## 1. Introduction

Ground clutter is a long-standing problem that limits use of weather radar observations. There are several approaches that one can take to mitigate ground clutter. Since the introduction of Doppler radars, the notch filter approach (Groginsky and Glover 1980) is a preferred option for the ground clutter suppression. The main drawback of applying notch filters is the error introduced in cases where precipitation and clutter spectra overlap. To mitigate this effect, frequency domain ground cancellers can be used. Passarelli et al. (1981) have studied different frequency domain clutter suppression algorithms that allow for adaptive selection of depth and width of a notch filter as well as for incorporation of the signal interpolation. Recently, Siggia and Passarelli (2004) and Bharadwaj et al. (2007) have demonstrated a real-time implementation of this methodology.

The ground clutter problem can also be addressed by identifying and rejecting radar range gates that are affected by clutter. Berenguer et al. (2006) and Cho et al. (2006) have used properties of single-polarization volumetric data to identify radar range gates that are contaminated by ground clutter. A number of authors have also shown that dual-polarization observations can also be used to identify such range gates. Giuli et al. (1991) have investigated a use of dual-linear-polarized measurements for mixed phase precipitation and ground clutter identification. Da Silveira and Holt (2001) have shown that neural networks can be used to discriminate between ground clutter and nonclutter echoes, where inputs to the network are the circular depolarization ratio and the degree of polarization. Gourley et al. (2007) have developed a fuzzy logic classification scheme that uses textures of differential reflectivity and differential phase to discriminate between clutter and nonclutter echoes. A main drawback of rejecting range gates, which are contaminated by ground clutter, is the data loss that can be severe in a widespread clutter case.

Dixon et al. (2006) have shown that many disadvantages of the above-listed techniques could be resolved by combining different methodologies. The authors have shown that by detecting range gates affected by clutter and applying a spectral clutter filter to those gates, a possible data loss as well as a computational burden of the procedure is reduced.

Several authors (e.g., Moisseev et al. 2000, 2002; Seminario et al. 2001; Unal and Moisseev 2004; Yanovsky et al. 2005; Moisseev and Chandrasekar 2007; Bachmann and Zrnić 2007) have demonstrated advantages of combining dual-polarization and spectral radar observations. Moisseev et al. (2000, 2002) have shown that for a polarimetric precipitation profiler an adaptive ground clutter spectral filter can be designed by using dual-polarization spectral decompositions. The limitation of this procedure, however, is that it is only applicable to the sidelobe clutter.

In this paper we extend upon Moisseev et al.’s (2000, 2002) work and propose a new methodology that allows for both main lobe and sidelobe adaptive clutter mitigation and can be used by dual-polarization-capable weather radars. The methodology uses a fuzzy logic classification algorithm applied to the textures of the spectral differential phase and reflectivity and the spectral decomposition of the copolar correlation coefficient to discriminate between noise, clutter, and precipitation spectral lines. Then, by rejecting spectral components that are classified as nonweather signals, a clutter and noise filter is defined.

In section 2 definitions of spectral decompositions of dual-polarization parameters are given. Properties of spectral decompositions of dual-polarization parameters are given in section 3. Based on these properties the fuzzy logic classification system is developed in section 4. Also in this section the filtering approach is introduced. In section 5 demonstration of the method on the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) observations is presented. A summary and conclusions are presented in section 6.

## 2. Dual-polarization spectral decompositions

### a. Estimation of Doppler power spectrum

*V*(

*n*), for each range gate is collected. Given this sequence, an autocorrelation function,

*n*), can be calculated as follows (Bringi and Chandrasekar 2001):

*N*is the length of the sequence. Normally the sequence length is equal to the number of samples collected during a dwell time. Then using the autocorrelation function the Doppler power spectrum,

*Ŝ*(

*k*), can be estimated as

*W*(

*n*) is a lag window function of length 2

*L*, which is smaller or equal to

*N*. The window function plays a dual role. It is used to reduce the leakage of strong spectral components into adjacent weaker ones and to control smoothness of the spectral estimates (Stoica and Moses 1997).

*Ŝ*

_{A}(

*l*) can be estimated as follows:

### b. Spectral decomposition of differential reflectivity, _{dr}(*k*)

*Ŝ*

_{hh}(

*k*) [or

*Ŝ*

_{vv}(

*k*)], are estimated by applying (1)–(3) to hh (vv) received voltage sequences.

### c. Copolar coherency spectrum, _{hv}(*k*)

*Ŝ*

_{hh,vv}(

*k*) by applying (2) and (3) to a cross-correlation function,

_{hh,vv}(

*n*), given as

### d. Spectral decomposition of differential phase, _{dp}(*k*)

_{hv}(

*k*) or

*Ŝ*

_{hh,vv}(

*k*):

## 3. Spectral decompositions of precipitation and clutter signals

Using spectral decomposition of dual-polarization observations one can create range–velocity spectrographs for each radial, as shown in Fig. 1. These spectrographs represent images, and therefore it is of interest whether image processing techniques can be applied to discriminate between clutter and precipitation spectral lines. In this paper we will show that using texture analysis of these spectrographs one can construct a spectral filter that rejects clutter and noise.

*x*

_{rk}represents either

_{dr}(

*k*) or

_{dp}(

*k*), and subscript r denotes the range gate counter. Here we use a 3 × 3 sliding window (

*m*= 2) to estimate textures SD[

*Z*

_{dr}(

*ν*)] and SD[Ψ

_{dp}(

*ν*)].

### a. Precipitation signal properties

It is commonly observed that small-scale variation in dual-polarization properties of weather echoes is relatively small. This information was used to discriminate between clutter and precipitation in the previous studies (Dixon et al. 2006; Gourley et al. 2007). To extend this analysis to spectral domain it is important to investigate statistical properties of spectral decompositions _{dr}(*k*), _{dp}(*k*), and _{hv}(*k*).

*P*

_{vv}are powers of hh and

*vv*signals,

*σ*denotes spectral width expressed in meters per second, and

_{ν}*ρ*

_{hv}(0) is the copolar correlation coefficient. If measurements are carried out in the alternating polarization mode, observed hh and vv time series are shifted with respect to each other and the resulting cross-correlation function in (5) cannot be estimated at zero lag. Therefore, the measured cross-correlation function can be written as

*T*and the interval between consecutive hh (or vv) samples is 2

_{s}*T*. Using the time-shifting property of DFT we can relate the copolar cross-spectral density in (11) to the one that corresponds to the cross-correlation function in (12):

_{s}One can see that the only difference between observations in STAR and alternating polarization modes is the (2*π*/*N*)*k* factor in (16). Unal and Moisseev (2004) have shown that by compensating for this factor one can estimate both the copolar correlation coefficient and differential phase from alternating mode observations. Therefore for the simplicity sake in the rest of the paper we will assume that measurements are carried out in the STAR polarization mode.

A peak due to weather contribution in the power spectrum resides over a span of Doppler frequencies. Polarimetric spectral decompositions at these Doppler frequencies are expected to have constant values of intrinsic differential reflectivity, copolar correlation coefficient, and differential phase. Therefore, deviations in observed _{dr}(*k*), _{dp}(*k*), and _{hv}(*k*) from constant values are caused by the presence of noise and by statistical variations.

### b. Observation of precipitation spectral properties

To study spectral properties of precipitation, dual-polarization time series observations were carried out in a severe thunderstorm on 30 May 2007 by the CSU–CHILL radar. Several RHI scans in alternating polarization mode were collected for this study.

Doppler spectra were estimated from sequences of 128 samples. For these calculations we have used Chebyshev window of length 64 and 50-dB sidelobe suppression level; hence, the resulting spectra have only 64 spectral lines. To further reduce the variance of the spectral estimate, averaging over five neighboring oversampled range gates was performed.

To estimate textures of _{dr}(*k*) and _{dp}(*k*) the expression in (8) was applied only to spectral lines with power spectral density values that are at least 20 dB above the level of the system noise spectral density. Since we are interested in precipitation properties, five spectral lines near zero Doppler frequency (one at zero and two on each side) were omitted to prevent a possible influence of ground clutter. The resulting distributions of _{dr}(*k*), and _{dp}(*k*) textures are shown by the dashed line in Fig. 2. The copolar coherency values were also calculated, the distribution of those is shown by the dashed line in Fig. 3. In the figures it can be seen that textures and coherency values of precipitation have narrow distributions. For the observed high signal-to-noise ration (SNR) cases precipitation textures of the spectral differential phase generally do not exceed 15°, and of the spectral differential reflectivity do not exceed 2 dB. Also, the copolar coherency values are larger than 0.9.

### c. Clutter properties

On 27 April 2007 CSU–CHILL radar was used to collect data in clear-air conditions for clutter evaluation. It is believed that most of echoes came from ground objects, but birds and insect echoes can also be present in the dataset. The estimated clutter properties, therefore, might not represent all the conditions and require a further study for a more complete picture of spectral clutter properties.

The observations were carried out in planned position indicator (PPI) mode with an elevation angle of 0.5°. As for the measurements taken on 10 October 2006 the range oversampling was used. From these observations, dual-polarization decompositions of _{dr}(*k*), _{dp}(*k*), and _{hv}(*k*) were calculated using the procedure described above. As mentioned before, we have used spectral lines where power spectral densities exceed system noise spectral density by at least 20 dB. The system noise is calculated from the “blue sky” measurements.

By applying (8) to the filtered spectrographs we have obtained distributions of SD[*Z*_{dr}(*ν*)] and SD[Ψ_{dp}(*ν*)] for ground clutter, as shown by the solid line in Fig. 2. From this study we can conclude that on average SD[*Z*_{dr}(*ν*)] exceeds 2 dB and SD[Ψ_{dp}(*ν*)] exceeds 20°. By comparing these values to textures of _{dr}(*k*) and _{dp}(*k*), which were obtained for precipitation measurements, one can see that there is a clear distinction between clutter and precipitation echoes. Furthermore, a distribution of the estimated copolar coherency spectrum values is depicted by the solid line in Fig. 3. It can be seen that ground clutter has a very wide distribution of the coherency values.

### d. Noise properties

The distribution of the textures and the copolar coherency spectrum values of noise were calculated using simulated observations. The simulations were based on a modified Chandrasekar et al. (1986) procedure, where the spectrum was assumed to be flat and the correlation between polarization channels zero. In Figs. 2 and 3 the resulting distributions of textures and coherency values for noise are shown by the dash–dotted line. One can observe that the distribution of the differential phase textures has a larger mean value than those of clutter and precipitation. The textures of the differential reflectivity on the other hand have a smaller mean value than those of clutter. The copolar coherency values have a distribution with a mean around 0.2 and spreads from 0 to 0.6. In common with a correlation coefficient the coherency spectrum estimate is biased and depends on number of independent samples used for the calculation.

Based on the observed distributions it can be concluded that it is possible to separate precipitation from noise and clutter in the spectral domain. The fuzzy logic classification methodology is a convenient approach for such type of problems and can be applied in this case as will be shown.

## 4. Methodology

### a. Textures calculation

The range-Doppler spectrographs are calculated for each range gate by applying discrete Fourier transform to the windowed correlation functions computed from time-sequence observations, using the procedure described in section 3b. From calculated cross and power spectra the copolar coherency spectrum, and textures of differential phase and differential reflectivity, as defined in (8), are computed. Prior to the copolar coherency spectrum calculation the power spectral densities are noise corrected by subtracting the system noise spectral density. This step is carried out to minimize effect of low SNR on spectral decomposition of the copolar correlation coefficient of a precipitation signal. In Fig. 4 examples of these calculations are shown. In this example same radar data were used as in Fig. 1. Visually textures provide a good distinction between precipitation and nonprecipitation components of the radar spectral signatures.

### b. Fuzzification

*Z*

_{dr}(

*ν*)], SD[Ψ

_{dp}(

*ν*)], and |

*ρ*

_{hv}(

*ν*) |, and produces three classes: precipitation, noise, and clutter. Similar to Liu and Chandrasekar (2000) and Lim et al. (2005), the transformation of crisp inputs, radar measurements, into fuzzy sets is carried out by using membership functions of the beta functional form,

*a*,

*b*,

*c*) for different inputs and classes are given in the Table 1.

The parameters of the membership functions are defined using observed distributions given in Figs. 2 and 3, with an exception of the precipitation membership functions.

The observed distributions of SD[*Z*_{dr}(*ν*)], SD[Ψ_{dp}(*ν*)], and | *ρ*_{hv}(*ν*) | are calculated from 30 May 2007 observations. These measurements are dominated by high reflectivity weather echoes. To include lower SNR cases the precipitation membership functions are extended over a greater range of values. In Fig. 5 proposed membership functions are shown.

### c. Inference

*j*th class,

*R*, can be written as

_{j}*j,*the proposition strength

*μ*is calculated using (17) for a given input. Here

_{j}*w*(

_{ij}*ν*)is the weight factor that is described below. The rule strength is calculated for each range-Doppler bin and each class.

The weight factors are Doppler velocity dependent and are introduced to slightly force the inference process toward the clutter class in cases where Doppler velocity is close to zero. The weight functions are selected such that, on one hand, the inference is forced to the clutter class in situations where rule strengths of different classes are similar and do not overpower the process otherwise.

*σ*= 0.4 m s

^{−1}.

The clutter weight function mimics an expected clutter spectrum shape in the region around zero Doppler velocity and is constant outside this region. The constant part of the weight function is introduced to include such effects as a phase noise that can spread a clutter signal to other frequencies.

As the final stage of the inference process, the class with the maximum *R _{j}* value for each cell in the range-Doppler domain is identified. That results in assigning one class out of three to each range-Doppler cell. An example of the classification is shown in Fig. 8. This figure is obtained from one radial of data collected on 16 October 2006.

In Fig. 8 one can see that the classification scheme correctly detects three classes. It is important to note that not all the cells around zero Doppler frequency are identified as clutter. For example, for ranges larger than 50 km, where the precipitation echo has zero frequency components, clutter is detected only for cells that are affected by clutter. This is an important result demonstrating that the proposed methodology allows for adaptive clutter filtering. Furthermore, the proposed technique not only detects ground clutter, but it appears to detect other contributions, such as bird, insects, and phase noise.

### d. Filtering

*σ*

_{N}^{2}is the noise power spectral density, and

*m*is the precipitation mask that is equal to 1 if a spectral line is classified as a precipitation signal and zero otherwise. The

_{k}*m*can be regarded as a frequency response of the clutter and noise rejection filter. To reduce the noise influence on the calculated moments even further the noise power spectral density subtraction is done. At CSU–CHILL noise power is estimated on daily basis from blue sky measurements or from the measurements with a turned off transmitter.

_{k}## 5. Application to CSU–CHILL observations

The proposed dual-polarization spectral filter was tested on CSU–CHILL observations of a snowstorm carried out on 16 October 2006. The observations were collected in the PPI mode with an elevation angle of 0.5°. Prior to the filtering, spectral decompositions of differential reflectivity, phase, and copolar coherency spectrum are calculated. The processing details are the same as described in section 3b.

In Fig. 9 PPI plots of original and filtered data are shown. For the comparison sake we have applied a standard infinite impulse response notch filter to the data and plotted the resulting PPI. The notch filter depth is 50 dB and the stop bandwidth is 4% of the Nyquist range. The difference in clutter suppression rates between notch and polarimetric spectral filters can be seen in Fig. 10. The suppression rates were computed by calculating differences in reflectivity values before and after clutter filtering. The new filter clutter suppression rate is observed to be in the order of 60 dB, while the notch filter yields around 35–40-dB suppression. So it can be concluded that the proposed dual-polarization spectral filter performs better that the notch filter. This difference can be explained by the ability of the proposed filter to reject not only ground clutter, but also phase noise, birds, insects, etc., contributions.

The spectral filter is designed not only to reject clutter, but also to reject parts of Doppler spectra that are dominated by noise. Therefore, it is expected that this processing would increase radar sensitivity. Since it was not a prime purpose of this study to evaluate sensitivity improvement of the procedure, only qualitative observations can be made. An effect of this processing is the most apparent on the copolar correlation coefficient observations (see Figs. 9j–l). One can observe that the polarimetric spectral filter produces copolar correlation coefficient observations with a least spatial variance. This can be attributed to both clutter suppression and to the noise processing. The effect of clutter suppression is most evident for ranges smaller that 10 km and ranges larger than 35 km in the western direction, where the radar signal is reflected from the Rocky Mountains.

An interesting effect can also be observed while comparing unfiltered | *ρ*_{hv}(0) | observations to the ones after the infinite impulse response (IIR) notch filter. It can be seen that after the standard filtering, range gates contaminated by ground clutter exhibit lower values of | *ρ*_{hv}(0) |. This effect cannot be attributed to a decrease in SNR, since the SNR values are comparable to the neighboring gates that do not show a decrease in | *ρ*_{hv}(0) |.

## 6. Summary and conclusions

A new clutter mitigation methodology that utilizes spectral decompositions of dual-polarization radar observations has been developed. The procedure is based on a fuzzy logic algorithm that is applied to range-Doppler spectrographs of differential phase and differential reflectivity textures and copolar coherency spectrum. The fuzzy logic system was developed based on observations of polarimetric spectral properties of clutter and precipitation signals. Also a theoretical consideration of precipitation spectral properties has been given.

On the example of the copolar correlation coefficient observations, it was shown that the proposed methodology results in more accurate estimates of polarimetric observables. This improvement is related to both clutter and noise suppression.

By comparing it to a traditional notch filter it was demonstrated that the new spectral filter can give up to 20 dB more in clutter suppression. The gain in the clutter suppression rate can be attributed to the rejection of all parts of spectra that are affected by clutter, and not only filtering around zero frequency. This property of the proposed methodology mitigates effect of system instabilities (i.e., phase noise), which spread clutter to other Doppler frequencies.

It is also expected that the filter rejects contributions from birds, insects, and other clutter signals that have nonzero Doppler velocity. However, we have not analyzed this aspect of the filter performance in sufficient details to draw any solid conclusions at the moment. It is still required to carry out more studies on the performance of the method in diverse conditions, where different types of nonweather echoes are present.

In the presented study, a relatively large number of FFT samples and range oversampling were used to demonstrate the capabilities of the proposed clutter filter. The filter performance depends on the number of samples; however, we expect that the proposed clutter suppression technique can be successfully applied to a smaller number of samples of nonoversampled measurements. An exact relation between sequence length and the resulting filter performance is a subject of a future study.

Similar to a standard spectral filter, the most computationally intensive step of the proposed adaptive clutter filter is the computation of dual-polarization spectral densities. Bharadwaj et al. (2007) have demonstrated that spectral filtering can be applied to dual-polarization observations in real time. Therefore, it is expected that the proposed clutter filter can be implemented for real-time applications.

## Acknowledgments

This work was supported primarily by the Engineering Research Centers Program of the National Science Foundation (NSF) under NSF Award 0313747. The CSU–CHILL facility is supported by the NSF.

## REFERENCES

Bachmann, S., and Zrnić D. , 2007: Spectral density of polarimetric variables separating biological scatterers in the VAD display.

,*J. Atmos. Oceanic Technol.***24****,**1186–1198.Berenguer, M., Sempere-Torres D. , Corral C. , and Sánchez-Diezma R. , 2006: A fuzzy logic technique for identifying nonprecipitating echoes in radar scans.

,*J. Atmos. Oceanic Technol.***23****,**1157–1180.Bharadwaj, N., Chandrasekar V. , and Junyent F. , 2007: Evaluation of first generation CASA radar waveform in the IP1 testbed. Preprints,

*Int. Geoscience and Remote Sensing Symp.*, Barcelona, Spain, IEEE, 2742–2745.Bringi, V. N., and Chandrasekar V. , 2001:

*Polarimetric Doppler Weather Radar: Principles and Applications*. Cambridge University Press, 636 pp.Bringi, V. N., Seliga T. A. , and Cherry S. M. , 1983: Statistical properties of the dual-polarization differential reflectivity (

*ZDR*) radar signal.,*IEEE Trans. Geosci. Remote Sens.***21****,**215–220.Chandrasekar, V., Bringi V. , and Brockwell P. , 1986: Statistical properties of dual-polarized radar signals. Preprints,

*23rd Conf. on Radar Meteorology,*Snowmass, CO, Amer. Meteor. Soc., 193–196.Cho, Y-H., Lee G. W. , Kim K-E. , and Zawadzki I. , 2006: Identification and removal of ground echoes and anomalous propagation using the characteristics of radar echoes.

,*J. Atmos. Oceanic Technol.***23****,**1206–1222.da Silveira, R. B., and Holt A. R. , 2001: An automatic identification of clutter and anomalous propagation in polarization-diversity weather radar data using neural networks.

,*IEEE Trans. Geosci. Remote Sens.***39****,**1777–1788.Dixon, M., Kessinger C. , and Hubbert J. C. , 2006: Echo classification within the spectral domain to discriminate ground clutter from meteorological targets. Preprints,

*22nd Int. Conf. on Interactive Information Processing Systems for Meteorology, Oceanography, and Hydrology,*Atlanta, GA, Amer. Meteor. Soc., 9.6. [Available online at http://ams.confex.com/ams/pdfpapers/105302.pdf.].Doviak, R. J., and Zrnić D. S. , 1993:

*Doppler Radar and Weather Observations*. Academic Press, 562 pp.Giuli, D., Gherardelli M. , Freni A. , Seliga T. A. , and Aydin K. , 1991: Rainfall and clutter discrimination by means of dual-linear polarization radar measurements.

,*J. Atmos. Oceanic Technol.***8****,**777–789.Gourley, J. J., Tabary P. , and Parent du Chatelet J. , 2007: A fuzzy logic algorithm for the separation of precipitating from nonprecipitating echoes using polarimetric radar observations.

,*J. Atmos. Oceanic Technol.***24****,**1439–1451.Groginsky, H. L., and Glover K. M. , 1980: Weather radar canceller design.

*Proc. 19th Conf. on Radar Meteorology*, Miami Beach, FL, Amer. Meteor. Soc., 192–198.Lim, S., Chandrasekar V. , and Bringi V. N. , 2005: Hydrometeor classification system using dual-polarization radar measurements: Model improvements and in situ verification.

,*IEEE Trans. Geosci. Remote Sens.***43****,**792–801.Liu, H., and Chandrasekar V. , 2000: Classification of hydrometeor based on polarimetric radar measurements: Development of fuzzy logic and neuro-fuzzy systems and in situ verification.

,*J. Atmos. Oceanic Technol.***17****,**140–164.Moisseev, D., and Chandrasekar V. , 2007: Nonparametric estimation of raindrop size distributions from dual-polarization radar spectral observations.

,*J. Atmos. Oceanic Technol.***24****,**1008–1018.Moisseev, D., Unal C. , Russchenberg H. , and Ligthart L. , 2000: Doppler polarimetric ground clutter identification and suppression for atmospheric radars based on co-polar correlation. Preprints,

*13th Int. Conf. on Microwaves, Radar and Wireless Communications,*MIKON-2000, Vol. 1, Wroclaw, Poland, 94–97.Moisseev, D., Unal C. , Russchenberg H. , and Ligthart L. , 2002: A new method to separate ground clutter and atmospheric reflections in the case of similar Doppler velocities.

,*IEEE Trans. Geosci. Remote Sens.***40****,**239–246.Passarelli R. E. Jr., , Romanik P. , Geotis S. G. , and Siggia A. D. , 1981: Ground clutter rejection in the frequency domain. Preprints,

*20th Conf. on Radar Meteorology,*Boston, MA, Amer. Meteor. Soc., 295–300.Sachidananda, M., and Zrnić D. , 1986: Zdr measurement considerations for a fast scan capability radar.

,*Radio Sci.***20****,**907–922.Sachidananda, M., and Zrnić D. , 1989: Efficient processing of alternately polarized radar signals.

,*J. Atmos. Oceanic Technol.***6****,**173–181.Seminario, M., Gojara K. , and Chandrasekar V. , 2001: Noise correction of polarimetric radar measurements. Preprints,

*30th Int. Conf. on Radar Meteorology,*Munich, Germany, Amer. Meteor. Soc., P1.7. [Available online at http://ams.confex.com/ams/pdfpapers/22049.pdf.].Siggia, A. D., and Passarelli R. E. , 2004: Gaussian model adaptive processing (GMAP) for improved ground clutter cancellation and moment calculation.

*Proc. Third European Conf. on Radar in Meteorology and Hydrology,*Visby, Sweden Copernicus, 67–73.Stoica, P., and Moses R. , 1997:

*Introduction to Spectral Analysis*. Prentice-Hall, 319 pp.Unal, C. M. H., and Moisseev D. N. , 2004: Combined Doppler and polarimetric radar measurements; correction for spectrum aliasing and nonsimultaneous polarimetric measurements.

,*J. Atmos. Oceanic Technol.***21****,**443–456.Yanovsky, F. J., Russchenberg H. W. J. , and Unal C. M. H. , 2005: Retrieval of information about turbulence in rain by using Doppler-polarimetric radar.

,*IEEE Trans. Microwave Theory Technol.***53****,**444–450.

Distributions of texture values of spectral differential (left) phase and (right) reflectivity for noise, clutter, and precipitation.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Distributions of texture values of spectral differential (left) phase and (right) reflectivity for noise, clutter, and precipitation.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Distributions of texture values of spectral differential (left) phase and (right) reflectivity for noise, clutter, and precipitation.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Distribution of spectrum coherency values for noise, clutter, and precipitation.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Distribution of spectrum coherency values for noise, clutter, and precipitation.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Distribution of spectrum coherency values for noise, clutter, and precipitation.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Range–velocity spectrographs of (left) copolar coherency *ρ*_{hv}(*ν*), and textures of (middle) differential reflectivity *Z*_{dr}(*ν*) and (right) differential phase Ψ_{dp}(*ν*). The spectrographs are calculated from the same data as in Fig. 1.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Range–velocity spectrographs of (left) copolar coherency *ρ*_{hv}(*ν*), and textures of (middle) differential reflectivity *Z*_{dr}(*ν*) and (right) differential phase Ψ_{dp}(*ν*). The spectrographs are calculated from the same data as in Fig. 1.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Range–velocity spectrographs of (left) copolar coherency *ρ*_{hv}(*ν*), and textures of (middle) differential reflectivity *Z*_{dr}(*ν*) and (right) differential phase Ψ_{dp}(*ν*). The spectrographs are calculated from the same data as in Fig. 1.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Membership functions for spectral differential (top) phase and (middle) reflectivity, and (bottom) copolar coherency for the three classes: noise, clutter, and precipitation.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Membership functions for spectral differential (top) phase and (middle) reflectivity, and (bottom) copolar coherency for the three classes: noise, clutter, and precipitation.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Membership functions for spectral differential (top) phase and (middle) reflectivity, and (bottom) copolar coherency for the three classes: noise, clutter, and precipitation.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Classification architecture.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Classification architecture.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Classification architecture.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Inference weight functions.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Inference weight functions.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Inference weight functions.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

An example of the classification in the spectral domain: (a) spectral reflectivity and (b) the corresponding three classes.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

An example of the classification in the spectral domain: (a) spectral reflectivity and (b) the corresponding three classes.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

An example of the classification in the spectral domain: (a) spectral reflectivity and (b) the corresponding three classes.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

PPI plots for (top to bottom) reflectivity, velocity, differential reflectivity, and copolar correlation coefficient. (left) The observed fields without any filtering applied to it. (middle) Results of the standard processing—the 50-dB IIR, the clutter filter, and the system noise power subtraction from the observed signal powers. (right) Resulting PPI after the polarimetric clutter and noise filter.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

PPI plots for (top to bottom) reflectivity, velocity, differential reflectivity, and copolar correlation coefficient. (left) The observed fields without any filtering applied to it. (middle) Results of the standard processing—the 50-dB IIR, the clutter filter, and the system noise power subtraction from the observed signal powers. (right) Resulting PPI after the polarimetric clutter and noise filter.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

PPI plots for (top to bottom) reflectivity, velocity, differential reflectivity, and copolar correlation coefficient. (left) The observed fields without any filtering applied to it. (middle) Results of the standard processing—the 50-dB IIR, the clutter filter, and the system noise power subtraction from the observed signal powers. (right) Resulting PPI after the polarimetric clutter and noise filter.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Clutter suppression rates for (a) standard notch and (b) polarimetric spectral filters.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Clutter suppression rates for (a) standard notch and (b) polarimetric spectral filters.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Clutter suppression rates for (a) standard notch and (b) polarimetric spectral filters.

Citation: Journal of Atmospheric and Oceanic Technology 26, 2; 10.1175/2008JTECHA1119.1

Parameters of the membership functions for the three different classes.