## 1. Introduction

Quantitative precipitation estimation (QPE) is one of the most important applications of weather radars. The QPE algorithms utilizing different combinations of reflectivity *Z*, differential reflectivity *Z*_{DR}, and specific differential phase *K*_{DP} were developed during the last two decades (e.g., Ryzhkov and Zrnić 1995; Brandes et al. 2002; Bringi et al. 2011; Wang et al. 2013). It was found that, although the methods using *Z* and *Z*_{DR} are able to provide robust estimation for different rainfall intensities, their performance heavily relies on the data quality and particularly on the accuracy of absolute calibration of *Z* and *Z*_{DR} and their correction for attenuation (e.g., Gorgucci et al. 1992; Scarchilli et al. 1996; Ryzhkov et al. 2014). The radar rain algorithms based on *K*_{DP}, on the other hand, are less sensitive to the drop size distribution (DSD) variations and immune to attenuation and radar miscalibration (Zrnić and Ryzhkov 1996). However, the *R*–*K*_{DP} estimates are increasingly noisy for lighter rain and their radial resolution is generally poorer than the ones obtained from *Z* and *Z*_{DR} (e.g., Ryzhkov and Zrnić 1995; Ryzhkov et al. 2005b).

Recently, a novel QPE method utilizing the specific attenuation *A* for rainfall rate *R* estimation was proposed by Ryzhkov et al. (2014). According to this approach, the *A* field is computed from *Z* and the path-integrated attenuation (PIA), which is generally used for attenuation correction (e.g., Bringi et al. 1990; Testud et al. 2000), and the rainfall rate is estimated using a power-law *R*(*A*) relation (Ryzhkov et al. 2014). It was found that the *R*(*A*) method is immune to biases caused by radar miscalibration, attenuation, partial beam blockage, and wet radome (Ryzhkov et al. 2014). Moreover, compared to the *R*–*K*_{DP} approach, the *R*(*A*) method also has better resolution along the radial direction. All these advantages make *R*(*A*) an attractive rainfall estimator for S-, C-, and X-band radars. The estimated radial profile of *A* is crucially dependent on the net ratio *R*(*A*) power-law relation are relatively insensitive to the DSD variability at S band as opposed to C and X bands, where such dependency is more pronounced. Hence, the parameters of the *R*(*A*) relations at C and X bands should also be optimized for local climate conditions.

The complex terrain in Taiwan poses a significant challenge for radar-based QPE because of abundant radar beam blockage. As indicated in Fig. 1, the Central Mountain Range (CMR) runs from the north of the island to the south, with the tallest peak of above 3800 m. The radar beam from lower antenna elevations of two C-band radars used in this study [0.5° for RCMK (located at Makung) and up to 3.4° for RCCK (located at Ching Chung Kong)] are significantly blocked by CMR, and the variables such as *Z* and *K*_{DP} from lower tilts become unavailable or biased. In this situation, the higher-tilt radar data have to be used in rainfall rate estimation, and the vertical variability of rainfall rate should be taken into account. For better estimation of the rainfall rate using higher-tilt radar data, the correction schemes utilizing vertical profiles of reflectivity (VPR) and specific differential phase (VPSDP) were developed and implemented for rainfall rate estimation (e.g., Andrieu and Creutin 1995; Marzano et al. 2004; Wang et al. 2013). Similar to the *Z* and *K*_{DP} data, the low-tilt *A* data are also unavailable or unreliable because of severe blockage, and the higher-tilt *A* measurements need to be used in the rainfall estimation.

In this study, the rainfall estimation using specific attenuation was performed using two C-band polarimetric radars in Taiwan for the first time. To ensure accurate and robust performance of the technique in this area, optimal values of the factor *R*(*A*) relation were derived based on the simulation using DSD and DSR data measured in Taiwan. The sensitivity of the algorithm to the temperature dependency of *A* was also investigated through a simulation. Corrections for vertical profiles of rain rate estimated from *R*(*A*) (VPRA) were then developed to mitigate the effects of beam blockage from CMR. The performance of the *R*(*A*) algorithm with the newly derived parameters and the VPRA correction scheme was evaluated for different precipitation types including typhoon, stratiform, and convective precipitations. This paper is organized as follows. Section 2 provides information on radar data sources and processing. The scheme for rainfall estimation using specific attenuation and testing of its performance for different rain events are described in sections 3 and 4, respectively. Summary and conclusions are provided in section 5.

## 2. Radar data sources and processing

Two C-band Gematronik polarimetric radars (RCMK and RCCK) used in the current work are deployed by the Weather Wing of the Chinese Air Force (WWCAF). Since 2008, the real-time data were made available to the Central Weather Bureau (CWB) of Taiwan to support the missions of flood monitoring and prediction. Both radars transmit and receive horizontally *H* and vertically *V* polarized waves simultaneously, and the key system characteristics are listed in Table 1 as a reference. Figure 1 shows the locations of C-band radars and four disdrometers used in the current study. The gauge network consisting of 495 gauges is also presented in Fig. 1, and the gauge measurements were used in the QPE performance evaluation.

Technical specifications of two C-band polarimetric radars (RCMK and RCCK) used in the current work.

Accurate absolute calibration of *Z* and *Z*_{DR} is an essential requirement to produce reliable and accurate radar rainfall products. For example, the accuracy of the *Z* calibration should be within 1 dB to ensure the bias of estimated rainfall rate around 15% for stratiform precipitation (Gourley et al. 2009). Different methods for absolute calibration were developed for both single- and dual-polarization radars during the past half century (e.g., Atlas and Mossop 1960; Chisholm 1963; Joss et al. 1968; Stratmann et al. 1971; Gorgucci et al. 1992, 1999; Ryzhkov et al. 2005a). After real-time data from two C-band radars were made available for the CWB, calibrations of RCMK and RCCK have been closely examined. It was found that *Z* measured by RCMK and RCCK is lower than the *Z* measurements from an adjacent operational S-band Weather Surveillance Radar-1988 Doppler (WSR-88D) RCCG located at Chi-Gu (also shown in Fig. 1), which is assumed to be well calibrated and not prone to attenuation (P.-L. Chang et al. 2009; Zhang et al. 2008b; Liou and Chang 2009; Xu et al. 2012). Figure 2 shows examples of the reflectivity fields from RCMK (0132 UTC), RCCK (0132 UTC), and RCCG (0131 UTC) on 9 August 2009. In this example, although the *Z* fields from RCMK and RCCK are corrected from attenuation using a standard method based on the measurements of total differential phase *Z* are still found compared to RCCG, and the inadequate absolute calibration could be the reason.

Reflectivity field sampled by (a) RCCG at 0131 UTC, (b) RCMK at 0132 UTC, and (c) RCCK at 0132 UTC 9 Aug 2009. The reflectivity fields from RCMK and RCCK are corrected for attenuation using differential phase with the attenuation coefficient of 0.088 dB (°)^{−1}.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Reflectivity field sampled by (a) RCCG at 0131 UTC, (b) RCMK at 0132 UTC, and (c) RCCK at 0132 UTC 9 Aug 2009. The reflectivity fields from RCMK and RCCK are corrected for attenuation using differential phase with the attenuation coefficient of 0.088 dB (°)^{−1}.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Reflectivity field sampled by (a) RCCG at 0131 UTC, (b) RCMK at 0132 UTC, and (c) RCCK at 0132 UTC 9 Aug 2009. The reflectivity fields from RCMK and RCCK are corrected for attenuation using differential phase with the attenuation coefficient of 0.088 dB (°)^{−1}.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

To quantify the calibration errors of these two C-band radars, an approach implemented in the radar reflectivity comparison tool (RRCT) was applied in the current work, and more details can be found on the RRCT website (http://rrct.nwc.ou.edu). Reflectivity along the equidistant line between RCMK (RCCK) and RCCG was measured by both radars and compared. The volume for comparison around the equidistant line has dimensions 120 km × 20 km × 20 km. The total reflectivities within this volume measured by both radars are calculated, and their difference represents the calibration mismatch. The calibration differences were estimated using 12-h data from typhoon Morakot (~0000–1200 UTC 9 August 2009) and 12-h data from a mixture of stratiform and convective precipitation (~0000–1200 UTC 18 July 2011). The results from typhoon Morakot are presented in Fig. 3, where the mean reflectivity differences of RCCG versus RCMK and RCCG versus RCCK are found to be 5.28 and 6.24 dB, respectively. Since RCCG is relatively well calibrated during this event based on a comparison between the RCCG QPE and gauge observations, these large mean reflectivity differences are likely an indication that RCMK and RCCK are miscalibrated. The miscalibration would result in an underestimation of rainfall intensity if an *R–Z* relation were used to derive rainfall estimation from these two radars.

The statistical RRCT results from (a) RCMK and (b) RCCK. The 12-h data from 0000 to 1200 UTC 9 Aug 2009 are used in this analysis. The time series reflectivity differences between RCCG and RCMK and between RCCG and RCCK are depicted as dots, and 12-h mean differences are depicted as solid lines. Std dev values

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The statistical RRCT results from (a) RCMK and (b) RCCK. The 12-h data from 0000 to 1200 UTC 9 Aug 2009 are used in this analysis. The time series reflectivity differences between RCCG and RCMK and between RCCG and RCCK are depicted as dots, and 12-h mean differences are depicted as solid lines. Std dev values

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The statistical RRCT results from (a) RCMK and (b) RCCK. The 12-h data from 0000 to 1200 UTC 9 Aug 2009 are used in this analysis. The time series reflectivity differences between RCCG and RCMK and between RCCG and RCCK are depicted as dots, and 12-h mean differences are depicted as solid lines. Std dev values

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The raw

## 3. Rainfall rate estimation with specific attenuation

### a. The R(A) algorithm

*A*derived using the ZPHI method (e.g., Testud et al. 2000), and the rainfall rate is estimated as (Ryzhkov et al. 2014)

*R*(

*A*) methodology has many advantages compared to the methods based on

*Z*,

*Z*

_{DR}, or

*K*

_{DP}because it is immune to radar miscalibration, attenuation, partial beam blockage, and impact of wet radome (Ryzhkov et al. 2014). The radial profile of

*A*is obtained by using measured

*Z*and total span of

*r*

_{1}and

*r*

_{2}along the radar beam as follows (Bringi et al. 1990; Testud et al. 2000; Ryzhkov et al. 2014):

*β*is the exponent in the

*A–Z*relation. It should be noted that

*Z*

_{a}in Eq. (2) is what is directly measured and not corrected for possible miscalibration and attenuation. The typical value of

^{−1}(Ryzhkov et al. 2014), but the optimal value of

### b. Taiwan DSD and DSR features and their impact on the R(A) algorithm

The coefficients

The DSD characteristics in Taiwan were investigated using data collected by four impact-type Joss–Waldvogel disdrometers (JWDs) shown in Fig. 1. Raindrop concentrations within the size range of 0.359–5.373 mm are measured in 20 size bins and with a temporal resolution of 1 min. There is a total of 7920 min of DSD data used in this study, including precipitation in typhoon systems in August 2011 and convective precipitation in May 2011. The forward scattering amplitudes [*f*_{a,b}(0)] at a temperature of 20°C were calculated with the T-matrix method (Waterman 1971). The *K*_{DP} and specific attenuation (*A*) are calculated using formulas proposed by Zhang et al. (2001). The optimal value of the factor ^{−1} is obtained using a linear least squares fit approach with simulated *K*_{DP} and *A* for *λ* = 5.3 cm (Fig. 4). It should be noted that the estimated ^{−1}; Ryzhkov et al. 2014]. Larger values of

Scatterplot of calculated *A* and *K*_{DP} using the T-matrix method at 20°C. DSD data from four JWDs: National Central University (NCU), Feitsui, Hsiayun, and Nankang are used in the calculation of *A* and *K*_{DP}, and the coefficient ^{−1} was obtained through a linear least squares fit approach.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Scatterplot of calculated *A* and *K*_{DP} using the T-matrix method at 20°C. DSD data from four JWDs: National Central University (NCU), Feitsui, Hsiayun, and Nankang are used in the calculation of *A* and *K*_{DP}, and the coefficient ^{−1} was obtained through a linear least squares fit approach.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Scatterplot of calculated *A* and *K*_{DP} using the T-matrix method at 20°C. DSD data from four JWDs: National Central University (NCU), Feitsui, Hsiayun, and Nankang are used in the calculation of *A* and *K*_{DP}, and the coefficient ^{−1} was obtained through a linear least squares fit approach.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The optimal intercept *R*(*A*) algorithm with the newly determined intercept will be evaluated in section 4.

### c. Temperature impact on the performance of the R(A) algorithm

*A*and factor

*R*(

*A*) relation increases with temperature (Ryzhkov et al. 2014). The temperature dependencies of these two variables may tend to balance each other in the resulting estimate of rainfall rate from the

*R*(

*A*) method, and the overall impact of temperature may be quite limited and can be probably ignored. Therefore, one pair of fixed values of

*R*(

*A*) algorithm, and the result is expected to be close to the rainfall estimate assuming

^{−1}below the melting layer. The corresponding radar reflectivity factor

*Z*was computed using the

*Z*–

*R*relationship optimized for Taiwan (W.-Y. Chang et al. 2009):

*K*

_{DP}and specific attenuation

*A*were obtained from assumed rain rate using the equations

*T*is temperature (°C) assuming a temperature lapse rate of 6.5°C km

^{−1}. Equations (5) and (6) are found to be optimal for typhoons in Taiwan (Wang et al. 2013). Equation (7) was derived using the same approach as described in section 3b at different temperatures. It is assumed that “true” rain rate decreases with height in such a way that the vertical gradient of

*Z*is equal to 1.7 dB km

^{−1}, which is a typical value of the gradient in typhoons in Taiwan (Wang et al. 2013).

*R*(

*A*) procedure with a temperature-dependent

*Z*and differential phase

*Z*(

*R*),

*A*(

*R*,

*T*), and

*K*

_{DP}(

*R*). A two-way path-integrated attenuation is estimated as an integral:

*A*is retrieved from attenuated

*Z*and PIA, it is converted to the rain rate using Eq. (7). Under the second scenario, the dependencies of

^{−1}and

*Z*. Vertical cross sections of the model (true) rain rate, the rain-rate estimate from

*R*(

*A*) with temperature-dependent coefficients

^{−1}(296) and 0.135 dB (°)

^{−1}(262) at 11° and 2°C, and these values are apparently different from the ones obtained at 20°C (Fig. 6b) However, the estimated rainfall rates from both versions of the

*R*(

*A*) algorithm are close to the model rainfall rate. Henceforth, we will use the

*R*(

*A*) algorithm with fixed parameters

(a) The model rainfall field estimated using ^{−1}. The rainfall rate estimated from the *R*(*A*) algorithm with (b) temperature-dependent and (c) fixed coefficients

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

(a) The model rainfall field estimated using ^{−1}. The rainfall rate estimated from the *R*(*A*) algorithm with (b) temperature-dependent and (c) fixed coefficients

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

(a) The model rainfall field estimated using ^{−1}. The rainfall rate estimated from the *R*(*A*) algorithm with (b) temperature-dependent and (c) fixed coefficients

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

(a) The comparison results from second tilt *R*(*A*) with temperature-dependent coefficients, and results from *R*(*A*) with fixed coefficients are denoted as *R*, *R*(*A*,*T*), and *R*(*A*), respectively. (b) The dependence of *T* based on the simulation results.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

(a) The comparison results from second tilt *R*(*A*) with temperature-dependent coefficients, and results from *R*(*A*) with fixed coefficients are denoted as *R*, *R*(*A*,*T*), and *R*(*A*), respectively. (b) The dependence of *T* based on the simulation results.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

(a) The comparison results from second tilt *R*(*A*) with temperature-dependent coefficients, and results from *R*(*A*) with fixed coefficients are denoted as *R*, *R*(*A*,*T*), and *R*(*A*), respectively. (b) The dependence of *T* based on the simulation results.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

### d. Correction of vertical profiles of rainfall using the R(A) method

In radar-based QPE, radar measurements at higher tilts can be used for rainfall rate estimation when radar beams at the lowest tilt are severely blocked. The vertical variations in radar measurements such as *Z* and *K*_{DP} and derived *A* need to be taken into account for accurate rainfall estimation at the surface. The methods of VPR and VPSDP correction were therefore developed and implemented for rainfall rate estimation based on *Z* and *K*_{DP} (e.g., Andrieu and Creutin 1995; Marzano et al. 2004; Zhang et al. 2008a; Wang et al. 2013). Although the *K*_{DP}- or *A*-based estimates of rain are immune to partial beam blockage, they are not useful if the blockage is too severe and the radar signal is entirely lost. Because of the severe beam blockage by CMR illustrated in Fig. 1, the reliable measurements of *A* at the lowest tilt may become unavailable. Therefore, measurements of *A* at higher tilts are used to fill the gaps, and the vertical variations in the estimated rainfall rate should be taken into account.

*R*(

*A*)–VPRA correction was developed to correct the vertical variations in the rainfall field. The new approach consists of two steps: generating the vertical profiles of rainfall field and correcting for vertical variations in the higher-tilt

*R*(

*A*) field. The VPRA is derived similar to the VPR approach proposed by Zhang et al. (2008a). In the VPRA derivation, the rainfall fields estimated with

*R*(

*A*) approach from all unblocked tilts (within the range between 20 and 80 km) are first grouped into evenly spaced vertical layers according to the central height of the bins. Within each layer (default depth of 200 m), the mean and standard deviation of all the

*R*(

*A*) values are computed. The vertical profile of

*R*(

*A*) is therefore derived with the mean

*R*(

*A*) value for each layer. Because the ZPHI estimate of

*A*is only valid for pure rain, the VPRA is only derived below the melting layer (approximately 5.5 km in the current study). An example of the derived VPRA is presented in Fig. 7, where the

*x*axis represents the mean rainfall rate [

*R*(

*A*)] and the

*y*axis represents the height above radar level (ARL). If

*k*

_{1}) is totally blocked and the

*k*

_{2}) is then used in the rainfall rate estimation, and the correction for the vertical profile of

*R*(

*A*) is performed according to the equation

_{1}and VPRA

_{2}are the vertical profiles of

*R*(

*A*) values at heights

*H*

_{1}and

*H*

_{2}, respectively. In this work, the vertical profile of

*R*(

*A*) is obtained after averaging of 1 h of data, and the VPRA correction is applied in real time. The performance of VPRA correction is further evaluated using real precipitation cases in section 4.

The vertical profile of the rainfall estimated from the *R*(*A*) algorithm (VPRA). Variables VPRA_{1} and VPRA_{2} are 1-h mean rain-rate estimates from the *R*(*A*) algorithm at the heights *H*_{1} and *H*_{2}, respectively.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The vertical profile of the rainfall estimated from the *R*(*A*) algorithm (VPRA). Variables VPRA_{1} and VPRA_{2} are 1-h mean rain-rate estimates from the *R*(*A*) algorithm at the heights *H*_{1} and *H*_{2}, respectively.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The vertical profile of the rainfall estimated from the *R*(*A*) algorithm (VPRA). Variables VPRA_{1} and VPRA_{2} are 1-h mean rain-rate estimates from the *R*(*A*) algorithm at the heights *H*_{1} and *H*_{2}, respectively.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

## 4. QPE performance evaluation

The performance of the *R*(*A*) and VPRA correction approach was evaluated for precipitation events in Taiwan during 2009 and 2011. These precipitation events include two typhoon events, Morakot (August 2009) and Nanmadol (August 2011), and a mixture of stratiform and convective precipitation events (July 2011). In the current work, the stratiform, convective, and typhoon precipitations were segregated based on the vertical structure of the reflectivity (Xu et al. 2008; Zhang et al. 2008a). Generally, a radar bin column is identified as convective if reflectivity at any height in the column is greater than 50 dB*Z* or if a reflectivity is greater than 30 dB*Z* at −10°C height or above (Zhang et al. 2008a). Classified as tropical precipitation, a typhoon system generally produces significantly heavier rainfall than stratiform and convective systems with the same reflectivity (Xu et al. 2008). The tropical precipitation is identified through examining the VPR characteristics. Two classes of VPR structures are considered to be tropical VPRs: 1) the reflectivity monotonically increases as the height decreases with a maximum at the lowest level and 2) the reflectivity increases or remains constant with the decrease in height below the bottom of the bright band (Xu et al. 2008). Usually, different rainfall estimators will be selected for different precipitation types. There are three questions we want to address through these experiments:

Is the newly derived

*α*–*γ*pair more appropriate for precipitation events in Taiwan than the*α*–*γ*pair derived previously for continental precipitations, and how much it can improve the accuracy of the estimated rainfall?Does the VPRA correction improve the accuracy of radar QPE? and

Can the

*R*(*A*) approach provide more robust and accurate rainfall estimation compared to other rainfall rate estimators such as*R*–*Z*and*R*–*K*_{DP}?

In each experiment, the hybrid-scan rainfall rate fields from individual radar were computed on polar grids. These fields were remapped onto a common Cartesian grid via a nearest neighbor approach and then merged into one regional/national rain-rate field using an inverse distance weighted mean scheme (Zhang et al. 2008b). The mosaicked accumulation was calculated and compared with gauge (as shown in Fig. 1) observations. The QPE performance was assessed using three scores: 1) the mean bias *R*_{p} and *G*_{p} are the 24-h radar and gauge accumulated rainfall for each pair *p*, and

### a. Impact of the choice of and on rainfall estimation

The impact of the coefficients *A* fields were first calculated using Eqs. (2)–(4), with ^{−1}, respectively. Rainfall rates were then estimated using Eq. (1), with *α*–*γ* pairs, only the radar–gauge pairs from the plain region (with gauge height below 500 m) were used in this evaluation.

Scatterplots of radar QPE vs gauge observations for typhoon precipitation. The coefficients are (a) ^{−1}, ^{−1}, ^{−1},

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Scatterplots of radar QPE vs gauge observations for typhoon precipitation. The coefficients are (a) ^{−1}, ^{−1}, ^{−1},

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Scatterplots of radar QPE vs gauge observations for typhoon precipitation. The coefficients are (a) ^{−1}, ^{−1}, ^{−1},

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The evaluation results for different values of *α* and *γ*.

It was found that the *R*(*A*) algorithm underestimates rain relative to gauge measurements in Expt I (MB = 0.59) and Expt II (MB = 0.76), and significant improvements were obtained in Expt III (MB = 1.07). The reason is the coefficients in Expt I and Expt II are derived based on the DSD and DSR observed in mostly continental precipitation, where DSD is generally different than in tropical rain and where raindrops are likely more oblate than the raindrops from typhoon precipitations in Taiwan (W.-Y. Chang et al. 2009). For the same rainfall rate, a lower radar reflectivity factor *Z* and lower differential phase ^{−1} and

The sensitivity of the *α*–*γ* pair to different precipitation types in Taiwan was also investigated using 24 h of precipitation that is characterized as a mixture of stratiform and convective rain (0000–2400 UTC 18 July 2011). The comparison results are presented in Fig. 9, and the scores are also included in Table 2. Similar to the results from the typhoon precipitation, rainfall underestimation was found in Expt I (MB = 0.56, RMSE = 25.63 mm, CC = 0.89), and Expt II (MB = 0.72, RMSE = 20.67 mm, CC = 0.89). The underestimation bias is significantly reduced if ^{−1} and *R*(*A*) algorithm (MB = 0.97, RMSE = 15.90 mm, CC = 0.90).

As in Fig. 8, but for the mixture of stratiform and convective precipitation (~0000–2400 UTC 18 Jul 2011).

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

As in Fig. 8, but for the mixture of stratiform and convective precipitation (~0000–2400 UTC 18 Jul 2011).

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

As in Fig. 8, but for the mixture of stratiform and convective precipitation (~0000–2400 UTC 18 Jul 2011).

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

### b. Performance of the VPRA correction

The VPRA is introduced and analyzed in section 3, and a clear trend of decreasing *R*(*A*) with height is shown in Fig. 7. In this section, two experiments (Expt IV and Expt V) were used to assess the performance of the VPRA correction in Taiwan. In Expt IV, the higher-tilt *A* field was directly utilized in the rainfall rate estimation when the lowest-tilt *A* is unavailable (mainly from the CMR region), and in Expt V, the higher-tilt *A* field was used in the *R*(*A*) relation and the obtained rainfall rate field was further corrected with the VPRA approach, as formulated in section 3c. The same dataset as in section 4a was utilized in this evaluation. Figure 10 shows an example of the spatial distribution of the radar QPE bias ratio without (Fig. 10a) and with (Fig. 10b) VPRA correction. In this example, 24-h data from typhoon Morakot (0000–2400 UTC 9 August 2009) were used. The size of the circles represents gauge-observed 24-h rainfall amounts and the color of the circles indicates the bias of radar QPE. White color represents a ratio between radar QPE and gauge measurement of 1.0 or no bias, orange color represents less than 1.0 or underestimation, and blue color represents greater than 1.0 or overestimation. Apparent underestimation is found along the CMR (within the white ellipse) in Expt IV (Fig. 10a), and the underestimation is significantly mitigated after the higher-tilt rainfall field is corrected using VPRA correction in Expt V (Fig. 10b). Compared to Expt IV, Expt V provides improvements of 41% in MB (0.89 versus 0.63), 11% in CC (0.93 versus 0.84), and 26% in RMSE (109 versus 148 mm). As indicated in Fig. 7, the apparent negative slope of the vertical profile could be found in the mean *R*(*A*) field when the height is below 4 km, and similar VPRA were also found at other times in this experiment. It implies that the rainfall rate increases as altitude decreases, and this may be caused by the orographic enhancement of the precipitation typical for the areas with complex terrain. Similar phenomena are also observed and reported in the precipitation in California (Zhang et al. 2012).

The spatial distribution of the radar QPE vs gauge observations (a) without and (b) with VPRA correction. The 24-h accumulated precipitation from typhoon Morakot (~0000–2400 UTC 9 Aug 2009) is used in this experiment. The size of the circles represents gauge-observed accumulated amount, and the color of the circles indicates the bias (QPE–Gauge). There are 123 gauges (within white circle) selected in this comparison. The underestimations (indicated by warm colors) within the white ellipse are significantly mitigated (indicated by white color) with the proposed VPRA approach.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The spatial distribution of the radar QPE vs gauge observations (a) without and (b) with VPRA correction. The 24-h accumulated precipitation from typhoon Morakot (~0000–2400 UTC 9 Aug 2009) is used in this experiment. The size of the circles represents gauge-observed accumulated amount, and the color of the circles indicates the bias (QPE–Gauge). There are 123 gauges (within white circle) selected in this comparison. The underestimations (indicated by warm colors) within the white ellipse are significantly mitigated (indicated by white color) with the proposed VPRA approach.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The spatial distribution of the radar QPE vs gauge observations (a) without and (b) with VPRA correction. The 24-h accumulated precipitation from typhoon Morakot (~0000–2400 UTC 9 Aug 2009) is used in this experiment. The size of the circles represents gauge-observed accumulated amount, and the color of the circles indicates the bias (QPE–Gauge). There are 123 gauges (within white circle) selected in this comparison. The underestimations (indicated by warm colors) within the white ellipse are significantly mitigated (indicated by white color) with the proposed VPRA approach.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The scatterplots of the radar QPE versus gauge measurements are displayed in Fig. 11 for the typhoon precipitation (Figs. 11a,b) and the mixture of stratiform and convective precipitation (Figs. 11c,d). For the mixture of stratiform and convective, although the maximum accumulation (200 mm) is much smaller than the typhoon precipitation (1500 mm), the enhancements of VPRA on QPE are still significant on MB (70%) and RMSE (34%). The comparison scores are listed in Table 3. Since the VPRA correction mainly applied in the region along the CMR region with altitude above 500 m, only those radar–gauge pairs with a gauge height above 500 m are examined in this evaluation. Compared to gauge observations, it was found that for both cases, Expt V yields smaller RMSE and closer to one CC and MB compared to Expt IV.

Scatterplots of radar QPE vs gauge observations for (a),(b) typhoon and (c),(d) a mixture of stratiform and convective precipitation. The results with (left) and without (right) VPRA correction are presented. The QPE–gauge pairs are mainly from the CMR and the gauge heights are >500 m ARL. The evaluation results in terms of MB, CC, and RMSE are also included.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Scatterplots of radar QPE vs gauge observations for (a),(b) typhoon and (c),(d) a mixture of stratiform and convective precipitation. The results with (left) and without (right) VPRA correction are presented. The QPE–gauge pairs are mainly from the CMR and the gauge heights are >500 m ARL. The evaluation results in terms of MB, CC, and RMSE are also included.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Scatterplots of radar QPE vs gauge observations for (a),(b) typhoon and (c),(d) a mixture of stratiform and convective precipitation. The results with (left) and without (right) VPRA correction are presented. The QPE–gauge pairs are mainly from the CMR and the gauge heights are >500 m ARL. The evaluation results in terms of MB, CC, and RMSE are also included.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The evaluation results for the vertical profile correction approach.

### c. Comparison between the R(A) approach and other rainfall estimators

The performance of the *R*(*A*) relationship with the VPRA correction approach was further compared with two other estimators: *R*–*Z* estimator, *Z* has been corrected for miscalibration and attenuation, as described in section 2a. When a radar beam at the lowest tilt is severely blocked, the VPSDP-based corrections and VPR corrections were applied following these two approaches to correct for the vertical variations in *K*_{DP} and *Z* fields, respectively (Wang et al. 2013). The comparison between the *R*(*A*), *R*–*K*_{DP}, and *R*–*Z* estimates is illustrated in Figs. 12 (typhoon event) and 13 (stratiform–convective events). The scores of MB, CC, and RMSE are shown in Table 4.

Scatterplots of QPE vs gauge observations using (a) *R* = 359*A*^{0.89}, (b) *R* = 207*Z*^{1.45}, and (c)

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Scatterplots of QPE vs gauge observations using (a) *R* = 359*A*^{0.89}, (b) *R* = 207*Z*^{1.45}, and (c)

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Scatterplots of QPE vs gauge observations using (a) *R* = 359*A*^{0.89}, (b) *R* = 207*Z*^{1.45}, and (c)

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Scatterplots of QPE vs gauge observations using (a) *R* = 359*A*^{0.89}, (b) *R* = 207*Z*^{1.45}, and (c)

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Scatterplots of QPE vs gauge observations using (a) *R* = 359*A*^{0.89}, (b) *R* = 207*Z*^{1.45}, and (c)

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Scatterplots of QPE vs gauge observations using (a) *R* = 359*A*^{0.89}, (b) *R* = 207*Z*^{1.45}, and (c)

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The evaluation results for the *R*(*A*), *R*–*Z*, and *R*–*K*_{DP} algorithms. The VPRA, VPR, and VPSDP corrections have been applied in the rainfall rate estimation.

In both typhoon and stratiform–convective events, the *R*(*A*) algorithm produced the most accurate estimation among the three estimators. For heavy rain, where *Z* might be significantly biased because of attenuation, its linear correction based on Eq. (4) is efficient and results in accurate rainfall estimation. The *R*(*A*)–VPRA approach can produce close to unit mean bias and correlation coefficient, and low RMSE. For light rain, where the *K*_{DP} field can be noisy and erratic, the radar reflectivity *Z* can still be used to provide optimal rainfall rate estimation (MB = 0.95, CC = 0.89, and RMSE = 21 mm) in the framework of the *R*(*A*) method (Ryzhkov et al. 2014). For C-band radar, the *R*–*K*_{DP} relation is more appropriate for heavier rain while the *R*–*Z* relationship works better for lighter rain. The reasons for underestimation of rain with *R*–*Z* may include the impact of the DSD variability and insufficient compensation of negative *Z* biases caused by attenuation and/or partial beam blockage. For these two cases, the *R*–*K*_{DP} estimate matches the gauges well when the precipitation is significant but overestimated the rainfall when the precipitation is light.

To further examine the quality of hourly total estimation by each method, the hourly radar QPEs and gauge observations were compared. Five QPE–gauge pairs are selected in this example, and their spatial distribution is shown in Fig. 14. The results of their comparison are presented in Fig. 15. The distances from these five gauges to RCMK are 69 (C1X090), 89 (467410), 109 (C1V410), 130 (C1R210), and 152 km (C1R240). The distance between two adjacent gauges is approximately 20 km. The 24-h accumulations observed by each gauge are 42 (C1X090), 89.5 (467410), 105.50 (C1V410), 96.5 (C1R210), and 61 mm (C1R240). Generally, the *R*(*A*) approach shows the best performance compared to *R*–*Z* and *R*–*K*_{DP} approaches, and the hourly QPE from *R*(*A*) (red line) approximately matches the gauge observation (black line). Although the *R*–*K*_{DP} approach can produce a good estimation for relative heavy rain (*R* > 5 mm h^{−1}), it may overestimate relatively light rain (*R* < 5 mm h^{−1}). For example, between 1000 and 1500 UTC (0500–1000 UTC), the accumulated precipitation estimated from *R*–*K*_{DP} is obvious larger than gauge C1X090 (467410) observation. On the other hand, the *R*–*Z* approach generally provides accurate estimation for relatively light rain (e.g., 0800–1300 UTC for gauge C1V410, 0800–2000 UTC or gauge C1R210), but significant underestimations result from the *R*–*Z* approach for relatively heavy rain (e.g., 2000–2400 UTC for gauge C1R210, and 2000–2400 UTC for gauge C1R240).

The spatial distribution of gauge observations vs radar-based QPEs from 24-h accumulation (0000–2400 UTC 18 Jul 2011). The relation of *R* = 359*A*^{0.89} is used in the rainfall rate estimation. The hourly performances from five gauges are examined and the results are presented in Fig. 15. The locations of these five gauges are indicated with black stars.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The spatial distribution of gauge observations vs radar-based QPEs from 24-h accumulation (0000–2400 UTC 18 Jul 2011). The relation of *R* = 359*A*^{0.89} is used in the rainfall rate estimation. The hourly performances from five gauges are examined and the results are presented in Fig. 15. The locations of these five gauges are indicated with black stars.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

The spatial distribution of gauge observations vs radar-based QPEs from 24-h accumulation (0000–2400 UTC 18 Jul 2011). The relation of *R* = 359*A*^{0.89} is used in the rainfall rate estimation. The hourly performances from five gauges are examined and the results are presented in Fig. 15. The locations of these five gauges are indicated with black stars.

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Hourly accumulation comparison between gauge observations and QPE using *R* = 359*A*^{0.89} (red line), *R* = 207*Z*^{1.45} (green line), and

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Hourly accumulation comparison between gauge observations and QPE using *R* = 359*A*^{0.89} (red line), *R* = 207*Z*^{1.45} (green line), and

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

Hourly accumulation comparison between gauge observations and QPE using *R* = 359*A*^{0.89} (red line), *R* = 207*Z*^{1.45} (green line), and

Citation: Journal of Hydrometeorology 15, 6; 10.1175/JHM-D-14-0003.1

## 5. Summary

To obtain accurate QPE products for the purpose of flood monitoring/prediction and water resource management, a new quantitative precipitation estimation approach based on the specific radar attenuation *A* was developed for two C-band polarimetric radars in Taiwan. The new QPE scheme was based on the formulations in Ryzhkov et al. (2014) but with different parameters that were optimized for Taiwan using local DSD and DSR observations. Furthermore, a vertical profile of rainfall rate from *R*(*A*) correction methodology was developed. At C band, the intercept *R*(*A*) relation as well as the net ratio ^{−1} and *R*(*A*) algorithm with fixed factors *A* fields from low tilts become unavailable or unreliable in the Central Mountain Range region, and the *A* fields from higher tilts need to be used for the surface rainfall estimation. Because of vertical variations of rainfall rates, the *R*(*A*) estimates obtained from the higher tilts may not match rainfall observed at the ground even if the *R*(*A*) relationship is accurate. For better estimation of the ground rainfall rate using higher-tilt *A* values, a VPRA correction approach was developed, in which a mean vertical profile of rainfall rate was computed in the unblocked region. The estimates of rain at higher-tilt *A* field in the blocked region are adjusted based on the mean VPRA to a lower reference altitude for QPE. The newly developed *R*(*A*) scheme was validated for different precipitation events including typhoons and the mixture of stratiform and convective rain. Based on these evaluations, the following conclusions can be drawn: 1) the newly derived coefficients *R*(*A*) algorithm are more appropriate for rainfall estimation in Taiwan for various precipitation types than the previously derived coefficients that are mostly valid for continental rain; 2) the underestimation along the CMR could be significantly mitigated with the newly developed VPRA correction approach; and 3) in comparison with conventional rainfall rate estimators such as *R*–*Z* (with VPR correction) and *R*–*K*_{DP} (with VPSDP correction), the *R*(*A*) algorithm with adjusted parameters and the VPRA correction could produce more accurate and robust rainfall rate estimation. It should be noted that this is the first validation study of the *R*(*A*) method in tropical rain at C band, and more studies and validations are expected in the future.

## Acknowledgments

This research is supported by funding from the Central Weather Bureau of Taiwan, Republic of China, and was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA110AR4320072, U.S. Department of Commerce. Authors would like to thank Dr. Lin Tang provided many helpful comments and that greatly improved the manuscript.

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