. 1 In my opinion this should not always be true. Qualitatively we have: P V = constant T therefore the volume only increases if the pressure stays constant 28

34 Figure 4.2: The Vantage Pro 2 receiver, [55] and [54] (p.1). Figure 4.3: The vantage pro 2 sensor suite on the rooftop of the NIKHEF (station 501). 29

35 4.1 HiSPARC weather software The HiSPARC weather station is controlled with a LabVIEW application. The basic structure of the software is outlined in the flowchart shown in figure 4.4. The software can be divided into four parts: Initialization Connect to weather station Select sensors Measure and send to database Figure 4.4: Basic structure of the weather station software. Initialization In the initialization phase the initial settings for data readout by the wheather station is retrieved from a file weather.user.settings.ini : COM port number Baud rate Start in data acquisition (daq) mode (True/False) Station ID These settings are also displayed at the front panel (figure 4.5). Connect to weather station In this phase the COM port specified in the initialization file is opened and the units for the weather variables are specified. We have chosen to use the factory chosen units (inch, degree Fahrenheit, mile per hour, mile). In the measure phase we convert them manually to more standard units (millimeter, degree Celsius, meter per second, and meter). In addition, the rain collector type is specified. Finally the dll version, weather station model number, software creation date and software version number are displayed on the front panel (figure 4.5). 30

36 Figure 4.5: Screenshots of the front panel of the weather stations software with a tab that displays the weather station settings (above left), a tab that displays the error settings (above right), a tab that displays current weather data (below left) and a tab where weather data is graphed for the last hour and the last 24 hours. Select sensors In this phase the sensors that are listed in the initialization file are displayed on the front panel. All available data is send to the database, the readings of which sensors the user decides to display on the front panel does matter. If the user changes the number of sensors it wants to display (on the settings tab figure 4.5) and presses save this information is overwritten in the initial settings file. Measure and send to database The measure phase is schematically described in figure 4.6. Weather data is read from the Vantage pro console, converted to standard units and the wind chill (using temperature and wind speed) and dew point (using temperature and relative humidity) are calculated. All data is displayed on the front panel (figure 4.5). Every once in a while, the difference between the computer time and GPS time (in seconds) is calculated by the HiSPARC DAQ software using the GPS antenna. This number is saved as plain text. We can use this difference to convert a computer weather timet PC into GPS timet GPS : T GPS = T PC. (4.1) All data is compacted in a weather data string that is send to the HiSPARC database. Weather variables The fifteen weather variables that are stored in the HiSPARC database are listed in table 4.1. Four variables (temperature inside, relative humidity inside and atmospheric pressure) are measured/registered by the Vantage Pro receiver that is located inside next to the HiSPARC computer. Seven variables (temperature outside, relative humidity outside, wind direction, wind speed, solar radiation, uv index and rain rate) are measured in the 31

37 Figure 4.6: Flow chart of the measure phase in the weather station software. sensor suite placed on the rooftop. Four variables (are measured by the sensor suite, evapotranspiration rate, heat index, dew point and wind chill) are derived from the other variables For more information about how to calculate the derived weather parameters you are referred to the Davis application note Derived variables see [56]. If there is an error this is displayed on the error tab. There are four possible errors: COM port connection error (the serial port could not be opened) weather station data connection error (data could not be send from the console to the COMPUTER) database error (data could not be send to the local database) console time error (console time does not equal computer time) For more information about software errors and how to resolve them you are referred to the installation manual included as appendix B. Temperature Data logger We can measure the outside air temperature, but the temperature of the HiSPARC setup itself is also interesting. There is a temperature sensor attached to the PMT of plate 1 of detection station 502 (Science Park Amsterdam). Moreover another temperature sensor was placed at the bottom of the ski box of detector 1. The temperature sensor attached to the PMT was of the type EL-USB-TC-LCD from Lascar electronics. The sensor placed at the bottom of the ski box was of the type EL-USB1, also from Lascar electronics. Both sensors have an accuracy of ±1 C. For more information about the temperature probes see [42] (p.89-93), [58] and [59]. 32

38 Variable Description Unit and Accuracy timestamp Unix timestamp in GPS time for every event. seconds temperature inside The temperature in the room of the receiver. ±0.5 C relative humidity inside The relative humidity of the air in the room of the receiver. This is a measure for the amount of water vapor a parcel of air contains as a percentage of the amount of water vapor this parcel maximally can contain under the given pressure and temperature. atmospheric pressure - ±1.0 hp a temperature outside The outside air temperature ±0.5 C relative humidity outside This is a measure for the amount of water vapor a parcel of air contains as a percentage of the amount of water vapor this parcel maximally can contain under the given pressure and temperature. wind direction - ±3 wind speed - ±1ms 1 solar radiation uv index This is the intensity of the suns radiation (direct and reflected) reaching a horizontal surface per second. This index is a number between 0 and 16 that is a measure for the current UV intensity. ±3% or±4% for RH > 90 %. ±3% or±4% for RH > 90 % ±90Wm 2 dimensionless±0.8 rain rate - ±1mmh 1 evapotranspiration rate heat index dew point wind chill The evapotranspiration rate is a measure for the amount of water vapor that goes back into a parcel of air. It is a combination of vapor that goes back through evaporation and transpiration. This variable can be seen as the opposite of rainfall and is calculated by the console. If the relative humidity is high, the air temperature feels higher. The combination of temperature and relative humidity is called the heat index. This variable is calculated by the console. Below the dew point temperature water vapor in the air will start to condensate. This variable is calculated by the LabVIEW weather software. The wind speed affects our sense of temperature. The combination of temperature and wind speed is called wind chill. This variable is calculated by the LabVIEW weather software. ±0.25 mm ±1.5 C ±1.5 C ±1 C Table 4.1: Weather variables measured by the Vantage Pro 2 weather station that are stored in the weather table of the HiSPARC database. Temperature inside, relative humidity inside and atmospheric pressure are measured by the console, temperature outside, relative humidity outside, wind direction, wind speed, solar radiation, uv index and rain rate are measured by the sensor suite, evapotranspiration rate, heat index, dew point and wind chill are calculated variables [57] (p ). 33

39 Chapter 5 Cosmic-ray and weather data analysis In order to build a model to describe the fluctuations in the shower data event rate and the Most Probable Value (MPV) of the PMT pulse heights data measured by the HiSPARC stations one has to acquire data, select data, and choose the tools for the analysis. In this chapter the data acquisition, data selection and the analysis tools are described. 5.1 Acquiring shower and weather data HiSPARC data is stored in the HiSPARC database. To make the data available for data analysis David Fokkema wrote a download script as a part of his HiSPARC framework [60]. This script was used to acquire shower and weather data. The data sets selected by the user are downloaded from the HiSPARC data base and saved as a HDF5 file (Hierarchical Data Format 5). These files can become quite large (1 GB for a year). Therefore I have divided the data into sets containing data of maximal one month. In this way the chance that these files will overload the RAM of the computer is much smaller. Once the data is downloaded duplicates are removed. Duplicate data exists because the HiSPARC computer connected to a HiSPARC detection station does not have a working internet connection at all times. If this is the case the HiSPARC DAQ software will keep trying to send the data to the database. It sometimes happens that the same data is send twice or more often. As a first step of the analysis, we have to clean the acquired data set. The data must lie between limits listed in table 5.1. The weather data limits are inspired by the Vantage Pro manual [57] (p ). 5.2 Number of events per hour One could calculate the number of events per time interval using the event rate stored in the HiSPARC database. However, this event rate is not always reliable. LabVIEW automatically calculates the event rate (in Hz) as mentioned in section If for example the HiSPARC detector computer is rebooted the calculated event rate is obscured. Therefore I calculate the number of events in another way. The number of registered pulse heights is equal to the number of events in a chosen time interval. As mentioned in section for a four-detector station it is important to realize that the trigger condition is satisfied for every event (two pulse heights above 70 mv or three pulse heights above 30 mv in an interval of 1.5 µs) and not for every individual pulse height. If the trigger condition is met all four PMTs are read. If two pulse heights were above 70 mv than the pulse heights measured by the other two PMTs don t have to be above 70mV. In short we can calculate the number of events by looking at the number of pulse height measurements even if an individual pulse height is below the threshold. This does not affect the number of events since the registrations in the other plates were responsible for the trigger. 34

40 Variable (s) Upper limit Lower limit Temperature -40 C 65 C Humidity 0 % 100 % Atmospheric pressure 540 hpa 1100 hpa Wind direction Wind speed 0ms 1 67ms 1 Solar radiation 0Wm Wm 2 UV index 0 16 Evapotranspiration 0 mm 2000 mm Rain rate 0mmh mmh 1 Heat index -40 C 74 C Dew point -76 C 54 C Wind chill -79 C 57 C Event rate 0 Hz 3.5 Hz Pulse heights 0 ADC counts ADC counts Integrals 0 ADC counts ns 10 9 ADC counts ns Table 5.1: Limits for weather data (lower limit weather value upper limit) [57] (p.49-50) and shower data (lower limit<shower value upper limit). For the number of events I have chosen intervals of one hour, because the most abrupt atmospheric pressure changes of 1 hpa take place in approximately one hour. The atmospheric pressure is the most important variable in the model that describes the number of events per hour. We are interested in the fluctuations in the number of events caused by changing atmospheric conditions. However, there are more factors that influence the event rate. If the high voltage of a PMT is changed its gain increases, hence more charge will reach its anode and consequently, more events will meet the trigger conditions. In addition, if one or more of the detectors do not function properly (as can be seen in figure 5.1), or if the computer is turned off, this has a direct effect on the measured event rate. These changes in the event rate are relatively large, while the fluctuations we are interested in are relatively small. Unusual changes can be identified by inspection of the development of the number of events against time. In figure 5.1, detector 3 does not function properly (this becomes clear from figure 5.2) and causes the number of triggers to drop substantially. In figure 5.3 the computer was turned off and rebooted, resulting in an abrupt change of the event rate. For the correlation analysis only data have been selected from those hours in time for which the recorded number of shower events is larger than In this way by looking at the time development of the number of events per hour and applying well chosen limits, data with abrupt changes in the number of events can be removed from the data set MPV of the pulse heights histogram One can look at individual pulse height measurements for every PMT. I looked at the changes in the pulse height histogram over time HiSPARC is mostly interested in charged particles. This makes the fluctuations of the Most Probable Value (see section 3.4.1) the most important feature of the histogram. Most of the particles (electrons and muons) that traverse the scintillation plate are MIPs, therefore we would expect the MPV peak of the pulse heights to be Landau distributed (figure 3.7). However, the distribution visible in the pulse heights histogram has a longer tail to the right and a steep falling curve to the left (e.g. see figure 5.4). This has to do with the following. 35

41 Figure 5.1: If one detector does not function properly, the number of events per hour drops substantially. Data from station 501. Figure 5.2: Pulse height histograms for the four detectors of station 501 on 8th of June, The MPV of one detector (detector three) moved towards the trigger level. Therefore, it does not function properly. Figure 5.3: If the computer is turned off for a period of time this results in a lower number of events for two data points of an hour. Data taken from detection station 501. The number of photons that reach the anode in the PMT for a given photon that reaches the photo cathode is not constant (for example on average only one out of four photons make it from the cathode to the first dynode) and is assumed to be normally distributed. Moreover, the position where the particle traverses the scintillation plate is uniformly distributed. The position of impact will determine the traversed distance by the photons through the scintillation plate to the PMT as was mentioned in section If the traversed distance and/or the number of reflections increase, less photons will reach the PMT due to absorption or because the photons do not arrive within the coincidence interval of 1.5µs. This results in normally distributed energies of the photons that reach the photocathode. The peak can therefore be described by a Landau distribution convoluted with a normal distribution. The fit of this function is displayed by the red line in the middle graph of figure 5.4. The tail of the data to the right of the peak is much longer than the tail of the fit. This is because more than one MIP can traverse the scintillation plate at the same time. The pulse height at which the distribution peaks is called the Most Probable Value (MPV) of the pulse height and the peak is called the MPV peak. Sometimes this peak is called the MIP-peak. The pulse height histogram to the left of the MPV peak is created by high energy photons (gamma s) either by pair creation, compton scattering or the photo electric effect. This part of the histogram can be described by a power 36

42 law: N(p) = N(0) e p p 0 (5.1) withn(p) the number of occurrences of pulse heightpandp 0 a constant. The fit of this function is displayed by the red line in the right graph of figure 5.4. From the local minimum the pulse height histogram rises and becomes very steep (see figure 3.13). This steepness can be explained by the threshold of 70mV in the trigger conditions. Pulse heights below this threshold are only registered if two (or more) other plates register an event above 70mV. Above this threshold the chance that there is a coincidence is higher, hence the steep rise of the histogram [61] (p.19-29), [1]). Figure 5.4: The pulse heights histogram (left) can be described by a Landau distribution convoluted with a normal distribution (middle) and a power law (right) [1]. The MPV peak in the pulse height histogram can be described by a Landau distribution. Since this peak resembles a parabolic shape I decided for simplicity to fit a parabola to the MPV peak in order to determine the pulse height corresponding to the peak. A similar analysis was conducted by Richard Bartels [38] using a Gaussian fit rather than a parabola. A pulse height histogram can only be made if there is sufficient data. For this, one must choose a time interval over which the MPV of the pulse heights must be determined. All pulse height values are accepted, so there are no pulse height limits specified. The data is split in time intervals. For every time interval a histogram is plotted. The pulse heights are split in a large number of bins in order to make all the features of the histogram visible. After trial an error it turns out that the choice for 150 linearly divided bins produces the desired result. A smaller number of bins obscures fluctuations and a much larger number of bins makes the position of the peak too sensitive for fluctuations. We are only interested in the peak. Therefore we make some cuts in the histogram to be able to make a good parabola fit. On the left side of the MPV peak we see the histogram falling according to the photon power law (equation (5.1)). Then the MIP contribution becomes dominant and the histogram starts rising. From this local minimum to the left the histogram is cut i.e. all pulse heights below the rising point are thrown away (figure 5.5). Now we can select the highest bin in the trimmed histogram. The pulse height belonging to the highest bin is the best guess for the MPV of the pulse heights. Only around the MPV of the pulse heights the peak looks like a parabola. Therefore we select all pulse heights in an interval around the peak (figure 5.6). This selection of pulse heights is split into 40 bins and a new histogram is plotted. For this interval a parabola is fitted: y = a (x b) 2 +c (5.2) withxthe pulse heights belonging to the bin centers andy the number of pulse heights in each bin. a is the steepness parameter,bis the horizontal translation parameter andcis the vertical translation parameter. The most optimized value for parameterbis the pulse height corresponding to the MPV peak. 37

43 Figure 5.5: A cut is applied to isolate the peak and determine the MPV of the pulse heights. Figure 5.6: Several different around the best guess (shown in green) of the peak value are selected for a parabolic fit. Here an interval of 200 ADC counts is shown. 38

44 For the fit the routine scipy.optimize.curve fit is used. Here a non-linear least squares procedure (the Levenberg- Marquardt algorithm) is applied to fit the parabolic function (5.2) to our data [62]. This fit is carried out for five different intervals around the obtained best guess for the MPV of the pulse heights. The fit where b and the initial guess differ the least is selected as the most optimal one. A trial and error approach resulted in the intervals of 200 (best guess ± 100), 160 (best guess ± 80), 120 (best guess ± 60), 80 (best guess ± 40) and 60 (best guess ± 30) ADC counts around the initial guess. In figure 5.7 a MPV peak fit is carried out for different time intervals. We can see that if we make the interval smaller than one hour the MPV peak becomes less visible and more sensitive to large fluctuations. This limits the effective time interval that can be chosen. For my analysis I have chosen a time interval of three hours. A compromise between the number of data points and the accuracy of the MPV fit Uncertainty in the MPV of the pulse heights The uncertainty of the MPV of the pulse heights is the uncertainty of parameter b in formula 5.2. σb 2 is produced by the curve fit routine as the diagonal elements of the estimated covariance matrix. In my opinion the produced variances are too low. This has consequences for the goodness of fit determination see section 7.2. The estimation off the variance of the MPV of the pulse heights may be improved if we fit another function such as a gaussian as Bartels [38] did. 5.4 Correlation analysis In my research I try to describe the fluctuations of the number of events per hour and the MPV of the pulse heights with a linear model using weather measurements. In order to determine which variables must be used in this model a linear correlation analysis can be executed. With a linear correlation analysis for two variables one can determine how well a linear least squares fit describes the measured data. If we have a data set with two variables (e.g. event rates and barometer values) a linear least squares fit is applied to the data with the module numpy.linalg.lstsq [63]. In the method of linear least squares a line: y = a x+b (5.3) is fitted through the data points (x 1,y 2 ),...(x n,y n ) in such a way that the sum of the squared vertical distances between the data points and the fit line is a minimum. This condition leads to the so called normal equations: yi = a x i +b n (5.4) xi y i = b x i +a x i 2 (5.5) where we sum overifrom 1 tilln, withnthe number of data points. If we solve the normal equations we obtain the values for parameters a and b that minimize the sum of the squared vertical distances between the data points and the fit line: a = n( x i y i ) ( y i )( x i ) n x i2 ( x i ) 2 (5.6) b = ( y i )( x i 2 ) ( x i )( x i y i ) n( x i2 ) ( x i ) 2 (5.7) An example of a linear least squares fit is shown in figure 5.8. Here the event rate is plotted against the atmospheric pressure. A negative correlation is clearly visible [64] (p ), [65] (p.284). 39

45 Figure 5.7: MPV fit for different time intervals. On the y-axis the logarithm of the number of pulse heights is plotted. On the x-axis the pulse heights is plotted in ADC counts. 40

46 Figure 5.8: Plot of (fictional) event rate and pressure data along with linear least squares fit line Correlation coefficient A linear least squares fit analysis can always be performed for two variable y and x. However, we would like to determine how well the found linear equation describes the relationship between the variables. The dependence between two variables is called a correlation. If y becomes larger if x becomes larger we speak of a positive correlation. If y becomes smaller ifxbecomes larger we speak of a negative correlation. A general impression of the strength of the correlation can be retrieved from the scatter plot for the two variables (figure 5.9). Figure 5.9: Different types of correlation [66]. 41

47 The strength of the linear correlation between the measurements x i and y i can be calculated with the correlation coefficient 1 r: r = n x i y i ( x i )( y i ) [ n x i2 ( x i ) 2][ n y i2 ( y i ) 2] (5.8) where we sum overifrom 1 tillnwith n the number of data points. The correlation coefficient varies between -1 and 1. A negative sign indicates a negative correlation, a positive sign indicates a positive correlation. The closer the correlation coefficient is to -1 or 1, the stronger the correlation is. A value close to zero indicates a weak linear correlation [65] (p ) Coefficient of determination The square of the correlation coefficientr 2 is called the coefficient of determination and is equal to: 2 r 2 = (yi model y) 2 (yi y) 2 (5.9) with y i model the values predicted by the linear fit and y is the mean value. We sum over i from 1 till n with n the number of data points. This ratio can be interpreted as the ratio of the explained variation to the total variation. It is the proportion of the variance of the y values that can be predicted from x values with the linear fit. Therefore the coefficient gives us an indication how good our model is. The value of the coefficient ranges between 0 and 1. If r 2 is close to 1, we have a good model. The coefficient of determination represents the percentage of the data that is close to the line of best fit. If we find a correlation coefficient r = 0.80 we calculate the coefficient of determination r 2 = (0.80) 2 = This means that 64% of the total variation in y can be explained by the linear fit line. The remaining 36% of the total variation in y can not be explained by the model. It is important to note that the existence of a correlation between variables y en x does not necessarily imply a causal relationship between the two variables. A correlation can mean the following: There is a causal relationship betweenxand y. There is a causal relationship between x and y, but this is not visible: an unknown variable makes this relationship difficult to prove. There is no causal relationship between x and y. The dependence that is observed is caused by the influence of other (hidden) variables onxand or y [67](p.94-95), [65] (p ), [68]. On the other hand, if the correlation coefficient is zero this does not have to mean that there is no correlation between variablesxandy. It means that there is not a linear correlation between them. It is still possible there exists a curvilinear relationship between the two variables. 1 The correlation is sometimes called the Pearson product moment correlation coefficient. 2 See for example [65] (p.325). 42

48 5.5 Models for the number of events per hour We are now ready to build a model that describes the fluctuations in the measured event rate A conventional model using the barometric coefficient Conventionally, the barometric effect is described by the barometric coefficient β with units of % hpa 1. We can describe the anticorrelation between event intensityi and the atmospheric pressurep by: or Integration leads to: or I di dp I 0 di I = β = βi (5.10) P P 0 dp (5.11) ( ) I ln = β(p P 0 ) (5.12) I 0 I = I 0 e β(p P0) (5.13) We can approximate this with a Taylor expansion, considering only first order 3 : I I 0 [1 β(p P 0 )] (5.14) where I 0 is the event intensity at standard pressure P 0. This model is essentially the same as the linear model described in section 5.5.2, where only the pressure is used [21] (p.39-40) An extended linear model We can try a linear model using four weather variables: N model = a P +b T +c H +d S +e (5.15) with N model the predicted number of events per hour, P the atmospheric pressure (in hpa), T the outside air temperature (in K) H the relative humidity outside (in %) and S the solar radiation (in W/m 2 ). a, b, c, d and e are numerical constants. The optimal values for the parameters a, b, c, d and e are the ones that minimize the value of χ 2 ( chi squared ). This test statistic is the quotient of the measured variance divided by the theoretical variance. χ 2 = i (N observed i N model i ) 2 σ 2 i (5.16) with N observed the observed number of events per hour, N model the number of events per hour as predicted by formula 5.15 andσ the uncertainty inn observed. We sum overifrom 1 tillnwithnthe number of measurements. 3 e x 1+x+ 43

49 The number of events is Poisson distributed (see section 3.4.2). Therefore the uncertainty in the observed number of events is given by: σ = N observed (5.17) In order to normalize our fit parameter we divide by the number of degrees of freedom: we useχ 2 r: the so called reducedχ 2 : χ 2 r = χ2 ν with ν the number of degrees of freedom. If χ 2 r 1 the model and the data match within the expected error variation and the model can be considered a good fit. If χ 2 r 1 this is called an over-fit. This can mean thatσ i are overestimated, or that our model contains too many variables. The last possibility is that χ 2 r 1. In this case, the model does not match the data well. This can mean that theσ i are underestimated. For the model of formula (5.15) we have five fit parameters, therefore: (5.18) ν = n 5 (5.19) withnthe number of measurements [69], [70] (p ), [1]. For the minimization process the routine scipy.optimize.fmin is used. Here a Nelder-Mead simplex algorithm is applied [71] Uncertainty in the model parameters We can find the uncertainty of a fit parameter a from the model by plotting χ 2 r χ 2 r0 against a a 0 with χ 2 r0 the minimum value of χ 2 r and a 0 the parameter value a corresponding to this minimum. We let a fluctuate around a 0 and keep the other parameters constant at the values that minimizeχ 2 r. The result is a plot of the form shown in figure 5.10 for parameter a along with a parabolic fit as described in section 5.3. The parabola has a minimum at a = a 0 and χ 2 r = χ 2 r0. Because we plotted a a 0 on the x-axis and χ 2 r χ 2 r0 on the y-axis this minimum will be at zero. χ 2 r is the observed variance divided by the expected variance. When χ 2 r = 1, the model and the data match exactly within the expected error variation. We let a fluctuate around a 0 and if the value for χ 2 r becomes 1 larger than zero we have found the uncertainty σ a. In the same way one can find the uncertainty in the parameters b, c, d andeby keeping the other parameters fixed at the value that minimizesχ 2 r [72] Model for the MPV of the pulse heights We can try a linear model to describe the fluctuations of the MPV of the pulsheights (calculated for intervals of three hours). The method is essentially the same as described in section For the MPV of the pulse heights we use two weather variables: MPV = a T out +b S +c (5.20) with MPV the most probable value of the pulse heights in ADC counts, T out the temperature of the outside air in Kelvin (K) ands the solar radiation in watt per square meter. a,bandcare numerical constants (a = d e,b = d f andc = d g +h). The results of this analysis is described in chapter 7. 44

50 Figure 5.10: The uncertainty in fit parameterais determined by plottingχ 2 r χ 2 r0 againsta a 0. If the value forχ 2 r becomes 1 larger than zero we have found the uncertaintyσ a. 45

51 Chapter 6 Correlation between the event rate and weather variables Figure 6.1: Event rate as a function of time, measured with station 501. The number of events that are registered by HiSPARC cosmic-ray detectors fluctuates over time. In figure 6.1 the fluctuations registered per hour are shown for July 2011 for station 501. The event rate is clearly not constant In my research I develop a model to describe the fluctuations in the measured number of events. In this model the fluctuations are assumed to be caused by changes in the atmospheric conditions. The shower data used are taken from five HiSPARC 4-plate detection stations: 501, 504, 506, 507 and For a description of the detectors see chapter 3. These stations are located at Science Park Amsterdam. The weather data is collected with a Davis Vantage Pro 2 weather station. For a description of this device and the atmospheric variables it measures see sections 4 and An unsuccessful attempt was made to describe the fluctuations of the number of events per hour for detection station

52 6.1 Number of events and weather variables The first step in the construction of the model is the selection of the atmospheric variables that are part of the model. To achieve this we have to vary only one variable and keep the others constant within a certain domain. The following atmospheric variables were taken into account: atmospheric pressure outside air temperature outside relative humidity solar radiation 2 In figure 6.2 histograms are shown of one year of data. In each histogram the bin size is chosen such that 20 bins contain all data. For the analysis only bins with more than 100 events are selected (the bins that rise above the horizontal red line). These bins for outside air temperature, outside relative humidity and solar radiation overlap. The part with the largest number of data points within the overlapping regions is selected. Using this procedure the correlations between the event rate and the individual weather variables are investigated. The results of this analysis are shown in figures 6.3 and through Atmospheric pressure Between the atmospheric pressure and the event rate a negative correlation is found as can be seen in figure 6.3. This plot contains almost a year of data from station 501. The data set is divided into 20 bins for the outside relative humidity, solar radiation and outside air temperature values. The domain for every constant variable is shown in figure 6.3. These bins overlap. The part with the largest number of data points (114 in this case) within the overlapping regions was selected for this regression analysis. The domain for the constant variables outside relative humidity, solar radiation and outside air temperature, along with the correlation coefficient and its corresponding two-tailed p-value 3 are shown in figure 6.3 (above). The correlation coefficient was found to be r = This is a strong correlation. The atmospheric pressure therefore has to be part of our model. As mentioned in chapter4 a negative correlation between the atmospheric pressure and the number of events is expected. In figure 6.3 (below) the residual points are presented. They show a flat distribution Outside relative humidity The correlation between the outside relative humidity and the event rate is found to be weak. The sign of this correlation fluctuates as can be seen in figure 6.4 (r = 0.18 and r = 0.25). Therefore the outside relative humidity might be part of the model that describes the fluctuations in the number of events Outside air temperature A very weak negative correlation (r = 0.12) is found between the outside air temperature and the event rate as can be seen in figure 6.4. Therefore the outside air temperature might be part of the model that describes the fluctuations in the number of events. 2 The variables wind speed, wind direction, UV index an rain rate were not considered as model variables, because there was no correlation observed or expected between these variables and the event rate. Dr. A.P.J. van Deursen from Technical University Eindhoven suspects a correlation between event rate the rain rate. I could not confirm this. 3 A p-value is an indicator for the probability of two uncorrelated sets of variables that produce the same correlation coefficient [73]. The calculation of a p-value is not an easy task. See for example [74]. 47

53 Figure 6.2: If one wants to investigate the correlation between the event rate and the atmospheric pressure one proceeds as follows: in each histogram the bin size is chosen such that 20 bins contain all data. Only bins with more than 100 events are selected (bins that rise above the horizontal red line). These bins for outside air temperature, outside relative humidity and solar radiation overlap. The part with the largest number of data points within the overlapping regions is selected. 48

54 Figure 6.3: Above: Correlation analysis between events per hour (y-axis) and atmospheric pressure (x-axis). Data taken from detection station 501 (from June 1, 2011 through May 13, 2012). For every constant variable the domain is shown along with the correlation coefficient and its corresponding two-tailed p-value. Below: The residual points are more or less scattered randomly around the horizontal axis. 49

55 Figure 6.4: Above left and right: Correlation between events per hour (y-axis) and outside relative humidity (x-axis). Left below: correlation analysis between events per hour and the outside air temperature. Right below: correlation analysis between events per hour and solar radiation. Data taken from detection station 501 (from June 1, 2011 through May 13, 2012). The somains for the constant variables are shown along with the correlation coefficient and its corresponding two-tailed p-value. 50

56 6.1.4 Solar radiation There is no correlation found (r = 0.01) between the solar radiation and the event rate as can be seen in figure 6.4. Therefore the solar radiation will probably not be part of the model that describes the fluctuations in the number of events Independence between variables One of the assumptions for building a model is that the variables used are independent. Dependence means that one variable can be described by a combination of the other variables. Not unexpectedly, some of the atmospheric variables mentioned above are correlated. The strength of the correlations between six couples of variables, for one year of data while keeping the other weather variables constant (as described in section 6.1) is displayed in figure 6.5. The best we can do is to select the most significant of the correlated variables and exclude the others from our model. For the plots below almost a year of data (from June 1, 2011 through May 13, 2012) is taken from detection station 501. This data set is divided into 20 bins for the three constant variables. The domains for every constant variable is shown above in every figure, along with the correlation coefficient and its corresponding two-tailed p-value are shown. These bins overlap. Every time the selection with the largest number of data points within the overlapping regions was selected for these regression analysis. The solar radiation and outside relative humidity are negatively correlated, a medium or strong correlation. An example is shown in figure 6.5 withr = The solar radiation and the outside air temperature are positively correlated, a medium correlation. An example is shown in figure 6.5 withr = The outside air temperature and the atmospheric pressure are negatively correlated, a medium correlation. An example is shown in figure 6.5 withr = The outside air temperature and outside relative humidity are positively correlated, a weak correlation. An example is shown in figure 6.5 withr = The atmospheric pressure and the solar radiation are not correlated. An example is shown in figure 6.5 with r = The atmospheric pressure and the outside relative humidity are not correlated. An example is shown in figure 6.5 withr =

57 Figure 6.5: Above left: correlation analysis between the solar radiation and outside relative humidity. Above right: correlation analysis between the solar radiation and the outside air temperature. Middle left: correlation analysis between the outside air temperature and the atmospheric pressure. Middle right: correlation analysis between the outside relative humidity and the outside air temperature. Below left: correlation analysis between the solar radiation and the atmospheric pressure. Below right: correlation analysis between the atmospheric pressure and the outside relative humidity. Data taken from detection station 501 (from June 1, 2011 through May 13, 2012). The somains for the constant variables are shown along with the correlation coefficient and its corresponding two-tailed p-value. 52

58 6.2 Building the model Selection of model variables We can use all available weather variables in our model, but we have learned in sections through that not all variables have a strong correlation with the event rate. We expect that the atmospheric pressure will be part of our model because of the strong correlation with the event rate. The outside relative humidity and the outside air temperature have a weak correlation with the event rate, therefore they might be part of the model. The solar radiation has no correlation at all with the event rate, therefore it is expected that the solar radiation will contribute not very much information to our model. We use seven different linear models. The atmospheric pressurep is part of all models A linear model for detection station 501 For detection station 501 we try to fit data from the weather station located near shower detection station 501 for three periods of time: one month (July 2011), two months (July and August 2011) and seven months of data (June up to and including December 2011). The models are listed in table 6.1. We see that if we describe the fluctuations of the event rate from July solely by the fitted values of the parameters and theχ 2 r of the fit using only the atmospheric pressure variations we get χ 2 r = Already a very satisfying result, since we used only one variable. If we also include the outside air temperaturet in our model the quality of the fit improves: χ 2 r = If we also include the outside relative humidity H χ 2 r does not improve. This could mean that the relative humidity does not add new information to our model. If we include the solar radiation in our model χ 2 r does improve, but if we look at a larger data set we see that this improvement disappears. Moreover the uncertainties in the solar radiation and outside relative humidity parameters are large, whereas the uncertainty in the outside air temperature is smaller (< 4%) and the uncertainty in the atmospheric pressure is very small (< 0.4%). In section we learned that outside air temperature, solar radiation en outside relative humidity are correlated. It is therefore no surprise that adding more than one of these three variables does not improve our model, since we do not add additional information. One concludes that a model that includes only the atmospheric pressure and the outside air temperature variations describes the fluctuations in the event rate best. The data from station 501 for July 2011 is plotted against time (solid blue line) in figure 6.6, along with the model that contains only the atmospheric pressure N = ap + b (solid green line) and the model containing atmospheric pressure and outside air temperature N = ap + bt + c (red dashed line). The corresponding residues against time are plotted in figure 6.7. The residues show no pattern or structure. The residual points are more or less scattered randomly around the horizontal axis as they should be. The residues are small compared with the experimental values (95 % of the residues are smaller than 5 % of the experimental values for both models). The residues are normally distributed with a mean around zero as can be seen in figure 6.8 respectively. Therefore the models are acceptable. 53

59 Model N = a P +b N = a P +b T +c N = a P +b T +c H +d N = a P +b T +c H +d S +e N = a P +b T +c S +d N = a P +b H +c S +d N = a P +b S +c N = a P +b H +c 7 11 (731 data points) (1463 data points) (2911 data points) parameters χ 2 r parameters χ 2 r parameters χ 2 r a = 14.00±0.05 a = 14.15±0.05 a = 13.38± b = (1.671±0.005) 10 4 b = (1.686±0.005) 10 4 b = (1.601±0.005) 10 4 a = 13.73±0.05 a = 14.04±0.05 a = 13.52±0.05 b = 5.5± b = 6.4± b = 7.5±0.2 c = (1.803±0.005) 10 4 c = (1.860±0.005) 10 4 c = (1.839±0.005) 10 4 a = 13.57±0.05 a = 13.85±0.05 a = 13.46±0.05 b = 4.4±0.2 b = 5.6±0.2 b = 7.2± c = 0.4±0.7 c = 0.3±0.6 c = 0.2±0.6 d = (1.751±0.005) 10 4 d = (1.817±0.005) 10 4 d = (1.825±0.005) 10 4 a = 13.66±0.05 b = 2.0±0.2 a = 13.93±0.05 b = 4.5±0.2 a = 13.46±0.05 b = 6.9±0.2 c = 0.0± c = 0.1± c = 0.1±0.6 d = 0.1±0.2 d = 0.0±0.2 d = 0.0±0.2 e = (1.696±0.005) 10 4 e = (1.796±0.005) 10 4 e = (1.816±0.005) 10 4 a = 13.65±0.05 a = 13.90±0.05 a = 13.45±0.05 b = 1.9±0.2 b = 4.5±0.2 b = 6.8± c = 0.1±0.2 c = 0.0±0.2 c = 0.0±0.2 d = (1.693±0.005) 10 4 d = (1.791±0.005) 10 4 d = (1.813±0.005) 10 4 a = 13.62±0.05 a = 13.74±0.05 a = 13.05±0.05 b = 0.1±0.7 b = 0.2±0.6 b = 0.4± c = 0.1±0.2 c = 0.1±0.2 c = 0.1±0.2 d = (1.633±0.005) 10 4 d = (1.644±0.005) 10 4 d = (1.573±0.005) 10 4 a = 13.68±0.05 a = 13.84±0.05 a = 13.15±0.05 b = 0.1± b = 0.1± b = 0.1±0.2 c = (1.640±0.005) 10 4 c = (1.656±0.005) 10 4 c = (1.587±0.005) 10 4 a = 13.44±0.05 a = 13.52±0.05 a = 12.98±0.05 b = 1.0± b = 1.0± b = 1.2±0.6 c = (1.607±0.005) 10 4 c = (1.613±0.005) 10 4 c = (1.559±0.005) Table 6.1: Models (for explanation of the models see text) used that try to describe the fluctuations in the number of events per hourn of station 501 for three periods of time. 54

60 Figure 6.6: The event rate for station 501 for July 2011 (blue solid line), along with the model that contains only the atmospheric pressure (red dashed line), and the model that also contains the outside air temperature (green solid line). χ 2 r is shown for this last model. Figure 6.7: The residual points are more or less scattered randomly around the horizontal axis. 55

61 Period N = N 0 [1 β(p P 0 )] χ 2 r 7 11 (731 data points) N = 2551[1 (0.5 ± 0.3)(P 1011)] (1463 data points) N = 2545[1 (0.6 ± 0.3)(P 1012)] (2911 data points) N = 2530[1 (0.5 ± 0.2)(P 1014)] 2.79 Table 6.2: Models that try to describe the fluctuations in the number of events per hour N of station 501 for three periods of time using a barometric coefficientβ. Figure 6.8: The residues are normally distributed with a mean around zero.. A linear model using the barometric coefficient for detection station 501 One can also try a fit using the model with a barometric coefficient as described in section 5.5.1: N = N 0 [1 β(p P 0 )] (6.1) withn the event rate,n 0 the mean event rate,β the barometric coefficient (in%hpa 1 ),P the atmospheric pressure (in hpa) and P 0 the mean atmospheric pressure. The results for the three data sets are listed in table 6.2. This model is essentially the same as the linear model described above, where only the atmospheric pressure is used. These data for July 2011 from station 501 is plotted against time, along with the barometric coefficient model in figure 6.9. The corresponding residues against time and distribution of residues are plotted in figures 6.10 and This model is acceptable.. We can find the uncertainty of the barometric coefficient β in the same way we described in section We plot χ 2 r χ 2 r0 against β β 0 with χ 2 r0 the minimum value of χ 2 r and β 0 the barometric coefficient corresponding to this minimum. We let β fluctuate aroundβ 0. The result is a parabola that is shown in figure

62 Figure 6.9: The event rate for station 501 for July 2011 (blue), along with the model that contains only the atmospheric pressure (red). Figure 6.10: The residual points are more or less scattered randomly around the horizontal axis.. 57

63 Figure 6.11: The residues are normally distributed with a mean around zero. Figure 6.12: The uncertainty in fit parameterβ is determined by plottingχ 2 r χ 2 r0 againstβ β 0. If the value forχ 2 r becomes 1 larger than zero we have found the uncertaintyσ β. 58

64 Model N = a P +b N = a P +b T +c N = a P +b T +c H +d N = a P +b T +c H +d S +e N = a P +b T +c S +d N = a P +b H +c S +d N = a P +b S +c N = a P +b H +c 1/7-18/7 11 (404 points) 15/9-11/12 11 (928 points) 13/ /2 12 (1634 points) parameters χ 2 r parameters χ 2 r parameters χ 2 r a = 9.95±0.05 a = 10.08±0.05 a = 12.57± b = (1.219±0.005) 10 4 b = (1.211±0.005) 10 4 b = (1.502±0.005) 10 4 a = 9.73±0.05 a = 10.04±0.05 a = 12.67±0.05 b = 10.7± b = 1.1± b = 0.4±0.2 c = (1.508±0.005) 10 4 c = (1.238±0.004) 10 4 c = (1.522±0.005) 10 4 a = 10.81±0.05 a = 9.98±0.04 a = 12.54±0.05 b = 16.4±0.2 b = 0.2±0.1 b = 0.4± c = 1.6±0.6 c = 1.0±0.5 c = 0.5±0.6 d = (1.793±0.005) 10 4 d = (1.197±0.004) 10 4 d = (1.507±0.005) 10 4 a = 10.68±0.05 b = 12.3±0.2 a = 9.73±0.04 b = 0.4±0.1 a = 12.53±0.05 b = 0.4±0.2 c = 2.1± c = 0.3± c = 0.5±0.6 d = 0.1±0.1 d = 0.1±0.3 d = 0.0±0.6 e = (1.667±0.005) 10 4 e = (1.162±0.004) 10 4 e = (1.505±0.005) 10 4 a = 9.39±0.05 a = 9.72±0.05 a = 12.62±0.05 b = 6.3±0.2 b = 0.3±0.1 b = 0.3± c = 0.1±0.1 c = 0.1±0.3 c = 0.0±0.6 d = (1.347±0.005) 10 4 d = (1.166±0.004) 10 4 d = (1.517±0.005) 10 4 a = 9.60±0.05 a = 13.74±0.05 a = 12.43±0.05 b = 0.6±0.6 b = 0.2±0.5 b = 0.4± c = 0.1±0.1 c = 0.1±0.3 c = 0.0±0.6 d = (1.190±0.005) 10 4 d = (1.175±0.004) 10 4 d = (1.485±0.005) 10 4 a = 9.25±0.05 a = 9.72±0.04 a = 12.53±0.05 b = 0.1± b = 0.1± b = 0.0±0.6 c = (1.150±0.005) 10 4 c = (1.175±0.004) 10 4 c = (1.499±0.005) 10 4 a = 9.20±0.05 a = 9.98±0.04 a = 12.44±0.05 b = 1.0± b = 1.0± b = 0.5±0.6 c = (1.135±0.005) 10 4 c = (1.192±0.004) 10 4 c = (1.485±0.005) Table 6.3: Models that try to describe the fluctuations in the number of events per hour N of station 504 for three periods of time A linear model for detection station 504 The results for all eight models for the data of station 504 are shown in table 6.3. We conclude that apart from the July data set the atmospheric pressure alone is significant to describe the fluctuations in the number of events per hour. Outside air temperature, outside relative humidity and solar radiation do not add more information when we look at the largest dataset. The data from station 504 of the period December 13, 2011 through February 28, 2012 is plotted against time, along with the model that contains only the atmospheric pressure N = ap + b in figure The corresponding residues against time are plotted in figure The residues do not show a pattern or structure. The residual points are more or less scattered randomly around the horizontal axis as they should be. The residues are small compared with the experimental values (95 % of the residues are smaller than 5 % of the experimental values). The residues are normally distributed with a mean around zero as can be seen in figure Therefore the model is acceptable... However, the parameter values for the atmospheric pressure variable from the first two data sets differ a lot from the parameter value for the last data set: -9.95, against If we merge the last two data sets this difference becomes remarkably clear in the plot of the model against time and its residues. All the residues before December 2011 are negative and all residues after this date are positive. A look at the high voltage learns that the high voltage for the PMT of plate 3 was changed from 794 V to 836 V on December 11, It is clear that an 59

65 Figure 6.13: The event rate for station 504 of the period December 13, 2011 through February 28, 2012 (blue line), along with the model that contains only the atmospheric pressure (red line). Figure 6.14: The residual points are more or less scattered randomly around the horizontal axis. change in the High Voltage of one plate has a remarkable effect and we can see that reflected in the value of the atmospheric pressure parameter. 60

66 Figure 6.15: The residues are normally distributed with a mean around zero. 61

67 Figure 6.16: If we try to describe the data (blue) from station 504 for the period October 2011 through February 2012 with our model (red) we get a misfit. Figure 6.17: The residues show a pattern. 62

68 Period N = N 0 [1 β(p P 0 )] χ 2 r 1/7-18/7 11 (404 data points) N = 2123[1 (0.5 ± 0.3)(P 1011)] /9-11/12 11 (928 data points) N = 1873[1 (0.5 ± 0.3)(P 1015)] /12-28/2 11 (1634 data points) N = 2191[1 (0.6 ± 0.2)(P 1021)] 1.43 Table 6.4: Models that try to describe the fluctuations in the number of events per hour N of station 504 for three periods of time using a barometric coefficientβ. A linear model using the barometric coefficient for detection station 504 Again one can also try to fit the data using the model with a barometric coefficient just as we did in section The results for the three data sets are listed in table 6.4. This model is essentially the same as the linear model described above, where only the atmospheric pressure is used. This data for December 13, 2011 through February 28, 2012 from station 504 is plotted against time, along with the barometric coefficient model in figure Its corresponding residues against time and the distribution of residues are plotted in figures 6.14 and This model is acceptable. 63

69 Model N = a P +b N = a P +b T +c N = a P +b T +c H +d N = a P +b T +c H +d S +e N = a P +b T +c S +d N = a P +b H +c S +d N = a P +b S +c N = a P +b H +c 16/ /1 12 (488 data points) 23/5-17/06 12 (612 data points) 19/1-26/2 12 (901 data points) parameters χ 2 r parameters χ 2 r parameters χ 2 r a = 14.16±0.04 a = 11.89±0.05 a = 8.85± b = (1.652±0.005) 10 4 b = (1.416±0.005) 10 4 b = (1.110±0.004) 10 4 a = 13.08±0.05 a = 10.99±0.04 a = 14.38±0.04 b = 13.6± b = 21.7± b = 12.3±0.2 c = (1.923±0.005) 10 4 c = (1.952±0.005) 10 4 c = (2.016±0.004) 10 4 a = 13.10±0.05 a = 10.81±0.04 a = 13.60±0.04 b = 13.5±0.2 b = 20.6±0.2 b = 10.8± c = 0.8±0.5 c = 0.4±0.6 c = 1.3±0.6 d = (1.931±0.005) 10 4 d = (1.899±0.005) 10 4 d = (1.884±0.004) 10 4 a = 13.10±0.05 b = 13.5±0.2 a = 10.46±0.04 b = 17.4±0.2 a = 13.03±0.04 b = 10.0±0.2 c = 2.1± c = 0.3± c = 1.1±0.6 d = 0.8±0.5 d = 0.1±0.2 d = 0.2±0.4 e = (1.931±0.005) 10 4 e = (1.778±0.005) 10 4 e = (1.805±0.004) 10 4 a = 13.08±0.05 a = 10.36±0.04 a = 13.67±0.04 b = 13.7±0.2 b = 16.9±0.2 b = 11.2± c = 0±1 c = 0.0±0.1 c = 0.2±0.4 d = (1.928±0.005) 10 4 d = (1.750±0.005) 10 4 d = (1.912±0.004) 10 4 a = 14.15±0.05 a = 9.69±0.04 a = 8.33±0.04 b = 1.4±0.5 b = 0.9±0.6 b = 3.0± c = 0±1 c = 0.2±0.1 c = 0.2±0.4 d = (1.664±0.005) 10 4 d = (1.189±0.005) 10 4 d = (1.035±0.004) 10 4 a = 14.15±0.05 a = 9.92±0.04 a = 8.47±0.04 b = 0± b = 0.2± b = 0.3±0.4 c = (1.651±0.005) 10 4 c = (1.220±0.005) 10 4 c = (1.072±0.004) 10 4 a = 14.18±0.05 a = 10.14±0.04 a = 8.58±0.04 b = 1.1± b = 3.0± b = 3.6±0.6 c = (1.663±0.005) 10 4 c = (1.215±0.005) 10 4 c = (1.057±0.004) Table 6.5: Models that try to describe the fluctuations in the number of events per hour N of station 506 for three periods of time A linear model for detection station 506 The results for all eight models for the data of station 506 are shown in table 6.5. The data from station 506 for December 16, 2011 through January 5, 2012 is plotted against time (solid blue line) in figure 6.18, along with the model that contains only the atmospheric pressure N = ap + b (green line) and the model containing atmospheric pressure and outside air temperaturen = ap +bt +c (red dashed line). Its corresponding residues against time are plotted in figure The residues show no pattern or structure. The residual points are more or less scattered randomly around the horizontal axis as they should be. The residues are small compared with the experimental values (95 % of the residues are smaller than 4 % of the experimental values). The residues are normally distributed with a mean around zero as can be seen in figure Therefore the models are acceptable. A description of the 506 data using atmospheric pressure and outside air temperature gives a better result than a model using only the atmospheric pressure. If we add other parameters such as the solar radiation and the outside relative humidity our model improves, but the the uncertainty in the solar radiation and outside relative humidity parameters is large, whereas the uncertainty in the outside air temperature is smaller (< 2%) and the uncertainty in the atmospheric pressure is very small (< 1%). Although one could chose to incorporate outside relative humidity and/or solar radiation I choose the models 64

70 with less parameters and conclude that a model that includes only the atmospheric pressure and the outside air temperature variations is the best one to describes the fluctuations in the event rate. Figure 6.18: The event rate for station 506 of the period December 16, 2011 through January 5, 2012 (blue solid line), along with the model that contains only the atmospheric pressure (green solid line) and the model that contains the atmospheric pressure and the outside air temperature (red dashed line). χ 2 r is shown for this last model. Figure 6.19: The residual points are more or less scattered randomly around the horizontal axis.. 65

71 Figure 6.20: The residues are normally distributed with a mean around zero. Period N = N 0 [1 β(p P 0 )] χ 2 r 16/ /1 12 (488 data points) N = 2200[1 (0.6 ± 0.2)(P 1012)] /5-17/06 12 (612 data points) N = 2085[1 (0.6 ± 0.3)(P 1015)] /1-26/2 12 (901 data points) N = 2024[1 (0.4 ± 0.2)(P 1025)] 2.48 Table 6.6: Models that try to describe the fluctuations in the number of events per hour N of station 506 for three periods of time using a barometric coefficientβ. A linear model using the barometric coefficient for detection station 506 Again one can also try a fit using the model with a barometric coefficient just as we did in section The results for the three data sets are listed in table 6.6. This model is essentially the same as the linear model described above, where only the atmospheric pressure is used. This data for December 16, 2011 through January 5, 2012 from station 506 is plotted against time, along with the barometric coefficient model in figure 6.18 (green solid line). The residues are small compared with the experimental values (95 % of the residues are smaller than 6 % of the experimental values). The residues are normally distributed with a mean around zero as can be seen in figure However, if we look at the residues plotted against time (figure 6.22) we see a wavelike pattern, therefore we are probably missing a variable (we learned that including the outside air temperature may work). Therefore this model is not acceptable.. 66

72 Figure 6.21: The residues are normally distributed with a mean around zero. Figure 6.22: We see a wavelike pattern among the residues. Therefore there is probably a variable missing in this model. 67

73 Model N = a P +b N = a P +b T +c N = a P +b T +c H +d N = a P +b T +c H +d S +e N = a P +b T +c S +d N = a P +b H +c S +d N = a P +b S +c N = a P +b H +c 23/5-17/6 11 (612 data points) 20/6-31/08 12 (1706 data points) 15/9-5/11 11 (858 data points) parameters χ 2 r parameters χ 2 r parameters χ 2 r a = 1.66±0.03 a = 1.81±0.03 a = 2.07± b = (2.64±0.03) 10 3 b = (2.77±0.03) 10 3 b = (3.01±0.03) 10 3 a = 1.68±0.03 a = 1.83±0.03 a = 2.20±0.03 b = 0.6± b = 1.8± b = 1.7±0.1 c = (2.49±0.03) 10 3 c = (2.28±0.03) 10 3 c = (2.66±0.03) 10 3 a = 1.92±0.03 a = 2.08±0.03 a = 2.21±0.03 b = 0.9±0.1 b = 0.8±0.1 b = 1.4± c = 0.5±0.4 c = 0.5±0.4 c = 0.3±0.4 d = (3.19±0.03) 10 3 d = (2.85±0.03) 10 3 d = (2.76±0.03) 10 3 a = 13.10±0.05 b = 1.3±0.1 a = 2.07±0.03 b = 0.7±0.1 a = 2.2±0.03 b = 1.4±0.1 c = 0.4± c = 0.4± c = 0.3±0.4 d = 0.0±0.1 d = 0.0±0.1 d = 0.0±0.2 e = (3.34±0.03) 10 3 e = (2.87±0.03) 10 3 e = (2.76±0.03) 10 3 a = 1.84±0.03 a = 1.89±0.03 a = 2.22±0.03 b = 0.6±0.1 b = 1.1±0.1 b = 1.5± c = 0.02±0.06 c = 0.0±0.1 c = 0.0±0.2 d = (2.99±0.03) 10 3 d = (2.53±0.03) 10 3 d = (2.73±0.03) 10 3 a = 1.91±0.03 a = 2.11±0.03 a = 2.16±0.03 b = 0.3±0.4 b = 0.5±0.4 b = 0.3± c = 0.01±0.09 c = 0.0±0.1 c = 0.0±0.2 d = (2.91±0.03) 10 3 d = (3.11±0.03) 10 3 d = (3.12±0.03) 10 3 a = 1.82±0.03 a = 1.91±0.03 a = 2.17±0.03 b = 0.02± b = 0.0± b = 0.1±0.2 c = (2.79±0.03) 10 3 c = (2.87±0.03) 10 3 c = (3.10±0.03) 10 3 a = 1.89±0.03 a = 2.13±0.03 a = 2.13±0.03 b = 0.4± b = 0.6± b = 0.4±0.4 c = (2.90±0.03) 10 3 c = (3.14±0.03) 10 3 c = (3.10±0.03) Table 6.7: Models that try to describe the fluctuations in the number of events per hour N of station 507 for three periods of time A linear model for detection station 507 The results for all eight models for the data of station 507 are shown in tables 6.7 and 6.8. For this station it was possible to describe the whole dataset of almost a year using the linear models. The data from station 507 for July 2011 is plotted against time in figure 6.23, along with the model that contains only the atmospheric pressure N = ap + b (solid green line) and the model containing atmospheric pressure and outside air temperaturen = ap +bt +c (dashed red line). For the model containing both the atmospheric pressure and the outside air temperature the residues against time are plotted in figure The residues show no pattern or structure. The residual points are more or less scattered randomly around the horizontal axis as they should be. The residues are small compared with the experimental values (95 % of the residues are smaller than 7 % of the experimental values). The residues are normally distributed with a mean around zero as can be seen in figure Therefore the model is acceptable. 68

74 Model N = a P +b N = a P +b T +c N = a P +b T +c H +d N = a P +b T +c H +d S +e N = a P +b T +c S +d N = a P +b H +c S +d N = a P +b S +c N = a P +b H +c 5/11-9/12 11 (472 data points) 16/ /3 12 (1645 data points) 10/3-13/05 12 (609 data points) parameters χ 2 r parameters χ 2 r parameters χ 2 r a = 1.56±0.03 a = 2.38±0.03 a = 1.55± b = (2.47±0.03) 10 3 b = (3.36±0.03) 10 3 b = (2.42±0.03) 10 3 a = 1.55±0.03 a = 1.96±0.03 a = 1.66±0.03 b = 1.7± b = 1.6± b = 2.6±0.1 c = (1.97±0.03) 10 3 c = (2.47±0.03) 10 3 c = (1.80±0.03) 10 3 a = 1.40±0.03 a = 2.06±0.03 a = 1.56±0.03 b = 1.5±0.1 b = 1.6±0.1 b = 2.5± c = 0.4±0.4 c = 0.4±0.4 c = 0.3±0.6 d = (1.92±0.03) 10 3 d = (2.61±0.03) 10 3 d = (1.74±0.03) 10 3 a = 1.44±0.03 b = 1.4±0.1 a = 2.09±0.03 b = 1.6±0.1 a = 1.56±0.03 b = 2.4±0.1 c = 0.4± c = 0.3± c = 0.3±0.6 d = 0.0±0.5 d = 0.0±0.4 d = 0.0±0.1 e = (1.99±0.03) 10 3 e = (2.65±0.03) 10 3 e = (1.76±0.03) 10 3 a = 1.58±0.03 a = 2.02±0.03 a = 1.65±0.03 b = 1.6±0.1 b = 1.6±0.1 b = 2.7± c = 0.1±0.5 c = 0.0±041 c = 0.0±0.1 d = (2.04±0.03) 10 3 d = (2.55±0.03) 10 3 d = (1.74±0.03) 10 3 a = 1.42±0.03 a = 2.51±0.03 a = 1.47±0.03 b = 0.4±0.4 b = 0.3±0.4 b = 0.5± c = 0.1±0.5 c = 0.0±0.4 c = 0.0±0.1 d = (2.36±0.03) 10 3 d = (3.51±0.03) 10 3 d = (2.35±0.03) 10 3 a = 1.60±0.03 a = 2.44±0.03 a = 1.60±0.03 b = 0.1± b = 0.1± b = 0.0±0.1 c = (2.51±0.03) 10 3 c = (3.41±0.03) 10 3 c = (2.47±0.03) 10 3 a = 1.37±0.03 a = 2.48±0.03 a = 1.43±0.03 b = 0.5± b = 0.4± b = 0.4±0.6 c = (2.32±0.03) 10 3 c = (3.49±0.03) 10 3 c = (2.31±0.03) Table 6.8: Models that try to describe the fluctuations in the number of events per hourn of station 507 for another three periods of time. 69

75 Figure 6.23: The event rate for station 507 of the period July 2011 (blue solid line), along with the model that contains only the atmospheric pressure (green solid line) and the model that contains the atmospheric pressure and the outside air temperature (red dashed line). χ 2 r is shown for this last model. Figure 6.24: The residual points are more or less scattered randomly around the horizontal axis. 70

76 Period N = N 0 [1 β(p P 0 )] χ 2 r 23/5-17/6 11 (612 data points) N = 951[1 (0.2 ± 0.4)(P 1015)] /6-31/08 12 (1706 data points) N = 943[1 (0.2 ± 0.5)(P 1012)] /9-5/11 11 (858 data points) N = 899[1 (0.2 ± 0.4)(P 1021)] /11-9/12 11 (472 data points) N = 892[1 (0.2 ± 0.3)(P 1013)] / /3 12 (1645 data points) N = 929[1 (0.3 ± 0.3)(P 1021)] /3-13/05 12 (609 data points) N = 842[1 (0.2 ± 0.3)(P 1015)] 1.27 Table 6.9: Models that try to describe the fluctuations in the number of events per hour N of station 507 for six periods of time using a barometric coefficientβ. Figure 6.25: The residues are normally distributed with a mean around zero.. A linear model using the barometric coefficient for detection station 507 Again one can also try a fit using the model with a barometric coefficient just as we did in section The results for the six data sets are listed in table 6.9. This model is essentially the same as the linear model described above, where only the atmospheric pressure is used. This data for June 20 through August 31, 2011 from station 507 is plotted against time, along with the barometric coefficient model in figure 6.23 (green solid line). The residues show no pattern or structure (figure 6.26). The residual points are more or less scattered randomly around the horizontal axis as they should be. The residues are small compared with the experimental values (95 % of the residues are smaller than 7 % of the experimental values). The residues are normally distributed with a mean around zero as can be seen in figure Therefore the model is acceptable. 71

77 Figure 6.26: The residual points are more or less scattered randomly around the horizontal axis. Figure 6.27: The residues are normally distributed with a mean around zero.. 72

78 Model N = a P +b N = a P +b T out +c N = a P +b T in +c 28/1-14/2 12 (407 data points) parameters χ 2 r a = 1.89±0.03 b = (2.84±0.03) a = 0.57±0.03 b = 3.2±0.1 c = (6.1±0.3) 10 2 a = 1.23±0.03 b = 20.8±0.1 c = ( 3.96±0.03) Table 6.10: Three models that try to describe the fluctuations in the event raten for station 507. Using temperature as a model variable. Station 507 is located inside the hall of NIKHEF, whereas the other stations are located outside on rooftops. For the models containing the air outside air temperature we can now use the temperature inside too. The outside air temperature and the inside air temperature are plotted against time in figure 6.28 by blue and red lines respectively. The mean temperatures are plotted by horizontal lines. We can see that the inside air temperature remains fairly constant, whereas the outside air temperature fluctuates more. Figure 6.28: The air temperature outside and inside with its mean plotted against time. We notice a large difference between the outside air temperature and the inside air temperature in the period January 28 through February 14. For this period we try to fit three linear models (table 6.10). One without the temperature, one with the atmospheric pressurep and the inside air temperaturet in and one with the atmospheric pressure P and the outside air temperature T out. The results from table 6.10 and shown in figure They show that the model using the inside temperature describes the data better than the one suing the outside temperature. The temperature influence probably has more to do with the temperature of the detector, than the temperature of the atmosphere. It has more to do with the temperature effect of the PMT described in section 3.2 than the atmospheric effects described in chapter 4. 73

79 Figure 6.29: The event rate for station 507 is fitted using the outside air temperature and the inside air temperature. 74

80 Model N = a P +b N = a P +b T +c N = a P +b T +c H +d N = a P +b T +c H +d S +e N = a P +b T +c S +d N = a P +b H +c S +d N = a P +b S +c N = a P +b H +c 28/6-26/7 11 (663 data points) 26/7-31/8 11 (875 data points) 15/9-2/11 11 (821 data points) parameters χ 2 r parameters χ 2 r parameters χ 2 r a = 1.66±0.03 a = 9.41±0.04 a = 10.50± b = (1.048±0.04) 10 4 b = (1.122±0.04) 10 4 b = (1.227±0.04) 10 4 a = 7.69±0.04 a = 10.39±0.04 a = 9.65±0.03 b = 16.0± b = 17.9± b = 10.0±0.1 c = (1.423±0.04) 10 4 c = (1.741±0.04) 10 4 c = (1.427±0.04) 10 4 a = 6.32±0.04 a = 8.95±0.04 a = 9.49±0.04 b = 10.75±0.1 b = 14.0±0.1 b = 8.2± c = 2.2±0.6 c = 1.9±0.5 c = 1.8±0.5 d = (1.116±0.04) 10 4 d = (1.469±0.04) 10 4 d = (1.345±0.04) 10 4 a = 6.64±0.04 b = 7.6±0.1 a = 9.13±0.04 b = 11.2±0.1 a = 2.2±0.03 b = 7.0±0.1 c = 0.5± c = 0.8± c = 0.7±0.5 d = 0.2±0.1 d = 0.1±0.2 d = 0.1±0.2 e = (1.072±0.04) 10 4 e = (1.416±0.04) 10 4 e = (1.299±0.04) 10 4 a = 6.93±0.04 a = 9.57±0.04 a = 9.28±0.04 b = 8.4±0.1 b = 11.8±0.1 b = 7.2± c = 0.2±0.1 c = 0.1±0.2 c = 0.2±0.2 d = (1.128±0.04) 10 4 d = (1.485±0.04) 10 4 d = (1.312±0.04) 10 4 a = 6.24±0.04 a = 7.82±0.04 a = 9.58±0.04 b = 1.4±0.6 b = 1.48±0.5 b = 1.1± c = 0.2±0.1 c = 0.2±0.1 c = 0.2±0.2 d = (8.06±0.04) 10 3 d = (9.52±0.04) 10 3 d = (1.126±0.04) 10 4 a = 7.01±0.04 a = 8.60±0.04 a = 9.59±0.04 b = 0.2± b = 0.2± b = 0.3±0.2 c = (8.94±0.04) 10 3 c = (1.043±0.04) 10 4 c = (1.137±0.04) 10 4 a = 5.66±0.04 a = 6.91±0.04 a = 9.99±0.04 b = 3.9± b = 3.9± b = 2.9±0.5 c = (7.24±0.04) 10 3 c = (8.38±0.04) 10 3 c = (1.152±0.04) Table 6.11: Models that try to describe the fluctuations in the number of events per hour N of station 509 for three periods of time A linear model for detection station 509 The results for all eight models for the data of station 509 are shown in tables 6.11, 6.12 and For this station it was possible to describe the whole dataset of almost a year using the linear models. The data from station 509 for the period of November 14, 2011 through January 5, 2012 is plotted against time in figure Its corresponding residues against time are plotted along with the model containing the atmospheric pressure and the outside air temperature in figure The residues show no pattern or structure, except for a small trend near the end of the period. There the residues are more negative than positive. The rest of the residual points are more or less scattered randomly around the horizontal axis as they should be. The residues are small compared with the experimental values (95 % of the residues are smaller than 5 % of the experimental values). The residues are normally distributed with a mean around zero as can be seen in figure Therefore this model is acceptable. 75

81 Model N = a P +b N = a P +b T +c N = a P +b T +c H +d N = a P +b T +c H +d S +e N = a P +b T +c S +d N = a P +b H +c S +d N = a P +b S +c N = a P +b H +c 14/ /1 12 (1006 data points) 9/1-27/2 12 (1147 data points) 26/3-21/04 12 (821 data points) parameters χ 2 r parameters χ 2 r parameters χ 2 r a = 13.66±0.04 a = 7.28±0.04 a = 10.02± b = (1.610±0.05) 10 4 b = (9.52±0.05) 10 3 b = (1.202±0.04) 10 4 a = 13.15±0.04 a = 12.37±0.04 a = 8.11±0.04 b = 11.0± b = 12.0± b = 18.9±0.2 c = (1.866±0.05) 10 4 c = (1.804±0.05) 10 4 c = (1.539±0.04) 10 4 a = 13.03±0.05 a = 12.20±0.04 a = 7.90±0.04 b = 11.2±0.2 b = 11.7±0.2 b = 17.9± c = 0.7±0.6 c = 0.9±0.6 c = 2.0±0.8 d = (1.868±0.05) 10 4 d = (1.772±0.05) 10 4 d = (1.500±0.04) 10 4 a = 13.03±0.05 b = 11.2±0.2 a = 12.1±0.04 b = 11.6±0.2 a = 8.2±0.04 b = 10.0±0.2 c = 0.7± c = 0.8± c = 0.9±0.8 d = 0.0±0.9 d = 0.0±0.5 d = 0.2±0.2 e = (1.868±0.05) 10 4 e = (1.764±0.05) 10 4 e = (1.310±0.04) 10 4 a = 13.16±0.05 a = 12.2±0.04 a = 8.34±0.04 b = 11.0±0.2 b = 11.8±0.2 b = 9.9± c = 0.0±0.9 c = 0.0±0.5 c = 0.2±0.2 d = (1.868±0.05) 10 4 d = (1.786±0.05) 10 4 d = (1.313±0.04) 10 4 a = 13.59±0.05 a = 7.11±0.04 a = 8.95±0.04 b = 0.3±0.6 b = 1.38±0.6 b = 0.8± c = 0.1±0.9 c = 0.1±0.5 c = 0.3±0.2 d = (1.605±0.05) 10 4 d = (9.25±0.05) 10 3 d = (1.102±0.04) 10 4 a = 13.64±0.05 a = 7.11±0.04 a = 9.04±0.04 b = 0.0± b = 0.1± b = 0.4±0.2 c = (1.608±0.05) 10 4 c = (9.35±0.05) 10 3 c = (1.108±0.04) 10 4 a = 13.62±0.05 a = 7.22±0.04 a = 9.54±0.04 b = 0.2± b = 1.6± b = 3.1±0.8 c = (1.608±0.05) 10 4 c = (9.35±0.05) 10 3 c = (1.168±0.04) Table 6.12: Models that try to describe the fluctuations in the number of events per hour N of station 509 for three periods of time. 76

82 Model N = a P +b N = a P +b T +c N = a P +b T +c H +d N = a P +b T +c H +d S +e N = a P +b T +c S +d N = a P +b H +c S +d N = a P +b S +c N = a P +b H +c 2/5-13/5 12 (223 data points) parameters χ 2 r a = 10.74±0.04 b = (1.252±0.04) a = 11.2±0.04 b = 19.3±0.1 c = (1.845±0.04) 10 4 a = 11.34±0.04 b = 18.8±0.1 c = 0.3±0.9 d = (1.848±0.04) 10 4 a = 10.92±0.05 b = 14.1±0.1 c = 1.4±0.9 d = 0.2±0.2 e = (1.670±0.04) 10 4 a = 10.38±0.04 b = 16.8±0.1 c = 0.1±0.2 d = (1.697±0.04) 10 4 a = 11.08±0.04 b = 3.2±0.9 c = 0.3±0.2 d = (1.276±0.04) 10 4 a = 9.56±0.04 b = 0.2±0.2 c = (1.136±0.04) 10 4 a = 11.96±0.04 b = 2.2±0.9 c = (1.366±0.04) Table 6.13: Model that tries to describe the fluctuations in the number of events per hour N of station 509 for one period of time. 77

83 Figure 6.30: The event rate for station 509 for November 14, 2011 through January 5, 2012 (blue), along with the model that contains atmospheric pressure and outside air temperature (red). χ 2 risshownforthislastmodel. Figure 6.31: The residual points are more or less scattered randomly around the horizontal axis. However, there is trend visible near the end of the period. 78

84 Figure 6.32: The residues are normally distributed with a mean around zero.. A linear model using the barometric coefficient for detection station 509 Again one can also try a fit using the model with a barometric coefficient just as we did in section The results for the seven data sets are listed in table The data from station 509 for the period November 14, 2011 through January 5, 2012 is plotted against time, along with the barometric coefficient model in figure The residues are shown in figure Except for this period all periods show trends in the residual plot. Moreover, even in this period there is a trend visible at the end of the data period. The residues are small compared with the experimental values (95 % of the residues are smaller than 6 % of the experimental values). The residues are normally distributed with a mean around zero as can be seen in figure Therefore the model in this period is questionable. However, the models using the barometric coefficient in the other periods are not acceptable. 79

85 Period N = N 0 [1 β(p P 0 )] χ 2 r 28/6-26/7 11 (663 data points) N = 1817[1 (0.5 ± 0.3)(P 1011)] /7-31/8 11 (875 data points) N = 1694[1 (0.6 ± 0.5)(P 1013)] /9-2/11 11 (821 data points) N = 1590[1 (0.7 ± 0.3)(P 1017)] / /1 12 (1006 data points) N = 2275[1 (0.6 ± 0.2)(P 1012)] /1-27/2 12 (1147 data points) N = 2059[1 (0.4 ± 0.2)(P 1025)] /3-21/04 12 (821 data points) N = 1851[1 (0.5 ± 0.2)(P 1015)] /5-13/5 12 (223 data points) N = 1643[1 (0.7 ± 0.3)(P 1013)] 3.88 Table 6.14: Models that try to describe the fluctuations in the number of events per hour N of station 509 for seven periods of time using a barometric coefficientβ. Figure 6.33: The event rate for station 509 for November 14, 2011 through January (blue), along with the model using the barometric coefficient (red). 80

86 Figure 6.34: The residual points are more or less scattered randomly around the horizontal axis. However, there is trend visible near the end of the period. Figure 6.35: The residues are normally distributed with a mean around zero. 81

87 Chapter 7 Correlation between the MPV of the pulse heights and weather variables The most probable value (MPV) of the pulse heights registered by HiSPARC cosmic-ray detectors fluctuates over time. In figure 7.1 the fluctuating MPV for plate 1 of detection station 502 is shown. The MPVs of the pulse heights are determined with a parabola fit of the MPV peak in a 3 hour pulse height histogram as described in section 5.3. Figure 7.1: MPV of the pulse heights fluctuations registered by scintillation plate 1 of detection station 502 for July In my research I develop a model that describes the fluctuations of the measured MPV of the pulse heights 1. In this model the fluctuations are ascribed to changes in atmospheric variables. The shower data is taken from HiSPARC detection station 502, equipped with four detectors, located at Science Park Amsterdam. The choice is made for station 502, because plate 1 has a temperature sensor attached to its PMT. Moreover there is a temperature sensor lying at the bottom of the ski box as mentioned in section 4.1. For a description of detector 502 see section 3. The weather data for the conditions outside the ski box is collected with a Davis Vantage Pro 2 weather station. For a description of this device see section 4. 1 A similar analysis was performed by Richard Bartels [38]. 82

88 7.1 Correlation between the MPV of the pulse heights and individual weather variables The same variables were taken into account in the model building as for the event rate: outside air temperature solar radiation outside relative humidity atmospheric pressure In the case of the model describing the event rate (section 6.1) we could look at a correlation between two of these variables while holding the other variables constant within a certain domain. With the MPV of the pulse heights this was more difficult. The MPV is calculated for three hour intervals, whereas the event rate was calculated for one hour intervals. Moreover it is harder to find a stable period for a PMT for which the high voltage was not adjusted. I did not succeed in finding a period that resulted in more than 800 data points. If we divide this data set into intervals keeping two, or more variables constant we are left with very low statistics. Therefore it was not able to perform a correlation analysis between the MPV of the pulse heights and individual weather variables while holding the other variables constant. However, performing a correlation analysis between the MPV of the pulse heights and individual weather variables was still possible. The MPV of the pulse heights where taken from plate 1 of station 502 in the period of July 1 through October 18, The results are shown in figure 7.2. This results in correlation coefficients of r = 0.32 (outside air temperature, 788 data points), r = 0.42 (solar radiation, 788 data points), r = 0.42 (outside relative humidity, 811 data points) and r = 0.14 (atmospheric pressure, 788 data points). As mentioned in section these weather variables are not uncorrelated. Most importantly a correlation analysis between the solar radiation and the outside relative humidity results in a correlation coefficient of r = 0.65 (833 data points). This correlation is also shown in figure 7.2. We conclude that the outside air temperature and solar radiation probably will be included in a model that describes the fluctuations of the MPV of the pulse heights. The outside relative humidity might be part of this model and the atmospheric pressure will probably not be included in this model. 83

89 Figure 7.2: Above left: correlation between the MPV and the outside air temperature. Above right: correlation between the MPV. Middle left: correlation between the MPV and the outside relative humidity. Middle right: correlation between the MPV and the atmospheric pressure. Below: correlation between the outside relative humidity and the solar radiation. Data is taken from scintillation plate 1 of detection station 502 and the Vantage pro weather station 501 for July 1 through October 18,

90 7.2 Correlation between the MPV of the pulse heights and the ambient temperature of the detector A PMT is sensitive to temperature variations as described in section 3.2. We can use three different temperatures: PMT temperature Ski box temperature Outside air temperature These temperatures are correlated, as they should be in this case. This is shown in figure 7.3. All three temperatures follow the same pattern. The temperatures of PMT and ski box are at their extremities always higher or lower than the outside air temperature. This probably has to do with the difference in heat capacity of air being relatively higher than for example the metal of the PMT or the ski box itself. Figure 7.3: The temperature of the outside air, the temperature of the ski box and the PMT temperature plotted against time. Data taken from detector 1 of station 502. A correlation analysis between the MPV of the pulse heights and the outside air temperature, ski box temperature and PMT temperature results in correlation coefficients of r = 0.47 (461 data points), r = 0.60, (395 data points) and r = 0.60, (461 data points) respectively 2. This anticorrelation between the MPV of the pulse heights and the temperature measured by a sensor attached to the PMT can be seen in figures 7.4 and 7.5. It does matter if we take the outside air temperature or the temperature inside the ski box. However, it does not seem to matter if we take the PMT temperature or the temperature at the bottom of the ski box. 2 The number of data points is less than in the correlation analysis carried out in section 7.1. The reason for this is that data for different variables was invalid or not available. If we compare the data for all variables we have to ignore the measurements of all variables for a timestamp if a measurement of one variable for that timestamp is not present. 85

91 Figure 7.4: MPV fluctuations of the pulse heights registered by scintillation plate 1 of detection station 502 for July 2011 along with the PMT temperature. Figure 7.5: Anticorrelation between the MPV fluctuations of the pulse heights registered by scintillation plate 1 of detection station 502 for July through October 2011 and the PMT temperature. 86

92 We can use the PMT temperature in a linear model to describe the MPV fluctuations: MPV = a T PMT +b (7.1) with MPV the most probable value of the pulse heights in ADC counts and T PMT the temperature of the photomultiplier in Kelvin (K).aand b are numerical constants. The result is shown in figure 7.6. Figure 7.6: Linear model that describes the fluctuations of the MPV of the pulse heights using the temperature of the PMT. Data is taken from detection station 502. For the models describing the fluctuations in the event rate in sections through a χ 2 r was calculated. In order for this to work σ MPV has to be known for every determined MPV of the pulse heights. This value is determined by the fit routine curve fit. As was mentioned in section these values are too low (in my opinion) and result in a χ 2 r that is too high (in the order of 4 to 10). Therefore I decided to use the correlation coefficient as a goodness of fit test. The model is not perfect model with a correlation coefficient of r = This means with a coefficient of determination r 2 = 0.29 that only 29 % of the variance of the MPVs of the pulse heights can be predicted from the model. Not every PMT can be equipped with a temperature sensor. However, if we have a HiSPARC weather station present we can calculate the PMT temperature from the outside air temperature using the following model: T PMT = a T out +b S +c (7.2) witht PMT the temperature of the photomultiplier in Kelvin (K),T out the outside air temperature in Kelvin (K) and S the solar radiation in watt per square meter (Wm 2 ). a, b andcare numerical constants. This model is graphed with the measured PMT temperature in figure 7.7. The correlation coefficient between the modelt PMT model and the measured valuest PMT isr = This is an excellent model. We can use model (7.2) for the PMT temperature in model (7.1) to describe the fluctuations in the MPV of the pulse heights: or MPV = d (e T out +f S +g)+h (7.3) 87

93 Figure 7.7: Linear model that describes the fluctuations of the PMT temperature using the outside air temperature and the solar radiation. Data is taken from detection station 502. MPV = a T out +b S +c (7.4) with MPV the most probable value of the pulse heights in ADC counts, T out the outside air temperature in Kelvin (K) and S the solar radiation in watt per square meter. a, b and c are numerical constants (a = d e, b = d f and c = d g +h). The two models (7.1) in red and (7.4) in dashed black are used to describe the fluctuations of the MPV of the pulse heights for station 502 in July 2011 (in blue). The result is shown in figure 7.8. For the model using the PMT temperature T PMT we have a correlation coefficient of r = 0.60 as mentioned earlier. The model that uses the outside air temperature T out and the solar radiation S results in a correlation coefficient of r = These are not perfect models. In the best case we have a coefficient of determination r 2 = This means that only 29 % of the variance of the MPVs of the pulse heights can be predicted from the model. We can use model (7.4) to describe the MPV fluctuations of other PMTs. It turns out that the other plates of detection station 502 did not show a stable MPV fluctuation pattern. Therefore we look at the detectors of detection station 501. A correlation analysis between the MPV of the pulse heights and the values calculated by model (7.4) results in correlation coefficients of r = 0.51 (plate 1), r = 0.64 (plate 2), r = 0.60 (plate 3) and r = 0.63 (plate 4) for data from July The MPV data (blue) is plotted in figure 7.9 along with the model (red) Extending the linear model with more weather variables We can try to extend the linear model (7.4) with the outside relative humidity and the atmospheric pressure. We can try to apply a linear least square fit to the MPV data using the extended models: MPV = a T out +b S +c H +d (7.5) MPV = a T out +b S +c H +d P +e (7.6) 88

94 Figure 7.8: Linear models that describe the fluctuations of the MPV of the pulse heights. Data is taken from detection station 502 for July Figure 7.9: Linear model that describe the fluctuations of the MPV of the pulse heights. Data is taken from plate 2 of detection station 501 for July The model does not improve the fit results. A correlation analysis between the MPV of the pulse heights and the values calculated with the models results in correlation coefficients ofr = 0.65 (model (7.5)),r = 0.66 (model (7.6)). However, this is not an large improvement from r = 0.64 (model (7.4)). We conclude that this last model that uses the outside air temperature and the solar radiation describes the fluctuations of the MPV of the pulse heights best. 89

95 Chapter 8 Conclusions I observed fluctuations in the event rate and the MPV of the pulse heights (for three hour intervals) measured by HiSPARC cosmic-ray detectors. During my research project I investigated to what extent these fluctuations could be explained by by changing weather conditions. I found a strong negative correlation between the event rate per hour and the atmospheric pressure and a weak negative correlation between the event rate and the outside air temperature. No correlation was found between the event rate per hour and the outside relative humidity or the solar radiation. I have developed a linear model to describe the fluctuations in the event rate for intervals of an hour measured by detection stations 501, 504, 506, 507 and 509 located at Science Park Amsterdam in the period of June 2011 through May Shorter intervals than one hour did not produce effective models. The atmospheric pressure has the largest influence in all version of this model for all detection stations investigated. The outside air temperature plays a part in most versions of the model. This model was not perfect (χ 2 r ranges from 1.15 to 1.60) and was only valid for limited periods of time. For each new time period a new model had to be constructed with different parameter values for atmospheric pressure and outside air temperature at sea level. Moreover, the parameter values varied from detection station to detection station. The fluctuations of the event rate of detection station 502 could not be described by the model. I found a medium correlation between the most probable value of the pulse heights for a three hour period and the temperature measured by a sensor attached to the photomultiplier (PMT). The PMT temperature can be described using a linear model that incorporates the outside air temperature and the solar radiation at sea level. Consequently, we should describe the MPV fluctuations using the same variables. The linear model was used to describe the MPV fluctuations for stations 502 and 501 in the period July 1 through October 18, The model resulted in correlation coefficients in the ranger = 0.54 to r = The models could only be developed if we acquired weather data. Therefore I developed a LabVIEW application that sends weather data from a Davis Vantage Pro or Vantage Pro 2 weather station to the local HiSPARC database. Eight weather stations are now sending weather data to the database and more high schools will follow when more high schools that possess a Vantage Pro weather station become aware of the existence of the software. Moreover, if lesson materials will be developed that physics teachers can incorporate easily into their curriculum, more high schools will be willing to purchase a Vantage Pro 2 weather station. While I was doing my analysis I combined my profession as a high school physics teacher with my research by developing correlation software for high school students. It was already possible for students to analyze data for one hour intervals using Microsoft Excel. However, Excel is not designed for the analysis of large data sets, whereas Python is. With this software high school students can download, plot and perform a correlation analysis on their data. For this, they only have to answer yes or no questions and enter the specifications of the data they want to analyze. Python runs in the background, so high school students do not have to understand Python to use the software. If they want to dig deeper they do have to learn Python and they can use the Python source code scripts of the software as nice examples. 90

96 Recommendations The models I developed may be used to monitor the stability of a HiSPARC detection station by analyzing the variations of the model parameters for event rate and the MPV of the pulse heights for a three hour period. I would like to see the correlation software become part of HiSPARC educational materials. Among others Niek Schulteiss, Koos Kortland and Cor Heesbeen developed educational materials for HiSPARC (see [75], [76] and [77]). By developing more lesson materials that easily can be incorporated into the lessons of high school physics teachers we can make HiSPARC more than the detection array that is used by gifted high school students and universities. Several additional functions may be implemented into the correlation software: A script that enables the user to choose its own time interval that can be used in its analysis. Plotting with multiple axes that enables the user to spot correlations more easily. A script that enables high school students to look at a correlation between two variables while keeping other variables constant within a chosen domain. A script that enables high school students to build models that describe the shower data. Of course some guidance for student must be offered. Therefore the following educational materials may be produced: Write a high school student booklet about correlation analysis where the they are guided through carefully worded questions, using the socratic method. This booklet is aimed at the upper level secondary education (in Dutch: bovenbouw havo/vwo). Write a Python introduction high school student booklet. The analysis software does not require a lot of programming knowledge. This is its strength and its weakness. If high school students want to conduct their own analysis with their own specific wishes, they have to learn the basics of Python. Write a student booklet about the weather using the HiSPARC weather station. This booklet is aimed at lower and upper level secondary education (in Dutch: onderbouw en bovenbouw havo/vwo). 91

97 Bibliography [1] David F. Fokkema. personal communication, [2] January [3] January [4] induction.png/250px-electroscope_showing_induction.png, July [5] January [6] V.F. Hess. Origin of penetrating radiation (translation). Phys. Zeitschr., 13(1084), [7] B. Rossi. Cosmic Rays. McGraw-Hill, New York, [8] M. S. Longair. High energy astrophysics vol. 1. Cambridge University Press, Cambridge, second edition, [9] J. Cronin, T.K. Gaisser, and S.P. Swordy. Cosmic rays at the energy frontier. Scientific American, 276(1):44, [10] January [11] T.K. Gaisser. Cosmic rays and particle physics. Cambridge University Press, Cambridge, [12] G. Taubes. Science, 262:1649, [13] July [14] N. Vercruyssen. Read-out systeem voor een kosmische stralingsdetector. grouppages/master/thesis_nathan.pdf, [15] D.F. Torres and L. A. Anchordoqui. Astrophysical origins of ultra-high energy cosmic rays. Reports on Progress in Physics, 67: , [16] A. M. Hillas. Ann. Rev. Astron. Astrophys., 22:425, [17] M. C. Miller A. Venkatesan and A. V. Olinto. Astrophys. J., 484:323, [18] Prof dr. R.A.M.J. Wijers. personal communication, [19] July [20] E. C. Sutton. Observational Astronomy. Cambridge University Press, Cambridge, [21] Irina James. Study of cosmic transient phenomena with the scaler mode technique in the argo-ybj experiment. July

98 [22] J. W. van Holten. jan-willem_/eas_struc.pdf, July [23] D.F. Fokkema. PhD thesis (in preparation). PhD thesis, NIKHEF, [24] R. Engel et al. Extensive air showers and hadronic interactions at high energy. annualreviews.org/doi/pdf/ /annurev.nucl , [25] A. W. Wolfendale. Cosmic rays [26] K. Nakamura et al. Pdg booklet. J. Phys. G, 37(075021), [27] January [28] January [29] S. Tavernier. Experimental Techniques in Nuclear and Particle Physics. Springer, Heidelberg, [30] January [31] M.A. Pomerantz. Cosmic rays. Van Nostrand, New York, [32] January [33] C. Grupen. Astroparticle Physics. Springer, Heidelberg, [34] C. Grupen and B. Shwartz. Particle detectors. Cambridge University Press, Cambridge, [35] W.R. Leo. Techniques for nuclear and particle physics experiments. Springer, Heidelberg, [36] January [37] 9125b series data sheet. my.et-enterprises.com/pdf/9125b.pdf, July [38] Richard Bartels. An analysis of the mpv and the number of events per unit time. nl/fileadmin/hisparc/werk_van_studenten/bartels2012_.pdf, [39] S. Thoudam et al. An air shower array for lofar: Lora [40] Bob van Eijk. personal communication, [41] January [42] B. van Eijk. Leraar in Onderzoek - Hoogenergetische Kosmische Straling. NIKHEF, [43] J. W. van Holten. Statistics of coincidences. Lesmateriaal_fysica jan-willem_/coinc.pdf, [44] L. Lyons. Practical guide to data analysis for physical science students. Cambridge University Press, Cambridge, [45] February [46] February [47] July [48] July [49] L. Myssowsky and L. Tuwim. Z. Physik, 39(2-3): ,

99 [50] E. Steinke. Z. Physik, 58: , [51] L.I. Dorman. Cosmic rays in the Earth s atmosphere and underground. Kluwer academic publishers, Dordrecht, [52] Davis instruments. August [53] July [54] Integrated sensor suite installation manual. weather/manuals/ _im_06152.pdf, July [55] January [56] Derived variables in davis weather products. weather/app_notes/an_28-derived-weather-variables.pdf, July [57] Vantage pro 2 console manual _IM_06312.pdf, July [58] Lascar el-usb-tc-lcd temperature sensor. temperaturedatalogger.php?datalogger=384, July [59] Lascar el-usb1 temperature sensor. php?datalogger=101, July [60] davidf/framework/, January [61] B. van Eijk. Leraar in Onderzoek - Hoogenergetische Kosmische Straling. NIKHEF, [62] html#scipy-optimize-curve-fit, February [63] March [64] E. Kreyszig. Advanced engineering mathematics. John Wily and sons, Singapore, [65] M. S. Spiegel and L. J. Stephens. Statistics - Schaums Outlines. McGraw-Hill, New York, [66] May [67] J. M. Utts and R. F. Heckard. Mind on statistics. Brooks Cole, Boston, [68] March [69] May [70] David M. Glover and William J. Jenkins. Modeling Methods for Marine Science. Cambridge University Press, [71] March [72] Ivo van Vulpen. personal communication, [73] html, August

100 [74] August [75] Niek Schultheiss. Routenet. routenet-lesbrieven/, [76] Koos Kortland. Kosmische straling [77] Cor Heesbeen et al. Kosmische straling. nlt/, [78] A. Cho. Forging a cosmic connection between students and science. Science, 310(5749):770, [79] March [80] 95

101 Samenvatting Wij worden gebombardeerd door kosmische straling. Vanuit alle richtingen komen deze deeltjes uit de ruimte op ons af. Enkele kosmische deeltjes hebben zoveel energie als een tennisbal die met 200 km/uur geserveerd wordt. Dit lijkt wellicht niet zoveel, maar deze energie is geconcentreerd in één atoomkern. En een atoomkern is heel klein. Als we een atoomkern zouden opschalen en zo groot zouden maken als een zandkorrel, dan zou die zandkorrel zo groot zijn geworden als de aarde. Zoveel energie in zo n klein deeltje is dus enorm! Als een kosmisch stralingsdeeltje botst op een deeltje boven in de atmosfeer, wordt een deel van zijn energie omgezet in nieuwe deeltjes (volgens de inmiddels bijna to cult verheven formulee = mc 2 die ons vertelt dat massa ook een verschijningsvorm van energie is, waardoor we energie kunnen omzetten in massa en omgekeerd). Die deeltjes botsen weer op andere deeltjes in de atmosfeer, waarbij opnieuw deeltjes worden geproduceerd en zo gaat dit proces door. Op deze manier onstaat er een douche (shower) van deeltjes. Niet alle deeltjesdouches bereiken het aardoppervlak. De beginenergie van het kosmische stralingsdeeltje is dan niet groot genoeg en de deeltjes die in de douche geproduceerd zijn, worden dan geabsorbeerd door de atmosfeer. Als de beginenergie van het kosmische stralingsdeeltje wel groot genoeg is, bereikt deze deeltjesdouche het aardoppervlak en kunnen wij dit meten. Hoe groter de energie van de kosmische straling, hoe groter het oppervlak is dat op het aardoppervlak beregend wordt door een deeltjesdouche. Dat oppervlak is bij kosmische straling met de hoogste energie ongeveer een vierkante kilometer. Dit is ongeveer de afstand tussen middelbare scholen in een stad. HiSPARC (High School Project on Astrophysics Research with Cosmics) is een project dat als doel heeft leerlingen van de middelbare school kennis te laten maken met wetenschappelijk onderzoek. Leerlingen bouwen op de universiteit onder begeleiding van wetenschappers zelf kosmische stralingsdetectoren. Deze detectoren worden op de daken van de scholen geplaatst. Er staan nu meer dan 100 meetopstellingen op daken van scholen en universiteiten in binnen- en buitenland. Leerlingen ijken de opstelling en kunnen de binnenkomende data analyseren. Al vele scholieren hebben hun profielwerkstuk, waarmee ze hun middelbare school afsluiten, gewijd aan HiSPARC. Ook ik deed dat in Een deeltje produceert een spanningspuls bij onze meetopstelling. De pulshoogte is een maat voor de energie die een deeltje afgeeft aan onze detector. Als we heel veel pulsen meten, blijkt het dat één geladen deeltje, waarschijnlijk een elektron of een muon (zwaar elektron) ongeveer dezelfde pulshoogte produceert. Als we een histogram maken van alle pulshoogtes die onze detector meet, zien we een duidelijke piek. Dit is de meest waarschijnlijke waarde of MPV (Most Probable Value) van de pulshoogte. De variabelen die wij meten met de kosmische stralingsdetectoren vertonen patronen. Zo fluctueren de MPV en het aantal pulsen dat we meten per uur flink in de tijd. De fluctuaties van het aantal pulsen per uur en de MPV waarde zijn een indicatie van de stabiliteit van onze detectoren. Het is bekend dat veranderende weersomstandigheden invloed hebben op onze meetopstellingen. Daarom is een twintigtal opstellingen ook uitgerust met een professioneel weerstation. De weergegevens werden nog niet opgestuurd naar de HiSPARC database, zoals dat wel gebeurt met de gegevens van de kosmische deeltjes waaraan wij meten. Mijn eerste taak was het operationeel maken van software die dit zou gaan doen. Vanaf 23 mei 2011 worden de weergegevens van opstelling 501 op Science Park Amsterdam volautomatisch opgestuurd naar de database. Inmiddels zijn er in Nederland acht HiSPARC weerstations operationeel. In mijn onderzoek heb ik geprobeerd de fluctuaties van het aantal pulsen per uur en de fluctuaties van de MPV 96

102 van de pulshoogtes te beschrijven met een model. In deze modellen zijn de weervariabelen luchtdruk, buitenluchttemperatuur en hoeveelheid zonnestraling opgenomen. Het aantal pulsen is sterk afhankelijk van de luchtdruk. De luchtdruk is een maat voor de hoeveelheid lucht en dus de hoeveelheid deeltjes boven de meetopstelling. Hoe meer deeltjes er zich boven de detector bevinden, des te groter is de kans op een wisselwerking met de inkomende deeltjes. Bij hogere luchtdruk zal het punt waar de eerste botsing plaatsvindt ook hoger liggen. Door deze effecten zullen er meer botsingen hebben plaatsgevonden, waardoor minder deeltjes het aardoppervlak zullen bereiken. Bij hogere luchtdruk verwachten we dus minder pulsen te meten. We zeggen ook wel dat er een negative correlatie bestaat tussen luchtdruk en het gemeten aantal pulsen per uur. Er bestaat ook een (zwakkere) negatieve correlatie tussen de luchttemperatuur en het gemeten aantal pulsen per uur. De gevoeligheid van de apparatuur (in het bijzonder de fotoversterkerbuis) voor de omgevingstemperatuur speelt hier waarschijnlijk een rol. Er bestaat een negatieve correlatie tussen de MPV van de pulshoogtes en de temperatuur van de fotoversterkerbuis. Deze werd gemeten door een sensor die aan de buis was vastgemaakt. Een hogere temperatuur resulteert dus in een lagere waarde voor de MPV van de pulshoogtes. De temperatuur van de fotoversterkerbuis kon worden beschreven met een model waarin de variabelen luchttemperatuur en hoeveelheid zonnestraling waren verwerkt. Dus konden we de fluctuaties van de MPV van de pulshoogtes beschrijven met dezelfde variabelen. Tijdens mijn analyse heb ik mijn beroep als docent natuurkunde gecombineerd met mijn onderzoek door software te ontwikkelen waarmee middelbare scholieren een correlatie analyse kunnen uitvoeren. Het was al mogelijk voor leerlingen om uurgemiddelden van de data te analyseren met Microsoft Excel. Dit programma is echter niet ontworpen voor het werken met grote hoeveelheden data. De programmeertaal Python biedt veel meer mogelijkheden. Bij mijn software draait Python op de achtergrond. Leerlingen kunnen nu data downloaden, plotten en een correlatie analyse uitvoeren. Ze hoeven hiervoor slechts ja-neevragen te beantwoorden en de specificaties van de door hen gewenste data in te voeren. Begrip van Python is dus niet nodig om de software te kunnen gebruiken. Als ze dieper willen gaan, zullen ze Python moeten leren en kunnen de Python scripts dienen als goede voorbeelden. 97

103 Acknowledgements This report contains my findings during the NIKHEF research project that I did with HiSPARC under the supervision of Prof. Bob van Eijk. It forms the finalization of my physics master s degree. In 2002 my high school physics teacher Jef Colle introduced me to the High School Project on Astrophysics Research with Cosmics (HiSPARC). With other high school students I built a set of scintillation detectors for the detection of cosmic rays. Besides that calibration measurements were conducted to find the optimal settings for the detectors. This process was guided by Henk Jan Bulten, Bob van Eijk and Sander Klous. In 2005 HiSPARC was awarded by the ALTRAN foundation. I was asked to give a presentation at the gathering where HiSPARC officially received the award. By then I was studying physics at the University of Amsterdam. HiSPARC inspired me to study physics and become a high school physics teacher. I was very proud that this was mentioned in Science magazine [78]. During my last years in high school HiSPARC paved the way for my physics study and I was very fortunate to be able to complete my physics masters degree with the same project. First of all I would like to thank my supervisor Bob van Eijk. With his project HiSPARC it was possible for me to combine my master research project with high school education. The combination of high school physics teaching with a physics masters was hard. There were times that I hardly had time to think. At those times Bob was there to keep me focused and to set my priorities straight: graduation comes before teaching students and my high school should support me in this. Bob has inside knowledge of (high school) teaching and is one of the few professors I know of that is not too proud to answer a stupid question. I also like his sense of humor. Doing hard work is OK, but he always made time for an anecdote a laugh or the occasional Windows bashing. For the nine years that I know him he inspired me to study physics and I will continue to do so, because you never stop learning. HiSPARC is a project for the long run, and I have the feeling that this is only the beginning. I would like to thank David Fokkema for sharing his sharp mind to solve the problems of the people around them. Despite the fact that he had no time because of his dissertation, he always found a moment where he could simplify computer code. I am glad to see that he will start teaching again at his local high school. In the last period of my masters Arne de Laat joined HiSPARC. I was fortunate to have another eclectic around that I could turn to for questions. I am very grateful that he took the time to critically review the first draft of my thesis. I also would like to thank Els de Wolf. She was kind enough to serve as a second supervisor for my thesis. I thank her for her time during the hectic last month of my masters. With her help I was able to graduate in time. Last but not least I would like to thank Fred Schimmel. Although he has advanced knowledge of LabVIEW, he was prepared to help me with every little pitfall I fell into. 98

104 Appendix A Cosmic-ray and weather data analysis software (in English) The event rate of a HiSPARC detection station data is around 0.3 Hz for a two detector station and around 0.7 Hz for a four detector station. Every day this results in and events respectively for the two setups. As a consequence the data files for the analysis of a month or a year become huge. Here mathematical environments such as Python, Matlab, or Mathematica become indispensable. It is possible to analyze the data with Excel from Microsoft Office. However, this can become rather frustrating since Excel is only designed for basic arithmetics. Advanced analysis can become very non-intuitive. At the NIKHEF institute the analysis is carried out by the more versatile scipy and numpy packages of the programming language Python. In short if one really wants to do research with HiSPARC data, learning Python is a must. In the HiSPARC philosophy high school students must be able to analyze the incoming data. However, learning a program language such as Python can become an untakeable barrier. Therefore I decided to create a user interface for high school students: HiSPARC data analysis. They must still install Python. After installing they only have to answer yes or no questions and enter the specifications of the data they want to analyze. Python runs in the background, so high school students do not have to understand Python to use HiSPARC data analysis. If they want to dig deeper they do have to learn Python. In this case the user interface served as a nice introduction. In this section the basic structure of the correlation analysis software is described. The software can be downloaded from [47] or from Github [48]. The software consists of several Python scripts that can be modified if the user wishes to do so. They can also serve as examples for the analysis high school students can conduct on their own. For high school students I wrote a quick start guide which is included as appendix C. Figure A.1: Introduction screen of HiSPARC Data Analysis. 99

105 The user interface HiSPARC data analysis can do essentially three things: Download HiSPARC shower and weather data Plot data Apply a simple linear correlation analysis. An overview of the capabilities of HiSPARC data analysis is shown in the flow chart of figure A.2. Figure A.2: Flow chart of HiSPARC Data Analysis. 100

106 A.1 Downloading data Figure A.3: Flow chart of the download part of HiSPARC Data Analysis. HiSPARC data is stored in the HiSPARC database. To make this data available for data analysis David Fokkema wrote a download script as a part of his HiSPARC framework [60]. This script is incorporated in the download part of HiSPARC data analysis. An overview of the download part of the software is shown in the flow chart of figure A.3. If the user specifies the HiSPARC station ID, start date and end date of his choice, this data is downloaded and saved as a so called HDF5 file. HDF5 stands for Hierarchical Data Format 5. It is a file format created to save and handle large amounts of data. These files can become quite large (1 GB for a year). The software cuts the required data in parts of a month maximum. In this way the chance that these files will overload the RAM of the user s computer is much smaller. After the data is downloaded the duplicates are removed. Duplicate data exists because the HiSPARC computer connected to a HiSPARC detection station does not have a working internet connection at all times. If this is the case the HiSPARC DAQ software will keep trying to send the data to the database. It sometimes happens that the same data is send twice or more often. Finally the filename of the data file and its location are printed along with the kind of data that the data file contains (shower data, weather data or both) as can be seen in figure A.4. Figure A.4: Screenshot of HiSPARC Data Analysis when data is downloaded 101

107 Figure A.5: Flow chart of the plot part of HiSPARC Data Analysis. A.2 Plotting data HiSPARC data analysis can plot the downloaded data against time. An overview of the plot part of the software is shown in the flow chart of figure A.5. If the user enters the desired variable and time interval, this data is plotted. Every variable that is present in the data file can be plotted (see section 3.4 for the available shower variables and section 4.1 for the available weather variables). For shower data the most interesting ones are the event rate, pulse heights and pulse integrals. A.2.1 Event rates LabVIEW automatically calculates the event rate (in Hz). If the user wants to plot these values the data is searched for bad data. This is necessary for the following reason. As mentioned in section sometimes the HiSPARC detector computer is rebooted. If this happens no data can be send to the database by HiSPARC DAQ. The LabVIEW software calculates the event rate as a running average for the last 90 seconds. If the computer was turned off this event rate becomes zero (because it takes longer than 90 seconds to boot the computer and restart the HiSPARC software) and then slowly increases to the actual value for the event rate. To remove this data the data set is scanned for the event rate of zero. If such an event is found data from 90 s before the timestamp of this event until 90 s after this timestamp is removed from the data set. The user also has the option to calculate the event rate for the time interval of his choice. If the user enters the desired time interval the data set is scanned for pulse height registrations within each desired time interval for plate 1 of the detection station. The number of registered pulse heights divided by the number of seconds in the time interval is equal to the mean event rate (in Hz). As was mentioned in section for a four-detector station it is important to realize that the trigger condition is satisfied for every event (two pulse heights above 70 mv or three pulse heights above 30 mv in an interval of 1.5 µs) and not for every individual pulse height. If the trigger condition is met all four PMTs are read. If two pulse heights were above 70 mv than the pulse heights measured by the other two PMTs don t have to be above 70 mv. In short we can calculate the event rate by looking at the number of pulse height measurements even if an individual pulse height is below the threshold. This does not affect the number of events since the registrations in the other plates were responsible for the trigger. A.2.2 Pulse heights The user can plot the individual pulse height measurements for every PMT against time. However, the changes in the pulse height histogram over time are more interesting. HiSPARC is mostly interested in charged particles. This makes the fluctuations of the Most Probable Value (see section 3.4.1) the most important feature of the histogram. The MPV peak in the pulse height histogram can be described by a Landau distribution. Since this peak resembles 102

108 Figure A.6: Screenshot of HiSPARC Data Analysis when the user selects a variable to plotting. a parabolic shape I decided for simplicity to fit a parabola to the MPV peak in order to determine the pulse height corresponding to the peak. A similar analysis was conducted by Richard Bartels [38] using a gaussian fit rather than a parabola. The user can specify the time interval over which the MPV of the pulse heights must be determined. A pulse height histogram can only be plotted if there is enough data to get a distribution of values so this interval cannot be too small. All pulse height values are accepted, so there are no pulse height limits specified. The data is split in time intervals specified by the user. For every time interval a histogram is plotted. The pulse heights are split in a large number of bins in order to make all the features of the histogram visible. After trial an error it turns out that the choice for 150 linear divided bins produces the desired result. A smaller number of bins obscures fluctuations and a much larger number of bins makes the position of the peak too sensitive for fluctuations. We are only interested in the peak. Therefore we make some cuts in the histogram to be able to make a good parabola fit. On the left side of the MPV peak we see the histogram falling according to the photon power law (equation 5.1. Then the MIP contribution becomes dominant and the histogram starts rising. From this local minimum to the left the histogram is cut i.e. all pulse heights below the rising point are thrown away (figure A.7). Now we can select the highest bin in the trimmed histogram. The pulse height belonging to the highest bin is the best guess for the MPV of the pulse heights. Only around the MPV of the pulse heights the peak looks like a parabola. Therefore we select all pulse heights in an interval around the peak (figure A.8). 103

109 Figure A.7: A cut is applied to isolate the peak and determine the MPV of the pulse heights. Figure A.8: Several different intervals around the best guess (shown in green) of the peak value are selected for a parabolic fit. Here an interval of 200 ADC counts is shown. 104

110 This selection of pulse heights is split into 40 bins and a new histogram is plotted. For this interval a parabola is fitted: y = a (x b) 2 +c with x the pulse heights belonging to the bin centers and y the number of pulse heights in each bin. a is the steepness parameter, b is the horizontal translation parameter and c is the vertical translation parameter. The most optimized value for parameter b is the pulse height corresponding to the MPV peak. For the fit the routine scipy.optimize.curve fit is used. Here a non-linear least squares procedure (the Levenberg-Marquardt algorithm) is applied to fit the parabolic function (A.1) to our data [62]. This fit is carried out for five different intervals around the obtained best guess for the MPV of the pulse heights. The fit where b and the initial guess differ the least is selected as the most optimal one. A trial and error approach resulted in the intervals of 200 (best guess ± 100), 160 (best guess±80), 120 (best guess±60), 80 (best guess±40) and 60 (best guess±30) ADC counts around the initial guess. In figure A.9 a MPV peak fit is carried out for different time intervals. We can see that if we make the interval smaller than one hour the MPV peak becomes less visible and more sensitive to large fluctuations. This limits the effective time interval that can be chosen by the user for correlation analysis with weather variables. (A.1) 105

111 Figure A.9: MPV fit for different time intervals. 106

112 A.2.3 Pulse integrals The user can plot the individual pulse integrals for every trace. However, the pulse integral histogram is more interesting. The pulse height integral histogram is made by integrating the trace of every event. If we gather enough data a pulse integral histogram can be plotted. On data.hisparc.nl the pulse integral histogram for a day is displayed (figure A.10). Figure A.10: Pulse integral histogram of station 501 January 12, [41]. The pulse integral histogram looks a lot like the pulse heights histogram. This is expected since a larger pulse height will result in a larger pulse integral. The peak in the pulse height integrals histogram is the MPV peak of the pulse integrals histogram (figure A.10). The pulse integral corresponding to this peak can be determined by a parabolic fit as was described in section A.2.2. Some parameters in the fit procedure are changed: The initial histogram for the user specified time interval is split in 750 bins. The intervals around the initial guess for the MPV of the pulse integrals are 3000 (best guess ± 1500), 2500 (best guess±1250), 2000 (best guess±1000), 1500 (best guess±750) and 1000 (best guess±500) ADC counts nanoseconds. In the end the reduced histogram where the parabola fit is applied is split in 500 bins. 107

113 A.3 Correlation analysis Figure A.11: Flow chart of the correlation part of HiSPARC Data Analysis. With HiSPARC data analysis the user can carry out a linear correlation analysis for two variables of his choice. In the analysis it is determined how well a linear least squares fit describes the measured data. An overview of the correlation part of the software is shown in the flow chart of figure A.11. If one variable of his choice is the pulse height or the pulse integral he can let the software choose to either use one of these variables or determine the MPV by using the method described in sections A.2.2 and A.2.3. When the names of the variables are entered the bad data is removed. The weather data must lie between limits listed in table A.1: lower limit weather value upper limit. For shower data there is a different criterion for the lower limit, because the measured value can not be equal to zero: lower limit < shower value upper limit The shower data must lie between limits listed in table A.2. These limits are inspired by the Vantage Pro manual [57] (p ). After the bad data is removed the user can choose to average the variable values. For this the time interval must be entered over which the average value must be calculated. Then the averages for the two variables can be used in the correlation analysis. However, if the variables are not averaged linear interpolation might be necessary. If one wants to use variables from different detectors the (e.g. shower event rate and atmospheric pressure value) the corresponding timestamps will be different. On average there is a shower event every second, whereas the weather variables are read every three seconds. Although we do not have the exact atmospheric pressure reading for every shower event we can use interpolation to approximate this value. This is accomplished with the numpy.interp module [79]. (A.2) (A.3) 108

114 Variable (s) Upper limit Lower limit Temperature -40 C 65 C Humidity 0 % 100 % Atmospheric pressure 540 hpa 1100 hpa Wind direction Wind speed 0 ms 1 67 ms 1 Solar radiation 0 Wm Wm 2 UV index 0 16 Evapotranspiration 0 mm 2000 mm Rain rate 0 mmh mmh 1 Heat index -40 C 74 C Dew point -76 C 54 C Wind chill -79 C 57 C Table A.1: Limits for weather data: lower limit weather value upper limit [57] (p.49-50). Variable (s) Upper limit Lower limit Event rate 0 Hz 3.5 Hz Pulse heights 0 ADC counts ADC counts Integrals 0 ADC counts ns 10 9 ADC counts ns Table A.2: Limits for shower data: lower limit<shower value upper limit. 109

115 Table A.3: Shower data and weather data that needs interpolation. For every event rate we are going to find the nearest pressure value. GPS timestamp (s) Event rate (Hz) GPS timestamp (s) Pressure (hpa) A.3.1 Interpolation If a shower measurement (e.g. an event rate with timestamp x) falls between two weather weather measurements (x a,y a ) and (x b,y b ) (e.g. two atmospheric pressures) we can use interpolation to approximate the weather value corresponding to the shower measurement. For two data points (x a,y a ) and (x b,y b ) we can calculate the linear interpolated valuey for known value x to be: y = y a +(y b y a ) (x x a) (x b x a ) (A.4) For example if we have two pressure measurements (x a,y a ) = ( s, hpa) and (x b,y b ) = ( s, hpa) and an event rate with a timestamp in between( s,0.7 Hz) we can find the pressure corresponding to the event rate timestamp(x,y) = ( s,y) by interpolation: y = ( ) ( ) = hpa ( ) (A.5) The interpolated pressure hp a lies in between the pressure measurements as expected. In the same way the pressure data in table A.3 is interpolated to find the interpolated pressure data corresponding to the event rate measurements. The results are shown in table A.4 and plotted in figure A.12. Note that the interpolated values lie on the blue line connecting the measurements (hence the name linear interpolation) [80]. 110

116 Table A.4: Event rates with interpolated pressure values. Event rate (Hz) Pressure (hpa) Figure A.12: Plot of the data (blue) with linear interpolation superimposed (red). 111

117 A.3.2 Least squares fit After the data is interpolated or averaged if necessary, we have a data set with two variables (e.g. event rates and atmospheric pressure values). Now a linear least squares fit is applied to the data with the module numpy.linalg.lstsq [63]. In the method of linear least squares a line: y = a x+b (A.6) is fitted through the data points (x 1,y 2 ),...(x n,y n ) in such a way that the sum of the squared vertical distances between the data points and the fit line is a minimum. This condition leads to the so called normal equations: yi = a x i +b n (A.7) xi y i = b x i +a x i 2 (A.8) where we sum overifrom 1 tillnwith n the number of data points. If we solve the normal equations we obtain the values for parameters a and b that minimize the sum of the squared vertical distances between the data points and the fit line: a = n( x i y i ) ( y i )( x i ) n x i2 ( x i ) 2 (A.9) b = ( y i )( x i 2 ) ( x i )( x i y i ) n( x i2 ) ( x i ) 2 (A.10) An example of a linear least squares fit is shown in figure A.13. Here the event rate is plotted against the Atmospheric pressure. A negative correlation is clearly visible [64] (p ), [65] (p.284). Figure A.13: Plot of (fictional) event rate and atmospheric pressure data along with linear least squares fit line. 112

118 A.3.3 Correlation coefficient A linear least squares fit analysis can always be performed for two variable y and x. However, we would like to determine how well the found linear equation describes the relationship between the variables. The dependence between two variables is called a correlation. If y becomes larger if x becomes larger we speak of a positive correlation. If y becomes smaller ifxbecomes larger we speak of a negative correlation. A general impression of the strength of the correlation can be gotten by inspection of the scatter plot for the two variables (figure A.14). Figure A.14: Different types of correlation [66]. The strength of the linear correlation between the measurements x i and y i can be calculated with the correlation coefficient 1 r: r = n x i y i ( x i )( y i ) [ n x i2 ( x i ) 2][ n y i2 ( y i ) 2] (A.11) where we sum overifrom 1 tillnwith n the number of data points. The correlation coefficient varies between -1 and 1. A negative sign indicates a negative correlation, a positive sign indicates a positive correlation. The closer the correlation coefficient is to -1 or 1 the stronger the correlation is. A value close to zero indicates a weak linear correlation [65] (p ). A.3.4 Coefficient of determination The square of the correlation coefficientr 2 is called the coefficient of determination and can be shown to be equal to: 2 r 2 = (yi model y) 2 (yi y) 2 (A.12) with y i model the values predicted by the linear fit and y is the mean value. We sum over i from 1 till n with n the number of data points. This ratio can be interpreted as the ratio of the explained variation to the total variation. It is the proportion of the variance of the y values that can be predicted from x values with the linear fit. Therefore this coefficients gives us an indication how good our model is. This coefficient ranges between 0 and 1. If r 2 is close to 1, we have a good model. The coefficient of determination represents the percentage of the data that is the closest to the line of best fit. If we find a correlation coefficient r = 0.80 we calculate the coefficient of determination r 2 = (0.80) 2 = This 1 The correlation is sometimes called the Pearson product moment correlation coefficient. 2 See for example [65] (p.325). 113

119 means that 64% of the total variation in y can be explained by the linear fit line. The remaining 36% of the total variation in y can not be explained by our model. It is important to note that the existence of a correlation between variables y en x does not necessarily imply a causal relationship between the two variables. A correlation can mean the following: There is a causal relationship betweenxand y. There is a causal relationship between x and y, but this is not visible: an unknown variable makes this relationship difficult to prove. There is no causal relationship between x and y. The dependence that is observed is caused by the influence of other (hidden) variables onxand or y [67](p.94-95), [65] (p ), [68]. On the other hand if the correlation coefficient is zero this does not have to mean that there is no correlation between variables x and y. It means that there is not a linear correlation between them. For example it is possible there still exists a curvilinear relationship between the two variables. A.4 Use at high school For high school students I wrote a quick start guide that is included as Appendix C. The software was tested at the Da Vinci college, a high school in Leiden during lessons NLT (Nature, Life and Technology) in a 5 vwo classroom (17 year olds). During the two lessons where the software was used a lot of bugs surfaced. Most of them are now fixed. Several additional functions may be implemented into the correlation software: A script that enables the user to choose its own time interval that can be used in its analysis. Plotting with multiple axes that enables the user to spot correlations more easily. A script that enables high school students to look at a correlation between two variables while keeping other variables constant within a chosen domain. A script that enables high school students to build models that describe the shower data. Naturally some guidance for student must be offered. Therefore the following educational materials may be produced: Write a high school student booklet about correlation analysis where the they are guided through carefully worded questions, using the socratic method. This booklet is aimed at the upper level secondary education (in Dutch: bovenbouw havo/vwo). Write a Python introduction high school student booklet. The analysis software does not require a lot of programming knowledge. This is its strength and its weakness. If high school students want to conduct their own analysis with their own specific wishes, they have to learn the basics of Python. Write a student booklet about the weather using the HiSPARC weather station. This booklet is aimed at lower and upper level secondary education (in Dutch: onderbouw en bovenbouw havo/vwo). 114

120 Appendix B Weather station software - Installation manual (in Dutch)

121 Appendix C Data correlation software - getting started guide for high school students (in Dutch)

122 Vantage Pro Software Documentatie Weerstation voor gebruik bij HiSPARC Loran de Vries Versie

123 Inhoud 1 Benodigdheden HetVantageProbasisstationverbindenmetdePC Ingebruiknemenvandeweerstationsoftware Installatie Weerstationautomatischopenenalsdepcopstart Desoftwarevoordeeerstekeeropstarten Benodigdegegevens Deweerstationsoftwarestarten Weerstationsoftwaregebruiken Detabladenstructuur Hettabblad Currentweatherdata Detweetabbladenmetgrafieken Hettabblad Error Hettabblad Settings Opgestuurdeweerdatauitdedatabasebekijken Weerdatadownloaden DataimportereninExcel Problemenoplossen...25 AppendixA Problemenmetdeprolificdriver...27 AppendixB-Handmatiginstallerenvandesoftware...29 B.1 Gebruikvanhetprogramma winzip...30 B.2 GebruikvandeuitpakfunctievanWindows...31 B.3 Belangrijk:bestandslocatievanhetweerprogramma...33 Appendix C Communicatieproblemenviadecompoort De basis van de Labview weerstation software is ontworpen door Floor Terra en in de huidige vorm gegoten door Loran de Vries. - Bij vragen, onduidelijkheden of suggesties kunt u contact opnemen met Loran de Vries (lvvries@science.uva.nl). 2

124 1 Benodigdheden Voor het gebruiken van de HiSPARC weerstation software zijn de volgende zaken nodig: DeHiSPARCPC EengeïnstalleerdweerstationvandefirmaDavistype Vantagepro of Vantagepro2. Figuur 1.1 Sensoren van de Vantage Pro Figuur 1.2 Vantage Pro Console Setvoorverbindingmetdepc. o Data logger(figuur 1.3) o Data loggerkabel(figuur 1.4) o Verbindingsstekker(figuur1.5) 1 Figuur 1.3 Data logger geplaatst in de achterkant van de console Figuur 1.4 Data logger kabel Figuur 1.5 Seriële verbindingsstekker 1 De mogelijkheid bestaat dat er geen seriële maar slechts een usb verbindingsstekker bij het weerstation is geleverd. Kijk voor verdere informatie hierover in de Davis documentatie zie -> support -> Go to Weather Support -> Instruction Manuals -> selecteer Vantage Pro of Vantage Pro 2 -> Vantage Pro2 Console onder het kopje system. 3

125 2 Het Vantage Pro basisstation verbinden met de PC Verwijderhetbatterijkapje(ziefiguur2.1) Verwijderdeadapteren/ofdebatterijen. N.B. Als de adapter of de batterijen niet verwijderd worden voordat de data logger geïnstalleerd wordt, kan het basisstation of de datalogger beschadigd raken. Verwijder de data logger nooit als het basisstation nog in bedrijf is. Drukdedataloggervoorzichtiginhetdaarvoorbestemdevakje. Sluithetbasisstationweeraanmetdeadapteren/ofplaatsdebatterijen(eerstdeadapteren daarna de batterijen). Verbinddedataloggermetdedatakabel. Verbinddedatakabelmetde9-pinconnector. Sluitde9-pinconnectoraanopdeseriëlepoortvandecomputer. Figuur2.1VerbindingvandeVantageProconsolemeteenPC. 4

126 Optioneel: Bij het ontbreken van een seriële poort kan er een verloopkabeltje nodig zijn van serieel naar usb(de kabeltjes van de merken Prolific en Sweex zijn getest en werken). Als er een seriële poort op de pc aanwezig is, verdient het aanbeveling deze poort ook te gebruiken. Figuur 2.2 Serieel naar USB verbindingskabeltje van het merk Prolific. BijdeleveringvanhetweerstationishetverloopstekkertjevanProlificmeegezonden.Voorde correcte werking moet er wellicht een driver worden geïnstalleerd. Mocht u de mini-cd met de driver kwijt zijn, is deze te downloaden. DownloaddelaatsteversievandeProlificPL-2303USBtoSerialdriver.Hetbestandheeftde naam PL2303_Prolific_DriverInstaller_v1417.zip en is te vinden op: Unzip PL2303_Prolific_DriverInstaller_v1417.zip en installeer de driver door het programma PL2303_Prolific_DriverInstaller_v1417.exe te openen en de stappen op het scherm te volgen Startdepcopnieuwop. N.B. Op enkele computers waar de Prolific verloopstekkers worden gebruikt, zijn driverproblemen opgetreden. Mocht dit optreden, volg dan de stappen in appendix A. 5

127 3 In gebruik nemen van de weerstation software 3.1 Installatie De weerstation software is al op uw HiSPARC pc geïnstalleerd via HiSPARC update. Hiervoor hoeft u dus zelf niets te doen. In de map Z:\user\hisparcweather zouden in ieder geval de onderstaande bestanden moeten staan: Als dit niet het geval is, kan de laatste versie van de weerstation software gedownload worden van: De instructie voor handmatige installatie staat beschreven in appendix B. 3.2 Weerstation automatisch openen als de pc opstart Als de HiSPARC pc opstart, zal het batchbestand StartHiSPARCSoftware draaien. Tot nog toe stond daar altijd: HiSPARC weather station disabled. Figuur 3.9 batchbestand StartHiSPARCSoftware. Dit was voorheen ook de bedoeling, want er was nog geen weerstation software geïnstalleerd. We gaan dit nu veranderen. Hierdoor zal het weerprogramma automatisch opstarten wanneer de pc wordt aangezet, net als het programma HiSPARC DAQ II. 6

128 Omditteveranderendoenwehetvolgende: Ganaardemap Z:\persistent\configuration enopenhetbestand config.ini methetprogramma Notepad of Wordpad. Figuur 3.10 Het configuratiebestand config.ini staat in de bestandsmap Z:\persistent\. Inhetbestand config.ini staatbijdekop[weerstation]: Enabled=0. Dezewaardemoetwordenvervangenvan0naar1. Slahetbestandconfig.iniop. Figuur3.11Inconfig.inivervangenwedewaardebijhetweerstationvan0naar1. Inhetbestand config.ini staatbovenaanookhethisparcstationsnummer.inhetvoorbeeldis dat 96. Dit getal is nodig als weatherstation.exe opgestart wordt. Deweerstationsoftwareisnuklaarvoorgebruik! 7

129 4 De software voor de eerste keer opstarten 4.1 Benodigde gegevens Voorhetopstartenvandesoftwarevanhetweerstation(ditdoenwein 4.2)iseenaantalgegevens nodig: -hetnummervandecompoortwaarhetweerstationopaangeslotenis; - de baudrate van het weerstation; - het HiSPARC stationsnummer. Com poort De weerstation software moet het nummer weten van de seriële communicatiepoort(com poort) waarop het weerstation is aangesloten. Dit nummer is als volgt te achterhalen: Ganaar systeemeigenschappen.ditkandoor(inhetmenustart)metderechtermuisknopop Deze computer en daarna met de linkermuisknop op eigenschappen te klikken. Figuur 4.1 Het venster systeemeigenschappen openen via menu start. Hetvenster systeemeigenschappen zalopenen.ditvensterisooktebereikenvia Configuratiescherm-> Systeem. Klikbijhettabblad Hardware op Apparaatbeheer. Figuur 4.2 De optie apparaatbeheer openen bij het tabblad hardware. 8

130 Klaphetkopje Poorten(COM&LPT) uitdoorophetplustekenernaastteklikken.hierstaan decompoortenvermelddieingebruikzijn.inhetvoorbeeldisditcompoort7(com7).ditgetal hebben we nodig. Figuur 4.3 Achterhalen van het compoort nummer in het venster apparaatbeheer. Baudrate De baudrate is de overdrachtssnelheid van een seriële verbinding; de hoeveelheid bits die per seconde via een serieel kanaal kan worden verzonden. DebaudratevoordeVantageProendeVantagePro2isaltijd19200bits/sec. Stationsnummer Dit nummer is af te lezen in het bestand Z:\persistent\config.ini zoals is beschreven in 3.2 Weerstation automatisch openen als de pc opstart. 9

131 4.2 De weerstation software starten Als de pc opnieuw wordt opgestart, zal de weerstation software automatisch openen. Het programma kan ook handmatig gestart worden door in de map Z:\user\hisparcweather op het programma hisparcweather.exe te klikken. Figuur 4.4 De software voor het weerstation handmatig starten. Als hisparcweather.exe opstart,zaleen COMError vensterverschijnen. Vulhierdejuistecompoort,debaudrateenhetstationsnummer(zie 4.1)inendrukop OK. Figuur 4.5 Bij de eerste keer opstarten zal er een COM error verschijnen. Desoftwarezounumoetenwerken! 10

132 Opmerkingen: Deeerstekeerdatdeweerstationsoftwarestart,kunnendegrafieken( 5.3)nognietdirect zichtbaar zijn. Dit komt doordat er voor de grafieken slechts elke minuut een nieuw punt getekendwordt.hetzalduscirca2minutendurenvoordatdeeerstetweedatapuntendooreenlijn verbonden zijn. Ophettabblad Settings kuntuzienoferdatabinnenkomt,doorbij PClasttimedata te kijken. Wat het venster com error doet, is de ingevoerde waarden van Com port number, Baud rate en Station ID wegschrijven naar het bestand weather.user.settings.ini. Dit bestand kunt u vinden in de map Z:\user\hisparcweather en kan geopend worden met notepad of wordpad(figuur 4.6). U kunt dus ook in dit bestand een waarde veranderen(bijvoorbeeld het COM-poortnummer) en dezewijzigingopslaan.udoetdaninfeitehetzelfdealshetvenstercomerrordoet,nadatuop OK heeft geklikt. Naast de bovengenoemde gegevens staat in weather.user.settings.ini ook of de weerstation software moet starten in data acquisitie modus(daq_mode) en welke sensoren uitgelezen dienen te worden. Figuur 4.6 In het weather.user.settings.ini staan de beginwaarden die de software inleest bij opstarten. 11

133 5 Weerstation software gebruiken 5.1 De tabladenstructuur De weerstation software heeft een tabbladenstructuur. Er zijn vijf tabladen die hieronder zijn afgebeeld. Op het tabblad Current weather data zijn de waarden van de verschillende weervariabelen uit te lezen. Figuur 5.1 Tabblad Current weather data. Op het tabblad Graphs from last hour worden de meetwaarden van (maximaal) het laatste uur in grafieken weergegeven. Figuur 5.2 Tabblad Graphs from last hour. Op het tabblad Graphs from last 24h worden de meetwaarden van (maximaal) de laatste 24 uur in grafieken weergegeven. Figuur 5.3 Tabblad Graphs from last 24h. 12

134 Ophettabblad Error valtte zien of het weerstation goed functioneert. Figuur 5.4 Tabblad Error. Op het tabblad Settings zijn enkele gegevens van het weerstation af te lezen en enkele zaken in te stellen. Figuur 5.5 Tabblad Settings. 13

135 5.2 Het tabblad Current weather data Op het tabblad Current weather data zijn de waarden van de verschillende weervariabelen uit te lezen. Vantage Pro meet een aantal parameters direct via sensoren en berekent andere variabelenzelfaandehandvandegemetenvariabelen. Gemeten weervariabelen: buitentemperatuur(temperatureoutside); binnentemperatuur(temperatureinside); debarometrischedruk(barometer); derelatieveluchtvochtigheidbinnen(humidityinside); derelatieveluchtvochtigheidbuiten(humidityoutside); dehoeveelheidneerslag(rainrate); deuvindex(uvindex); windrichting(winddirection); windsnelheid(windspeed); zonnestraling(solarradiation). Berekendeweervariabelen: 2 dauwpunt(dewpoint); hitteindex(heatindex); gevoelstemperatuur(windchill); verdamping(evapotranspiration). Inhetmiddenvanhettabbladbevindtzichdeknop.Alshieropgedruktwordt,zal het programma stoppen met het opvragen van data van het weerstation. Het programma kan weer gestart worden met de knop (linksboven in het scherm). Figuur 5.6 Tabblad Current weather data. 2 Voor meer informatie over het formulewerk achter deze weervariabelen verwijzen we naar de Davis documentatie op support -> Go to Weather Support -> Application Notes -> selecteer Vantage Pro of Vantage Pro 2 -> Derived Variables in Davis Weather Products.pdf 14

136 5.3 De twee tabbladen met grafieken Er zijn twee tabbladen met grafieken. Op het eerste tabblad Graphs from last hour worden de meetwaarden van (maximaal) het laatste uur in grafieken weergegeven. Op het tweede tabblad Graphsfromlast24h wordthetzelfdegedaanmaardanvoordelaatste24uur. Het tabblad is onderverdeeld in vier grafieken. Elke grafiek heeft meerdere verticale assen. Linksboven: buitentemperatuur(temperatureoutside); derelatieveluchtvochtigheidbuiten(humidityoutside); debarometrischedruk(barometer). Linksonder: zonnestraling(solarradiation); verdamping(evapotransipration); deuvindex(uvindex). Rechtsboven: binnentemperatuur(temperatureinside); derelatieveluchtvochtigheidbinnen(humidityinside). Rechtsonder: windrichting(winddirection); windsnelheid(windspeed). Inhetmiddenvanhettabbladbevindtzichdeknop.Alshieropgedruktwordt,zal het programma stoppen met het opvragen van data van het weerstation. Als het programma dan weer gestart wordt met de knop (linksboven in het scherm) zullen de grafieken opnieuw beginnen met tekenen. De meetgegevens zijn dan enkel gewist in de grafiekvensters. De data is wel opgestuurd naar de database. Figuur 5.7 Tabblad met grafieken. 15

137 5.4 Het tabblad Error Op het tabblad Error valt te zien of het weerstation goed functioneert. Figuur 5.8 Tabblad met grafieken. Bij het vak sensor status kan de toestand van elke weervariabele worden afgelezen. Het indicatielampje naast elke sensor kan de volgende kleuren groen, rood en grijs hebben: Kleur Betekenis Sensor OK BAD DATA Sensor handmatig uitgeschakeld door de gebruiker 16

138 Rechts van het paneel sensor status bevindt zich een viertal indicatielampjes die rood(probleem) of groen(alles OK) kunnen branden. Lampje Betekenis Mogelijk oplossing bij probleem Het scherm COM ERROR zal waarschijnlijk verschijnen. Is er een verbinding tussen de Vantage Pro console en de PC via de seriële poort? -ZitdeverbindingskabelindePCen in de console? -Vul je de goede com poort in (kijk bij apparaatbeheer voor het correcte com port nummer)? Ishetgeluktomdataop tevragenvandevantage Pro console? -Resetdeconsoledoor maanenuit te zetten (batterijen en adapter er 10secuittehalen). Is de opgevraagde data verstuurd naar de database? -Is het knopje DAQ mode op het tabblad settings aan(groen)? - Draait het batch bestand HiSPARC monitor? Zo niet, start de Hisparc DAQ software. Staat de klok van de Vantage Pro console gelijkmetdeklokvande PC? - Zal zich automatisch aanpassen en weer groen worden. Inhetmiddenvanhettabbladbevindtzichdeknop.Alshieropgedruktwordt,zal het programma stoppen met het opvragen van data van het weerstation. Het programma kan weer gestart worden met de knop (linksboven in het scherm). 17

139 5.5 Het tabblad Settings Figuur 5.9 Tabblad Current weather data. Bijdeindicatorsvaltdoordegebruikernietsintestellen,maarenkelietsaftelezen. Indicator COM port Baud rate Weather station model Station ID DLL Version Database name Hier staat het nummer van de seriële communicatiepoort(com poort) waarop het weerstation is aangesloten. De overdrachtssnelheid van de seriële verbinding met de Vantage Pro van bits/sec. Model type. HiSPARC stationsnummer Versienummer van de gebruikte bibliotheek met functies(dll) die door de weerstation software gebruikt wordt. Naam van de HiSPARC database Bijdecontrolszijnenkelezakenintestellen: door een sensor aan of uit te vinken, kan de gebruiker bepalen of die sensor uitgelezen moet worden. Als een sensor uitgevinkt staat, zal het lampje op het tabblad Error grijs worden. De wijziginggaatdirectin,maarpasalseropdeknop SAVEsettings gedruktwordt,zalhetaantal sensoren dat de gebruiker wil uitlezen, opgeslagen worden in het bestand weather.user.settings.ini. Dit betekent dat bij de volgende keer opstarten de opgegeven sensoren uit het bestand zullen worden gelezen. Het bestand weather.user.settings.ini kunt u vinden in de map Z:\user\hisparcweather en kan geopend worden met notepad of wordpad. 18

140 Doordeknop DAQmode aanofuittezetten,kandegebruikerbepalenofdeweerdatadoorgestuurd dient te worden naar de database. De wijziging gaat direct in(het lampje Buffer OK? zal roodofgroengaankleuren),maarpasalseropdeknop SAVEsettings gedruktwordt,zalde optie data acquisitie modus (aan of uit) opgeslagen worden in het bestand weather.user.settings.ini. Dit betekent dat bij de volgende keer openen in de opgegeven modus gestart zal worden. Inhetmiddenvanhettabbladbevindtzichdeknop.Alshieropgedruktwordt,zal het programma stoppen met het opvragen van data van het weerstation. Het programma kan weer gestart worden met de knop (linksboven in het scherm). 19

141 6 Opgestuurde weerdata uit de database bekijken 6.1 Weerdata downloaden Figuur 6.1 Op staat de data per dag per weervariabele. Op is het station van de school de weerdata per uur op een dag te bekijken. De data is voor elke weervariabele op te halen door rechtsboven op de tekst Source teklikken.jekrijgtdandedataals.csvbestand(commaseperatedvalues).ditisuittelezenmet Excel. Figuur 6.2 Een deel van het.csv bestand voor de luchtdruk, uitgelezen in Excel. Op dit moment worden er alleen grafieken en opvraagbare data gegenereerd voor de luchtdruk en de buitentemperatuur. In de nabije toekomst zal dit ook mogelijk worden voor de andere weervariabelen. 20

142 6.2 Data importeren in Excel Het CSV-formaat bestaat enkel uit tekstgegevens. Waarden worden gescheiden door komma's, en regels door het nieuwe-regelteken. Nederlandstalig spreadsheet-programma's gebruiken vaak de puntkomma als scheidingsteken, omdat de komma als decimaalteken en de punt als separeerteken voor de duizendtallen wordt gebruikt. In Engelstalige landen is het gebruikelijk dat de komma als cijfergroeperingssymbool en de punt als decimaalteken te gebruiken. AlsubeschiktovereenNederlandseversievanExcelkanhetopenenvanditsoortbestandeneen probleem opleveren bij de data. Bij de data komen opeens enorme getallen. Als dit gebeurt, moet de data geïmporteerd worden. Volg daartoe de volgende stappen: KlikinExcelop Data -> Externegegevensimporteren -> Gegevensimporteren (figuur6.3). Figuur 6.3 Importeren van een csv bestand in Excel Erzaleen verkennervensteropenen waarin u naar de mapkuntgaan waarhet csv bestand zich bevindt(figuur 6.4). Figuur6.4Ganaardemapwaarhetcsvbestandzichbevindt. 21

143 Deeerstestapvande'WizardTekstimporteren zalverschijnen(figuur6.5).bijdeeerstestap dient het Oorspronkelijke gegevenstype op Gescheiden te staan. Klik nu op Volgende. Figuur 6.5 Bijdetweedestapvande'WizardTekstimporteren (figuur6.6)dienthet Scheidingsteken opdepuntkommatestaan.kliknuop Volgende. Figuur

144 Klikbijdederdestapvande'WizardTekstimporteren op Geavanceerd (figuur6.7). Figuur 6.7 Hetvenstermetgeavanceerdeinstellingenzalverschijnen(figuur6.8). Zet hier het Decimaalteken op de punt en het Scheidingsteken voor duizendtallen op de komma. Klik vervolgens op OK. Figuur

145 Ubentweerterugbijdederdestapvandewizardtekstimporteren(figuur6.9). Klik hier op Voltooien. Figuur 6.9 Het venster Gegevens importeren zal verschijnen (figuur 6.10). Hier kunt u kiezen voor invoegen van de gegevens op het bestaande werkblad, of invoegen in een nieuw werkblad. Kliknauwkeuzeop OK. Figuur 6.10 Dedatasetzalnuverschijneninhetgoedeformaat! 24

146 7 Problemen oplossen Hoewel de weerstation software correct zou moeten functioneren, kunnen er zaken mis gaan. Wees zo goed problemen(en eventueel gevonden oplossingen voor deze problemen) te melden via Voor problemen met het weerstation zelf verwijzen we naar hoofdstuk 4 Troubleshooting and Maintenance van de Vantage pro Manual te downloaden van: -> support -> Go to Weather Support -> Instruction Manuals -> selecteer Vantage Pro of Vantage Pro 2 -> selecteer wat u wilt hebben waarschijnlijk het bestand Vantage Pro2 Console onder het kopje system. Probleem Oplossing Weerstation sofware start niet automatisch bij opnieuw opstartenpc De weerstation software is niet geïnstalleerd op de pc. In de map Z:\user\hisparcweather zouden in ieder geval de onderstaande bestanden moeten staan: Als dit niet het geval is, kan de software gedownload worden van: De instructie voor handmatige installatie staat beschreven in appendix B. Inhetbestand config.ini indemap Z:\persistent\configuration staatbij bij de kop[weerstation]: Enabled=0 i.p.v. Enabled=1. Hetvenster comerror verschijnt. Het juiste nummer van de com poort is niet bekend, of de juiste baud rateisnietingevuld.zie 4.1e.v. Alshetvensterblijftverschijnen,zouditkunnenbetekenen,datereen probleem is met het toewijzen van een com-poortnummer. Voer hiertoe destappenuitinappendixc. Hetzouookkunnenbetekenendatereenprobleemismetdedrivervan de usb naar serieel converter. Zie appendix A. Op het tablad Error kleurt het lampje Com port connection rood Het scherm COM ERROR zal waarschijnlijk verschijnen. ZitdeverbindingskabelindePCenindeconsole? Vuljedegoedecompoortin(kijkbijapparaatbeheervoorhetcorrecte Op het tablad Error kleurt het lampje weather station connected rood Resetdeconsoledoor maanenuittezetten(batterijenenadapterer10 secuittehalen). 25

147 Probleem Oplossing Op het tablad Error kleurt het lampje weather station connected rood Ishetknopje DAQmode ophettabbladsettingsaan(groen)? Draait het batch bestand HiSPARC monitor? Zo niet, start de Hisparc DAQ software. Op het tablad Error kleurt het lampje weather station connected rood Zalzichautomatischaanpassenenweergroenworden. 26

148 Appendix A Problemen met de prolific driver Bij gebruik van de Prolific verbindingskabel(zie figuur A.1) van serieel naar usb, zijn er op enkele pc s driverproblemen opgetreden. De pc kan dan geen verbinding maken met het weerstation via de seriële poort. Daardoor zal het venster COM Error verschijnen. Als na het controleren van het correcte com poort nummer, baudrate en stationsnummer(zie 4.1), het venster com error blijft verschijnen, kan dit duiden op driver problemen. Mocht dit gebeuren, kan het onderstaande stappenplan een oplossing bieden. Figuur A.1 Serieel naar USB verbindingskabeltje van het merk Prolific. Poging 1 driver opnieuw installeren VerwijderdeProlificPL-2303uitdeUSBpoortvandeHiSPARCpc. VerwijderdeProlificdriver,alsdezeopdeHiSPARCpcgeïnstalleerdis,via configuratiescherm -> software DownloaddelaatsteversievandeProlificPL-2303USBtoSerialdriver.Hetbestandheeftde naam PL2303_Prolific_DriverInstaller_v1417.zip en is te vinden op: Unzip PL2303_Prolific_DriverInstaller_v1417.zip en installeer de driver door het programma PL2303_Prolific_DriverInstaller_v1417.exe te openen en de stappen op het scherm te volgen Startdepcopnieuwop,deweerstationsoftwarezounugewoonmoetenstarten. Poging 2 De-installatie niet geslaagd Mogelijk is bij het de-installeren van de driver niet alles goed gegaan. Prolific erkent dit probleemenraadtaanhetvolgendetedoen: VerwijderdeProlificPL-2303uitdeUSBpoortvandeHiSPARCpc. VerwijderdeProlificdriver(opnieuw)via configuratiescherm -> software Downloadhetbestand PL2303DRemover_v1001.zip van: 27

149 Downloadhetbestand PL2303DRemover_v1001.zip van: Unzip PL2303DRemover_v1001.zip enopenhetprogramma PL2303DRemover.exe,volgde stappen op het scherm. Startdepcopnieuwop. InstalleerdelaatsteversievandeProlificPL-2303USBtoSerialdriver Startdepcopnieuwop,,deweerstationsoftwarezounugewoonmoetenstarten. 28

150 Appendix B- Handmatig installeren van de software De weerstation software is al op uw HiSPARC pc geïnstalleerd via HiSPARC update. Hiervoor hoeft u dus zelf niets te doen. U kunt altijd de laatste versie hisparcweather.zip downloaden van: Volg de onderstaande stappen om de weerstation software te laten werken: GaachterdecomputerzittenwaardeHiSPARCsoftwareopisgeïnstalleerd. OpenbestandsmapZ:\userenkopieerhetbestand hisparcweather.zip naardezelocatie. Figuur B.1 De map Z:\user met het bestand hisparcweather.zip. Pak het bestand hisparcweather.zip uit met Winzip, of de zip-uitpakfunctie van windows. Hieronder staan de twee methoden beiden beschreven. 29

151 B.1 Gebruik van het programma winzip (Voor gebruik van het programma winrar kunnen dezelfde stappen worden gevolgd.) Klikmetderechtermuisknopop hisparcweather.zip,gametdemuisnaar Winzip enklikop Extract to here. De map hisparcweather zal gecreëerd worden. Figuur B.2 Selecteren van de uitpakoptie van winzip. Nahetuitpakkenzaldemap hisparcweather gecreëerdzijn. Figuur B.3 Na het unzippen zal de map hisparcweather verschijnen. Hetbestand hisparcweather.zip isnuoverbodigenmagwordenverwijderd. 30

152 B.2 Gebruik van de uitpakfunctie van Windows Klikmetderechtermuisknopop hisparcweather.zip enklikop ExtractAll. Figuur B.4 Selecteren van de uitpakoptie van windows. De ExtractionWizard zalverschijnen.klikop Next. Figuur B.5 Welkomstscherm van de extraction wizard. 31

153 Inhetinvulvakwaarindeuitpakdirectorykanwordenopgegeven,dient Z:\user testaan. Klik vervolgens op Next. Figuur B.6 In dit venster specificeren we in welke bestandsmap de bestanden uitgepakt moeten worden. Alsdebestandenuitgepaktzijn,zalhetonderstaandevensterverschijnen.Klikop Finish om het venster te sluiten. Figuur B.7 Laatste venster van de extraction wizard. 32

154 B.3 Belangrijk: bestandslocatie van het weerprogramma Alshetuitpakkengeslaagdis,zalereenmap hisparcweather gecreëerdzijnmet7bestanden: Figuur B.8 bestanden uit de uitgepakte map hisparcweather. Demap hisparcweather moetkomentestaanindemap Z:\user\. Dit is heel belangrijk, want de hisparc software verwacht dat de map hier staat. 33

155 Appendix C Communicatieproblemen via de com poort Alshetvenster ComError blijftverschijnenendestappenin 4.1en 4.2gevolgdzijn,kandit duiden op een probleem rond het toewijzen van een COM-poortnummer. Op enkele PC s is gebleken dat een COM-poortnummer groter dan 9 niet werkt. Na het uitvoeren van de onderstaande stappen is het probleem mogelijk verholpen. Ganaar systeemeigenschappen.ditkandoor(inhetmenustart)metderechtermuisknopop Deze computer en daarna met de linkermuisknop op eigenschappen te klikken(figuur C.1). Figuur C.1 Het venster systeemeigenschappen openen via menu start. Hetvenster systeemeigenschappen zalopenen(figuurc.2).ditvensterisooktebereikenvia Configuratiescherm-> Systeem. Klikbijhettabblad Hardware op Apparaatbeheer. Figuur C.2 De optie apparaatbeheer openen bij het tabblad hardware. 34

156 Klaphetkopje Poorten(COM&LPT) uitdoorophetplustekenernaastteklikken.hierstaan de com poorten vermeld die in gebruik zijn(figuur C.3). Figuur C.3 De COM-poorten die in gebruik zijn, worden weergegeven bij apparaatbeheer. Klik met de rechtermuisknop op de USB converter en daarna met de linkermuisknop op Eigenschappen (figuur C.4). Figuur C.4 35

157 Klikophettabblad Poortinstellingen endaarnaopdeknop Geavanceerd (figuurc.5). Figuur C.5 Het venster met eigenschappen van één van uw COM poorten. Erzaleenvenstermetgeavanceerdeinstellingenverschijnen(figuurC.6).Linksonderkuntu het com-poortnummer instellen. Als u klikt op het pijltje naast COM-poortnummer klapt er eenmenuuitwaarinuhetnummerkuntkiezenvoordecompoort. OpenkelePCsisgeblekendateenCOM-poortnummerbovende9nietwerkt.Kiesdaaromeen ander nummer. Enkele nummers kunnen al in gebruik zijn(bijvoorbeeld door HiSPARC Master en Slave kastjes en uw GPS systeem). Deze COM-poortnummers kunt u niet gebruiken. Als windows een COM-poortnummer al heeft toegewezen, staat er achter COM#(in gebruik). Ditbetekentnietaltijddateropdatmomentookechteenapparaatopdezepoortaangesloten is. Bij apparaatbeheer kunt u zien op welke COM-poortnummers daadwerkelijk een apparaat is aangesloten. Figuur C.6 Kies zelf het nummer van een COM-poort. 36

158 Kies een COM-poortnummer waar geen apparaat op is aangesloten. Als u een COMpoortnummeruitdelijstkiestwaardekreet ingebruik bijstaat,zalnahetklikkenopde knop OK eenfoutmeldingverschijnen(figuurc.7).alsuzekerweetdateropdatmoment geen apparaat op dit COM-poortnummer is aangesloten, kunt u deze waarschuwing negeren, doorop Ja teklikken. Ubevestigtdewijzigingdoornogeenaantalkerenop OK teklikken. Figuur C.7 Als Windows vermoedt dat een COM-poortnummer reeds toegewezen is, volgt een waarschuwing.. VulhetdoorugekozenCOM-poortnummerinbijhetvenster COMError.Vulookdebaudrate (19200)enuwstationsnummerinenklikop OK Deweerstationsoftwarezounumoetenwerken! Mochthetvenster COMError nogmaalsverschijnen,kuntudestappenuitdezeappendixopnieuw uitvoeren, waarbij u een ander COM-poortnummer kiest. Figuur C.8 Het venster COM error. 37

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