Abstract

This paper presents new methods for rainfall estimation from X-band dual-polarization radar observations along with advanced techniques for quality control, hydrometeor classification, and estimation of specific differential phase. Data collected from the Hydrometeorology Testbed (HMT) in orographic terrain of California are used to demonstrate the methodology. The quality control and hydrometeor classification are specifically developed for X-band applications, which use a “fuzzy logic” technique constructed from the magnitude of the copolar correlation coefficient and the texture of differential propagation phase. In addition, an improved specific differential phase retrieval and rainfall estimation method are also applied. The specific differential phase estimation is done for both the melting region and rain region, where it uses a conventional filtering method for the melting region and a self-consistency-based method that distributes the total differential phase consistent with the reflectivity factor for the rain region. Based on the specific differential phase, rainfall estimations were computed using data obtained from the NOAA polarimetric X-band radar for hydrometeorology (HYDROX) and evaluated using HMT rain gauge observations. The results show that the methodology works well at capturing the high-frequency rainfall variations for the events analyzed herein and can be useful for mountainous terrain applications.

1. Introduction

In the last decade, dual-polarization radars have become an important tool for meteorological applications such as quantitative precipitation estimation (QPE) and hydrometeor classification. Dual-polarization radars offer an advantage by enabling more accurate physical models of precipitation by providing information on size, shape, phase, and orientation of hydrometeors (Bringi and Chandrasekar 2001). In addition, some of the dual-polarization measurements are immune to absolute radar calibration and partial beam blockage (Zrnić and Ryzhkov 1996; Vivekanandan et al. 1999a), as well as help in quality control. By taking advantage of these characteristics of dual-polarization radar, QPE performance can be improved in comparison to single-polarization-radar-based QPE (Cifelli and Chandrasekar 2010). Dual-polarization techniques have been applied to S- and C-band radar systems for several decades; however, higher-frequency systems such as X band are now widely available to the radar community and QPE applications at this frequency band are becoming increasingly popular (Matrosov 2010; Wang and Chandrasekar 2010; Anagnostou et al. 2010).

This study is based on data collected from the National Oceanic and Atmospheric Administration (NOAA) dual-polarization X-band radar for hydrometeorology studies (HYDROX) during the NOAA Hydrometeorology Testbed (HMT)-West 2005–06 season in California [see Matrosov et al. (2007) for a description of the radar deployment and sampling during HMT-West 2005–06]. HMT conducts research on precipitation and weather conditions that can lead to flooding and fosters the transition of scientific advances and new tools into forecasting operations (http://hmt.noaa.gov). The suite of instruments deployed in HMT-West includes radars, profilers, disdrometers, and gauges, and provides an ideal framework to develop, test, and validate new QPE techniques. HMT-West is the first regional demonstration of the HMT project, with emphasis on cold-season precipitation in the American River basin (ARB) of the Sierra Nevada near Sacramento, California. Precipitation in the ARB during the cold season is typically stratiform in nature with snow at higher altitudes, often transitioning to rain at lower elevations. The combination of steep orography and variable precipitation types makes the ARB an especially challenging environment for radar QPE. During the HMT-West 2005/06 field season, the X-band radar was deployed at Auburn, California, at an elevation of 460 m above mean sea level (MSL).

In this paper, an integrated precipitation processing system is described that combines quality control, hydrometeor classification, specific differential phase (Kdp) retrieval, and rainfall estimation at X band. Recent hydrometeor classification systems provide identification for precipitation types as well as nonmeteorological targets such as clutter or insects and birds by integrating various classification systems such as data quality and hydrometeor classification (Chandrasekar et al. 2013). In hydrometeor classification, discrimination of meteorological and nonmeteorological targets can be an important component of the overall radar processing. Giuli et al. (1991) used the difference in the texture of reflectivity factor (Zh, hereafter reflectivity) and differential reflectivity (Zdr) to identify clutter regions. Moreover, a fuzzy classification scheme for discriminating meteorological from nonmeteorological targets was developed at S band in the Joint Polarization Experiment (JPOLE), which uses texture parameters of Zh and the differential propagation phase (φdp) (Ryzhkov et al. 2005).

In this paper a new classification method is developed for application to the NOAA Earth System Research Laboratory (ESRL) X-band dual-polarization radar [see Matrosov et al. (2005) for a description of the radar characteristics]. The technique uses the copolar correlation coefficient (ρ), the texture of φdp, and the signal-to-noise ratio (SNR). The reason for using SNR is to distinguish variability in dual-polarization parameters due to changes in the SNR. For example, in rain regions at high SNR, ρ values are usually large (i.e., close to 1) compared to ρ in regions with mixed precipitation types (e.g., the melting region). However, at low SNR ρ in rain can actually be smaller than the corresponding value in melting precipitation (i.e., at 10-dB SNR in rain ρ may be 0.93, whereas at 35-dB SNR in the melting region ρ could be 0.95). Therefore, by combining the SNR information with the ρ, it is possible to distinguish rain from mixed precipitation over the full range of SNR. This method can work at any frequency from S to X band (Lim and Chandrasekar 2011). However, it is more useful at higher frequencies such as X band because of the increased sensitivity of ρ and φdp at X band. The Kdp at X band tends to be ∼3 times that of Kdp at S band.

The Kdp is an important parameter for rainfall estimation because it is not affected by propagation attenuation, and it is closely related to rain rate, even in the presence of hail (Aydin et al. 1995; Chandrasekar et al. 2008). Current techniques to retrieve Kdp include range filtering, regression analysis, or both (Golestani et al. 1989; Hubbert and Bringi 1995). However, these methods may reduce the local extrema in Kdp in the estimation because of filtering (Wang and Chandrasekar 2009) and retrieve negative Kdp values on the rear side (i.e., the side farthest from the radar) of intense convective cells (Ryzhkov and Zrnić 1996). To overcome these issues, a new combined Kdp retrieval algorithm that adopts a conventional filtering method for the propagation path through the melting region and an alternate method that distributes Kdp in a manner self-consistent with Zh for the rain region is introduced herein. Using Kdp calculated by the proposed algorithm, the rainfall estimation is performed and evaluated using data from the NOAA HMT program.

The paper is organized as follows: Section 2 introduces briefly microphysical properties of the rain medium and dual-polarization radar measurements used for classification and rainfall estimation. In section 3 the hydrometeor classification, especially for rainfall preclassification, is described, and section 4 describes the new Kdp retrieval algorithm. In section 5 the rainfall estimation based on new Kdp is evaluated, and the important conclusions are summarized in section 6.

2. Background

Microphysical properties of the rain medium can be described by the drop size distribution (DSD). To study the shape of the DSD with widely varying rainfall rates, the natural variation of DSD can be expressed by the normalized gamma function as (Sekhon and Srivastava 1971; Willis 1984; Testud et al. 2001; Bringi and Chandrasekar 2001)

 
formula
 
formula
 
formula

where D0 is the equivolumetric median volume diameter (mm), μ is the shape parameter, and Nw (mm−1 m−3) is the normalized intercept parameter of the exponential distribution with the same water content and D0.

Radar observations in the rain medium can be expressed in terms of the DSD, and Zh,υ (hereafter reflectivities) at horizontal (h) and vertical (υ) polarizations are defined as

 
formula

where λ is the wavelength of the radar; σh,v represents the radar cross sections at horizontal or vertical polarizations; Kw is the dielectric factor of water defined as , where ɛr is the complex dielectric constant of water; Zdr is defined as the ratio of reflectivity factors at horizontal and vertical polarizations (Seliga and Bringi 1976), which is sensitive to mean drop shape; and Kdp is proportional to the real part of the difference in the complex forward scatter amplitudes f at horizontal and vertical polarizations. It can be expressed as

 
formula

where φdp between two range locations r1 and r2 is expressed in terms of Kdp as

 
formula

The measured differential propagation phase (ψdp) can be defined as

 
formula

where δ is the backscatter phase that is the difference between arguments of the complex backscattering amplitudes for horizontal and vertical polarizations; ρ is the correlation between the signal at horizontal and vertical polarizations, and ρ is expressed as

 
formula

where Shh, Sυυ refer to elements of the backscattering matrix, the asterisk is the complex conjugate, and the bars indicate expectation of elements.

The polarimetric radar variables provide information about the microphysical and other properties of precipitation such as hydrometeor size, shape, orientation, phase state, and fall behavior. The φdp is proportional to the forward scatter property of hydrometeors, which is the difference between horizontal and vertical propagation phases. For horizontally oriented hydrometeors such as raindrops, a horizontal propagation phase shift (i.e., the radial derivative) is larger than a vertical polarization phase shift (i.e., Kdp > 0° km−1). In addition, in regions of nonmeteorological echoes, because of poor correlation between signals on horizontal and vertical polarizations, φdp fluctuations are significantly higher than in precipitation. The ρ is affected by the variability in the ratio of the vertical to horizontal size of individual hydrometeors. Values of ρ are close to unity for rain and pristine ice crystals. In the case of melting and mixed-phase conditions, ρ is smaller than unity. Low values of ρ can be used for detecting hail and mixed-phase precipitation and contamination by ground clutter and nonmeteorological scatterers.

3. Hydrometeor classification

During the last decade, various advanced methods for hydrometeor classification, which are based on dual-polarization radar variables, have been proposed (Vivekanandan et al. 1999b; Liu and Chandrasekar 2000; Straka et al. 2000; Zrnić et al. 2001; Lim et al. 2005; Baldini et al. 2005, Ryzhkov et al. 2005; Keranen et al. 2007; Park et al. 2009). These methods were mainly developed and demonstrated for S-band and C-band weather radars and were described briefly in Chandrasekar et al. (2013). Recently, Dolan and Rutledge (2009) and Snyder et al. (2010) have proposed methods utilizing characteristics of dual-polarization observables specific to X band. In contrast, the proposed hydrometeor classification described herein is a robust technique that can be applied to S band, C band, and even higher frequencies, such as X and Ku bands. The classification technique uses the ρ and the texture of ψdp along with SNR as inputs, and produces four simple categories of nonmeteorological target, rain, rain/ice mixture, and ice particles as outputs. The ρ is sensitive to precipitation phase state and is a good indicator for melting particles and nonmeteorological targets. The ρ in precipitation does not have a wide dynamic range, mostly varying between 0.9 and 1 [however, it can significantly drop below 0.9 in regions of mixed precipitation or hail, as HYDROX measurements show (e.g., Matrosov et al. 2007, 2013)]. The expression 10ρ is used in the hydrometeor classification technique, to expand the scale of ρ in precipitation. The texture of ψdp may also be efficient for discriminating between precipitation, ground clutter/anomalous propagation, and biological scatters (Ryzhkov et al. 2005). The use of this texture value can also be extended to detect melting particles. Texture information can be obtained using the root-mean-square difference of radar observations in the azimuth and in range directions (Gourley et al. 2007). In this study, texture is estimated only in the range direction, calculated using

 
formula

where r indicates the range of the gate length and N represents the number of resolution gates in the range. In this study seven gates with 150-m resolution are used. The proposed algorithm consists of four principal aspects, namely, 1) melting-layer detection, 2) fuzzification, 3) inference, and 4) defuzzification.

In dual-polarized S- and C-band radars, Zdr, ρ, and the linear depolarization ratio (LDR) have been extensively used to detect melting layers. In stratiform precipitation, Zrnić et al. (1993) and Matrosov et al. (2007) used a constant ρ threshold approach to detect the melting layer for S-band and X-band radar measurements. As the radar beam transitioned from the rain region below to the melting region above, ρ dropped sharply, and this information could be used to determine the height of the melting layer. This approach works well for higher SNRs. For lower SNR values (as shown in Fig. 1), ρ exhibits significant sensitivity to SNR. Even in the rain region, smaller ρhυ values (such as 0.9) can exist compared to ρ values (such as 0.93) in mixed precipitation for higher SNR [note that the noise level for the HYDROX radar during HMT 2006 (HMT-06) operations was around −102 dBm]. Figure 1 shows the distribution of ρ with SNR during a combined stratiform/convective rainfall [2053:49 UTC 30 December 2005; see Matrosov et al. (2007) for a more detailed description of this event] with a pronounced bright band (shown in Fig. 4). The blue dots in Fig. 1 indicate all data above 0.8 km MSL, including rain, snow, and mixed-phase precipitation, and red dots are data for the rain region only (a height between 0.8 and 2.3 km MSL). The data in Fig. 1 show considerable overlap in the ρ distributions of the rain-only category versus the all-precipitation category, indicating that melting-layer detection using a constant ρ threshold may not work properly at low SNR. During frontal passages some increased convective activity may make detection of the bright band more difficult.

Fig. 1.

Scatterplot of (a) SNR vs 10ρ and (b) SNR vs σ(ψdp) for the 2053:49 UTC 30 Dec 2005 case as shown in Fig. 4. Blue dots are from heights > 2.5 km MSL, and red dots are data for the rain region (0.8 < height < 2.5 km).

Fig. 1.

Scatterplot of (a) SNR vs 10ρ and (b) SNR vs σ(ψdp) for the 2053:49 UTC 30 Dec 2005 case as shown in Fig. 4. Blue dots are from heights > 2.5 km MSL, and red dots are data for the rain region (0.8 < height < 2.5 km).

To overcome this problem, an advanced melting-layer detection technique is proposed, as described below. The melting layer is determined from the combined characteristics of σ(ψdp)-SNR and 10ρ-SNR, as shown in Fig. 2. First, melting snow and/or rain/ice mixture regions are identified by their location in the two-dimensional space shown in Figs. 2a and 2b. Next, the heights of melting region are calculated. An estimate of the median height of the melting level is then obtained. The detected melting level is subsequently used for the hydrometeor classification system as an environment factor (temperature). Another advancement of the hydrometeor classification is introduced via two two-dimensional beta membership functions (2D-MBF) by using the SNR, σ(ψdp), and 10ρ variables. [Readers should refer to Liu and Chandrasekar (2000) for a description of beta membership functions.]

Fig. 2.

Classification decision boundary for the NOAA X-band radar (HYDRO-X): (a) SNR vs 10ρ and (b) SNR vs σ(ψdp). The area between the red solid lines indicates single-phase particles such as rain or snow, whereas the area within the black dotted lines are melting particles or rain/hail mixtures.

Fig. 2.

Classification decision boundary for the NOAA X-band radar (HYDRO-X): (a) SNR vs 10ρ and (b) SNR vs σ(ψdp). The area between the red solid lines indicates single-phase particles such as rain or snow, whereas the area within the black dotted lines are melting particles or rain/hail mixtures.

Figure 2 shows the classification boundary of 2D-MBFs for the HYDROX data. The σ(ψdp) as a function of SNR is shown in Figs. 2a and 2b, and shows the corresponding relation between 10ρ and SNR. The classification boundary was obtained with HYDROX data collected during the 2005–06 season, including the data shown in Fig. 1. The procedure included estimation of the mean value of σ(ψdp) and 10ρ according to SNR and obtaining a best-fit relation to the data. Note that these MBFs depend on the characteristics of the radar system such as signal fluctuation. Therefore, adjustment of MBFs is needed for each radar system. Subsequently, the inference (rule strength) is defined as

 
formula

where f denotes the fuzzification function and H is the height from MSL. In the equation, 2D − MBF1 and 2D − MBF2 indicate the two-dimensional membership function for σ(ψdp) − SNR and 10ρ − SNR, respectively. At the defuzzification stage, if the maximum rule strength (MR) is less than 0.2 (this is an empirical threshold), then the target is identified as nonmeteorological or low signal targets. The block diagram of the classification method is shown in Fig. 3. Figures 4a–c depict Zh, ψdp, and ρ from an RHI collected on 2053:49 UTC 30 December 2005. This RHI was performed during the same period of combined convective/stratiform precipitation shown in Fig. 1, with rain occurring below about 2.8 km from MSL and snowfall above this height. Both the HYDROX data and observations from a nearby S-band vertically pointing profiler indicated the presence of a pronounced melting layer approximately 2.8 km above MSL. This event provided an excellent opportunity to test the hydrometeor classification algorithm. The classification results from the proposed method are shown in Fig. 4d. The detected melting layer, depicted by a black line in each panel, was compared to the S-band profiler observation collected at a range of approximately 18 km from the X-band radar. Good agreement between the melting region observed in the S band and the X band was found (not shown). Based on the melting-layer characteristics, it can be seen that the classification results shown in Fig. 4d are reasonable.

Fig. 3.

Schematic diagram of hydrometeor classification.

Fig. 3.

Schematic diagram of hydrometeor classification.

Fig. 4.

Radar observations (2053:49 UTC 30 Dec 2005) and classification result: (a) Zh, (b) ψdp, (c) ρ, and (d) hydrometeor types (red: rain, green: melting particles/mixture, blue: ice particles such as snow or ice crystal, white: nonmeteorological or low-signal targets). Black solid lines indicate detected melting layer.

Fig. 4.

Radar observations (2053:49 UTC 30 Dec 2005) and classification result: (a) Zh, (b) ψdp, (c) ρ, and (d) hydrometeor types (red: rain, green: melting particles/mixture, blue: ice particles such as snow or ice crystal, white: nonmeteorological or low-signal targets). Black solid lines indicate detected melting layer.

4. Kdp retrieval

A number of studies have shown that Kdp can provide relatively accurate estimates of rainfall because it is less sensitive to variations in the DSD compared to a traditional Z–R approach (Z is the radar reflectivity factor; R is the rain rate in mm h−1) (Sachidananda and Zrnić 1986; Matrosov et al. 2006; Cifelli and Chandrasekar 2010). Moreover, the Kdp technique is relatively insensitive to hail (Chandrasekar et al. 1990). Because of the increased sensitivity of ψdp at X band compared to S or C band, Kdp can often outperform rainfall estimation from Z–R approaches at this frequency (Matrosov et al. 2002, 2006). However, a disadvantage of Kdp is that it is traditionally calculated over a pathlength as opposed to each individual range gate.

Conventionally, Kdp is calculated as a mean slope of range profiles of the ψdp measurement and is a best fit across a specified pathlength. To estimate Kdp from a ψdp profile, Golestani et al. (1989) and Hubbert and Bringi (1995) used such a filtering technique. These methods can work well in rain regions where microphysical properties are changing smoothly such as stratiform rain. However, for intense convective regions, the method can result in underestimating peak Kdp and negative Kdp values, and the estimated Kdp fluctuates much in low rain-rate regions because of significant signal fluctuations (Wang and Chandrasekar 2009). Wang and Chandrasekar (2009) proposed an adaptive algorithm to suppress noise-associated fluctuations in small Kdp segments and to reduce estimation biases in large Kdp segments. The method incorporates the regression errors adaptively through scaling for estimation of Kdp. This method can retrieve improved peak Kdp values in heavy rainfall regions as well as in light rainfall regions with higher signal fluctuation. However, this method is based on filtering techniques and may not be efficient for eliminating backscatter phase shift and negative Kdp values.

An advanced Kdp estimation technique that combines the conventional filtering method for the melting region and a new self-consistent method for rain only is proposed here. The reason for using the filtering method in the melting region is that variations of particle density and DSD may be too significant to produce reliable results with the profiling method. The Kdp distribution method is incorporated with attenuation-corrected Zh and total ψdp in the rain region (in order to provide a Kdp estimate at every range gate as described below). To retrieve Kdp using the self-consistent method, an attenuation-corrected is first estimated using Eqs. (9) and (10) (Testud et al. 2000). Note that, for this study, the values of β and γ are 0.76 and 0.31, respectively, and these values are obtained from theoretical simulation with the Brandes et al. (2004) drop shape model at a temperature of 10°C for widely varying drop size distributions ,

 
formula
 
formula
 
formula

where Z′(r) is attenuated reflectivity and r0 and rm indicate the beginning and end range of precipitation echo, respectively, and

 
formula

After the attenuation correction is completed, Kdp is retrieved as

 
formula

In the Kdp–Zh relation, the value of b is relatively constant, whereas the value of a varies significantly according to drop shape distribution and temperature. Here, the value of b is 0.76. The parameter a is obtained for each radar ray from corrected Zh and total ψdp within the rain region.

The schematic diagram of the Kdp retrieval system is shown in Fig. 5. The specific attenuation coefficient (αh) is also a very useful parameter for rainfall estimation, and this application has been pursued in the literature (Bringi and Chandrasekar 2001; Ryzhkov et al. 2011).

Fig. 5.

Schematic diagram of the new Kdp estimation technique.

Fig. 5.

Schematic diagram of the new Kdp estimation technique.

To test the proposed algorithm, HYDROX radar data for 1459:21 UTC 31 December 2005 were used. Figure 6 shows an example ray of Kdp estimations in stratiform rain. Figures 6a and 6b present ray profiles of observed and corrected Zh and Zdr (note that the attenuation correction is performed after smoothing the observed Zh with a 1.5-km range filter). Figures 6c and 6d show the corresponding ψdp ray profile and standard deviation of ψdp at a running 1.5-km interval, respectively. Figure 6e depicts the estimated Kdp using the proposed method (blue solid line) and conventional filtering method (red dotted line; Hubbert and Bringi 1995). The conventional filtering method was carried out for all data along the ray with ρ exceeding 0.9 (Matrosov et al. 2007) with a 4.5-km range width. The elevation of the ray was below the melting level over the entire pathlength, so that the precipitation shown in Fig. 6 corresponds to rainfall. With the exception of the spike shown in Figs. 6a and 6c at a range of approximately 2 km from the radar, the data show relatively stable Zh with ψdp increasing at a relatively uniform rate over the pathlength as anticipated for stratiform rain. The large Zh and ψdp values at a 2-km range represent ground clutter. Using ρ, most of the ground clutter region can be filtered out. However, not surprisingly, the Kdp estimate using the conventional filtering technique in Fig. 6e shows large values of Kdp in the vicinity of the ground clutter. It is induced by smoothing the large values ψdp at neighboring range gates within the ground clutter region after filtering by ρ. Note that some simple ground clutter filtering based on the absolute values of ρ and the Doppler velocity constraint is also typically used for conventional Kdp estimations from the HYDROX data (Matrosov 2010).

Fig. 6.

An example ray profile illustrating the performance of the Kdp estimation technique using data collected at 1459:21 UTC 31 Dec 2005, elevation: 2.6°, azimuth: 41.0°. Observed and corrected (a) Zh, (b) Zdr, (c) ψdp, (d) standard deviation of ψdp within 2-km range, and (e) estimated Kdp (blue solid line indicates new Kdp from the proposed method, and red dotted line is Kdp from the conventional filtering method). Circles refer to area of interest described in the text.

Fig. 6.

An example ray profile illustrating the performance of the Kdp estimation technique using data collected at 1459:21 UTC 31 Dec 2005, elevation: 2.6°, azimuth: 41.0°. Observed and corrected (a) Zh, (b) Zdr, (c) ψdp, (d) standard deviation of ψdp within 2-km range, and (e) estimated Kdp (blue solid line indicates new Kdp from the proposed method, and red dotted line is Kdp from the conventional filtering method). Circles refer to area of interest described in the text.

The new method is not significantly affected by ψdp of ground clutter because it uses Zh in the retrieval process and Zh are not affected by neighboring ground clutter to the same degree as ψdp. In addition, the new method provides more reasonable Kdp values at 5–10- and 25–30-km ranges as compared to attenuation-corrected Zh. The reason for the larger Kdp variation in the conventional method at the 25–30-km range (circled region in Figs. 6c–e) is that sharp DSD variation induces large backscatter phase change and provides significant ψdp fluctuations. As shown in Fig. 6b, there is some increased variability in Zdr between about 25 and 32 km. Hence, we can say that the drop size variability is enhanced at these ranges and that the backscatter phase shift changes should be more pronounced there. For ranges outside the 20–30-km range, the standard deviation of ψdp is generally between 1° and 2°, which is indicative of good stable phase measurements.

Figure 7 shows radar observations (observed Zh, ψdp, and ρ) and Kdp estimation results for the entire RHI scan, including the ray shown in Fig. 6. Figures 7a–c are Zh,ψdp, and ρ, respectively, whereas Kdp retrieved by the new technique and the results of the conventional method are shown in Figs. 7d and 7e, respectively. The melting level is at a height of 2.8 km MSL, so that the RHI includes rain only (below the melting level), mixed (within the melting layer), and snow (above the melting layer), as indicated by the gradient in ρ (Fig. 7c). The Kdp retrieval method proposed here was used in both the rain-only region and in the melting region. In contrast, the conventional method was applied in all regions where ρ exceeded 0.95.

Fig. 7.

RHI scan example of Kdp estimation (1459:21 UTC 31 Dec 2005, azimuth: 41.0°). (a) Observed Zh, (b) ψdp, (c) ρhv, (d) estimated Kdp from the proposed method, and (e) Kdp from the conventional filtering method.

Fig. 7.

RHI scan example of Kdp estimation (1459:21 UTC 31 Dec 2005, azimuth: 41.0°). (a) Observed Zh, (b) ψdp, (c) ρhv, (d) estimated Kdp from the proposed method, and (e) Kdp from the conventional filtering method.

For further evaluation, the new Kdp retrieval methodology and the filtering method (Hubbert and Bringi 1995) are compared for an entire event observed during 30–31 December 2005. This was the most significant event for the 2005/06 HMT-West field season, with major flooding occurring on both sides of the Sierra Nevada (Matrosov 2011). During this 24-h event, 160–200 mm of rainfall fell in the ARB, which caused local heavy flooding. Figure 8 shows a comparison of Kdp retrieved by both Kdp estimation methods and from a ground instrument [a Joss–Waldvogel disdrometer (JWD)] at a resolution gate above the HMT-West Colfax (CFC) site (at 2.4° radar elevation). The CFC site is located at distance of about 18 km from the HYDROX radar. Figures 8a and 8b depict time series and a scatterplot of Kdp retrieval results for the 30–31 December 2005 event, respectively, and Fig. 8c shows a scatterplot of retrieved Kdp and Kdp calculated from JWD DSDs. The solid line is the new Kdp, and the dotted line shows Kdp from the conventional filtering method. The time range on the x axis is approximately 24 h, starting at 2053:00 UTC 30 December 2005 and ending at 1953:00 UTC 31 December 2005. For statistical analysis, the normalized bias (NB), the normalized absolute error (NAE), the correlation coefficient, and the linear regression parameters are used. The NB and the NAE between two parameter series X and Y can be defined as

 
formula
 
formula

where angle brackets mean averaging

Fig. 8.

(a) Time series, (b) scatterplot of Kdp retrieved by the new method and the filtering method (Hubbert and Bringi 1995), and (c) scatterplot of retrieved Kdp and Kdp calculated from JWD DSDs. Solid line in (a) is the new Kdp and dotted line is the Kdp from the filtering method. Time range on the x axis is approximately 24 h, starting at 2053:00 UTC 30 Dec 2005 and ending at 1953:00 UTC 31 Dec 2005.

Fig. 8.

(a) Time series, (b) scatterplot of Kdp retrieved by the new method and the filtering method (Hubbert and Bringi 1995), and (c) scatterplot of retrieved Kdp and Kdp calculated from JWD DSDs. Solid line in (a) is the new Kdp and dotted line is the Kdp from the filtering method. Time range on the x axis is approximately 24 h, starting at 2053:00 UTC 30 Dec 2005 and ending at 1953:00 UTC 31 Dec 2005.

The NB, the NAE, and the correlation coefficient between the new Kdp and the filtered Kdp are −0.92%, 32.89%, and 0.87, respectively. The linear regression is derived as

 
formula

From the results of Figs. 6e, 7d, and 8, it can be seen that the proposed algorithm produces less noise and more stable results compared to the conventional filtering technique. In addition, the proposed method produces only positive values of Kdp throughout the rain region.

5. Rainfall estimation

The use of Kdp derived from ψdp for the QPE application has been studied by a number of researchers (e.g., Bringi and Chandrasekar 2001; Ryzhkov et al. 2005; Matrosov et al. 2005; Matrosov 2010; Wang and Chandrasekar 2010) and has shown promising results. As these previous studies indicated, Kdp has several advantages for QPE compared to other radar variables such as Zh and Zdr, especially at higher frequencies such as X band; Kdp is not significantly affected by beam blockage and is not sensitive to the uncertainty of radar calibration as well as attenuation effects. The relation between rainfall rate (mm h−1) and Kdp (° km−1) is described as . In this paper, 17 and 0.73 are used for parameters (c and d, respectively) from Matrosov (2010). For evaluation of Kdp-derived rainfall, the estimation includes a comparison of both instantaneous and cumulative rainfall using the conventional, filtered Kdp and the proposed method with surface rain gauge and disdrometer data. Data used for the evaluation are from the HMT event mentioned above.

Figure 9 shows a comparison of the instantaneous rainfall estimation from the R–Kdp relation using the two different Kdp methods. Figure 9a depicts the rainfall estimation by the new Kdp (as shown in Fig. 7d), and Fig. 9b is the rainfall estimation by the conventional Kdp (as shown in Fig. 7e). The results of Fig. 9 indicate that the rain rates derived from the new Kdp method have a smoother vertical texture. Figure 10 shows a comparison of instantaneous rainfall and rainfall accumulations from R–Kdp estimation corresponding to Fig. 8 and ground instruments (a JWD and a standard 0.01″ tipping-bucket rain gauge at the CFC site). From the results of Fig. 10, it can be seen that the new Kdp performs well compared to the ground instrumentation. The NB and the NAE between the rainfall estimation from the new Kdp are −0.19% and 39.28%, respectively, where the NB and the NAE between rainfall estimation from the filtered Kdp are −1.24% and 42.41%, respectively. Note also the tipping-bucket gauge data are in good agreement with accumulations derived from a collocated JWD.

Fig. 9.

RHI scan example of rainfall estimation (1459:21 UTC 31 Dec 2005) corresponding to Figs. 7d and 7e. Estimated rainfall using (a) the new Kdp and (b) Kdp from the conventional filtering method.

Fig. 9.

RHI scan example of rainfall estimation (1459:21 UTC 31 Dec 2005) corresponding to Figs. 7d and 7e. Estimated rainfall using (a) the new Kdp and (b) Kdp from the conventional filtering method.

Fig. 10.

Comparison of (a) time series, (b) scatterplot of instantaneous, and (c) cumulative rainfall from RKdp estimation corresponding to Fig. 8 and ground instruments (JWD and rain gauge) at the CFC site. Time range on the x axis is approximately 24 h, starting at 2053:00 UTC 30 Dec 2005 and ending at 1953:00 UTC 31 Dec 2005.

Fig. 10.

Comparison of (a) time series, (b) scatterplot of instantaneous, and (c) cumulative rainfall from RKdp estimation corresponding to Fig. 8 and ground instruments (JWD and rain gauge) at the CFC site. Time range on the x axis is approximately 24 h, starting at 2053:00 UTC 30 Dec 2005 and ending at 1953:00 UTC 31 Dec 2005.

6. Summary and conclusions

Rainfall estimation using Kdp measurements at X band have been shown to be relatively successful (Wang and Chandrasekar 2010; Matrosov et al. 2006). This paper presents a further enhancement to this class of applications, improving the robustness of the rainfall estimation process, especially for complex terrain applications due to reduced ground clutter contamination at Kdp retrieval. New methods for hydrometeor classification and estimation of Kdp for X-band dual-polarization radar are presented. The advanced techniques developed in this paper were evaluated in an area of complex terrain using data from the 2005–06 HMT-West field project. The main novelty in the hydrometeor classification comes from the use of two 2D membership functions established by integrating signal-to-noise ratio and other radar variables such as σ(ψdp) and 10ρ. This method does not use attenuation-affected factors such as Zh and Zdr. Therefore, this algorithm is robust and can be used effectively for preprocessing the radar data (e.g., identifying rain region) in attenuation correction and precipitation estimation, especially for a higher frequency such as X band. A Kdp distribution method is also introduced that incorporates attenuation-corrected Zh and total ψdp in the rain region. This algorithm has an advantage that it is not significantly affected by backscatter phase shift compared to the conventional filtering method. Also, the technique allows for retrieval of Kdp at every range gate. When a radar echo is narrow, however, the presence of significant δ at the beginning or ending ranges of the echo may significantly affect changes in ψdp. The analysis shows that this new Kdp method, which does not use data from adjacent range bins, should better capture gradients in rain rate when compared to Kdp calculated using the traditional method. In addition, rainfall estimation based on the new Kdp is evaluated. The evaluation shows that the rainfall estimation results agree well with ground instruments.

Acknowledgments

The HYDROX radar operations were supported by the Physical Sciences Division (PSD) at NOAA/ESRL. The authors would like to acknowledge the hard work and dedication of the PSD staff in the collection and processing of the HMT data used in this study. The participation of Lim in this study is partially supported by a grant from a Strategic Research Project (Development of flood warning and snowfall estimation platform using hydrological radars) funded by the Korea Institute of Construction Technology. The participation of Chandrasekar in this study is supported by the CASA NSF ERC program.

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