Evaluation of a weather clutter simulation

Evaluation of a weather clutter simulation

A.D.Thomson and E.S.Riseborough

Abstract: The output of a high-fidelity weather clutter simulation, designed to model low-PRF X-, C-, or S-band phased array radar, is compared with measurements made by three radar systems. The first comparison demonstrates the simulation’s ability to replicate real horizon search measurements in terms of various signal properties. The second comparison demonstrates the simulation’s ability to generate signals that reflect the vertical dynamic and thermodynamic structure of stratiform precipitation. The third comparison demonstrates the simulation’s ability to create weather clutter signals with exotic power spectrum shapes that do exist in nature. In all three cases the simulation output is found to compare well with the real radar measurements. Thus, this simulation is a very good tool for generating realistic weather clutter signals and as such provides a valuable source of data for applications requiring such signals. In addition, this simulation can be used to add controllable weather clutter to existing experimental measurements that may have been affected by weather if it had been present at the time of measurement. This allows the effects of weather clutter to be considered when analysing any experimental data set.

1 Introduction

Early detection, tracking, and engagement of sea-skimming anti-ship missiles are extremely important functions of modern naval radar. X-band phased array radar is currently being developed to perform these functions [ 11. Operation at X-band frequencies provides good horizon search performance with respect to multipath propagation. However, target detection using X-band radar can be greatly affected by weather. For example, the power backscattered by precipitation can occupy a large portion of the X-band Doppler spectrum (for low PRF) and can significantly exceed the power backscattered by targets that have small radar cross section. Thus, it is important to assess the performance of such a radar system in an environment containing precipitation.

Simulation is a useful approach for developing an initial assessment of radar performance, since acquiring real shipborne radar measurements of approaching sea- skimming missiles in precipitation is a major undertaking. Furthermore, weather systems cannot be controlled. Consequently, it would be very difficult to acquire, experimentally, a data set encompassing the full range of weather conditions that shipborne radar must operate in.

A high-fidelity simulation of the weather clutter measurements that would be made by low-PRF X-, C-, or S-band phased array radar has been developed at the Defence Research Establishment Ottawa (DREO) in Canada [2]. A unique feature of this simulation is the ability of the defined radar and environment to control the spectral properties of the weather clutter signals. This

0 Canadian Crown copyright 2001 IEE Proceedings online no. 20010383 DUI: 10.1049/ip-rsn:20010383 Paper first received 12th September 2000 and in revised form 23rd February 2001 The authors arc with the Defence Research Establishment Ottawa, 3701 Carling Avenue, Ottawa, Ontario, Canada, KIA 024

IEE Proc.-Rudai: Sonar Navig., Vol. 148. No. 3, June 2001

allows detection algorithms operating in the Doppler domain to be tested against more flexible and realistic weather clutter spectra. The simulation is currently being used to investigate the detection performance of an X-band radar system when operating in horizon search mode against sea-skimming anti-ship missiles in an environment containing precipitation. It will eventually be combined with sea and land clutter simulations of similar fidelity to provide a data source of littoral clutter.

This paper presents a brief description of the approach used to generate the simulated signals. Complete details are given in [ 2 ] . The main objective of this paper is to demonstrate the capability of the simulation to generate realistic weather clutter signals. This is achieved by comparing simulated signals with experimental measurements and theoretical expectations. First, simulated weather clutter signals corresponding to a horizontal radar beam are compared, in terms of various signal properties, with measurements made by an experimental array radar system (EARS). Then, vertically pointing radar measurements are simulated and examined for expected dynamic and thermodynamic properties associated with a stratiform precipitation field. Finally, the weather clutter simulation is used to replicate exotically shaped power spectra that have been found experimentally by [3].

2 Weather clutter simulation

The weather clutter simulation requires a number of input parameters that are used to describe the environment, the relative location and characteristics of the observing radar system, and a single measurement ray along which the radar views the environment. From these inputs the simulation provides as output discrete in-phase (I) and quadrature (Q) signals, and the corresponding power density (S) and phase (@) spectra, at many range bins along the measurement ray.

The environment is modelled as a stratiform precipitation field above a rough spherical sea surface. A stratiform

119

precipitation model was initially chosen to simplify coniparison of the simulated data with real radar measurements. However, the approach used can be generalised to model any structure of precipitation if the necessary information specifying the precipitaticin field is available for input. The precipitation consists of horizontally homo- geneous layers of snow, mixed phase particles, and rain. A uniform cloud field is defined across the entire viewing volume of the radar within a specified height range. A uniform field of turbulence is also modelled. The wind field is limited to a horizontal flow having a magnitude and direction that can vary with height. Cnrrently, vertical air motion is neglected. Propagation effects are incorporated using an effective earth radius, which simplifies the multipath calculations required for the case of a reflective sea surface. Backscatter from the sea surface is not currently considered. However, a compatible sea clutter simulation whose output will be combined with that of the weather clutter simulation is currently under construction.

The computational approach used to create the output signals is graphically depicted in Fig. 1. Although the simulation calculates the weather clutter signals at many range bins along the specified measurement ray, for simpli- city, Fig. 1 only depicts the process for a single range bin. The depicted process begins with a physically based precipitation model and a statistical model.

The precipitation model calculates the mean contribu- tion of the precipitation field to the received radar signal. Specifically, _a mean noiseless power density spectrum (labelled as S in Fig. 1) is calculated as a function of radial Doppler velocity for each range bin along the measurement ray. The calculations consider attenuation of the signal due to atmospheric gases, clouds, and precipitation as it travels along the propagalion path, which is a straight line relative to the effective Earth radius. Multiple paths caused by reflection of the signal from the sea surface are also considered. The backscatter cross section of the precipitation is determined from the thermodynamic phases, the sizes, and the concentrations of the precipitation particles within a given radar resolution volume. The radial Doppler velocities of the precipitation particles are functions of gravity, the horizontal wind field, and turbulence. The antenna gain pattern and the transmit/receive

characteristics of the modelled radar determine the weighting applied throughout the resolution volume. The variation of this weighting and the variation of the precipitation field within the resolution volume control the shape of the calculated power spectrum.

There is typically a large number (-- lo9) of precipitation particles within the portion of the resolution volume that contributes the majority of backscattered power to the signal samples measured by the radar. The positions and velocities of these scatterers will be random with respect to each other. Consequently, the magnitude and phase of the signal samples will fluctuate in time because of the variation in the interference of the many backscattered waves that return from the scatterers and sum at the antenna port. The statistical model calculates fluctuations, or random numbers, representing the result of this interference. The output of the statistical model is a set of Gaussian distributed random numbers (f ’ and f Q ) corresponding to the fluctuations of each I and Q signal sample at each range bin along the measurement ray. If the measurement ray is defined such that adjacent resolution volumes overlap, then these random numbers will be appropriately correlated in range.

As shown in Fig. 1, the output of the statistical model is passed through a fast Fourier transform (FFT) to create fluctuations U” and f @), corresponding to the coefficients of the power and phase spectra of the radar signal. The spectral power fluctuations are then filtered by the output of the precipitation model to produce a Doppler velocity power density spectrum that incorporates statistical fluctuations. This spectrum is combined with the fluctuations corresponding to the phase spectrum to create a complex time series that is then passed through an inverse FFT. The result is a complex time series of noiseless in-phase (1’) and quadrature (Q’) components. Receiver noise is modelled by generating Gaussian distributed random numbers ( N I and NQ) based on the input noise power. These numbers are then added to the I’ and Q’ components.

The power spectrum measured by a real radar system will consist of the convolution of the spectrum due to the precipitation signal with that of the spectrum of the window function implicitly applied by the radar to the measured I and Q time series. The precipitation model

statistical model

range correlated statistical fluctuations

for I and Q

range correlated statistical fluctuations

for S and @

V

I

L l i density spectrum

precipitation

V

I’

t

L

t

inverse FFT I 1

output I and Q r

t

r

t

I I

I I I

Fig. 1

120

Ovewiav of computational approach used to generate weather clutter signals at a single range bin

IEE Proc -Radac Sonar Navig.. Vol. 148, No 3, June 2001

calculates the Doppler velocity power density spectrum directly in the frequency domain. Consequently, this spectrum does not incorporate the effects of a time domain window function. To include these effects the I’ + N‘ and Q’+NQ time series are truncated to a small fraction of their original lengths. This leaves the final output I and Q time series. Another FFT of this truncated complex time series gives the output power density and phase spectra.

3 Experimental measurements

The first tests of the weather clutter simulation’s ability to produce realistic signals were direct comparisons of simulated signals with real radar measurements. The data for these comparisons were acquired by field trials conducted during the period 18-22 June 1997 at a DREO site located on the edge of the Ottawa River (see Fig. 2).

The radar measurements were made by EARS, which is an X-band pulsed Doppler radar that uses an elliptical parabolic dish for the transmit antenna and a vertical and horizontal array of eight horns each for the receive antenna. The data corresponding to only one horizontal receive horn (NARDA 640 standard gain), however, were compared with simulated data. The phased array antenna model used in the weather clutter simulation was modified to model this horn prior to generating the simulated data. The environment was characterised by measurements made by a Joss-Waldvogel disdrometer and a balloon-borne radiosonde. Weather radar data, collected by the Environ- ment Canada radar at Carp, Ontario, were also purchased. Forecast support was provided by the Weather Services Centre at Canadian Forces Base Trenton.

I and Q signal samples were measured by EARS at many range bins along a horizontal ray overlooking the river. Several data sets were acquired for each precipitation event using different waveform parameters. The power and phase spectra, as well as the effective reflectivity factor, Z [4], were derived from the I and Q data.

The effective reflectivity factor is essentially a measure of the backscatter cross section of the precipitation. It is defined by

where y is the backscatter cross section per unit volume of the precipitation field, A is the transmitted radar wave-

Fig. 2 DREO experimental site located on the Ottawa River EARS is inside the building marked ‘EARS‘. The insets show the radiosonde and the Joss-Waldvogel disdrometer setup

IEE Proc.-Ruduc Sonar Nuvig.. Vol. 148, No. 3, June 2001

length, lK,I2 is a function of the complex index of refrac- tion for water. A height profile of Z is a required input of the weather clutter simulation. The experiment plan was to derive this profile from the Carp radar data. However, the Carp radar data corresponding to the EARS site were not saved due to the limited data transfer rate between the Carp radar and the Environment Canada archiving site. This unfortunate circumstance was only discovered after the field trials were completed. Consequently, the simulation was altered to accept a range profile o f 2 instead of a height profile, and this range profile was based upon the Z values extracted from the EARS data.

The EARS data were also used to estimate the horizontal wind speed at the surface, which is another input required by the weather clutter simulation. This was necessary because the radiosonde could not provide accurate measurements below 400 m altitude.

The radiosondes were launched at the EARS site. For each case, the EARS measurements were made during the time of a radiosonde flight. The radiosonde provided profiles of the horizontal wind speed and direction, which are required inputs of the weather clutter simulation. In addition, the 0°C level was extracted from the temperature profiles measured by the radiosonde. This information is required by the weather clutter simulation to define the boundaries of the regions containing the different precipitation types (snow, mixed phase, rain).

The disdrometer made measurements throughout the entire time period of the field trials. It calculated the diameters and impact times of the raindrops hitting its sensor head. This information was used to calculate Z, and the rain rate, R. A power law relationship, Z=aRb, was then determined from the Z-R data for each precipitation event. This relationship is used by the weather clutter simulation to calculate the attenuation of the radar signal in the rain region, and also to determine the sizes and concentrations of the raindrops in the modelled environment.

4 Comparison of EARS measurements with simulated weather clutter signals

During the field trials of 18-22 June 1997, the EARS setup was designed to emulate a shipborne horizon search radar. The weather clutter simulation [2] was set up to model a similar horizon search radar. A comparison of the real and simulated data corresponding to the measurements made at 14:00:51 on 18 June 1997 is given in this Section. At that time the surrounding precipitation consisted of light rain and drizzle.

The EARS parameters and the corresponding inputs to the weather clutter simulation for this case are given in Tables 1-3. The modelled Z field used by the weather clutter simulation was based on the range profile derived from EARS. The modelled wind field was based on profiles of horizontal wind speed and direction constructed from the EARS measurements and the radiosonde profile. The portions of the horizontal wind speed and direction profiles in the height range between the valid radiosonde data (above approximately 400 m) and the EARS measurements at the surface were interpolated considering the horizontal acceleration of the balloon and the measured variability of the radiosonde profile. The two constructed profiles used as inputs to the weather clutter simulation are shown in Fig. 3, which also shows the 0°C level measured by the radiosonde.

121

Table 1: Parameters describing radar system ~~

Symbol Sample value Description

ha 10.0 m antenna system height above sea level

O6 ,3.27" antenna system 6 dB elevation beamwidth

4 6 3.66" antenna system 6 dB azimuth beamwidth

G, 23.9 dB antenna system gain on boresight

Pf 68.5 dBm transmitted power

ff '3.0 GHz transmitted frequency

0 0.0 (horizontal) polarisation

"c 128 number of pulses in a coherent burst

Ts 500 ps pulse repetition interval

z 1.0 ps pulse width

r 1 pulse compression ratio

G,, 54.2 dB receiver system gain

B6 5.0 MHz 6 dB receiver bandwidth

-12.2 dBm noise power pn

Table 2: Parameters describing the measurement ray


0.925 km Rmin

Rmax 9.91 km

N" 600 0, 0.0" (D 329.0"

minimum range

maximum range

number of range bins

elevation angle

azimuth angle

Table 3: Parameters describing the environment


3.0 x IO8 m s-' 9.8 m s-'

1.38 x I 0-23 J K-'

(4/3) x 6370 km

0.1 g r r 3

0.92 0.2 239 mm6 m-3 ( m m h-')-b

1.37 3.17 k m

4.7 km

10 m 300 m

0.38 m s-' 0.29 n i s-' 290 K 18°C 0 ppt'*

1

speed of light

acceleration due to gravity

Boltzmann constant

effective earth radius

cloud liquid water content

complex refractive index function for water

complex refractive index function for ice

Z-R power law coefficient*

Z-R power law exponent*

height of 0°C level

maximum height of precipitation

cloud base height

thickness of the melting layer

spectral width of snow spectrum

spectral width of turbulence spectrum

reference temperature

sea (or river) surface temperature

sea (or river) surface salinity

sea (or river) state

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* Z= aRb

** ppt parts per thousand

IEE Proc.-Rudur; Sonar Nuvig., Vol. 148. No. 3, June 2001

4 1 0% level

3 E Y

0 Ik 0 2 4 6 8 1 0 1 2 1 4

U, ms-’ a

5 r

. . . . . . . . _t 0 100 200 300

0

deg b

Fig. 3 The dashed line marks the height of the 0°C level

Profiles of horizontal wind speed, U, and direction, a,,

Fig. 4 shows a comparison of the in-phase signal samples, measured by EARS and generated by the weather clutter simulation. The Q data (not shown) display a very similar picture. Both images of Fig. 4 show similar wavy features. However, the EARS I image appears noisier and contains some features that are not seen in the simulated I image. These features are even more apparent when the data are compared as power spectra. Fig. 5 shows the corresponding power spectral density data as a function of range and Doppler velocity. The phase spectra (not shown) consist of a mostly random pattern of values between --71

and 71, except for some evidence of range correlation. The features found in the EARS data that are not

replicated by the weather clutter simulation were mostly caused by spectral impurities in the transmitted waveform, which were caused by a ‘YIG’ filter that was applied to the waveform prior to transmission. The significant effects that this filter had on the transmitted signal spectrum can be seen in Fig. 6. In particular, the YIG filter created two prominent peaks on either side of the main peak at 9 GHz. Each of these peaks was approximately 1 kHz away from

IEE Proc -Radar; Sonar Navig , Vol 148, No 3, .June 2001

the main peak and had a magnitude only 10 dB below that of the main peak. When the YIG filter is not used, EARS measures much ‘cleaner’ weather clutter spectra. Unfortu- nately, EARS used the YIG filter for all measurements made during the field trials of 18-22 June 1997.

The weather clutter simulation models a radar system that transmits a single frequency. As seen in Fig. 5 , the vast majority of the received power due to backscattering of this frequency (9GHz, see Table 1) is found in the simulated spectra within the velocity range of 0 to 7 m s-’. The EARS spectra contain similar features in this velocity range. These features were mainly due to backscattering of the frequencies in the transmitted signal spectrum near 9GHz. The features of the EARS spectra that are not replicated in the simulated spectra were caused by the backscatter of other transmitted frequencies by precipitation and ground clutter. For example, at ranges less than 2 km, the EARS spectra show a secondary peak between -17 and -lOm s-l that has a magnitude approximately 10 dB less than that of the region between 0 and 7 m SKI.

The Doppler shift frequencies corresponding to these two peaks differ by about 1 kHz. Thus, the two peaks were almost certainly caused by backscatter from the same precipitation, but the secondary peak was caused by backscattering of the frequencies of the secondary peaks in the transmitted signal spectrum. Thus, assessment of the weather clutter simulation should be based on comparison of the features within the spectral region between 0 and 7 m s-l only.

In the velocity region between 0 and 7 m s-’, the power due to weather clutter extends throughout the measurement range (1-10 km). There is some indication of slight broadening with range in this portion of the clutter spectrum. However, this is very difficult to see in Figs. 5 and 7 because of the low clutter to noise ratio beyond ranges of about 5 km. Broadening and other range effects will be more significant at the larger ranges where horizon search radar is tasked to detect targets. The weather clutter simulation does account for these effects, as demonstrated in [2].

The first three moments of the power spectra, and the weather clutter to noise ratio, were calculated as a function of range. Data outside of the 0 to 7 m s-’ velocity interval were filtered out for these calculations. Fig. 7 shows a comparison of the moments corresponding to the real and simulated data. The power and clutter to noise ratio plots each show good agreement. The agreement in terms of the variation of the mean power level with range is expected since the range profile of mean reflectivity factor input into the simulation was derived from the EARS data. However, even with this forcing of agreement in mean power level, the plots still qualitatively show good unbiased agreement in terms of the magnitude of the statistical fluctuations, and that the radar system noise has been correctly modelled. The forcing of agreement in mean power level was a necessary compromise brought on by a lack of independent data. However, achieving a good comparison in terms of the variation of power with range, due to variation of the precipitation intensity with range, is not a test of the simulation’s ability to produce realistic weather clutter signals, but rather a test of the observational system’s ability to accurately measure the characteristics of the environment, which is not the objective of this work. The mean velocity and spectral width plots also show good agreement at the shorter ranges. It is more difficult to compare the mean velocity and spectral width at the far ranges because the clutter to noise ratio is too low to get accurate estimates of these moments.

123

EARS I simulated I

E ai

F

Y

m

E Y

ai

2 m

time, ms time, ms

-0 18 -0 13 -0 09 -0 04 0 004 0.08 013 017

I! v Fig. 4 EARS measurements were made at 14 00.5 1 on 18 June 1997

Comparison of EARS I with simulated I

EARS S simulated S

E

ai

2

Y

D

E

ai

2 D

-15 -10 -5 0 5 10 15 radial velocity, m sel

-15 -10 -5 0 5 10 15 radial velocity, m s-'

-44 0 -36.7 -29 4 -22 1 -148 -7 6 -0 3 6 9 14 2 S, dBm (m SI)-'

Fig. 5 EARS measurements were made at 14 00 51 on 18 June 1997

124

Comparison of EARS S with simulated S

IEE Proc.-Radar; Sonur Nuvig., Vol. 148, No. 3. June 2001

I I I I I I I I

I I

-1 0 -5 0 5 10 frequency relative to 9 GHz, kHz

Fig. 6 without YIG filter Thin black line: with YIG filter Thick grey line: without YIG filter

Comparison of the EARS transmitted signal spectrum with and

The statistics of the EARS and simulated I data are compared in Fig. 8. The upper portion of the Figures compares time series of I data that were measured and simulated at a range of 1.36 km. The clutter to noise ratio for this range bin was high at approximately 18 dB. The probability density fhnctions for the samples corresponding to this range bin are shown in the lower plots. Each of these lower plots shows a thick grey line which is a Gaussian function with zero mean, and a standard deviation determined from the actual I data it is being compared with. The comparisons show that both the measured and simulated I data had Gaussian statistics. Similarly, the Q data were also found to have Gaussian statistics. As would be expected based on these results, the coefficients of the power and phase spectra were found to have exponential and uniform probability density finctions, respectively.

a

2 4 6 a range, km

C

The EARS time series of Fig. 8 is less smooth than that of the simulated time series. The additional structure is attributed to backscattered signals corresponding to transmitted frequencies other than 9 GHz. Fig. 8 also show that the standard deviation of the EARS data (54.2mV) is larger than that of the simulated data (37.0mV). This was caused by a slight difference (- 3 dB) in the power of the two signals. Almost all of this difference can be attributed to the way in which the weather clutter simulation calculates the power. To reduce computational require- ments to acceptable levels, the weather clutter simulation only considers the portion of the resolution volume that receives a weight by the antenna and receiver that is within 6 dB of that applied to the centre of the resolution volume on boresight. This truncation of the resolution volume results in a loss of about 3 dB of power for this case. This power difference can be reduced if the weather clutter simulation is set up to consider a larger resolution volume.

Fig. 9 shows a quantitative comparison of the range correlation of the in-phase signal samples and the power spectral coefficients. The calculations have been limited to ranges (1.33 to 3.625 km) where the clutter to noise ratio is greater than 0 dB.

The upper-left plot shows the correlation of the range series of I samples received for each transmitted pulse for a lag of 15 m, which is equal to the distance between the centres of adjacent resolution volumes. These range correlation values are then averaged over time to produce the data point at 15 m range lag in the upper-right plot. The other points in the upper-right plot are similar averages at different lags.

Both of the average curves show strong correlation at short lags and a similar decrease in correlation with increasing lag. The strong correlation was caused by the large range overlap between adjacent resolution volumes of the measurement ray. The range correlation of the simulated I data, however, was lower than that of the EARS data at all lags. This was related to the spectral impurities introduced into the transmitted waveform by the YIG filter. The range correlation calculation for the EARS

2 4 6 a range, km

b 3.01-, . . , , . . . . . . , , , , , . , . . . , , , . , , , , A

1.0 1.5 2.0 2.5 3.0 3.5 range, km

d Fig. 7 Thin black lines: simulated data Thick grey lines: EARS data No points are plotted at ranges where the estimated clutter power is zero

IEE Pmc.-Radur: Sonuv Navig., Vol. 148, No. 3, June 200I

Comparison of spectral moments and clutter-to-noise ratio for EARS and simulated data

125

EARS I simulated I

160

EO

E O

-EO

-160

> -

time, ms

-200 -100 0 100 200 -200 -100 0 100 200 I, mV I, mV

Fig. 8 Probability density functions were generated using 32 time senes having 128 samples each. The thick grey lines are Gaussian functions having zero mean and standard

Statistics of EARS and simulated I datu at the 1 36 km range bin

deviations equal to that of the I data they are compared with

data considered all of the weather and ground clutter power that was backscattered by the various frequency components of the transmitted spectrum, and the power of the uncorrelated radar system noise. However, the correlation of the simulated data was dependent upon the weather clutter power resulting from backscatter of only the 9 GHz transmitted frequency and uncorrelated system noise. The greater proportion of uncorrelated system noise reduced the range correlation of the simulated data. This difference

1 0

08 c

m 0

P 0 6 -

2 0 4

m a, cn

0 2

0 -.A . 10 20 30 40 50 60

time, ms

1 .o

0.8 0 .- c - E 0.6 8 c

2 0.4

m a, cn

0.2

0

is greatly reduced if the range correlation calculation is limited to the velocity interval corresponding to the 9 GHz transmit frequency (1 to 5 m s-'1.

The lower-left plot in Fig. 9 shows the range correlation of the power spectral coefficients for a lag of 15 m. Here it can be seen that the correlation of the spectral coefficients within the 1 to 5 m s-' velocity interval (shaded region) is the same for both the EARS and simulated data. Outside of this velocity interval, the correlation of the simulated

c ._ c - ??

0

m m cn El

c

al cn $ P

1 .o

0.8

0.6

0.4

0.2

20 40 60 EO 100 120 range lag, m

-14 -7 0 7 14 radial velocity, m s-'

Fig. 9 Thick grey lines: EARS data Thin black lines: simulated data Data points within the shaded regions of the left plots are averaged to produce the data points of the right plots

Comparison of range correlation in the EARS and simulated I and S data

range lag, m

126 IEE Proc-Radar: Sonar Navig., Vol. 148, No. 3, June 2001

spectral coefficients drops to zero because these coefficients correspond to radar system noise only. The EARS spectral coefficients outside of the 1 to 5 m s-l interval were correlated because they contained power backscattered at frequencies other than 9 GHz.

The data points shown in the lower-right plot are averages of only those data points in the lower-left plot that are within the shaded region. By limiting the calculations to this velocity interval, much better agreement was achieved between the EARS and simulated average correlation. Thus, the weather clutter simulation is properly simulating the range correlation of the signals resulting from the backscatter of the 9 GHz frequency.

A second data set measured on 18 June 1997, using different waveform parameters, was also analysed using the above comparisons. Similarly favourable results (not shown) were achieved.

5 Comparison with vertically pointing measurements

The comparison presented in this Section is designed to demonstrate the weather clutter simulation’s ability to properly model dynamic and thermodynamic vertical structure associated with stratiform precipitation.

The inputs to the weather clutter simulation were set to produce data corresponding to a stratiform precipitation case that is discussed in the literature [ 5 ] . In this case, the University of Toronto X-band radar made vertically pointing measurements of stratiform precipitation at Torbay Newfoundland on 1 March 1992. The data discussed in [5] were saved in terms of reflectivity factor spectra as a function of height. Since the data output by the weather clutter simulation are provided as power density spectra, these data were converted to reflectivity factor spectra to allow for a more straightforward qualitative comparison. This was done by approximating the radar equation as

simulated

-15 -10 -5 0 5 10 15 velocity, m s-’

where P,. is the received power, Y is the range to the centre of the resolution volume, K is a constant of proportionality, and v is the radial Doppler velocity. A reflectivity factor spectrum was then formed by multiplying S by 9 and then scaling the result so that the peak value of the simulated data matched the peak value of the real data, i.e.

(3)

where K‘ is the scaling constant. The resulting reflectivity factor spectra (dZ/dv) are compared with the real data in Fig. 10.

The simulated spectra are shown as a function of range (or altitude) in the left-hand plot. The two horizontal dashed white lines mark the upper and lower boundaries of the melting layer, i.e. the region where snow melts to rain. The data discussed in [5] are shown in the right-hand

Some major differences in the two plots are evident. The real data show a prominent reflection in the positive velocity region, caused by a gain imbalance between the I and Q channels, and a DC spike at zero velocity for all ranges. No attempt was made to simulate these features.

Both plots, however, show similar properties of the precipitation field. In the snow region (above the upper dashed white line) the vast majority of the reflectivity factor is found in a narrow velocity interval between 0 and 3 m s-l in both plots. Snowflakes are known to have fall speeds in this range. At the top of the melting layer, where the snowflakes would begin to melt, both plots show a shift of the spectral peak to higher velocities. In addition, the reflectivity factor increases significantly inside the melting layer. The velocity shift is due to the larger fall speeds associated with mixed phase particles or newly formed raindrops. The increase in power is due to the larger backscatter cross section associated with the melting layer (see [6]). At the bottom of the melting layer the spectra of both plots broaden significantly and the spectral widths remain constant with altitude down to the ground. This is due to the larger range of velocities (typically -10 to 0 m s-I) associated with the range of possible raindrop sizes (typically 100 pm to 6 mm).

plot.

real

velocity, m s-1

-20 -15 -10 -5 0 5 10 15 20 25 dZ/dv, dBZ [m SI]

Fig. 10 Measurement of the real data IS discussed in [5] The honzontal dashed white lines shown in the left-hand plot mark the upper and lower boundaries of the melting layer

IEE Proc -Radar, Sonar Navig , Vol 148. No 3, June 2001 127

Comparison of real and simulated re$ectivity factor spectra corresponding to vertically pointing measurements

Thus, the weather clutter simulation lis capable of realis- tically modelling vertical dynamic and thermodynamic structure found in stratiform precipitation.

6 Exotic spectra

It has been found that a large portion of the power spectra corresponding to weather clutter measurements have spectral shapes that can be approximated by a Gaussian function [3,4]. However, there are instances in which this shape can be very different from that of a Gaussian. This Section is intended to show that the weather clutter simulation is capable of generating non-Gaussian spectral shapes that do exist in nature.

The weather clutter simulation was set up to model the C-band radar described in [3]. The information needed to derive the environmental inputs required by the weather clutter simulation to model the precipitation observed in [3] were not available. Consequently, the simulation used a generic stratiform precipitation field to generate exotic spectral shapes. This precipitation field contained a well- defined melting layer and a horizontal wind that increased in speed with increasing height. The radar system used horizontal and vertical 3 dB beamwidths of 4" to view a ray

simulated

3.0 km

-60 r ' ' " I ' ' " ' ' ' ' ' " " ' I

-10: 7 . 6.51 km - .

vi : -60 ' ' " I ' ' ' " ' ' ' " " " '

.- -33r 19.3215 km

E m -48 D

20.0235 km R

-500 -250 0 250 500 frequency, Hz

that passed through the melting layer along an elevaiioti of 3". This single ray was simulated 50 times under identical conditions. The average power spectra for each of five selected range bins are shown in Fig. 11. Immediately to the right of each of these average spectra is a real spectrum reproduced from [3] that shows a similar shape.

The simulated spectrum at 3.0km (Fig. 11) resulted from a resolution volume that contained rain only. 'The spectrum to its right is stated in [3] to also correspond to rain only. The two spectra have very similar shapes. The other spectra of Fig. 11, both simulated and real, all corresponded to resolution volumes that straddled the melting layer. In the case of the simulated data, it cat1 be said with certainty that it was the straddling of the melting layer that created the very non-Gaussian spectral shapes. For example, the simulated spectral shape at 4.9305 km is a broad pedestal with a superimposed peak at the high- velocity end. The broad pedestal was caused by vertical wind shear and the large range of raindrop fall-speeds. The superimposed peak was caused by the large vertical gradient of reflectivity at the bottom of the melting layer and the collocated vertical gradient of horizontal wind velocity. This spectrum and the other simulated spectra at 6.51, 19.3215, and 20.0235 km also have shapes that are similar to the real spectra they are compared with. Some minor

real

40c 35 C

401: 101 d

20 -

0 -

-20

0 250 500 - 4 0 1 ' ' ' ' I ' ' " I " ' " " " I

-500 -250

Fig. 11 The simulated spectra, shown on the left, are averages of 50 individual spectra generated under identical conditions. The real data of [3], shown on the right, were reproduced by permission of the IEEE Transactions on Aerospace and Electronic Systems. The top two plots correspond to radar resolution volumes containing rain only The other 8 plots correspond to resolution volumes that span across the 0°C level

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Comparison of real and simulated exotic spectral shapes

IEE Proc.-Radal; Sonar Navig., Vol. 148, No. 3, June 2001

differences are apparent. However, this is not surprising since the modelled environment was not exactly the same as that corresponding to the real measurements, and the ranges corresponding to the simulated spectra were not the same as those of the real spectra that they were compared with.

7 Summary and conclusions

A high-fidelity weather clutter simulation has been eval- uated by comparing simulated signals with real radar measurements made in three different geometries. In the first case, the simulated in-phase and quadrature components, as well as the corresponding power and phase spectra, were compared with real measurements made by an experimental array radar system (EARS) that observed a horizontal ray above the Ottawa River. Some notable differences between the real and simulated signals were discovered. However, it was shown that these differences were caused by a particular filter (YIG) used in the EARS transmitter. The use of this filter created a significant spectrum of transmitted signals instead of a signal dominant frequency as modelled by the simulation. When the measured data were adjusted to remove the effects of this filter the real and simulated signals compared well in terms of statistics, spectral moments, and range correlation. Comparison of the simulated data with the adjusted real data allows for a good assessment of the weather clutter simulation for the case when a real radar using a single dominant transmit frequency is to be modelled. This is the case for EARS when the YIG filter has been removed, and also the case for most operational radars. The second case compared simulated signals with vertically pointing radar measurements. In this case, the simulated spectra were found to exhibit changes in the spectral shape resulting from the modelled thermodynamic phase changes of the precipitation with height. These expected changes were the same as those found in the real data. In the third case, the simulation was used to create data along a radar beam that passed through the melting layer at 3” elevation. The straddling of the melting layer by the simulated radar resolution volume created very non-Gaussian spectral shapes. These shapes were found to be very similar to those corresponding to real radar measurements in which the resolution volume contained the 0°C level.

The favourable results of the three comparisons demonstrate that the weather clutter simulation is a very good tool for creating realistic weather clutter signals. In particular,

the ability of the simulated radar and environment to control the shape of the weather clutter spectrum in a realistic way has been shown. Thus, this simulation can provide a valuable source of data for applications requiring weather clutter signals, such as the assessment or devel- opment of detection algorithms designed to perform well in an environment containing precipitation. Since this simulation is capable of replicating real radar measurements, it should also be useful for assessing the accuracy of more simple weather clutter models. In addition, the presence of precipitation during experimental measurements cannot be controlled. However, the weather clutter simulation can be used to add controllable weather clutter to existing experimental measurements that were made in the absence of precipitation. This can be done by adding simulated I and Q signal samples, generated without radar system noise, directly to the real I and Q samples. In this way, the effects of precipitation on radar performance can be examined, even if the experimental data used for analysis were initially collected in fair weather.

8 Acknowledgments

The authors are grateful to the Canadian Atmospheric Environment Service at the King City Research Facility for the loan of the Joss-Waldvogel disdrometer. They are also grateful to Professor R. List of the University of Toronto Cloud Physics Group for providing the radar data used in the comparison of Section 5. The authors acknowledge the IEEE for giving permission to reproduce portions of the figures of [3]. They also acknowledge G.C. Duff, D.O. Lamothe, Dr. B. Wong, and E.D. Brookes of DREO for their help in the collection of the EARS data.

9 References

1

2

LOK, J.J.: ‘Intemational APAR radar aims for 2000’, Janeb Defence Weekly, 10 January 1996, pp. 27-29 THOMSON, A.D.: ‘Simulation of weather clutter as measured by X- band phased array radar’. Technical report DREO TR 1999-077, 1999, Defence Research Establishment, Ottawa, Canada JANSSEN, L.H., and VAN DER SPEK, G.A.: ‘The shape of Doppler spectra from precipitation’, IEEE Trans. Aerosp. Electron. Syst., 1985,

4 DOVIAK, R.J., and ZRNIC, D.S.: ‘Doppler radar and weather observa- tions’ (Academic Press, Inc., 1993, 2nd edn.)

5 THOMSON, A.D., and LIST, R.: ‘Raindrop spectra and updraft deter- mination by combining Doppler radar and disdrometer’, 1 Atmos. Ocean. Technol., 1996, 13, pp. 4 6 5 4 7 6 ROGERS, R.R., and YAU, M.K.: ‘A short course in cloud physics’ (Pergamon Press, 1989, 3rd edn.)

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21, pp. 208-219

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Evaluation of a weather clutter simulation

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