Radar Comparison Study

Radar Comparison Study NPN Wind Profilers Paloma Farias Gutierrez, Johannes Wiig

Contents 1. Introduction... 3 2. The Atmosphere as a Target... 3 2.1 Kolmogorov micro scales... 4 2.2 Refractive Index Gradient... 4 2.3 Atmospheric Attenuation... 4 2.4 Frequency Choice... 4 3. The Radar System... 6 3.1 System Overview... 6 3.2 Antenna Design... 7 3.2.1 Antenna Pattern... 8 3.2.2 Antenna Gain... 9 3.2.3 The Beam Swinging Technique... 9 3.2 Radar Equation... 10 3.3.1 Rayleigh Radar Equation... 10 3.3.2 Soft Target Radar Equation... 11 3.4 Radar Pulses and Resolution... 13 4. Data Processing... 14 5. Discussion Multi Mode Observations... 16 6. References... 17 Appendix:... 18 2

1. Introduction The NOAA Profiler Network (NPN) consists of a network of 35 sites with phased array antennas that produces wind profiles and atmosphere turbulence measurements available for the general public online in near real time. The project started in 1990 and consisted originally of 31 profilers operating at 404 MHz. Today it has grown with one additional 404 MHz profiler in central United States and three new profilers operating at 449 MHz in Alaska. This report focuses on the most common profiler, the 404 MHz configuration. The NPN embraces numerous scientific applications such as atmospheric wave propagation, precipitation research and metrological studies to mention a few. The report is divided in major 4 parts. The first part treats the atmosphere as a radar target; explains the scattering process and how it is reflected in the radar design. The following section covers the radar system: the antenna, the radar equation including a method of atmospheric turbulence estimation, and finally how the wind is derived. Next the data processing is described. Ending the report there is a discussion about multi mode observations using the AMISR. 2. The Atmosphere as a Target In the early years, echoes from apparently clear air were referred to as angels due to its inexplicable nature. According to K.S Gage and B.B Balsley (1978), Booker and Gordon (1950) and Megaw (1950) developed theoretical foundations for turbulent scattering of radio waves motivated by the need to explain long distance tropospheric radio propagation. Turbulence in the atmosphere is caused by air masses of different temperature and humidity. The NPN radar can detect these fluctuations in atmospheric density by using the air masses varying index of reflection as tracers. The volume target reflecting the transmitted energy in a certain range gate is the small scale atmospheric turbulence. The turbulence, or eddies, changes the refractive index (eq. 1) as it creates a different combination of the parameters in eq 1. than in a stratified fluid. The most favorable condition for backscattering is when the spatial scale of an eddy is equal to half the radar wavelength. This scattering type is called Bragg scattering. The simple concept of Bragg scattering can be described with the help of the below figure 1, where irregularities in the refractive index of scales near half the wavelength creates constructive interference. Equation 1 and figure 1 shows that when d is equal to λ/2 (or a multiple) the reflected wave experience constructive interference. In the NPN radar case, θ is close to 90 degrees.. 2 sin θ [eq.1] Figure 1: Bragg scatter illustration [from Encyclopedia Britannica] 3

2.1 Kolmogorov micro scales It is difficult to set a certain number on the volume reflectivity for clear air as it is proportional to the eddy dissipation ( ε) rate and the kinematic viscosity (ν) of the atmosphere. This relationship is described by the Kolmogorov micro scale ( λ k ) in equation 2, setting a minimum wavelength limit on the radar system for observationss of turbulent scales within the inertial subrange. Wavelengths smaller than this micro scale limit are strongly damped and would not provide sufficient signal returns. [eq.2] Figure 2: Height distribution of Kolmogorov Figure 2 1 shows the height distribution of this short NPN micro scale. [After Balsley and Green 1978] wavelength limit with the atmospheric regions indicated. is marked with a red star on this scale (and AMISR with a blue), together with a number of other famous radar systems. It is clear that the operating point is chosen far below the Kolmogorov limit, setting system parameters as the limiting factor for detection and not the nature of the scatter. 2.2 Refractive Index Gradient The return signal power for clear air is related to the vertical gradient of the refractive index. According to Gage 1 the gradient of the index of refraction in the atmosphere can be described by: [eq.3] where p is the atmospheric pressure, T is the absolute temperature, θ is the potential temperature, and q is the specific humidity. A stronger gradient will generate a stronger return, but only as long as the Bragg condition is met, whichh it will always be as long as the radar operates within the inertial subrange. 2.3 Atmospheric Attenuation The troposphere extends from the ground up to ~ 20km above the earth surface. This region is dominated by air parcels were density, pressure, temperature, and vapor content act as a function of the refractive index gradient separating the air masses. All these factors contribute to a radar loss of the transmitted signal know as the atmospheric attenuation. Vapor content is the most influence term, hence precipitation often determine if observations are possible at all. According to Peebles (fig 2.3 10) the atmospheric losses for a 404 MHz system is 1.8 db in a standard atmosphere. 2.4 Frequency Choice In theory any frequency between 40 1400 MHz can be use for clear air radar, but frequency allocations in these ranges (VHF UHF) are hard to come by, hence most commonly used frequencies for this purpose are restricted to around 50, 400 or 1000 Mhz. At the upper range hydrometors (rain) will dominate the return if present while at the lower range even if hyrdometeors are detectable they will not dominate the respond. The observing altitude 1 Gage K. S. and B. B. Balsley, Doppler Probing of the Clear Atmosphere, Bulletin American Meteorological Society, Vol. 59, No. 9, September 1978 4

decreases with increased frequency but this also limits the lowest observable altitude. This implies that typically 50 MHz radar can receive echoes from up to 20 km but it lowest observable altitude is 2 km, while at 1000 MHz a radar may see echoes from 100 meters but only up to around 3 km 23, these ranges of course also depend on antenna sizes and type and transmitted power. No single frequency is suitable for all application, frequencies around 400 Mhz are a good trade off. The minimum observable ranges are around 500 meters and they can penetrate the atmosphere up to 10 km. At 400 MHz the return can also tolerate clear air echoes with some interference of hydormeteors but anything more than light rain will dominate the response. The antenna choice of phase array is largely determined by economical factors. They are normally a less expensive alternative to steerable dishes and also easier to maintain. 2 R. R. Rogers et. al Research Applications of a Boundary Layer Wind Profiler, Bulletin American Meteorological Society, Vol. 74, No. 4, April 1993 3 http://mst.nerc.ac.uk/intro_wind_prof.html 5

3. The Radar System This chapter covers the antenna, beam swinging technique, the radar equation including a method of atmospheric turbulence estimation, and finally how the wind is derived. System Overview The NPN radar use a phased array antenna with a transmitting frequency of 404 Mhz with a maximum power of 6 kw 4. The system is able to operate in 2 modes, 3.3µs (low mode) or 20µs (high mode) pulses (see chapter 3.4 Radar Pulses and Resolution for further information about the pulses). According to the NPN website 4 the radar uses a 128 point fast fourier transform (FFT) to perform spectral analysis and extrapolate velocity estimates. The beam swinging chapter explains further how the winds are extracted. The receiver system consists of a mono static super heterodyne receiver. Figure 3: Block System diagram of the NPN [from the NPN website] 4 http://www.profiler.noaa.gov/npn/ 6

Figure 4: 404 MHz Coaxial Colinear Antenna other. Each array consists of 20 rows of coaxial colinear elements fed by several RF power dividers. This configuration enables a 16.3 degree tilt from the vertical axis (zenith). The transmitting frequency is 404 MHz. The figure below illustrates the antenna two elements and three element row configurations (left) and the layout of the antenna (right). The beam with of the antenna is 4 degrees. 3.2 Antenna Design The antenna choice of phase array is largely determined by economical factors. They are normally a less expensive alternative to steerable dishes and also easier to maintain. As described on the NPN webpage, the NPN profile uses a fixed beam antenna (not to be confused with a fixed beam pattern) for optimal low maintenance operation in occasionally harsh weather conditions. The antenna is a phased array of a physical size of 40 x 40 ft with an element spacing of 0.711λ and row spacing of 0.711λ, placed orthogonally against each Figure 5: Complete Layout of a 404 MHz Co Co Antenna from the NPN website. 7

3.2.1 Antenna Pattern Using Mahafza rect_array.m [Radar Systems Analysis and Design Using Matlab B.R. Mahafza, chapter 10 ] the simulation in figure 6 and 7 are obtained. In the simulation the antenna is pointed at zenith and the beam pattern produced is normalized. The maximum tilting of the beam (13.6 degrees) determines the limit for where the grating lobes start moving in to the real space. Figure 6: NPN Antenna Array Pattern (contour) Figure 7: NPN Array Pattern (mesh) 8

3.2.2 Antenna Gain The antenna gain is directly proportional to the aperture: [eq.4] where G is the gain, λ the wavelength (c/404 MHz=74.2 cm) and A e the antennas effective aperture defined as A e =Aρ where A is the physical aperture (40x40 ft =12.191x12.192m) and ρ is the aperture efficiency (0 ρ 1 ). In this report ρ is assumed to be 1.... =3.39x10 3. [eq.5] 3.2.3 The Beam Swinging Technique In order to derive 1 hour horizontal wind profiles from the radial wind detection a Beam Swinging Technique is utilized. The figure 8 below shows the geometry of the three beam pointing directions (Zenith, North, and East) contributing by the radial wind velocities (V RZ,V RN,V RE ) to the final wind vector (eq. 7) at any given range using the off zenith angle as described by the set of equations in eq. 6. [eq.6] sincos sin cos [eq.7] Each pointing direction s integration time is 1 minute for high mode and 1 minute for low mode, thus switching between directions every 2 minutes. The steering time is short hence a wind vector measurement is produced in just over 6 minutes for each mode. However, 10 of these measurements are averaged to form one final wind profile measurement every hour as described in chapter 4. Data Processing. Figure 8. Beam Swinging Technique 9

3.1 Radar Equation When considering the radar equation in the case of the wind profiler it is necessary to use two different types of scattering processes leading to slightly different radar equations. Both scattering cases are volume scatter, but a Rayleigh return (chapter 3.3.1) is received from hydro meteors or biota, and a soft return (chapter 3.3.2) is resulting from the turbulent mixed atmosphere creating refractivity gradients fulfilling the Bragg condition. 3.3.1 Rayleigh Radar Equation The NPN has a wide range of targets with different cross section and number density (rain drops sizes, bugs etc). This section is included as a comparison; hence the cross section and number density are specific for AMISR targets. For volume scattering targets the radar equation for received power P r takes the form: The noise power P N is expressed as:, where the bandwidth B is:, and the system temperature T sys is: 100. 104 [eq.8] [eq.9] [eq.10] [eq.11] From the above equations the final expression for the SNR can be expressed as:. [eq.12] Table 1 below shows NPN and AMISR system parameters. The SNR is calculated for both systems. The AMISR values for cross section and number density are used in both cases for the sake of comparison. NPN range used for calculations is high mode max. Marked in green are the AMISR calculations using the NPN range. Parameter Symbol NPN AMISR Unit Transmitted Power P t 6 2200 kw Effective Aperture A e 50 400 m 2 Antenna Efficiency ρ 0.9 0.9 Cross section σ 0 Obj. dependent 3x10 29 m 2 Speed of light c 299792458 299792458 m/s Pulse duration τ 20 300 μs Number density N Obj. dependent 10 11 m 3 Loss L 1.8 1.8 db Range R High Mode: 7.5 16.25 >80 km Low Mode: 0.5 9.25 Boltzmann Constant k 1.3806503 10 23 1.3806503 10 23 J/K Transmit frequency f 404 449.3 MHz Transmit wavelength λ 74.2 66.7 cm Bandwidth B 63.5 50 khz System temperature T sys 154 100 K Received power P r High Mode: 7.17x10 15 8.01x10 16 R=16.5km: 1.94x10 14 W Noise power P N 1.35 10 16 6.90x10 17 W Signal to noise ratio SNR High Mode:17.3 10.6 R=16.5km: 24.5 db Table 1. 10

3.3.2 Soft Target Radar Equation [eq.13] 5 Where Parameter Symbol NPN Unit Average transmitted power 6 kw Effective Aperture A e 50 m 2 Fraction rx power passing through the receiver filter. F 1 1 Fraction rx power passing through the coherent integration. F 2 1 Speed of light c 299792458 m/s Pulse duration τ 20 μs Volume reflectivity of the atmospheric scattering process. η 1x10 14 1x10 5 m 3 Transmission line efficiency. α 1 Range R High Mode: 7.5 16.25 km Low Mode: 0.5 9.25 Boltzmann Constant k 1.3806503 10 23 J/K Number of spectra averaged together to reduce noise fluctuations n i 10 Bandwidth B 63.5 khz System temperature T s 154 K Cosmic noise temperature at the antenna terminals. T e 104 K Table 2. The SNR is calculated as a function of volume reflectivity at a range of 6 km in chapter 3.3.3 3.3.3 SNR and Reflectivity of Clear Air Figure 9: One week of spectral peak power at Platteville The signal power is a measure of the amount of the radar's energy that has been reflected and returned from the atmosphere. Very 5 Balsley, 1978a Figure 10: Weather station data from Platteville. 11

weak (blue) 20 db to very strong (red) returns of 100dB is indicated in the spectral peak power in figure 9. From the low mode around 6km altitude a typical value of about 60dB is observed from this week long plot of spectral peak power (fig. 9). The returns are mostly clear air scatter as precipitation was moderate during this particular week. The weather station data from the same period is also included for the curious. By plotting the SNR (code in appendix) as a function of reflectivity (fig. 11) using the soft target radar equation (eq. 13) with the parameters in table 2 at the 6km range in fig 9. The typical clear air reflectivity at 6km is estimated to 6.17x10 10 m 3. Although it is difficult to verify if this number is representative, it is seen (Venema, 2000) 6 that clear air reflectivity can fall within this range, but this is probably an under estimate of the reflectivity as the system parameters used for the calculations are ideal. 100 NPN Volume Reflectivity vs. SNR @ 6km 80 60dB @ 6km SNR [db] 60 40 20 10-14 10-12 10-10 10-8 10-6 Figure 11: NPN Volume Reflectivity vs. SNR @ 6km Volume reflectivity [m -3 ] To further link the volume reflectivity to the turbulent refractive index variations in the atmosphere, the relationship by Ottersten 7 can be used (eq. 14).. 1.4710 / [eq.14] where is a measure of the total variance of the spatial refractive index variations. 6 Venema V., Russchenberg H., Ligthart L., Clear air scattering observations: downdraft and angels. Physics and Chemistry of the Earth, special issue for the first European radar meteorology conference (ERAD) in Bologna, Italy, 4 8 September 2000. 7 Ottersten, H. Radar backscattering from the turbulent clear atmosphere. Radio Sci., 4, pp. 1251 1255, 1969. 12

3.4 Radar Pulses and Resolution The solid state power amplifier provides 6 kilowatts of peak power, radiating 3.3µs in low mode, or 20µs in high mode, pulses at a frequency of 404 MHz. When the radar operates in the high mode, a longer transmitted pulse is used, i.e. average power is increased. As a result the sensitivity in the high mode is increased by a factor of about 16 db. The table 3 below summarizes the radar operating parameters. Parameter Symbol High Mode Low Mode Unit Pulse width τ 20 3.3 µs Tx Frequency f 404 404 MHz Tx Power P t 6000 6000 W Phase code 3 chips of 6.67µs 2 chips of 1.67µs Number of range gates n 36 36 FFT length N 128 128 Range Resolution ΔR 900 320 m Max Range Limit R max 16.25 9.25 km Min Range Limit R min 7.5 0.5 km Table 3. The inter pulse period (IPP) and the FFT length (N) determines the Doppler resolution and the Doppler pass band which must cover the expected radial velocities, being detected in the beams at satisfying detail. The atmospheric radial winds detected are within + 25m/s and at an unambiguous range of 16.25 km the inter pulse period becomes: 108 [eq.15] And the Doppler shift resolution becomes: Δ 72.1 [eq.16], giving the final velocity resolution: Δv Δf λ 26.7 m/s [eq.17], which correspond to the atmospheric wind range. Figure 12: NPN Beam, Mode and Resolution Illustration [from NPN website] 13

4. Data Processing To achieve the final data product of 1 hour wind profiles with sufficient accuracy and resolution the NPN uses a data processing mode which is a combination of coherent and non coherent integration of the received range gated pulses at three different beam pointing directions (see beam swinging technique section). Coherent integration keeps the phase information and builds up signal amplitude over 10 coherently integrated pulses to produce one spectrum, which is the squared magnitude of the Fourier transformed data of 128 points. This integration step increases the SNR by 10dB at 100% efficiency. To increase the SNR even more 10 of the 128 point spectrums are non coherently integrated as depicted in figure 13. Assuming a probability of detection P D =0.5 and a false alarm number of n fa =2, a resulting improvement factor of 7dB is achieved as described by an empirically derived expression for the improvement factor in Peebles 8. Figure 13: Non coherent integration of range resolved spectrums. (Figure from lecture notes of Optical Remote Sensing with Coherent Doppler LIDAR by Sara Tucker, Alan Brewer, Mike Hardesty, CIRES NOAA, Optical Remote Sensing Group, Earth System Research Laboratory The total SNR improvement achieved by data processing alone is the sum of the coherent and non coherent integration improvements, 10+7=17dB, which translates into an improved detectable range from 10km to 16.5km in high mode, and from 5.8km to 9.2km in low mode. The radial velocity in each range gate is found by fitting the frequency shifted intensity peak in the spectrum. This peak frequency corresponds to the Doppler shifted transmit frequency, and the shift Δ is proportional to the scatter s mean radial velocity V R according to eq. 18 below. Δ [eq.18] The width of the peak is also derived and indicates the spread of Doppler velocities present in each range gate. This measure is proportional to the intensity of the atmospheric turbulence 9. Before the non coherent integration is performed a consensus method 10 is used to remove measurements containing large deviations between the three beams in the corresponding range bins. This produces a more reliable mean wind data product, kicking out erroneous samples caused by either sporadic noise sources or sudden instrument operation instabilities. One drawback of this method is that any real large and sudden deviations above the accepted range are also removed. The wind etc. will not be presented if too few valid samples are collected. 8 Peebles Jr., P. Z., Radar Principles, John Wiley & Sons, Inc., 1998 9 The Nerc MST Radar Facility at Aberystwyth: Beam Broadening of Radar Return Spectral Widths 10 Weber B. L. et al 1992: Effects of Small Scale Vertical Motion on Radar Measurements of Wind and Temperature Profiles, J. Atmos. Oceanic Technol., Vol. 9, No. 3 14

The NPN data is available on line in near real time. Three of the many parameters available on line are shown below, where the most descriptive graph might be the one showing wind speed and direction, also called a waterfall plot. The three graphs are from the same time interval. Figure 14: Wind speed and direction at Platteville [from NPN website] Figure 15: Spectral peak power at Platteville Figure16: Velocity variance at Platteville 15

5. Discussion Multi Mode Observations AMISR is a new modular incoherent scatter radar for upper atmospheric research. Its primary scientific purpose is to observee the ionosphere. The question was raised if AMISR could be used in a multi mode observation scheme to measuree lower atmospheric winds concurrent as collecting ionospheric data. The AMISR design is based on the NPN wind profiler. It is a phased array configuration transmitting at 449 MHz. The largest difference are the higher transmitting power for the AMIRS (2.2 MW see table 1 in chapter 3.3.1) and the data processing procedures aimed towards the ionized part of the atmosphere (above 80 km) having free electron as its scattering target. Farley et. al. showed in the sweet year of 1977 that an ionospheric radar( the Arecibo Observatory operating at 430MHz) has excellent capabilities as a clear air wind profiler. The results 11 in figure 17 shows the winds measured are well correlated with the wind measurements from a rawinsonde at a 70 km longitudinal distance. The AO results indicate AMISR s potential for multi mode observation to aid the understanding of the atmospheric coupling. Figure17: Comparison of vertical profiles of wind speedss and direction observed by Arecibo Radar on 6th April 1977 with nearly simultaneous NWS rawinsonde observation from San Juan (after Farley et. al., 1978) As indicated in Figure 2 (chapter 2.1), the inertial subrange limits the clear air return for the AMISR transmitting frequency at a height of ~35km, leading to a gap in the profile until sufficient electron density is reached at AMISR normal operating height. 11 Farley, D. T., B. B. Balsley, W. E. Swartz, and C. LaHoz, 1978: Winds aloft in the Tropics Measured by the Arecibo Radar. (Submitted to J. Appl. Meteor) 16

6. References Farley, D. T., B. B. Balsley, W. E. Swartz, and C. LaHoz, 1978: Winds aloft in the Tropics Measured by the Arecibo Radar. (Submitted to J. Appl. Meteor) Gage K. S. and B. B. Balsley, Doppler Probing of the Clear Atmosphere, Bulletin American Meteorological Society, Vol. 59, No. 9, September 1978 Mahafza B.R Radar Systems Analysis and Design Using Matlab The Nerc MST Radar Facility at Aberystwyth: Beam Broadening of Radar Return Spectral Widths Ottersten, H. Radar backscattering from the turbulent clear atmosphere. Radio Sci., 4, pp. 1251 1255, 1969. Peebles Jr., P. Z., Radar Principles, John Wiley & Sons, Inc., 1998 R. R. Rogers et. al Research Applications of a Boundary Layer Wind Profiler, Bulletin American Meteorological Society, Vol. 74, No. 4, April 1993 Venema V., Russchenberg H., Ligthart L., Clear air scattering observations: downdraft and angels. Physics and Chemistry of the Earth, special issue for the first European radar meteorology conference (ERAD) in Bologna, Italy, 4 8 September 2000. Weber B. L. et al 1992: Effects of Small Scale Vertical Motion on Radar Measurements of Wind and Temperature Profiles, J. Atmos. Oceanic Technol., Vol. 9, No. 3 http://mst.nerc.ac.uk/intro_wind_prof.html http://www.profiler.noaa.gov/npn/ Acknowledgments Dr. Christopher Williams, for literature guidance and informative coffee break. 17

Appendix: MATLAB Code to generate figure 11. % Radar SNR Calc clc; clear all; close all; % Constants c = 299792458; % [m/s] speed of light kb = 1.380658e-23; % [J/K] Boltzmann constant % Radar System Parameters f = 404e6; % [Hz] Tx frequency lambda = c./f; % [m] Tx Wave length Pt = 6e3; % [W] Average output power Ae = 50; % [m2] Effective aperture F1 = 1; % Fraction receiver power passing through the receiver filter F2 = 1; % Fraction receiver power passing through the coherent integration process. tao = 3.3e-6; % [s] Pulse width eta = 1e-14:1e-8:1e-5; % [m^-3] Volume reflectivity of the atmospheric scattering process. alfa = 0.8; % Transmission line efficiency. ni = 10; % Number of spectra averaged together to reduce noise fluctuations B = 63.5e3; % Bandwidth Tsys = 154; % [K] System temperature Tc = 104; % [K] Cosmic noise temperature at the antenna terminals. R = 6000; % [m] Range to target % Single Pulse Signal-to-Noise ratio with tropospheric loss SNR = (Pt.*Ae.*F1.*F2.*c.*tao.*eta.*alfa^2.*sqrt(ni))./(16*sqrt(2)*pi*R^2*kB*(Tsys+alfa*Tc)*B); semilogx(eta, 10.*log10(SNR)) xlabel('volume reflectivity [m^{-3}]') ylabel('snr [db]') grid axis tight 18