Noise attenuation directly under the flight path in varying atmospheric conditions

Transcription

1 UNCLASSIFIED Nationaal Lucht- en Ruimtevaartlaboratorium National Aerospace Laboratory NLR Executive summary Noise attenuation directly under the flight path in varying atmospheric conditions Report no. NLR-TR Author(s) V. Sindhamani Report classification UNCLASSIFIED Date Spetember 2012 Knowledge area(s) Vliegtuiggeluidseffecten op de omgeving Descriptor(s) Noise Propagation Cabauw Measurements Weather Problem area In many countries, airport operations are constrained by noise restrictions to protect the people living in the vicinity of the airports. These restrictions help to create the desired eco-friendly environment by monitoring the noise levels using noise metrics such as L DEN or DNL. These noise doses (on a yearly basis) are typically expressed using noise contours plotted around an airport. The contours calculated are an approximation of the actual noise levels. In order to get a high quality result, the noise contours should be validated with the measurements. While doing so, the large gap between measured and calculated aircraft noise data directly under flight path was observed. This gap can be minimized by improving the accuracy of noise contour calculation methods. There are many factors that influence the accuracy of the noise contour calculations such as source variation, sound propagation path and receiver variation. The influence of these factors should be modelled and included in the noise contour calculations. Henceforth the UNCLASSIFIED

2 UNCLASSIFIED Noise attenuation directly under the flight path in varying atmospheric conditions main goal of this research is to improve the accuracy of noise contour calculation. Description of work In this research, one of the factors is considered that is the influence of weather conditions on sound propagation directly under the flight path. It is analysed and included in the noise contour calculations. In order to do so, an experiment setup was built at Cabauw by the NLR to isolate the influence of weather conditions on the sound propagation directly under flight path. The data obtained from this experiment was compared with standard noise contour prediction methods and correction methods were derived considering multiple weather parameters. Multi linear regression analysis was used to determine the correction factors which can be used to update existing noise contour calculation methods. In the end, the effectiveness of the correction methods is found by comparing it with measurements. Results and conclusions This research shows that the effect of varying temperature and humidity has a major influence on the noise attenuation directly under flight path in comparison with the variations in the other weather parameters. In the end, it was observed that the results found using the varying atmospheric conditions did not considerably improve the accuracy of the predicted noise levels. This implies that the varying atmospheric conditions do not have a significant impact on the deviations between the measured and the calculated noise data. Thus, the large deviations between the measured and the calculated noise data is to be sought in noise variations due to the aircraft itself. Applicability Currently noise contour calculation methods typically use fixed and average weather conditions. The results of this thesis show that noise contour calculations need to be done considering temperature and humidity to be dynamic factors as opposed to fixed parameters. The results of this research partially bridge the gap between the measured and calculated. This research paved the way for the further steps that need to be taken to address the main problem. It also recommends a fruitful step for further research that is the variations at the source of the noise should be obtained and be included in the noise modelling calculations as it influences the noise contour considerably. Nationaal Lucht- en Ruimtevaartlaboratorium, National Aerospace Laboratory NLR UNCLASSIFIED Anthony Fokkerweg 2, 1059 CM Amsterdam, P.O. Box 90502, 1006 BM Amsterdam, The Netherlands Telephone , Fax , Web site:

3 Nationaal Lucht- en Ruimtevaartlaboratorium National Aerospace Laboratory NLR NLR-TR Noise attenuation directly under the flight path in varying atmospheric conditions V. Sindhamani No part of this report may be reproduced and/or disclosed, in any form or by any means without the prior written permission of NLR. Customer National Aerospace Laboratory NLR Contract number Owner National Aerospace Laboratory NLR and TU Delft Division NLR Air Transport Distribution Limited Classification of title Unclassified September 2012 Approved by: Author V. Sindhamani Reviewer D.H.T. Bergmans, and M. Arntzen Managing department R.W.A. Vercammen. Date: Date: Date:

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5 Master thesis NLR-TR By Vivekanandhan Sindhamani 27 th September 2012 Prof. Dr. D. G. Simons Ir. M. Arntzen Ir. D.H.T Bergmans Graduating Professor First Supervisor Second Supervisor TU Delft TU Delft / NLR NLR 3

6 Noise attenuation directly under the flight path in varying atmospheric conditions Vivekanandhan Sindhamani 4

7 Preface This thesis titled Noise attenuation directly under the flight path in varying atmospheric conditions has been submitted in partial fulfilment of the requirements for the Degree of Master of Science in Aerospace Engineering, at the department of Air Transport & Operations (ATO) at Delft University of Technology in the Netherlands. First and foremost, I would like to thank my Professor Dr. D.G. Simons for giving me the opportunity to carry out my thesis work in the ATO department. I would like to sincerely express my gratitude to my first supervisor Ir.M.Arntzen for his extensive and unconditional support throughout my thesis. I am thankful to my second supervisor Ir. Dick Bergmans for sharing his valuable time and bringing out the professional in me. I am very grateful to all the NLR employees at the Department of Environment and Policy Support (ATEP) for including me in their team. I would also like to thank my internship supervisors Roel Hogenhuis and Sander Heblij for supporting me initially at the NLR.I would also thank Dr.ir.M.Voskuijl for accepting to be on the panel to judge my thesis. I would like to express my appreciation for my friend Varun Raman for proof reading my thesis and giving me constructive criticism. I would like to thank my friends Vishal, Sreenath, Satish kumar, Thilak and many others for their unwavering belief in me. Last, but definitely not the least, I am indebted to my parents and my girlfriend for their unconditional love and support. Delft, 20 August 2012 Vivekanandhan Sindhamani 5

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9 Abstract Aircraft noise levels around the airports are limited by noise regulations in order to protect the inhabitants living in the vicinity of the airports. Hence, noise level predictions in the vicinity of the airport are a must. The noise level predictions are made based on the standard methods and are compared with the measured noise levels. While doing so, large deviations were observed between predicted and measured aircraft noise data directly under the flight path. These deviations may be attributed to the uncertainties in source noise levels, influence of atmospheric conditions and/or uncertainties at the receiver s end. In this thesis, the influence of the atmospheric conditions on sound propagation directly under the flight path was examined. In order to examine this phenomenon, an experiment setup was built by the NLR in the KNMI tower at Cabauw in The set-up was designed to measure simultaneously the varying atmospheric conditions and their influence on sound propagation directly under flight path. The data obtained from this experiment was compared with standard noise contour prediction methods and a correction method was derived considering multiple weather parameters. Multiple linear regression analysis was used to determine the correction factors which were used to update existing noise contour calculation methods. The results obtained correspond to an altitude of up to 100 meters. To determine the noise contours for altitudes above 100 meters, the results generated using the measured values up to a height of 100 meters were scaled. In the end, it was observed that the results computed using the newly formulated methods did not considerably improve the accuracy of the predicted noise levels. This implies that the varying atmospheric conditions do not have a significant impact on the deviations between the measured and the calculated noise data. Thus, the large deviations between the measured and the calculated noise data is to be sought in the noise variations due to the aircraft itself. 7

10 Contents 1 Introduction Problem definition Focus Steps Research questions Research approach Report outline 18 2 Framework Experimental setup Background Information 22 3 Inputs and Methods Acoustic data Weather parameters Statistical Analysis Correction method Scaling Method 33 4 Results and Discussion Seasonal effect of weather parameters on AGSP Influence of wind parameters at different frequency bands Effectiveness of different noise contour calculation methods Effectiveness of noise contour calculation methods at higher altitudes 48 5 Conclusion 51 6 Recommendations 52 References 53 Appendix A 55 Appendix B 61 8

11 Appendix C 66 Appendix D 70 Appendix E 72 9

12 List of terms and symbols The important terms and metrics used in this thesis are tabulated in this section. Terms Description 1/3 rd Octave bands 1/3rd Octave bands are used to analyse the broad-band frequency AGSP ANOMS ANP Database A-weighting A-weighted sound level, L A,i Airport noise contours Decibel KNMI NLR Noise Noise Power Distance (NPD) content of sound. It divides the frequency range into bandwidths. The ratio of two adjacent bandwidth centre frequencies is 2(1/3). Air-to-ground sound propagation path Airport Noise and Operations Monitoring System The international Aircraft, Noise and Performance database ( A standard frequency weighting or correction used to reflect the frequency response of the average human ear over a wide range of listening conditions. The unit of the A-weighted sound levels is displayed by dba or db(a) A-weighted sound pressure level, unit is db (A) where i is the frequency band (which ranges from 1 to 31 for 1/3rd octave bands with centre frequency from 10Hz to 10kHz). Lines on a map which represents equal noise exposure levels. Amplitude of the sound signal described on a logarithmic (Decibel) scale. Royal Netherland Meteorological Institute ( National Aerospace Laboratory, Amsterdam, the Netherlands ( ) Noise is defined as unwanted sound which results in annoyance, sleep disturbance or health problems during high and long exposures. The terms noise and sound are sometimes used interchangeably in this thesis. Noise event levels are tabulated as a function of perpendicular distance vertically below an airplane in steady level flight at a reference speed in a reference atmosphere, per aircraft and engine type. The data account for the effects of sound attenuation due to 10

13 Terms Sound Sound Attenuation Sound Pressure Level Sound Exposure Level L, overall A-weighted A sound level L A,max, maximum overall A-weighted sound level Relative Humidity (RH) Transmission loss (TL) Excess transmission loss (ExTL) Refraction Description spherical wave spreading (inverse-square law) and atmospheric absorption in SAE AIR-1845 Atmosphere [1]. Sound is a pressure variation in an elastic medium (i.e. liquid or gas). Sound energy propagates in an elastic medium by longitudinal wave motion which is sensible to ear. Decrease of sound energy along the propagation path. Difference in actual pressure in the sound wave to the standard reference pressure ( Pascal). The constant sound level which has the same amount of sound energy in one second as the original noise event; the standard single event descriptor is described in ISO The logarithmic summation of A-weighted sound energy. The resultant value depends on the spectrum Maximum value of LA over a period of time, The ratio of prevailing water vapour pressure in the air at a given temperature divided by saturated vapour pressure at that temperature times 100 percent [2]. The amount of attenuation of the sound energy due to air-to-ground sound propagation. The difference between the measured and calculated transmission loss (TL). This phenomenon describes the bending of sound waves when the wave passes from one medium to the other. 11

14 Metrics Units Description L DEN db(a) Day-evening-night level DENL, a noise index adopted by the European Commission which penalizes evening noise by 5dB and night-time noise by 10dB. SPL db Sound pressure level DNL db(a) Day-night average sound level is primary metric adopted by Federal aviation administration. It is a 24- hour average noise level. A 10 db penalty is applied to night-time (10:00 p.m. to 7:00 a.m.). SEL db(a) Sound Exposure Level 12

15 1 Introduction The world is moving towards an eco-friendly environment by reducing various forms of pollution. One of the single biggest challenges confronting us today is the mitigation of noise pollution. Increase in aircraft movements have resulted in increasing noise pollution. This alarming increase in noise levels has resulted in noise reduction becoming a top environmental and political priority. In many countries, airport operations are already constrained by noise restrictions to protect the people living in the vicinity of the airports. These restrictions help to create the desired ecofriendly environment by monitoring the noise levels using noise metrics such as LDEN or DNL. These noise doses (on a yearly basis) are typically expressed using noise contours plotted around an airport. The contours calculated are an approximation of the actual noise levels. Firstly in this chapter, the problem will be explicitly defined. Subsequently, earlier research and knowledge gaps are discussed. Finally the general framework and the steps of this master thesis are discussed. 1.1 Problem definition As mentioned above, noise contours are the most widespread means used to determine the noise levels. Prediction methods that are used to calculate noise contours in the vicinity of airports are the ECAC.Doc.29 [3] or Integrated Noise Model (INM) [4]. In order to get high-quality results, noise contours are validated with measurements. But it is seldom possible to match the hundreds of noise measurements made in the vicinity of airports with the theoretically computed values. In order to improve the accuracy between aircraft noise measurements and predictions, the assumptions made in the prediction models and the corresponding inaccuracies have to be addressed. The important factors that influence the accuracy in the prediction models include: Source (aircraft): o Aircraft type o Aircraft weight o Aircraft setting (thrust, flaps etc.) o Directionality of sound emission (from engine, airframe, landing gear, etc.) Propagation through the atmosphere: o Distance o Atmospheric effects (rain, wind, turbulence, etc.) o Obstructions (shielding) 13

16 Receiver: o Ground effects o Measurement aspects In-depth research, focused on these factors will improve the quality of the noise contours. This thesis focuses on one of the factors the noise attenuation directly under the flight path in varying atmospheric conditions with the ultimate aim of partially bridging the gap between measured and calculated aircraft noise. The gap between measured and calculated aircraft noise levels are attributed to two main reasons; the uncertainty in the measurements and the errors in aircraft noise modelling. Today s precision measurement equipment ensures that a deviation in the measurements in the order of ±0.5 dba [5] can be achieved. This illustrates that the large deviations between measured and calculated results is due to deficiencies in the theoretical calculations. Therefore the uncertainty in the measurements is not questioned in this research. In Figure 1, Miller et al., [6] shows predicted sound exposure levels (SEL) of 21,166 departures of eight common aircraft types (predicted using INM) against actual measurements of those same operations made by noise monitoring system at the Minneapolis Airport. Differences in the order of +/- 15dB between predicted and observed SEL s are common. The magnitude and bias of the difference are reduced when they are combined to estimate long term integrated yearly doses (LDEN). Figure 1 Predicted versus measured SELs for 20,000+ individual aircraft departures Fidell et al. [7] quoted from Miller et al. [6] state that especially at long ranges and small angles of incidence the errors are in the order of 3-4 db (95% bound on data). They also compared Day- Night-Average Levels (DNL) of two years, measured at 29 locations in major airports and 14

17 predictions were made by INM of the DNL value at the same locations. The standard deviation for 95% of the difference between monitored and predicted levels was about 4 db. After their review, they suggested that such errors in prediction are minimal compared to prediction errors associated with inadequate representation of flight trajectory, flight operational information, the seasonal variation, meteorological condition, and runway use that lead to very different noise exposures in airport neighbourhoods. The similar difference between the measured and calculated noise levels of individual events are mentioned in report CDV-NLR-TNO in January 2006 [8]. 1.2 Focus As mentioned, this thesis is about the noise attenuation directly under the flight path. From here on, this path is referred to as air-to-ground propagation. In contour calculations this path is taken from a Noise Power Distance (NPD) table. For a given power setting and distance between the source and the receiver, the noise value is taken (e.g. interpolated) from the table. Directly under the flight path implies a sound angle of incidence greater than 60 degrees. At smaller elevation angles a lateral correction is applied. The air-to-ground attenuation directly under the flight path is embedded in the NPD tables and includes the inverse square law together with a correction for atmospheric absorption under standardised atmospheric conditions (SAE AIR-1845 Atmosphere). In 2008 Okada et al. [9] & [10] studied the influence of atmospheric conditions on air-to-ground sound propagation by considering the air temperature, humidity and air pressure. They found that atmospheric absorption (function of temperature and humidity) tends to increase with increasing altitudes, and hence sound exposure levels (SEL) for aircraft decreases with increasing altitudes. Also the variation in winter was higher than that in summer as shown in [9]. Figure 2 Calculated A-weighted SPLs near the ground at horizontal distances (---- calculated values under the standard atmospheric conditions 25 C, 70%) [9] 15

18 Even before this particular study, Okada et al. [11] statistically investigated the influence of atmospheric absorption on environmental noise propagation (traffic, constructions, airconditioning system in building and birds) instead of aircraft noise propagation. They conducted an experiment for a period of one year (208 days of valid measurements) by measuring the Sound Pressure Level (SPL) and meteorological data simultaneously. Ambient noise levels and meteorological data measured at every second were averaged over 10 minutes. They found that the effects of atmospheric absorption are larger in the winter than in the summer. They analysed that the correlation between atmospheric absorption and SPL become high when the observation time is short, meaning that the correlation obtained for an hour is higher when comparing with those obtained for day and night or a whole day. As a result of their study, it has been found that the effect of atmospheric absorption on environmental noise propagation is large and cannot be neglected in sound spectrum analysis of the total noise in residential areas. Although Okada identified the influence of a varying atmosphere on air-to-ground attenuation, their validation is based on noise simulations with measured weather data, not noise measurements. Thereby varying wind and turbulence conditions were not taken into account leaving mismatches with measurements partly unexplained. 16

19 1.3 Steps To include dynamic atmospheric conditions into noise contour calculations one should first know what the real impact of the atmosphere on sound propagation is and what data is available to estimate the differences due to the effect of the atmosphere on sound propagation. If no significant improvement is found, then there is no need to improve the noise contour calculations. The first step involves measuring the aircraft noise and determining if any trends are found while plotting the weather parameters against measured noise levels. However the variation of aircraft noise measurement also includes aircraft settings inclusive of noise variations from the source. Thus it is meaningless to measure the aircraft noise directly [NLR-CR ]. Therefore, an experimental setup should be designed to isolate the effect of varying atmosphere on air-toground sound propagation. Therefore the National Aerospace Laboratory (NLR) in the Netherlands decided to explore this aspect in detail. In 2010 the NLR started to assess the effect of atmosphere on aircraft sound propagation from air-to-ground and built a set-up in the KNMI tower at Cabauw. The set-up was designed to eliminate all other influences but the varying atmosphere, while determining the sound attenuation. If a trend is found between the weather parameters and measured noise levels, then the next step is to formulate a correction method to improve noise contour calculations. With the aim of carrying out this thesis in a structured manner, the aforementioned steps are formatted into research questions. A research approach was developed to answer the research questions in an orderly manner. 1.4 Research questions The steps mentioned above were framed into three research questions, 1. Can a trend be determined for varying atmospheric conditions using real noise measurement on the air-to-ground propagation path? 2. If a trend is found, can it be incorporated into the noise contours calculations? 3. Does the formulated correction method significantly improve the noise contour calculations? 17

20 1.5 Research approach To develop initial steps for this thesis, an overview of the experimental setup and initial assessment done by the NLR is briefly explained. Secondly, further assessment of varying atmospheric conditions on sound propagation is done to answer the first research question. The results of the assessment are formulated into a correction method and incorporated in the noise contour calculations to answer the second research question. Finally, the latter method and standard noise contour method are compared to answer the third research question. The results are expected to provide a solution to the problem defined earlier. 1.6 Report outline Figure 3 below shows the build-up of this report, Figure 3 Report Outline 18

21 2 Framework In this chapter, the elements required for the development of the initial steps of this thesis are described. Firstly the experimental setup built by the NLR is described. Subsequently the initial assessment done by the NLR and the associated measurements taken are discussed. 2.1 Experimental setup In this section, the requirements of the experimental setup, selection of the location for the experiment, and an overview of the setup and a description of each part are discussed in detail Requirement for the setup The purpose of the experiment is to isolate the effect of varying atmosphere while determining airto-ground sound attenuation. The requirements to that end are listed below, 1. The sound spectrum used for the experiment should be similar to aircraft flyover noise. 2. The air-to-ground sound propagation directly underneath the flight path should be considered. This means that the elevation angle of the sound propagation path should be higher than 60 degrees. 3. The noise should be measured at the ground level. Simultaneously, weather parameters should be measured along the sound propagation path. 4. The variation in the sound source should be eliminated. 5. The effect of background noise should be eliminated from the measurements. 6. The effect of ground reflections should be eliminated from the measurements.(in accordance to Annex 16 [12]) 7. The emitted noise levels should stay within the accepted noise levels to avoid disturbances to the local residence around the experimental site Selection of the location The location of the setup is at Cabauw where the KNMI has a measurement tower for meteorological experiments. The tower is the third tallest tower in the Netherlands (213 m high) and is shown in Figure 4. It is located in the western mid part of the Netherlands. The location is shown in the Appendix A.1. This tower was chosen as it satisfies the main requirements of the experimental setup mentioned earlier due to its height and availability of instruments for measuring weather parameters along the air-to-ground path. 19

22 Figure 4 KNMI-Meteorological measurement tower, Cabauw Overview of the setup Mic 3 M Mic Mic 5 Mic Top-view (a) Isometric view (b) Figure 5 Schematic diagram of the experimental setup The setup consists of a loudspeaker (see Appendix A.2 for loud speaker specifications) which is positioned at 100 meters above the ground at one side branch of the tower pointing 240 from North as shown in Figure 5 (a). The loud speaker is programmed to transmit an hourly audio signal. The emitted sound is recorded by five microphones which are positioned directly under and 25 20

23 meters away in the directions of 40, 130, 220 and 310. The emitted sound is recorded by a microphone placed 1 meter in front of the speaker and this is used as the reference sound. (As shown in Figure 5 (b)) (See Appendix A.3 for types of microphones used). Simultaneously, the atmospheric parameters like wind speed, wind direction, temperature, humidity and their variation are measured at different heights. A broadband audio signal of 15 seconds is emitted every hour by the loudspeaker. With the aim of capturing the background noise, the recording is started a few seconds prior to the loudspeaker emissions and it is stopped a few seconds post the emission Description of the setup In this section the individual parts of the setup are explained. Sound Source: The sound power output of an aircraft flyover is usually distributed over a wide range of frequencies. The aircraft sound contains equal power within a fixed bandwidth at any centre frequencies which has similar characteristics of broadband noise. The loud speaker is programmed to transmit an audio signal of broadband noise (frequency ranges from 250 Hz to 4000 Hz) every hour mimicking an aircraft flyover. The extent to which the loudspeaker mimics the aircraft flyover noise is shown in Appendix A.4.Thus the speaker spectrum is assumed to represent the aircraft spectrum. Air-to-ground path: To focus only on the air-to-ground sound propagation path, the ground microphones are placed directly under the loud speaker and 25 meters away in four different directions. By doing so, the elevation angle of sound propagation is 75 as shown in Figure 5 (b) and subsequently the sound is measured in four different directions. Weather parameters: The weather parameters are measured by the KNMI at different heights ranging from 10m to 200m above ground level. Simultaneously, the emitted sound is recorded by the NLR experimental setup. The weather data retrieved from the KNMI and acoustic data recorded are stored in a database. The retrieval method of the weather and acoustic data together with the database formulation are explained in Appendix A.3.1. Source variation: To eliminate the variation at the source itself, a reference measurement is placed at a distance of one meter below the speaker. The position of the reference measurement is shown in Figure 5 (b). 21

24 Background Noise: To reduce the effect of background noise, the overall A-weighted sound level measured at the ground should be greater than 60dB (A), which is 10 db higher than the average background noise. Since the loud speaker produces a noise of 102 db (A), it is placed at 100 meters above the ground. The reduction in the noise level due to spherical spreading is equal to 40 db (A). If the reduction of sound due to weather parameters is assumed to be less than 2dB (A) then the initial noise level at the ground is about = 60 db (A). Ground reflection: The effect of ground reflection has influence on the noise measurement. The ground effects are defined as the difference between the measured sound pressure level and the measured sound pressured level in free field conditions. The physical and geometrical explanation of ground effect was explained in chapter 8 of reference [2]. In this experiment the emitted sound is recorded under full ground reflection conditions (i.e. measuring flush using a 40 cm metal plate laying on sand foundation, as described by ICAO Annex 16 [12]). Therefore the receiver is placed directly on a full reflecting surface (shown in A.3.1). This results in the difference in path length between the direct and reflected signal becoming zero. Under this condition, both direct and reflected signals arrive in phase and interfere constructively. To eliminate full ground reflection, the theoretical amplification of 6 db is subtracted from the recorded noise levels for all the frequencies. 2.2 Background Information The above described experimental setup was operational from 1st of August The data collected until April 2011 was used initially by the NLR to assess the effects of the atmosphere on sound propagation. In this section, an overview of initial assessment results and steps taken in this thesis to continue NLR s work are explained Initial assessment The initial assessment work was carried out by Dick Bergmans, Michel Arntzen and Wim Lammen at the NLR. The figures used in this section are taken from their conference paper [13]. The results of the initial assessment were based on the visualization of the data showing the variation in AGSP under dynamic atmospheric conditions. Here, the AGSP is quantified as the transmission loss which is denoted by R. The transmission loss is the subtraction of the overall A- weighted sound level recorded on the ground from overall A-weighted sound level (LAeq) recorded by a reference microphone at 100m height. 22

25 First, the weather parameters such as temperature and humidity, measured at 10m height were compared with the measured transmission loss at each microphone position. For the Microphone positioned at 310, the variation is shown in Figure 6.. Figure 6 Variations in Temperature and Humidity The variation in temperature and humidity shows no clear trend with the variation in the transmission loss. Similarly, variation of other weather parameters such as wind velocity, wind direction and turbulence (parameterization of turbulence is explained in Appendix A.5) were considered individually. Even then, no clear correlation was found between weather parameters and transmission loss. Finally to express the importance for further research, the variation between predicted and measured transmission loss were illustrated by Figure 7. Figure 7 Differences between theoretical values vs. measured distribution at position 310 º (Solid red line represents the predicted reference; dashed magenta line represents the measured mean) 23

26 The theoretically computed transmission loss was found based on spherical wave spreading and atmospheric absorption (method prescribed in ISO ). The absorption was calculated based on local temperature and humidity. The measured transmission loss was subtracted from the predicted transmission loss and shown using blue dots). No scientific explanation could be given for the variation seen in Figure 7. However, the authors recommended a statistical approach with different parameterization to assess the effects of atmosphere on sound propagation and use the complete dataset of an entire year for analysis. Apart from the above recommendations, the filtering of the dataset should be improved to remove the invalid data points for the analysis. This initial set of results, its limitations and recommendations have paved the way for this research. From the initial assessment results, limitations and recommendations, the subsequent steps for this research are constructed and are described in the block diagram given below. Figure 8 Steps undertaken 24

27 3 Inputs and Methods The description of the set-up and the main objectives of the thesis are explained in the previous chapters. From the description of setup, it is perceived that large sets of audio recordings and weather parameters are collected for this thesis. There are several ways to analyse the collected data. In this chapter the input required for the analysis and the analysis methods are explained in the context of the objectives. 3.1 Acoustic data As mentioned in the previous chapter, acoustic data is extracted from audio recordings. There are several ways to do this. The extraction method used in the initial assessment (section 2.2.1) has drawbacks; therefore the extraction method has been changed in the current assessment to overcome the drawbacks. The difference between the extraction methods used in initial (section 2.2.1) and current assessment are explained in appendix B.1. In the end, the acoustical data are censored in a way to exclude the data points with high background noise. Any disturbances are left out (as good as possible). An automated process has been defined to censor the acoustical data and can be found in the appendix B.2. The audio signal desired from the speaker is broadband (white) noise. The emitted sound, however, depends on the speakers specifications. As the speaker is made for speech purposes this changes the broad band noise characteristics. The selection of frequency bands used for the analysis is depicted in Figure 9. Figure 9 A-weighted sound levels at 1/3rd octave bands (Centre frequency ranges from 250 Hz to 4 khz) 25

28 The loudspeaker was programmed to emit the audio signal whose frequencies ranges from 250 Hz to 4 khz. In the above figure it is shown that the sound levels between 500 Hz to 3150Hz (represented in blue lines) contain most energy. The sound levels at 4 khz (represented in green lines) and the sound levels between 250 Hz to 400Hz (represented in red lines) do not contain as much sound energy. The variation in the sound energy is mainly due to the emitted sound spectrum of the loudspeaker as shown in Appendix A.4 (Figure 27). In further analysis the frequency bands range from Hz are the ones considered, since they contain enough sound energy. 3.2 Weather parameters In addition to the acoustical data, weather parameters are part of the analysis. In this section, the selections of weather parameters are explained. The weather parameters used to represent varying atmospheric conditions are temperature, humidity, wind speed, wind direction, turbulence, wind speed gradient and temperature gradient (gradients w.r.t to altitude). In this thesis, however, only five were considered and provided by the KNMI. All weather parameters provided by the KNMI are mentioned in Appendix A.5. From that, the weather parameters measured at 10m height are used for the analysis. The 10 metres height was deliberately chosen. The KNMI uses this height to measure common weather conditions at different sites. Data at this height is therefore widely available throughout the Netherlands (e.g. around Amsterdam Airport Schiphol). This availability has a practical benefit, especially when weather variations (i.e. findings of this research) are aimed to be incorporated into the noise contour calculations for different kind of airports. The selected weather parameters are listed below, 1. Temperature 2. Humidity 3. Wind speed 4. Wind direction 5. Turbulence The temperature and humidity is represented by a single acoustical parameter called atmospheric absorption. The absorption is function of temperature and humidity. This is calculated using the method prescribed by Society of Automotive Engineers Aerospace Recommend Practice 866A (SAE ARP 886A) [1]. The mean wind speed (WS) and turbulence (the standard deviation of wind speed over 10 minutes) parameter are used in the same format as provided by the KNMI and is defined in Appendix A.5 26

29 Table A- 1. Nevertheless, the wind direction is used in a different format. The wind can be split up into upwind and down wind direction with respect to the sound propagation. The conversion of wind direction parameter provided by the KNMI to the respective format used in this thesis is explained schematically using Figure 10. The upwind condition is that when wind is blowing against the sound propagation direction and downwind condition is that when wind is blowing in the direction of the sound propagation. Figure 10 Wind direction parameter The wind direction parameter is denoted as WR and is dimensionless. The wind direction parameter w.r.t to sound propagation direction is calculated using the formula given in (3.9), (3.9) Here, Figure 10. For downwind conditions, WR value ranges from 0 < WR < 1. For upwind conditions, WR value range from -1 < WR < Statistical Analysis In this section, the need and selection of a statistical method to analysis the influence of the atmosphere on sound propagation is briefly explained. As mentioned in the previous chapter, the results of the initial assessment made by the NLR couldn t draw a clear scientific explanation on the given problem. Nevertheless, one of the 27

30 recommendations is to follow a statistical approach with different parameterization for the further assessment. Generally the statistical methods are mainly used as a tool to find an influence of one variable on the others. Therefore, the statistical approach is considered as one of the worthy step to start with the analysis Selection of the statistical method In the process of selecting a statistical method, first the definition and categories of statistics are briefly explained. After that, one of the categories is chosen based on the type of the solution required for a problem. The complete breakdown of the categories of general statistical analysis is shown in Figure 11. Figure 11 Categories of statistics The two main broad categories of statistics are, 1. Descriptive Statistics 2. Inferential statistics The descriptive statistics allows a researcher to organize and summarize the information. The inferential statistics allows a researcher to draw a conclusion about data. In this thesis, the latter category is needed to draw a conclusion about the influence of atmosphere on AGSP. 28

31 The inferential statistics category is further subdivided into two main types, 1. Estimation 2. Hypothesis testing Estimation statistics are used to make estimates about the values based on the given sample data. Hypothesis testing statistics are used to make a statistical inference to check whether or not data supports a particular hypothesis. In this thesis, the quantity of the atmospheric influence needs to be found. For that, the estimation statistics needs to be used to estimate the quantity of atmospheric influence on AGSP. Further down, estimate statistics is subdivided into two types, 1. Parameter estimation 2. Confidence interval Parameter estimation is used to describe the relationship between variables in a population. Confidence interval is used to indicate a reliability of an estimate. In this thesis, the solution to the problem is to formulate a relation between the atmospheric parameters and the acoustic parameters. To be sure that a trend is found, the formulated relation should have a high reliability. Therefore estimation statistics is selected for the analysis in this thesis. Eventually, there are many mathematical models developed based on the estimation statistics method The primary statistical models developed based on estimation statistics are linear-regression models and multi-linear regression models. In precise, a linear-regression model is used to analyse the relationship between two individual variables. The multi-linear regression model is used to analyse the relationship between an individual variable and a group of variables. The relationship between an individual acoustic parameter and individual weather parameters needs to be found. Similarly, the relationship between an individual acoustic parameter and group of weather parameters needs to be found. Hence, linear-regression analysis and multi-linear regression model is selected and used. The high level statistical models are not considered for the selection process to avoid complications. The definition, formulation and description of the estimation statistics and multi linear regression model are given in Appendix B.1. In line with one of the main research questions, the results of the statistical analysis are used to formulate a correction method. This is explained in the next section. 29

32 3.4 Correction method In this section, the description of the correction method used to estimate the transmission loss along AGSP for a slant distance of 100m height is explained Categorisation The dataset was divided based on seasonal variation prior to the statistical analysis. The effects of seasonal variation were determined by dividing the year into four common seasons and the data was collected for the following periods given in Table 1. Table 1 Seasonal periods Seasons Periods Number of Valid data points Autumn 01-Sep-10 to 30-Nov Winter 01-Dec-10 to 28-Feb Spring 01-Mar-11 to 31-May Summer 01-Jun-11 to 31-Aug (Total) Formulation of equation for a single frequency band The estimation method to determine the transmission loss in the Cabauw set-up is similar for all the one third octave bands ranging from 500 Hz to 3150 Hz. Thus, the calculation of the transmission loss at a single one-third octave band is explained in the following paragraphs. The standard method to calculate general transmission loss includes spherical spreading and atmospheric absorption at standard temperature and humidity condition according to SAE ARP- 866A and it is given in (3.10). (3.10) 30

33 Where, GTL General transmission loss f Centre frequency of 1/3 octave band (Hertz) Sp Transmission loss due to spherical spreading (db) α Atmospheric absorption coefficient (db/m) in SAE AIR-1845 Atmosphere r Distance between the source and the receiver Based on the above, the transmission loss would theoretically always be the same in the Cabauw set-up. However there are variations between the measured and calculated transmission loss. This variation is assessed by estimating the seasonal excess transmission loss (difference between measured and calculated transmission loss) due to weather parameters excluding temperature and humidity. Atmospheric absorption has been excluded in the estimated formulation as they have been accounted for in the standard formula. The format of the equation for excess transmission loss is given in (3.11). The coefficients of the weather parameters are not the same for all seasons as the analysis is carried out for each season individually. (3.11) Where, ExTL Excess transmission loss f Centre frequency of 1/3 octave band (Hertz) n Season number (n = 1, 2, 3, 4) WR Wind direction (value ranges from -1 to 1) WS Wind Speed (m/s) Tur Turbulence factor (standard deviation of wind speed for 10 min) B1 to B4 are the found coefficients of weather parameters using statistical analysis. The final transmission loss is composed of spherical spreading, atmospheric absorption at varying temperature and humidity and the excess transmission loss found by statistical analysis. (3.12) 31

34 3.4.3 Equation formulation The following steps, briefly explains the process of finding the above mentioned final transmission loss equation: 1. By using multi-linear regression analysis, equation (3.12) was found by analysing the excess transmission loss and the combination of weather parameters for three different microphone positions and each season. The microphone positions (310, 130, 40 ) were considered as they were the only ones which provided sufficient data points. Total numbers of equations are, 4 (seasons) 3 (Microphone positions) = 12 equations 2. Next, the equations for three microphone positions are reduced to one general equation for each season by taking the mean of respective weather parameter coefficients. It reduces the number of equations to 4. This approach is used because the difference between the coefficients B1 and B2 of microphones is negligible. The effect of turbulence is independent of direction. As mentioned earlier, turbulence is represented as variation in wind speed, it doesn t dependent on the wind direction. The influence of these weather parameters are discussed in the next chapter Formulation of equations for different frequency bands In the previous step, the transmission loss for a single 1/3 rd octave band from 100m altitude to ground level was calculated using four different equations representing the seasonal variation. The same methodology was carried out to formulate the equation for the other third octave bands whose centre frequency range from 500 to 3150Hz. For some 1/3rd octave bands, the coefficients (like B1, B2, B3, and B4) of weather parameters are unacceptable (insignificant). Those coefficients are interpolated between the adjacent one third octave bands that are significant. 32

35 3.5 Scaling Method The NASA report of 1975 [14] on the variation of the excess attenuation has been instrumental in the analysis of the excess transmission loss at heights above 100meters. It is determined that the excess attenuation is more pronounced near the earth's surface than at higher altitudes. Figure 12, taken from [15] shows the altitude dependence of the excess attenuation schematically. The data point in this curve at a particular altitude indicates the excess attenuation coefficient at that height. The gradient of the curve varies inversely with the height up to a height h o from the ground and remains virtually constant above that altitude. The value of h o was provided as approximately 200 m (600 ft) i.e. the excess attenuation prominently changes below this altitude. Figure 12 Schematic diagram of variation of excess attenuation with altitude (dimensionless) The graph shown above was utilized to obtain the equation which explains the variation of the excess transmission loss with altitude. The equation representing the linear portion of the graph was already explained in the NASA report. The equation of exponential part was not available and has been determined from the graph. The equation found is given in (3.13). (3.13) 33

36 The excess transmission loss for AGSP at 100 meters was available from the results of the experiment. In order to scale the excess transmission loss (at 100 meters) for different altitudes, there are two conditional equations that need to be used. Conditional 1 equation (3.13) is used to scale the ExTL up to 200 meters altitude. Condition 2 equation (addition of linear portion, explained in NASA report) is used to scale the ExTL above 200 meters altitude. The scaling of excess transmission loss for AGSP (above 100 meters) is explained in the next section. Condition 1 (Altitude below 200m): ; dba (3.14) ) ExTl = excess transmission loss at specified altitude (dba) Y (d) = Numeric excess transmission loss value from the graph (dimensionless) X (d) = Numeric altitude value from the graph (Dimensionless) The above equation is valid up to an altitude of 200 meters. For altitudes above 200 meters condition 2 is applicable. Condition 2 (Altitude above 200m): The residual attenuation coefficient shown below was obtained from the NASA Report and it is equal to the slope of the linear variation. Thus as mentioned earlier this value has added to the equation of the exponential section of the graph. (Condition 1) For d > 200m; = 200m; Residual attenuation coefficient 34

37 (3.15) (3.16) Y (d ) is obtained using condition 1. The results and the discussion of the multi linear regression analysis are explained in the next chapter. 35

38 4 Results and Discussion In this chapter, the results of the statistical analysis performed for this thesis are presented. The first and second sections focus on the seasonal effect of weather parameters and its dependence on the frequency of the AGSP at a height of 100 meters. The third and fourth sections focus on the effectiveness of the devised noise contour calculation method. The dataset used for the analysis is collected from the setup (described in chapter 2) between August 2010 and Dec Seasonal effect of weather parameters on AGSP As mentioned in the previous chapter, the weather parameters considered for the analysis are temperature, relative humidity, wind speed, wind direction and turbulence. The seasonal effect of weather parameters is studied by analysing its effects on a single 1/3 rd octave band (2000 Hz). The effect of weather on the other 1/3 rd octave bands (ranges from 500 Hz to 3150 Hz) is not considered, in order to study only the seasonal effect of weather parameters on transmission loss for AGSP. In section 4.2, the influence of weather parameter on different frequency bands are studied. Although the analysis is carried out on the entire dataset, this section focuses on the results obtained from microphone position 5 (shown in Figure 5a). Figure 13 shows the correlation coefficients found using the linear regression analysis for a transmission loss of 2000Hz at Microphone position 5 versus individual weather parameters. Microphone position 4 is excluded as it provided insufficient data points. The correlation coefficients found using linear regression analysis for the Microphone position 2 and 3 are not shown. The values found between the individual weather parameters and transmission losses measured at the microphone positions were insignificant for certain seasons. Figure 13 Seasonal effect of weather parameters (Microphone position 5) 36

39 In Figure 13, the zero correlation coefficient means no dependency; the magnitude gives the dependency of the weather parameter on the transmission loss for AGSP. The positive or negative correlation, points out whether the phenomena increases or decreases (e.g. if R > 0, the increase in the value of a weather parameter increases TL and if R < 0, then the increase in the value of a weather parameter decreases TL). The blue line shows the correlation coefficient found between measured transmission losses versus atmospheric absorption at different seasons. The other lines represents correlation coefficients found between measured excess transmission loss (excluding the spherical spreading and atmospheric absorption) versus wind parameters for different seasons. In the following section, effect of temperature, humidity and wind parameters are discussed with the results shown in Figure 13. To derive the dependencies of the weather parameter on AGSP, a linear regression analysis and multi-linear regression analysis was carried out. These methods are explained in appendix C. Hence, only the linear dependency is considered, meaning non-linear behaviour is left out in this analysis Effect of temperature and relative humidity on AGSP As mentioned earlier, the temperature and humidity are represented as atmospheric absorption. The effect of atmospheric absorption gradually increases from autumn to winter as shown in Figure 14.From here on in all figures, the mean values are represented as markers (, ) and standard deviations values are represented as bars ( ). It is mainly due to the fact that the variation in humidity and temperature dominates the excess transmission loss during the winter. This dominance slowly fades towards the summer period (The mean and variation in the temperature and humidity measured at the Cabauw site for different seasons is shown in Figure 14). One general case, the transmission loss due to atmospheric absorption is high when the relative humidity is high and when the temperature is low. This is due to the fact that with an increase in the density (i.e. increase in the amount of water vapour in air) damping of sound occurs. There are other general cases, such as temperature is high and humidity is low, so those cases are not explained in this section. The detailed theoretical explanation of variation of atmospheric absorption with respect to the relative humidity and temperature is explained in the fourth chapter of reference [2]. 37

40 Figure 14 Variation in Relative Humidity and Temperature Effect of wind parameters The effect of wind direction on excess transmission loss is high during autumn compared to other seasons as shown in Figure 13. The variation of wind direction is shown in Figure 15 (top left). It can be seen, that the amount of variation (standard deviation) in wind direction during different seasons are more or less the same. From Figure 13 it can be inferred that during autumn the dominance of atmospheric absorption is less than the wind parameters. Therefore the effect of wind direction in autumn is high compared to other seasons on the transmission loss. Thus it can be inferred that, influence of wind direction is independent of seasonal variation, however it is dependent when the atmospheric absorption is dominant. Figure 15 The average and standard deviation of wind speed and turbulence (w.r.t 310 ) 38

41 As mentioned in the previous chapter, the wind direction (WR) value for the upwind condition ranges from 0 to -1 and for the downwind condition ranges from 0 to 1. When there is an upwind, the sound energy is apparently transported away from the receiver towards the source and vice versa in the case of downwind. This cannot be explained as a refraction effect (bending of sound rays); the wind speed also plays a major part in refraction. The mean wind speed has minimal effect irrespective of the season. (Only the summer season shows a significant correlation, see Figure 13 ). From this it is inferred that, the mean wind speed doesn t influence the transmission loss for propagation directly under the flight path. This supports the observation that the transportation of sound energy towards and away from the receiver is not explained by refraction. Turbulence is composed of inertial and thermal fluctuations. The net effect of turbulence is the scattering of sound waves and this can be explained using the Bragg diffraction phenomena. The theoretical modelling of turbulence and its effects on sound propagation are explained in NASA report [14]. Turbulence is defined here as the variation of wind speed at the time of measurement. The variation in wind speed has a non-linear behaviour; therefore the turbulence does not have a strong linear correlation with the variation in transmission loss. This is seen in Figure 13 where the correlation between turbulence and transmission loss for AGSP is minimal compared to other weather parameters. Turbulence also does not have seasonal effect which is shown in Figure 15 (bottom left). The individual influence of each weather parameter on the propagation of a sound of 2000 Hz frequency are summarised as follows. The atmospheric absorption has a seasonal effect as opposed to the wind parameters. The atmospheric absorption is dominant compared to the wind parameters. The mean wind speed and turbulence have no clear effect on the propagation of a broad band sound at a 1/3 rd octave band with a centre frequency of 2000 Hz. 39

42 4.2 Influence of wind parameters at different frequency bands The influence of temperature and humidity at different frequency bands is a well-known physical phenomenon. The wind parameters are combined and the influence on sound propagation is analysed using multi-linear regression analyses. The microphone positions 2 and 3 which were excluded for linear regression analysis were included for multi-linear regression analysis. As the results obtained from multi linear regression analysis was significant for all seasons. The analysis resulted in the generation of a linear equation for each 1/3 rd octave band (independent of microphone position) as discussed in section These equations were used to estimate the excess transmission loss due to wind parameters. The coefficients of the linear equation (3.11) vary for different frequency bands as shown in Figure 16 and are tabulated in Appendix E.1. The magnitude and sign of the coefficient implies the frequency dependence of wind parameter on excess transmission loss. Figure 16 Frequency dependency of transmission loss due to effect of wind parameters The influence of the wind direction (which is gradually increasing from the lower frequency band to the higher frequency band) has a frequency dependency as shown in Figure 16 (top left). The effect of mean wind speed is near zero and can be neglected. It doesn t have a frequency dependency which is shown in Figure 16 (top right). The influence of turbulence is independent of frequency according to the results since the major part of turbulence is explained as variation of wind speed. 40

43 The constant term in the generated linear equation (3.11) refers to the amount of unexplained transmission loss which is shown in Figure 16 (bottom right). Figure 16 (bottom right) shows that, from a frequency of 500Hz to 1000Hz, the unexplained TL is negative. This implies that the transmission loss is less than the standard predicted value (even if we consider only spherical spreading). This can also be observed from the Figure 17 where the difference between measured and calculated transmission loss at microphone position 5 is shown. The same phenomenon is seen at microphone 2 and 3, (Appendix E.3). This cannot confirm the problem is due to directivity. This can be due to the increase in the level of background noise or the imperfectness of the assumed Omni directional point source in the calculation while applying spherical spreading. Moreover, the reference sound level of 500Hz and 3150Hz are similar at 100m height as shown in Appendix E.2. So this is unlikely to be caused due to the differences in sound emitted from the speaker. Figure 17 Average of measured and calculated TL (at Microphone position 5) While moving from the 1250Hz to the 3150 Hz frequency band, the unexplained transmission loss increases. This shows that there are other unknown factors or non-linear behaviour of the weather parameters which can have a major influence. From the above results, the limitation of the formulated equation (3.12) is identified and stated below, The estimated influence of weather parameters from multi-linear regression analysis hold for the 1/3 rd octave band whose centre frequency range from 1250 Hz to 3150Hz ( as the B4 coefficient is positive for these 1/3 rd octave bands). Therefore, the overall sound levels are estimated by considering only these 1/3 rd octave band levels in the following results. 41

44 4.3 Effectiveness of different noise contour calculation methods In the previous section, the effect of individual and combined weather parameters on the AGSP up to 100 metres height was examined (all based on measured data). In this section the methods used to calculate the transmission loss (not measured) in the AGSP is studied while including the varying weather conditions. The standard methods used in noise contour calculation form the starting point and we work toward the new method where the estimated excess transmission loss equation (discussed in the previous chapter) is added. All this is done to bridge the gap between the measured and the calculated aircraft noise, the main objective of the thesis. Four different approaches are considered to estimate the transmission loss. Each approach accounts for a different combination of weather effects in order to estimate the transmission loss due to air-to-ground sound propagation. The first two methods are formed based on the standard methods. Last two methods are formulated by adding additional weather effects (that are estimated using the result of statistical analysis done in this thesis) to the standard methods. The four different methods are summarised in Table 2. 42

45 Table 2 Calculation methods Approaches C1 The estimation of transmission loss This approach uses the standard atmospheric conditions (i.e. the standard method in aircraft noise contour calculation [3]). This method is referred to as classical method. Factors considered are: Spherical spreading Standardised atmospheric absorption (T= 25 o C, RH=70%). C2 This approach uses the varying atmosphere (measured at Cabauw). Factors considered are: Spherical spreading Standardised atmospheric absorption (varying T and RH) C3 This approach uses the varying atmosphere (measured at Cabauw). Factors considered are: Spherical spreading Standardised atmospheric absorption (varying T and RH) The estimated excess transmission found using the varying wind parameters (wind direction, wind speed and turbulence) C4 This approach also uses the varying atmosphere (measured at Cabauw). Factors considered are: Spherical spreading Standardised atmospheric absorption (varying T and RH) The estimated excess transmission found using the varying wind parameters (wind direction, wind speed and turbulence) The estimated unexplained transmission loss. 43

46 Ultimately, the effectiveness of bridging the gap using the different methods is found by comparing the calculated results with the measured values. The noise is calculated for 100 metres height using the events (2383 events, see section 3.4.1) of Cabauw expressed in L DEN. The L DEN is the equivalent noise level with penalties for the night and evening. The L DEN represents the averages of a day for a full year and is used in the Netherlands to regulate environmental aircraft noise. The mathematical formulation is given in appendix D Difference between measured and calculated LDEN The effectiveness of the calculation method is analysed in two ways. 1. The differences in the measured and calculated overall sound levels are analysed. The overall sound levels are found by considering only the 1/3 rd octave bands (whose centre frequency ranges from 1250Hz to 3150 Hz) as prescribed in the previous section. The difference between the mean levels of measured and calculated overall TL are analysed. Then, the estimated overall TL is used to calculate the L DEN. In the end, the effectiveness of the calculation methods is derived by analysing the difference between the measured and calculated L DEN. 2. The correlation between the measured and calculated ( daily ) L DEN using the four methods is analysed. Figure 18 Difference between Measured and Calculated TL, L DEN for C1 approach (Microphone position5) 44

47 Figure 18 (top) represents the differences between measured and calculated transmission loss at every data point throughout the year for microphone position 5, whereas the bottom picture shows the difference in L DEN. The solid red line in both plots represents the calculated reference and the dashed magenta line represents the mean of the difference between measured and calculated value. The symbol η is used to represent the number of data points in the plot. The mean of the difference between measured and calculated TL and L DEN are also represented in the plot along with the respective standard deviations. Figure 18 represents the first calculation method (C1). Instead of showing similar figures for the other calculation methods, the variation in the mean of the difference between measured and calculated L DEN using the four different methods is shown in one single plot for clarity purposes. Figure 19 Difference and correlation between Measured and Calculated L DEN (Microphone position 5) Figure 19 (left side) shows the mean and standard deviation of the difference between the measured and the calculated L DEN using the four different methods. Figure 19 (right side) shows the correlation coefficient found between each measured and calculated L DEN using different calculation methods. The correlation coefficient tells how good the calculated L DEN follows the measured L DEN fluctuations (Figure 18 below). C1 includes no varying atmospheric conditions. It uses the fixed SAE AIR-1845 Atmosphere conditions. The 45

48 correlation coefficient of C1 is therefore zero and ultimately the reference. C2 includes varying atmospheric conditions while calculating the absorption. C2 is therefore non zero. Similarly, it adheres with other calculation methods (C3, C4). Further, detailed interpretation of Figure 19 is explained in the following section. To get an insight of the differences between the calculation methods, the variations in measured TL and calculated TL using three different methods (C2, C3, and C4) are shown in Figure 20 for microphone position 5. The calculation method C1 is excluded in Figure 20, since there is no variation in the TL throughout the year (as fluctuations in weather parameters are not considered). Figure 20 Difference between Measured and Calculated TL (Microphone position 5) Figure 18 to Figure 20 represent the results for microphone position 5. Also, similar results are seen at other microphone positions and therefore support the findings above. Hence, the figures representing the other microphone positions are shown in Appendix E.4. 46

49 4.3.2 Interpretation The effectiveness of the calculation methods and the explanation of the results presented in the previous section are discussed below. From Figure 19 (left side), it is seen that L DEN is higher for the calculation method C2 compared to C1 method (where only a fixed absorption value is considered). This is due to the fact that, in the Netherlands the temperature is below the SAE AIR-1845 atmosphere conditions and the humidity is above the SAE AIR-1845 condition. Thus the transmission loss estimated using method C2 is lower than that found using method C1. Therefore L DEN calculated using the C2 method is high compared to L DEN calculated using the C1 method. Hence the L DEN found using C2 method is higher. Comparing C2 and C3 methods it is noticed that calculation method C3 improves the prediction by 0.11 db (A) which is about 12% compared to C2. This also indicates that the improvement in the noise contour calculation will be around 0.11dBA (e.g. for 2382 flights a year all at 100 meters height). The L DEN is zero for C4 method as per definition (it includes the constant term). From Figure 19 (right side) it can be seen that the correlation coefficient (R) (between measured and calculated LDEN) increases from C1 method to C3 method. From this, it can be inferred that the effectiveness of the calculation methods is increasing from C1 to C3 method. But this trend does not hold for C4, as the correlation coefficient found for C4 method is decreasing. This is due to the addition of the unexplained excess transmission loss term in the linear equation found using C3 method. The effectiveness of the calculation methods are summarized as follows The effectiveness of the calculation methods is increasing from C1 to C3 method. The C4 method is not considered as it holds the estimated excess TL due to unknown factors. The effectiveness of the calculation methods also shows the improvement in the noise contour calculation. From the study, it indicates that, the improvement in the noise contour calculation will be around 0.11dBA (e.g. for 2382 over flights a year all at 100 meters height). To get a better picture of the improvement also when the aircraft flies at higher and different altitudes, the improvement is scaled to greater heights in the next section. 47

50 4.4 Effectiveness of noise contour calculation methods at higher altitudes In the previous section, the effectiveness of the calculation method at 100 meters altitude was discussed. In this section, the effectiveness of the calculation methods at altitudes above 100 meters is discussed. This is done by studying the difference between the measured and the calculated L DEN (estimated using C1, C2 and C3 methods). As pointed out in section 4.3, the C1 method uses standard absorption parameter. Method C1 is to be referred to as a classical method that is included in standard noise models. The C2 method includes the influence of varying absorption. The C3 method includes the influence of varying absorption and wind parameters. As mentioned in the section 4.3.1, the L DEN is calculated by using the transmission loss. The measured and calculated transmission loss (above 100 meters) for each Cabauw noise event is found by the using the scaling method mentioned in section 3.5. First, the effectiveness of the classical method (C1 method) is found by finding the difference between the measured and the calculated L DEN and this is shown in Figure 21. L DEN refers to the difference between the measured and the calculated L DEN. Both the mean difference and the standard deviation are plotted against the altitude. The solid red line in the graph represents the reference level (zero) for clarity. Figure 21 Difference between measured and calculated L DEN (C1 method) 48

51 From Figure 21, it is inferred that the mean L DEN is increasing with altitude and goes up to 3.74 dba at 1000 meters height. Further, it starts decreasing towards 1500 meters. This decrease in L DEN above 1000 meters is mainly due to the effect of using the scaling factor which is a frequency dependent curve (shown in section 3.5, Figure 12 ). On the other hand, the standard deviation is increasing up to 1000 meters and then decreasing. This shows the fluctuations in the measured L DEN values at different altitudes. These fluctuations cannot be explained by the C1 method since it uses the standard absorption values. On the whole, the difference between measured and calculated L DEN (using the classical method) is high. In the similar manner, the difference between the measured and calculated L DEN (using C2 and C3) is found and shown in Figure 22. Figure 22 Difference between measured and calculated L DEN (C2 and C3 method) By comparing Figure 21and Figure 22, it can be seen that the methods C2 and C3 estimates the measurements better than C1. Now, from Figure 22, it can be inferred that the mean L DEN (found using C2 method) peaks at 200m altitude and it reduces virtually to zero at an altitude 1500m. This shows that calculation method C2 gives a better estimation of the measured values at higher altitudes rather than at lower altitudes. This can be due to the fact that at the lower altitudes the influence of the varying atmospheric absorption has very little impact on AGSP. At higher altitudes, the influence of varying atmospheric absorption dominates other factors. Moreover, the C2 method does not explain the variation in the range of the L DEN values on a day to day basis. 49

52 This is mainly due to the fact that the C2 method is derived by the linear regression analysis, i.e. the non-linear variations are not taken into consideration. From Figure 22, it can be seen that method C3 also follows the same trend as the C2 method. In addition to that, it can be inferred from Figure 22 that the influence of wind parameters on the AGSP is minimal as the difference between C3 and C2 method is negligible. From the above paragraphs, it can be determined that method C2 is the most suitable and viable method (among the calculation methods considered in this thesis) for the future noise contour calculations. Thus we can ultimately deduce from this study that, The effect of wind parameters on the mean sound level (L DEN) is negligible and all noise contour computations which will be carried out in the future may be done so using method C2 which only factors in the variations in temperature and humidity. 50

53 5 Conclusion The research questions upon which this thesis is based are: Can a trend be determined for varying atmospheric conditions using real noise measurement on the air-to-ground propagation path? If a trend is found, can it be incorporated into the noise contours calculations? Does the formulated correction method significantly improve the noise contour calculations? The questions mentioned above have been comprehensively explained as follows: Trend Determination A linear trend has been determined for varying atmospheric conditions along the AGSP. This was determined by analysing the variation in the weather parameters such as wind speed, wind direction and turbulence along the AGSP. Linear regression analysis and multi-linear regression analysis was utilized to determine the linear trend mentioned. Trend Incorporation The determined trend has been incorporated into a representative noise calculation for doing contour calculation in the vicinity of airports. This is done by demonstrating three different noise calculation methods. The first two methods were formulated by considering the standard parameters (spherical spreading and atmospheric absorption). The last method was formulated by factoring in additional parameters such as wind direction, wind speed, turbulence. This addition constitutes to the excess transmission loss equation which was determined statistically from the Cabauw data set. In this way trends are incorporated into noise (contour) calculations used for the air-to- ground sound propagation path. Improvement in the noise contour calculation The suggested methods do show an improvement over the standard methods considering varying weather condition, but the degree of the improvement is quite small. The overall improvement for an altitude of 100 meters is only 0.11 dba assuming Dutch weather conditions. For greater altitudes above, there was considerable improvement. 51

54 6 Recommendations The following recommendations are hereby made: 1. Currently noise contour calculation methods typically use fixed and average weather conditions. The results of this thesis show that noise contour calculations need to be done considering temperature and humidity to be dynamic factors as opposed to fixed parameters. Although the addition of the wind parameters improves the noise contour, it can be neglected as the improvement is negligible. 2. The conclusions drawn from this thesis are based on the sound ranging from Hz. Thus in the future, other sound frequencies may be explored to obtain more results. 3. The wind parameter may be modelled using a nonlinear relation (rather than using linear relation given in equation 3.11) to obtain better results. 4. Variations at the aircraft as noise source should also be included in the noise modelling calculations as it influences the noise contour considerably. 5. A manned experimental setup must be utilized in the future. Apart from the setup being manned, periodic calibration, equipment maintenance and regular maintenance of the surroundings are a must. After all, the results of an experiment are only as accurate as the quality of the input data recorded via the setup. 52

55 References [1] Society of Automotive Engineers, Standard values of atmospheric absorption as a function of temperature and humidity. SAE ARP 866A, Society of Automotive Engineers, [2] G. Ruijgrok, Elements of Aviation Acoustics, Delft : Delft University Press, [3] ECAC.CEAC Doc 29, Report on Standard method of Computing Noise Contours around Civil Airports, Volume 1&2, 3rd Edition, [4] Federal Aviation and Administration (FAA), Integrated Noise Model (INM) version 7.0 Technical Manual, [5] R. Payne, Uncertainties associated with the use of a sound level meter, NPL Report, April [6] N. Miller, G. Anderson, R. Horonjeff, S. Kimura, J. Miller, D. Senzig and R. Thompson, Examining INM accuracy using empirical sound monitoring and radar data, NASA Contractor Report CR , [7] S. Fidell and P. D. Schomer, Uncertainties in measuring aircraft noise and predicting community response to it, Noise Control Engineering Journal, vol. 55, no. 1, pp (7), 1 January [8] A. Eisses, J. Golliard, A. Mast and P. Balke, Onderzoek naar Verschillen tussen gemeten en berekend vliegtuiggeluid, Rapport CDV-TNO-NLR IS-RPT060017, CDV-TNO-NLR, January [9] T. Okada, K. Yoshihisa and T. Iwase, Effect of atmospheric absorption on aircraft noise propagation around airports in several world regions during a year, in Internoise, Shanghai, China., [10] T. Okada, K. Yoshihisa and T. Iwase, Temporal variability for atmospheric absorption of sound and its effect on aircraft noise propagation around an airport during a year, in Internoise, Shanghai, China., [11] K. Yoshihisa and Y. Okada, The Effect of Atmospheric Absorption on Environmental Noise Propagation in an Urban Area, Computer Science and Engineering, vol. 20, no. 1, October

56 [12] International Standard Organisation, Acoustics Description, measurement and assessment of environmental noise Part 1: Basic quantities and assessment procedures.iso , [13] D. Bergmans, M. Arntzen and W. Lammen, Noise attenuation in varying atmospheric condition, in Inter-noise, Osaka,Japan, [14] R. Deloach, On the excess attenuation of sound in the atmosphere, NASA Langley Research center, Hampton,Va, March [15] M. Burkhard, H. Karplus and H. Sabine, Sound propagation near the earth's surface as influenced by weather conditions,rep ,Part-II, WADC, U.S.Air Force, Dec [16] J. Cohen, Statistical power analysis for the behavioural sciences, 2nd Edition, Routledge Academic,ISBN-10: , [17] P. Teunissen, D. Simons and C. Tiberius, Lecture notes AE2E01, Probability and observation theory, Delft: Faculty of Aerospace engineering, Delft University of Technology., [18] D. Simons, M. Snellen and M. Ainslie, A Multivariate Correlate analysis of High-frequency bottom backscattering strength measurements with geotechnical parameters, Ocean Engineering, vol. 32, no. 3, pp , [19] G. Thomann, Uncertainities of measured and calculated aircraft noise and Consequences in Relation to Noise limits, in Acoustics, Paris, France., [20] P. D. Schomer, A Statistical description of ground to ground sound propagation, Noise Control Engineering, vol. 51, no. 2, pp , April [21] S. Stigle, Fisher and the 5% level, Mathematics and Statistics, vol. Volume 21, no. 4, p. 12,

57 Appendix A A.1 Location of the experimental setup Figure 23 Cabauw location in Map (Source Google Maps) Figure 24 Top view of experimental site 55

58 A.2 Loud speaker specifications 56

59 A.3 Microphones The types of microphones used in the experiment are shown in Figure 25, Figure 25 B&K 4952 outdoor microphone (left) and B&K 4949 surface microphone (right) The microphones placed at the ground level are Brüell & Kjaer (B&K) The ground microphones are connected to the NI-DAQ soundcard and measure the potential difference in Volts with a sampling rate of 48 khz simultaneously. The microphone placed at 1 meter in front of the speaker is B&K 4952 and it is connected to the TRITON soundcard. The B&K 4952 needs a higher electrical potential than the microphone type B&K Therefore B&K 4952 has been connected to another soundcard. A.3.1 Installation of ground microphone The installation of ground microphone is shown in Figure 26, Figure 26 Microphone mounted flush on a 40 cm metal plate placed on a sand foundation 57

60 A.4 Comparison of aircraft and loud speaker spectra A Boeing spectrum was chosen from the ANP database and the corresponding specifications used to collect the data from ANP database are given in Table A-1. The reference sound spectrum provided by the ANP Database are normalised to 70 db at 1000 Hz using the AIR-1845 atmosphere. The reference spectrum is A-weighted and corrected for the reference distance (100m) by following the standard method given in Appendix D of reference [3]. The resulted reference spectrum of the Boeing is shown in Figure 27 and values are given in Table A-2. The loudspeaker reference frequency spectrum is extracted from the loud speaker specifications from Appendix A.1 and normalised to 70 db at 1000 Hz is given in Table A-3. The emitted audio signal by loudspeaker is a random broadband noise having a flat power spectral density between Hz. The emitted noise is not flat due to the characteristics of the loudspeaker. The loudspeaker is designed as a public addressing system and radiates best at speech frequencies ranging from 500Hz to 4 khz. In turn it maintains minimum noise impact to the surrounding. Fortunately the loud speaker mimics the aircraft flyover noise spectrum to an extent between 500Hz to 4 khz which is shown in Figure 27. Although aircraft noise differs; differences or trends should physically be transferable to other frequencies. Table A- 1 Boeing NPD specifications ACFT_ID Description Engine Type Number Of Engines Departure Spectral Class ID Boeing /PW4056 Jet Table A- 2 Frequency spectrum data of Boeing at 100m height frequency LA db(a) Frequency LA db(a) Table A- 3 Frequency spectrum data of loud speaker at 100m height Frequency L A

61 Figure 27 Boeing and loud speaker frequency response curve at 100 m height A.5 Dataset A.5.1 Database The database consists out of two sets of data: acoustic and weather data. The acoustic data is provided by the data acquisition card through a NLR computer installed at the KNMI tower at Cabauw. The weather data is provided by the KNMI computers. The weather and acoustic data were transferred to the NLR daily or on a weekly basis via the internet and stored in a database. A Format of the database All the data which are extracted from the database are structured in an xls (MS-Excel) format. This excel sheet is used as the base information to determine uncertainties of atmospheric effects on AGSP. The parameters stored in the excel sheet are listed in Table A- 1. Parameters Event Datum Start Time Acoustic parameters (L A,max, L A,i, LA eq ) Wind direction (WR Content The serial number of the event. The date of the respective event. (dd-mmm-yy) The start time of the respective event. (hh:mm) The value of recorded acoustic parameters at the different microphone positions (Mic 1, Mic 2, Mic 3, Mic4, Mic 5 and Ref Mic shown in Figure 5). The average wind direction of 12 seconds ample over the event 59

62 mean) Wind speed (WS mean) Turbulence Relative Humidity (RH) Temperature (T) Atmospheric Pressure (PS) period (one minute) at the different heights (at 10m, 20m, 40m and 80m) and the different directions (at 0, 120, 240 ). Unit is Degrees. The average wind speed of 3 seconds sample over the event period (one minute) at the different heights (at 10m, 20m, 40m and 80m) and different direction (at 0, 120, and 240 ). Unit is m/s. The turbulence is denoted for different heights and different directions using the following parameters, 1. WS std, the Standard deviation of wind speed of 3 seconds sample over the event period. 2. WS std10min, the Standard deviation of wind speed of 3 seconds sample over the last 10 minutes (before and after the sound emission). 3. WR std, the Standard deviation of wind direction of 12 sample over the event period. 4. WR std10min, the Standard deviation of wind direction of 12 seconds sample over the last 10 minutes (before and after the sound emission). Unit is m/s. The average relative humidity (RH mean) and standard deviation of relative humidity (RH std) over the last 10 minute at 10m height. Unit is percentage. The average temperature (TA mean) and standard deviation of temperature (TA std) over the last 10 minute at the different heights (at 10m, 20m, 40m and 80m). Unit is C. The average atmospheric pressure (PS mean) and standard deviation of atmospheric pressure (PS std) over the last 10 minute at 10m height. Unit is kpa. Table A-5 1the fields in the Excel sheet 60

63 Appendix B B.1 Extraction methods of Acoustic data The acoustic data contains the two main acoustic parameters that are calculated from the recorded audio signal. The two main acoustic parameters that were used for the assessment are given below, 1. A weighted sound level (L A,i ) per one-third octave band, (i represents the band number of 1/3 rd octave bands) 2. Equivalent overall A weighted sound level (LA eq ) An example chosen to study the difference between the extraction methods used in the initial assessment and current assessment. The selected example case is given below. Here, the method used in the initial assessment is denoted as M1 and the method used in the current assessment is denoted as M2. Example Case The event date and time Microphone position : 310 : 23 th October, 2010 at 16:20hrs The recorded audio signal at the given microphone position is shown in Figure 28. The length of the recorded audio signal is 60 seconds which includes 15 seconds of emitted audio signal (termed as event noise) from the loud speaker and the remainder is background noise as shown in Figure 28. Figure 28 Audio signal received at ground microphone 61

64 The 60 second recorded signal is divided into equivalent parts of 0.25 second. This resulted in 240 parts but out of the 240parts only 200 parts were considered. This was done to eliminate overlapping of background noise and event noise periods. Those time periods are given in Table B-1. For each part of the recorded signal, the sound energy contained in 1/3 rd octave bands is extracted through a discrete Fourier transform at a sampling rate of 48 khz. Then for each part of the record signal, the A-weighted sound level L A,i per frequency band were calculated by applying corresponding A-weighting. The calculated acoustic parameters that are used for further analysis are represented in bold letters. Table B-1 Time divisions Category Time (s) Time period (t) in Total parts parts Background noise (1 to 15sec) and (1 to 60 parts) and 160 (35sec to 60sec) (140 to 240) Event noise 20 sec to 30 sec 80 to 120 parts 40 In the following section, the calculation methods of A weighted sound level (L A,i ) and equivalent overall A-weighted sound level (LA eq ) used in the M1 and the M2 are explained. B.1.1 Calculation method of A weighted sound level (L A,i ) In the M1 method, the maximum value of the overall A-weighted sound level (L A ) among 240 equivalent parts was found using (B.1). The corresponding L A,i values are extracted for 1/3 rd octave frequency bands using (B.2). (B.1) Where, t ranges from 1 to 240 parts considering the entire time period. (t max represents the time period when L A is maximum) (B.2) In the M2 method the mean value of L A,i for each 1/3 rd octave band during the event noise period are considered. Therefore per 1/3rd octave band is calculated using (B.3). 62

65 Where, t ranges from 80 to 120 considering only the sound levels during event noise period. (B.3) B.1.2 Calculation method of Equivalent overall A weighted sound level (LA eq ) In both the methods, the calculation of the equivalent overall A-weighted sound level (LA eq ) is similar. The general equation is given in (B.4). Nonetheless the overall A-weighted sound level (L A ) used for the calculation is different for two methods. (B.4) In the M1 method, the overall A-weighted sound level (L A ) for each part of the time period is calculated by logarithmic summation of A-weighted sound level (L A,i ) using (B.5). In this method, 1/3 rd octave bands whose centre frequencies range from 10 Hz to 10 khz are considered. (B.5) Where i represent band number of 1/3 rd octave bands In the M2 method, the overall A-weighted sound level (L A ) is calculated using (B.6). Here, 1/3 rd octave bands whose centre frequencies range from 500 Hz to 3150 Hz are considered. (B.6) The difference between the A-weighted sound level (L A,i ), as calculated using the M1 and M2 method, is shown in Figure 29 for the selected frequency ranges. 63

66 Oct , channel 6,dBA values per 0.25 s, V/Pa Previous Method Improved Method LA (dba) /3rd centre freq (Hz) Figure 29 L A calculated using the M1 and the M2 method The sound level extracted using the M1 method is slightly higher than the M2 method. This is due to the M1 that uses maximum sound levels within a period to calculate the overall sound level. Therefore, the extracted sound levels are minimized using the M2 method. B.2 Filtering Method The dataset was filtered to exclude the event that lies outside the designed window. The window used in the M1 and the M2 methods are mentioned in this section. In M1 method, an event is excluded when the difference between maximum value of overall A- weighted sound level (L A ) during the background noise period and the minimum value of L A during the event noise period is less than 10 dba. The condition of the window is given in (B.7). (B.7) Where, ); (t is the time period considered when event noise is recorded given in Table B-1) ; (t is the time period considered when background noise is recorded given in Table B-1) In M2, the sound levels at each third octave bands (centre frequencies range from 500 Hz to 3150 Hz) are considered, in spite of considering the overall level. An event is excluded when the difference between L A,i during the event noise period and the L A,i during the background noise period is less than 10 dba. The condition of the window is given in (B.8). 64

67 (B.8) Where (i ranges from 27 to 35 band numbers of 1/3 rd octave bands) Figure 30 LA eq calculated using M1 and M2 method The difference between the M1 and M2 filtering method can be compared using Figure 31. According to the M1 method, the minimum value of the event is not less than the maximum of the background noise if 10 db (A) is added. Therefore, the chosen event in this example would be excluded given the M1 method. However, the event is not excluded if the same condition is used in combination with the M2. Hence, by using the M2 method more valid events are included. 65

68 Appendix C C.1 Statistics In this section, first the statistical terms involved in estimation statistics are explained. Then, the multi linear regression model is explained. C.1.1 Linear correlation coefficient (ρ) The linear dependencies of one variable on the other are sort by linear regression analysis. The (linear) correlation coefficient is an indicator of the strength of a relationship between two variables used in regression analysis. For example, the importance of the individual atmospheric variable on the calculated transmission loss can be analysed by finding the correlation between those two factors. The correlation coefficient (ρ), for y (TL) and x (atmospheric variable), is given in (C.1) Cxy ρ xy = σ σ (C.1) x y Where C is the covariance, it is the measure of the linear relationship of the variable of interest which is related to the correlation coefficient shown in (B.9) and σ is the standard deviation. Many authors have many regulations for interpreting the correlation coefficient. However all those criteria s are in some ways arbitrary and should not be observed strictly [16].Hence, an absolute magnitude of the correlation coefficient of represents a weak correlation. Moderate correlations range from whereas strong correlations range from 0.7 to 1. The trustworthiness of a correlation coefficient is judged by its statistical significance. The definition and importance of statistical significance is explained in next section. The correlation coefficient not only quantifies relations, the square of the coefficient determines the percentage of scatter explained by the one variable on the other variable. C.1.2 Confidence interval, level of confidence and statistical significance In this section, the description of the confidence interval and its relation with level of confidence is explained. Then the definition and importance of statistical significance are explained. The confidence interval indicates the lower and upper range of the estimated correlation in the given sample size. The level of confidence is the indication of the probability that the estimated correlation can occur between two correlated data. The level of confidence is a percentage, typically 95% or 99%. It shows how confident the estimated correlation is within the confidence interval. The level of confidence represents the trustworthiness of the correlation coefficient. The confidence level is also represented in another form as significance level. The relation between confidence level and significance level is trivial and given in (C.2) 66

69 Confidence level = (1 significance level); (C.2) The significance is defined as the randomness of each correlation coefficient. For example consider a weak correlation coefficient such as 0.3, of significance level 0.40, confidence interval (0.2, 0.4) and sample size 100. This means that there is a probability of 40% that the observed correlation within the range (0.2 to 0.4) can occur between two uncorrelated data sequences. In other words, there is probability of 60% (confidence level) that the observed correlation within the range (0.2 to 0.4) can occur between two correlated data. In general, the higher level of confidence implies a larger confidence interval. Lower levels of confidence will have a short confidence interval. Normally, one would like to have lower confidence intervals with higher level of confidence. This is difficult to achieve. Nevertheless, the relation between confidence interval and confidence level has the dependency on the number of samples involved in the analysis. Since, the size of the sample is important in the analysis. The importance of sample size is explained by showing the dependency of the significance level on number of samples. In Figure 32, the examples show the importance of number of samples in finding the significance level for the obtained correlation coefficient (ρ). The η (number of samples) data pairs (x1, x2) are created randomly. Therefore, x1, x2 are independent and subsequently the correlation coefficient between x1, x2 should be zero but the resulting ρ value for different data pairs from Figure 32 shows that they are not equal to zero. To find the significance of correlation coefficient for data pairs (x1, x2) of different η s are analysed using Monte Carlo simulation. To analyse the variation in the correlation coefficient with respect to the number of samples, the entire process has been repeated for M times (here M = 10^5) for different η. For η (equal to 10, 30, 100 and 1000) data pairs and their corresponding probability distribution function of the correlation coefficients containing M values are shown as scatter plots and histograms respectively in Figure 32. From this, it can be seen that when number of samples increases, the histogram is more peaked around low values of ρ. The cumulative distribution function is determined from the histogram and shown in Figure 33 and the probability of the correlation coefficient that occurred by chance (statistical significance) is shown in for Figure 34 for different sample size. The method followed in this example is explained in [17]. From this figure the p value for corresponding correlation coefficient of η data pairs are found. 67

70 Figure 32 Simulation of the observed correlation coefficient between uncorrelated data pairs n = 10 n = 30 n = 100 n = F ρ (ρ) ρ Figure 33 Cumulative distribution function of the correlation coefficient of uncorrelated data pairs n = 10 n = 30 n = 100 n = P (mod(ρ) > ρ) ρ Figure 34 Statistical significance of the correlation coefficient of uncorrelated data pairs 68

71 From this analysis, it can be confirmed that for weak correlation coefficient when the number of sample size increases, the significance level decreases. In other words, when the number of sample size increases, the level of confidence increases and confidence interval decreases. This effect is seen in Figure 34. However for the strong correlation coefficient, the number of sample size has marginal effect on the significance level of correlation coefficient. C.1.3 Multiple linear regression model In this section, the mathematics behind the multiple linear regression model used in this thesis is explained. Multiple linear regression analysis is an application of estimation statistics. This is the extended version of linear regression analysis. In linear regression analysis, a single variable is related to one independent variable and it fits a line through a set of points based on one independent variable. In multiple linear regression, a single variable (y) is related to more than one independent variables (x 1, x 2,..., x n ) to find interdependencies. The fitted line equation given as [18], y= cx 1 1+ cx cx n n + c n+ 1 (C.3) The coefficients c i of (C.3) form a linear relationship between the independent variables (x i ) and the desired parameter (y i ). A is defined as a matrix containing the x i variables in each column. The final column is filled with 1 s to relate to the final entry like c n+1 in (C.3). As a result a linear combination is written as η x ( n+ 1) matrix, where η is number of samples and n is number of variables. y = Ac (C.4) Where, vector y is a column vector containing all measured transmission losses. The column vector c contains the coefficients as defined in (C.3) The system of equations in (C.4) is solved in the least squares sense yields, cˆ = ( A The variable ĉ T A) 1 A T y (C.5) represents the estimated set of coefficients. An empirical relation between y and x variable is formulated by substituting the estimated values in (C.5). 69

72 Appendix D D.1 Noise metrics calculation D.1.1 L DEN calculation First, the overall A weighted sound level (LA) at the receiver position for single event is calculated using transmission loss (TL) of each frequency band formulated from (D.1).The calculation method is shown in mathematical form below, ; dba (D.1) Where, LA ref is the A-weighted sound level at source and TL the estimated transmission loss at every 1/3 rd octave band. Then, L DEN for each day is formulated as shown below, T = 15secs, k = number of hours/events in day period. ; dba (D.2) T = 15secs, k = number of hours/events in evening period. ; dba (D.3) T = 15secs, k = number of hours/events in night period. ; dba (D.4) ; dba (D.5) The overall L DEN for a year or specified time period is calculated by taking the mean of the collective L DEN. ; dba (D.6) Where, n is the number of events within the specified time period. 70

73 D.1.2 Overall A weighted reference sound level An overall A-weighted reference equivalent sound level is calculated using the measured sound levels at the source altitude for different frequencies, ; dba (D.7) D.1.3 Overall A weighted Transmission loss Overall A weighted transmission loss is found by subtracting (D.7) with (D.1) for every event. (D.8) The mean TL for the whole year or specified time period is calculated using (D.9) ; dba (D.9) Where, n is the number of events within the specified time period. 71

74 Appendix E E.1 Coefficients of weather parameters Table C- 1 Coefficients of weather parameters for different seasons and different 1/3 octave frequency bands Autumn 500Hz 630Hz 800Hz 1000Hz 1250Hz 1600Hz 2000Hz 2500Hz 3150Hz B B B B Winter B B B B Spring B B B B Summer B B B B

75 E.2 Reference spectrum Reference spectrum of loud speaker E.3 Average of measured and calculated TL Figure 35 Average of measured and calculated TL (at Microphone position 2) 73

76 Figure 36 Average of measured and calculated TL (at Microphone position 3) E.4 Difference between measured and calculated TL and L DEN The differences between measured and calculated TL and LDEN for other microphone positions are shown in this section. E.4.1 Results of Microphone position 2 (40 ) Figure 37 Difference between Measured and Calculated TL, L DEN for C1 (Microphone position 2) 74

77 Figure 38 Difference and correlation between Measured and Calculated L DEN (Microphone position 2) Figure 39 Difference between Measured and Calculated TL (Microphone position 2) 75

78 E.4.2 Results of Microphone positioned at 130 degree Figure 40 Difference between Measured and Calculated TL, L DEN for C1 (Microphone position 3) Figure 41 Difference and correlation between Measured and Calculated L DEN (Microphone position 3) 76

79 Figure 42 Difference between Measured and Calculated TL (Microphone position 3) 77