## 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 (*K*_{dp}) 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 (*Z _{h}*, hereafter reflectivity) and differential reflectivity (

*Z*

_{dr}) 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

*Z*and the differential propagation phase (

_{h}*φ*

_{dp}) (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 _{hυ}*), the texture of

*φ*

_{dp}, 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

_{hυ}*ρ*in regions with mixed precipitation types (e.g., the melting region). However, at low SNR

_{hυ}*ρ*in rain can actually be smaller than the corresponding value in melting precipitation (i.e., at 10-dB SNR in rain

_{hυ}*ρ*may be 0.93, whereas at 35-dB SNR in the melting region

_{hυ}*ρ*could be 0.95). Therefore, by combining the SNR information with the

_{hυ}*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

_{hυ}*ρ*and

_{hυ}*φ*

_{dp}at X band. The

*K*

_{dp}at X band tends to be ∼3 times that of

*K*

_{dp}at S band.

The *K*_{dp} 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 *K*_{dp} include range filtering, regression analysis, or both (Golestani et al. 1989; Hubbert and Bringi 1995). However, these methods may reduce the local extrema in *K*_{dp} in the estimation because of filtering (Wang and Chandrasekar 2009) and retrieve negative *K*_{dp} 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 *K*_{dp} retrieval algorithm that adopts a conventional filtering method for the propagation path through the melting region and an alternate method that distributes *K*_{dp} in a manner self-consistent with *Z _{h}* for the rain region is introduced herein. Using

*K*

_{dp}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 *K*_{dp} retrieval algorithm. In section 5 the rainfall estimation based on new *K*_{dp} 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)

where *D*_{0} is the equivolumetric median volume diameter (mm), *μ* is the shape parameter, and *N _{w}* (mm

^{−1}m

^{−3}) is the normalized intercept parameter of the exponential distribution with the same water content and

*D*

_{0}.

Radar observations in the rain medium can be expressed in terms of the DSD, and *Z _{h}*

_{,}

_{υ}(hereafter reflectivities) at horizontal (

*h*) and vertical (

*υ*) polarizations are defined as

where λ is the wavelength of the radar; *σ _{h}*

_{,}

*represents the radar cross sections at horizontal or vertical polarizations;*

_{v}*K*is the dielectric factor of water defined as , where ɛ

_{w}_{r}is the complex dielectric constant of water;

*Z*

_{dr}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

*K*

_{dp}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

where *φ*_{dp} between two range locations *r*_{1} and *r*_{2} is expressed in terms of *K*_{dp} as

The measured differential propagation phase (*ψ*_{dp}) can be defined as

where *δ* is the backscatter phase that is the difference between arguments of the complex backscattering amplitudes for horizontal and vertical polarizations; *ρ _{hυ}* is the correlation between the signal at horizontal and vertical polarizations, and ρ

*is expressed as*

_{hυ}where *S _{hh}*,

*S*

_{υυ}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 *φ*_{dp} 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., *K*_{dp} > 0° km^{−1}). In addition, in regions of nonmeteorological echoes, because of poor correlation between signals on horizontal and vertical polarizations, *φ*_{dp} fluctuations are significantly higher than in precipitation. The *ρ _{hυ}* 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,

_{hυ}*ρ*is smaller than unity. Low values of

_{hυ}*ρ*can be used for detecting hail and mixed-phase precipitation and contamination by ground clutter and nonmeteorological scatterers.

_{hυ}## 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 K_{u} bands. The classification technique uses the *ρ _{hυ}* and the texture of

*ψ*

_{dp}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

_{hυ}*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 10

_{hυ}^{ρhυ}is used in the hydrometeor classification technique, to expand the scale of

*ρ*in precipitation. The texture of

_{hυ}*ψ*

_{dp}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

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, *Z*_{dr}, *ρ _{hυ}*, 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,

_{hυ}*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),

_{hυ}*ρ*exhibits significant sensitivity to SNR. Even in the rain region, smaller ρ

_{hυ}_{hυ}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

_{hυ}*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

_{hυ}*ρ*distributions of the rain-only category versus the all-precipitation category, indicating that melting-layer detection using a constant

_{hυ}*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.

_{hυ}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*(*ψ*_{dp})-SNR and 10^{ρhυ}-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(*ψ*_{dp}), and 10^{ρhυ} variables. [Readers should refer to Liu and Chandrasekar (2000) for a description of beta membership functions.]

Figure 2 shows the classification boundary of 2D-MBFs for the HYDROX data. The σ(*ψ*_{dp}) as a function of SNR is shown in Figs. 2a and 2b, and shows the corresponding relation between 10^{ρhυ} 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(*ψ*_{dp}) and 10^{ρhυ} 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

where *f* denotes the fuzzification function and *H* is the height from MSL. In the equation, 2*D* − MBF1 and 2*D* − MBF2 indicate the two-dimensional membership function for *σ*(*ψ*_{dp}) − SNR and 10^{ρhυ} − 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 *Z _{h}*,

*ψ*

_{dp}, 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.

_{hυ}## 4. *K*_{dp} retrieval

A number of studies have shown that *K*_{dp} 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 *K*_{dp} technique is relatively insensitive to hail (Chandrasekar et al. 1990). Because of the increased sensitivity of *ψ*_{dp} at X band compared to S or C band, *K*_{dp} can often outperform rainfall estimation from *Z–R* approaches at this frequency (Matrosov et al. 2002, 2006). However, a disadvantage of *K*_{dp} is that it is traditionally calculated over a pathlength as opposed to each individual range gate.

Conventionally, *K*_{dp} is calculated as a mean slope of range profiles of the *ψ*_{dp} measurement and is a best fit across a specified pathlength. To estimate *K*_{dp} from a *ψ*_{dp} 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 *K*_{dp} and negative *K*_{dp} values, and the estimated *K*_{dp} 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 *K*_{dp} segments and to reduce estimation biases in large *K*_{dp} segments. The method incorporates the regression errors adaptively through scaling for estimation of *K*_{dp}. This method can retrieve improved peak *K*_{dp} 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 *K*_{dp} values.

An advanced *K*_{dp} 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 *K*_{dp} distribution method is incorporated with attenuation-corrected *Z _{h}* and total

*ψ*

_{dp}in the rain region (in order to provide a

*K*

_{dp}estimate at every range gate as described below). To retrieve

*K*

_{dp}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 ,

where *Z*′(*r*) is attenuated reflectivity and *r*_{0} and *r _{m}* indicate the beginning and end range of precipitation echo, respectively, and

After the attenuation correction is completed, *K*_{dp} is retrieved as

In the *K*_{dp}*–Z _{h}* 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

*Z*and total

_{h}*ψ*

_{dp}within the rain region.

The schematic diagram of the *K*_{dp} retrieval system is shown in Fig. 5. The specific attenuation coefficient (α_{h}) 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).

To test the proposed algorithm, HYDROX radar data for 1459:21 UTC 31 December 2005 were used. Figure 6 shows an example ray of *K*_{dp} estimations in stratiform rain. Figures 6a and 6b present ray profiles of observed and corrected *Z _{h}* and

*Z*

_{dr}(note that the attenuation correction is performed after smoothing the observed

*Z*with a 1.5-km range filter). Figures 6c and 6d show the corresponding

_{h}*ψ*

_{dp}ray profile and standard deviation of

*ψ*

_{dp}at a running 1.5-km interval, respectively. Figure 6e depicts the estimated

*K*

_{dp}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

_{hυ}*Z*with

_{h}*ψ*

_{dp}increasing at a relatively uniform rate over the pathlength as anticipated for stratiform rain. The large

*Z*and

_{h}*ψ*

_{dp}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

_{hυ}*K*

_{dp}estimate using the conventional filtering technique in Fig. 6e shows large values of

*K*

_{dp}in the vicinity of the ground clutter. It is induced by smoothing the large values

*ψ*

_{dp}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

_{hυ}*ρ*and the Doppler velocity constraint is also typically used for conventional

_{hυ}*K*

_{dp}estimations from the HYDROX data (Matrosov 2010).

The new method is not significantly affected by *ψ*_{dp} of ground clutter because it uses *Z _{h}* in the retrieval process and

*Z*are not affected by neighboring ground clutter to the same degree as

_{h}*ψ*

_{dp}. In addition, the new method provides more reasonable

*K*

_{dp}values at 5–10- and 25–30-km ranges as compared to attenuation-corrected

*Z*. The reason for the larger

_{h}*K*

_{dp}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

*ψ*

_{dp}fluctuations. As shown in Fig. 6b, there is some increased variability in

*Z*

_{dr}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

*ψ*

_{dp}is generally between 1° and 2°, which is indicative of good stable phase measurements.

Figure 7 shows radar observations (observed *Z _{h}*,

*ψ*

_{dp}, and

*ρ*) and

_{hυ}*K*

_{dp}estimation results for the entire RHI scan, including the ray shown in Fig. 6. Figures 7a–c are

*Z*,

_{h}*ψ*

_{dp}, and

*ρ*, respectively, whereas

_{hυ}*K*

_{dp}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

_{hυ}*K*

_{dp}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.

_{hυ}For further evaluation, the new *K*_{dp} 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 *K*_{dp} retrieved by both *K*_{dp} 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 *K*_{dp} retrieval results for the 30–31 December 2005 event, respectively, and Fig. 8c shows a scatterplot of retrieved *K*_{dp} and *K*_{dp} calculated from JWD DSDs. The solid line is the new *K*_{dp}, and the dotted line shows *K*_{dp} 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

where angle brackets mean averaging

The NB, the NAE, and the correlation coefficient between the new *K*_{dp} and the filtered *K*_{dp} are −0.92%, 32.89%, and 0.87, respectively. The linear regression is derived as

## 5. Rainfall estimation

The use of *K*_{dp} derived from *ψ*_{dp} 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, *K*_{dp} has several advantages for QPE compared to other radar variables such as *Z _{h}* and

*Z*

_{dr}, especially at higher frequencies such as X band;

*K*

_{dp}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

*K*

_{dp}(° 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

*K*

_{dp}-derived rainfall, the estimation includes a comparison of both instantaneous and cumulative rainfall using the conventional, filtered

*K*

_{dp}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–K*_{dp} relation using the two different *K*_{dp} methods. Figure 9a depicts the rainfall estimation by the new *K*_{dp} (as shown in Fig. 7d), and Fig. 9b is the rainfall estimation by the conventional *K*_{dp} (as shown in Fig. 7e). The results of Fig. 9 indicate that the rain rates derived from the new *K*_{dp} method have a smoother vertical texture. Figure 10 shows a comparison of instantaneous rainfall and rainfall accumulations from *R–K*_{dp} 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 *K*_{dp} performs well compared to the ground instrumentation. The NB and the NAE between the rainfall estimation from the new *K*_{dp} are −0.19% and 39.28%, respectively, where the NB and the NAE between rainfall estimation from the filtered *K*_{dp} 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.

## 6. Summary and conclusions

Rainfall estimation using *K*_{dp} 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 *K*_{dp} retrieval. New methods for hydrometeor classification and estimation of *K*_{dp} 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*(*ψ*_{dp}) and 10* ^{ρ}^{hυ}*. This method does not use attenuation-affected factors such as

*Z*and

_{h}*Z*

_{dr}. 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

*K*

_{dp}distribution method is also introduced that incorporates attenuation-corrected

*Z*and total

_{h}*ψ*

_{dp}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

*K*

_{dp}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

*ψ*

_{dp}. The analysis shows that this new

*K*

_{d}

_{p}method, which does not use data from adjacent range bins, should better capture gradients in rain rate when compared to

*K*

_{dp}calculated using the traditional method. In addition, rainfall estimation based on the new

*K*

_{dp}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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