Utilization of Specific Attenuation for Tropical Rainfall Estimation in Complex Terrain

Yadong Wang Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma

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Pengfei Zhang Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma

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Alexander V. Ryzhkov Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma

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Jian Zhang NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma

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Pao-Liang Chang Central Weather Bureau, Taipei, Taiwan

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Abstract

To improve the accuracy of quantitative precipitation estimation (QPE) in complex terrain, a new rainfall rate estimation algorithm has been developed and applied on two C-band dual-polarization radars in Taiwan. In this algorithm, the specific attenuation A is utilized in the rainfall rate R estimation, and the parameters used in the R(A) method were estimated using the local drop size distribution (DSD) and drop shape relation (DSR) observations. In areas of complex terrain where the lowest antenna tilt is completely blocked, observations from higher tilts are used in radar QPE. Correction of the vertical profile of rain rate estimated by the R(A) algorithm (VPRA) is applied to account for the vertical variability of rain. It has been found that the VPRA correction improved the accuracy of estimated rainfall in severely blocked areas. The R(A)–VPRA scheme was tested for different precipitation cases including typhoon, stratiform, and convective rain. Compared to existing rainfall estimation algorithms such as rainfall–reflectivity (RZ) and rainfall–specific differential phase (RKDP), the new method is able to provide accurate and robust rainfall estimates when the radar reflectivity is miscalibrated or significantly biased by attenuation or when the lower tilt of the radar beam is significantly blocked.

Corresponding author address: Yadong Wang, CIMMS, 120 David L. Boren Dr., Norman, OK 73072. E-mail: yadong.wang@noaa.gov

Abstract

To improve the accuracy of quantitative precipitation estimation (QPE) in complex terrain, a new rainfall rate estimation algorithm has been developed and applied on two C-band dual-polarization radars in Taiwan. In this algorithm, the specific attenuation A is utilized in the rainfall rate R estimation, and the parameters used in the R(A) method were estimated using the local drop size distribution (DSD) and drop shape relation (DSR) observations. In areas of complex terrain where the lowest antenna tilt is completely blocked, observations from higher tilts are used in radar QPE. Correction of the vertical profile of rain rate estimated by the R(A) algorithm (VPRA) is applied to account for the vertical variability of rain. It has been found that the VPRA correction improved the accuracy of estimated rainfall in severely blocked areas. The R(A)–VPRA scheme was tested for different precipitation cases including typhoon, stratiform, and convective rain. Compared to existing rainfall estimation algorithms such as rainfall–reflectivity (RZ) and rainfall–specific differential phase (RKDP), the new method is able to provide accurate and robust rainfall estimates when the radar reflectivity is miscalibrated or significantly biased by attenuation or when the lower tilt of the radar beam is significantly blocked.

Corresponding author address: Yadong Wang, CIMMS, 120 David L. Boren Dr., Norman, OK 73072. E-mail: yadong.wang@noaa.gov

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 ZDR, and specific differential phase KDP 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 ZDR 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 ZDR 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 KDP, 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 RKDP estimates are increasingly noisy for lighter rain and their radial resolution is generally poorer than the ones obtained from Z and ZDR (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 RKDP 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 along the propagation path, which is used to convert total span of differential phase to PIA. It is instrumental to climatologically tune the factor using a regional statistic of DSD and the raindrop diameter–shape relations (DSR). Ryzhkov et al. (2014) showed that the parameters of the 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 KDP 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 KDP 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.

Fig. 1.
Fig. 1.

The locations of the C-band dual-polarization radars (marked with red squares), S-band RCCG single-polarization radars (marked with cyan squares), JWDs (marked with green asterisks), and the gauge network (marked with small white asterisks) used in the current study.

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

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 and the coefficients in the power-law 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.

Table 1.

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

Table 1.

Accurate absolute calibration of Z and ZDR 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 (e.g., Jameson 1992; Carey et al. 2000; Testud et al. 2000; Park et al. 2005), obviously lower values of Z are still found compared to RCCG, and the inadequate absolute calibration could be the reason.

Fig. 2.
Fig. 2.

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.

Fig. 3.
Fig. 3.

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 are also calculated and included.

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

The raw fields of RCMK and RCCK were processed with the new Selex–Gematronik family of digital receiver and signal processor (GDRX; Bringi et al. 2005). The GDRX processes the raw field using the field unwrapping, “good data” mask application, and finite impulse response (FIR) filtering. The details of the procedure could be found in Bringi et al. (2005). After the raw field was processed by the GDRX, linear interpolation, smoothing, and missing data filling were applied on the field.

3. Rainfall rate estimation with specific attenuation

a. The R(A) algorithm

Ryzhkov et al. (2014) proposed a novel rainfall rate estimation technique that directly utilizes the specific attenuation A derived using the ZPHI method (e.g., Testud et al. 2000), and the rainfall rate is estimated as (Ryzhkov et al. 2014)
e1
where the coefficients and depend on radar wavelength, temperature, and polarization. It was found that the R(A) methodology has many advantages compared to the methods based on Z, ZDR, or KDP 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 between ranges r1 and r2 along the radar beam as follows (Bringi et al. 1990; Testud et al. 2000; Ryzhkov et al. 2014):
e2
e3
and
e4
where and and β is the exponent in the A–Z relation. It should be noted that Za in Eq. (2) is what is directly measured and not corrected for possible miscalibration and attenuation. The typical value of at C band for continental rain is about 0.06–0.08 dB (°)−1 (Ryzhkov et al. 2014), but the optimal value of for subtropical islands is not well established. As mentioned before, the coefficients and in Eq. (1) are also affected by the precipitation type, and the intercept is generally larger for tropical than for continental rain. Herein, the optimal values of the coefficients , , and are derived based on the local DSD and DSR measurements in Taiwan as discussed in section 3b.

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

The coefficients , , and in Eqs. (1) and (4) depend on the DSD and DSR characteristics. Optimal coefficients for precipitation in Taiwan have to be derived based on the local DSD and DSR measurements. In this work, the used DSR is based on the study of W.-Y. Chang et al. (2009), which was obtained through the observations of 12 typhoon events in Taiwan. It was found that two factors affect the drop shape relation of raindrops in a typhoon system: the horizontal wind velocity and the rainfall intensity. Generally, the horizontal wind velocity was the major factor of influence for the DSRs, and the raindrops within typhoon precipitation in Taiwan are more spherical than the raindrops from typical maritime or continental precipitation systems. This unique feature can be caused by the terrain influences on the precipitation formation (W.-Y. Chang et al. 2009).

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 [fa,b(0)] at a temperature of 20°C were calculated with the T-matrix method (Waterman 1971). The KDP and specific attenuation (A) are calculated using formulas proposed by Zhang et al. (2001). The optimal value of the factor dB (°)−1 is obtained using a linear least squares fit approach with simulated KDP and A for λ = 5.3 cm (Fig. 4). It should be noted that the estimated is larger than the values generally used for continental rain [within 0.06–0.08 dB (°)−1; Ryzhkov et al. 2014]. Larger values of would result in higher rain-rate estimates for the same radial profiles of reflectivity and differential phase.

Fig. 4.
Fig. 4.

Scatterplot of calculated A and KDP 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 KDP, and the coefficient dB (°)−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 and exponent in Eq. (1) are found to be 359 and 0.88, respectively. The intercept value is significantly higher than derived by Ryzhkov et al. (2014) at 20°C for the Oklahoma DSD dataset, but exponent turns out to be almost the same ( = 0.89). This indicates that the precipitation type mainly affects , and its impact on is negligible. The performance of the 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

The specific attenuation A and factor decrease with increasing temperature, but the intercept in the 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 and could be used in the R(A) algorithm, and the result is expected to be close to the rainfall estimate assuming and vary with temperature. To verify this assumption, we performed simulations at C band for a model of a horizontally uniform storm with rainfall rate depending only on the height above the surface. We assumed a temperature lapse rate of 6.5°C km−1 below the melting layer. The corresponding radar reflectivity factor Z was computed using the ZR relationship optimized for Taiwan (W.-Y. Chang et al. 2009):
e5
Intrinsic values of specific differential phase KDP and specific attenuation A were obtained from assumed rain rate using the equations
e6
and
e7
where 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).
Two simulation scenarios are considered. For the first scenario, we computed the rain rates using the R(A) procedure with a temperature-dependent and . Attenuated Z and differential phase at each gate are calculated using intrinsic values of Z(R), A(R, T), and KDP(R). A two-way path-integrated attenuation is estimated as an integral:
e8
where the factor is a function of slant range due to dependence on rain rate and temperature. After 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 and on temperature are ignored and the default values = 0.088 dB (°)−1 and = 359 are used. In the simulations, the surface temperature is 25°C and the maximal reflectivity is 40 dBZ. Vertical cross sections of the model (true) rain rate, the rain-rate estimate from R(A) with temperature-dependent coefficients and , and the rain-rate estimate with fixed (default) values of and are displayed in Figs. 5a–c, respectively. It was found that the estimation results using fixed and were similar to the results using temperature-dependent coefficients, and both of them are close to the model rainfall rate field. At each tilt, the biases of rain-rate estimate using fixed and are within 15% compared to “true” rain. Radial profiles of three rain rates at second and third tilts are also presented in Fig. 6a, where the temperature drops to approximately 11°C (second tilt) and 2°C (third tilt) at 85 km. Based on the simulation results, the values of are approximately 0.113 dB (°)−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 and in our further analysis.
Fig. 5.
Fig. 5.

(a) The model rainfall field estimated using from a horizontally uniform reflectivity field with a vertical gradient of 1.7 dB km−1. The rainfall rate estimated from the R(A) algorithm with (b) temperature-dependent and (c) fixed coefficients and .

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

Fig. 6.
Fig. 6.

(a) The comparison results from second tilt and third tilt , where the model rainfall rate, results from 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 and on temperature 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 KDP 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 KDP (e.g., Andrieu and Creutin 1995; Marzano et al. 2004; Zhang et al. 2008a; Wang et al. 2013). Although the KDP- 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.

In this study, a new vertical profile of rainfall from the 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 at the lowest tilt (k1) is totally blocked and the is unavailable, the higher tilt from the same azimuth and same range but a higher tilt (k2) is then used in the rainfall rate estimation, and the correction for the vertical profile of R(A) is performed according to the equation
e9
where VPRA1 and VPRA2 are the vertical profiles of R(A) values at heights H1 and H2, 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.
Fig. 7.
Fig. 7.

The vertical profile of the rainfall estimated from the R(A) algorithm (VPRA). Variables VPRA1 and VPRA2 are 1-h mean rain-rate estimates from the R(A) algorithm at the heights H1 and H2, 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 dBZ or if a reflectivity is greater than 30 dBZ 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:

  1. Is the newly derived αγ pair more appropriate for precipitation events in Taiwan than the αγ pair derived previously for continental precipitations, and how much it can improve the accuracy of the estimated rainfall?

  2. Does the VPRA correction improve the accuracy of radar QPE? and

  3. Can the R(A) approach provide more robust and accurate rainfall estimation compared to other rainfall rate estimators such as RZ and RKDP?

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 , 2) the root-mean-square error , and 3) the correlation coefficient , where angle brackets indicate the mean of the samples, Rp and Gp are the 24-h radar and gauge accumulated rainfall for each pair p, and is the standard deviation of all the radar (gauge) pairs.

a. Impact of the choice of and on rainfall estimation

The impact of the coefficients and on the rainfall rate estimation was first evaluated using 72-h data from typhoon precipitation (Morakot, 0000–2400 UTC 8–9 August 2009; Nanmadol, 0000–2400 UTC 30 August 2011). In the evaluation, the A fields were first calculated using Eqs. (2)(4), with equal to 0.06, 0.08, and 0.088 dB (°)−1, respectively. Rainfall rates were then estimated using Eq. (1), with for experiments I and II (Expt I and Expt II) and for experiment III (Expt III). The 24-h rainfall amounts were estimated and compared with gauge measurements. The results of comparisons are presented in Fig. 8. The evaluation scores of MB, RMSE, and CC are listed in Table 2. It should be noted that in the mountain region, the radar beam from the lowest elevation angle is significantly blocked, and the higher-tilt radar data are applied in the rainfall rate estimation. However, because of the DSD (DSR) variability in orographic regions, the estimated rainfall rate is less correlated to the ground gauge observation, and a vertical profile of rainfall rate correction is needed. To eliminate the contamination from ground clutter (blockage) and focus on the impact of αγ pairs, only the radar–gauge pairs from the plain region (with gauge height below 500 m) were used in this evaluation.

Fig. 8.
Fig. 8.

Scatterplots of radar QPE vs gauge observations for typhoon precipitation. The coefficients are (a) dB (°)−1, ; (b) dB (°)−1, ; and (c) dB (°)−1, . The QPE–gauge pairs are from the plain region with the gauge’s heights are below 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

Table 2.

The evaluation results for different values of α and γ.

Table 2.

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 are measured in typhoons compared to the typical continental rain. The coefficients dB (°)−1 and better reflect the characteristics of DSD and DSR of precipitation in Taiwan.

The sensitivity of the αγ 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 dB (°)−1 and were used in the R(A) algorithm (MB = 0.97, RMSE = 15.90 mm, CC = 0.90).

Fig. 9.
Fig. 9.

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).

Fig. 10.
Fig. 10.

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.

Fig. 11.
Fig. 11.

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

Table 3.

The evaluation results for the vertical profile correction approach.

Table 3.

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: and . The coefficients in these two estimators are obtained based on the DSR and DSD measurements from typhoon precipitations in Taiwan (Wang et al. 2013). In the RZ 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 KDP and Z fields, respectively (Wang et al. 2013). The comparison between the R(A), RKDP, and RZ 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.

Fig. 12.
Fig. 12.

Scatterplots of QPE vs gauge observations using (a) R = 359A0.89, (b) R = 207Z1.45, and (c) . Two typhoon rain events, Morakot (0000–2400 UTC 8–9 Aug 2009) and Nanmadol (0000–2400 UTC 30 Aug 2011), are summarized in this example. 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

Fig. 13.
Fig. 13.

Scatterplots of QPE vs gauge observations using (a) R = 359A0.89, (b) R = 207Z1.45, and (c) . The 48-h (~0000–2400 UTC 17–18 Jul 2011) precipitation classified as the mixture of stratiform and convective is used in this example. 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

Table 4.

The evaluation results for the R(A), RZ, and RKDP algorithms. The VPRA, VPR, and VPSDP corrections have been applied in the rainfall rate estimation.

Table 4.

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 KDP 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 RKDP relation is more appropriate for heavier rain while the RZ relationship works better for lighter rain. The reasons for underestimation of rain with RZ 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 RKDP 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 RZ and RKDP approaches, and the hourly QPE from R(A) (red line) approximately matches the gauge observation (black line). Although the RKDP 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 RKDP is obvious larger than gauge C1X090 (467410) observation. On the other hand, the RZ 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 RZ approach for relatively heavy rain (e.g., 2000–2400 UTC for gauge C1R210, and 2000–2400 UTC for gauge C1R240).

Fig. 14.
Fig. 14.

The spatial distribution of gauge observations vs radar-based QPEs from 24-h accumulation (0000–2400 UTC 18 Jul 2011). The relation of R = 359A0.89 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

Fig. 15.
Fig. 15.

Hourly accumulation comparison between gauge observations and QPE using R = 359A0.89 (red line), R = 207Z1.45 (green line), and (blue line). The gauge observation is depicted by the black line. The 24-h data from 0000 to 2400 UTC 18 Jul 2011 is used in this example.

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 in the R(A) relation as well as the net ratio are quite susceptible to the variability of DSD and DSR (for ), and these parameters have to be optimized using local DSD and DSR. The optimal values of and have been obtained via simulations using the DSD and DSR observations in Taiwan. The newly derived dB (°)−1 and are larger than the corresponding coefficients found to be optimal for continental precipitation. The use of “continental” coefficients would produce underestimation of tropical rain that is typical for Taiwan. It is also demonstrated that the temperature dependencies of and can be ignored and the R(A) algorithm with fixed factors and would produce rainfall estimates with mean bias and correlation coefficient error less than 10% (i.e., MB = 0.9–1.1, and CC > 0.9). Because of the severe beam blockages caused by high mountains, the 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 and in the 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 RZ (with VPR correction) and RKDP (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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  • Andrieu, H., and Creutin J. D. , 1995: Identification of vertical profiles of radar reflectivity for hydrological applications using an inverse method. Part I: Formulation. J. Appl. Meteor., 34, 225239, doi:10.1175/1520-0450(1995)034<0225:IOVPOR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Atlas, D., and Mossop S. C. , 1960: Calibration of a weather radar by using standard target. Bull. Amer. Meteor. Soc., 41, 377382.

  • Brandes, E. A., Zhang G. , and Vivekanandan J. , 2002: Experiments in rainfall estimation with a polarimetric radar in a subtropical environment. J. Appl. Meteor., 41, 674685, doi:10.1175/1520-0450(2002)041<0674:EIREWA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., Chandrasekar V. , Balakrishnan N. , and Zrnić D. S. , 1990: An example of propagation effects in rainfall on polarimetric variables at microwave frequencies. J. Atmos. Oceanic Technol., 7, 829840, doi:10.1175/1520-0426(1990)007<0829:AEOPEI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., Thurai M. , and Hannesen R. , 2005: Dual-Polarization Weather Radar Handbook. 2nd ed. Neuss, 163 pp.

  • Bringi, V. N., Rico-Ramirez M. A. , and Thurai M. , 2011: Rainfall estimation with an operational polarimetric C-band radar in the United Kingdom: Comparison with a gauge network and error analysis. J. Hydrometeor., 12, 935954, doi:10.1175/JHM-D-10-05013.1.

    • Search Google Scholar
    • Export Citation
  • Carey, L. D., Rutledge S. A. , Ahijevych D. A. , and Keenan T. D. , 2000: Correcting propagation effects in C-band polarimetric radar observations of tropical convection using differential propagation phase. J. Appl. Meteor., 39, 14051433, doi:10.1175/1520-0450(2000)039<1405:CPEICB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chang, P.-L., Lin P.-F. , Jou B. J.-D. , and Zhang J. , 2009: An application of reflectivity climatology in constructing radar hybrid scans over complex terrain. J. Atmos. Oceanic Technol., 26, 13151327, doi:10.1175/2009JTECHA1162.1.

    • Search Google Scholar
    • Export Citation
  • Chang, W.-Y., Wang T.-C. C. , and Lin P.-L. , 2009: Characteristics of the raindrop size distribution and drop shape relation in typhoon systems in the western Pacific from the 2D video disdrometer and NCU C-band polarimetric radar. J. Atmos. Oceanic Technol., 26, 19731993, doi:10.1175/2009JTECHA1236.1.

    • Search Google Scholar
    • Export Citation
  • Chisholm, J., 1963: Frequency shift reflector. U.S. Patent 3108275. [Available online at www.google.com/patents/US3108275.]

  • Gorgucci, E., Scarchilli G. , and Chandrasekar V. , 1992: Calibration of radars using polarimetric technique. IEEE Trans. Geosci. Remote Sens., 30, 853858, doi:10.1109/36.175319.

    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., Scarchilli G. , and Chandrasekar V. , 1999: A procedure to calibrate multiparameter weather radar using properties of the rain medium. IEEE Trans. Geosci. Remote Sens., 37, 269276, doi:10.1109/36.739161.

    • Search Google Scholar
    • Export Citation
  • Gourley, J. J., Illingworth A. J. , and Tabary P. , 2009: Absolute calibration of radar reflectivity using redundancy of the polarization observations and implied constraints on drop shapes. J. Atmos. Oceanic Technol., 26, 689703, doi:10.1175/2008JTECHA1152.1.

    • Search Google Scholar
    • Export Citation
  • Jameson, A. R., 1992: The effect of temperature on attenuation correction schemes in rain using polarization propagation differential phase shift. J. Appl. Meteor., 31, 11061118, doi:10.1175/1520-0450(1992)031<1106:TEOTOA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Joss, J., Thams J. C. , and Waldvogel A. , 1968: The accuracy of daily rainfall measurements by radar. Preprints, 13th Radar Meteorology Conf., Montreal, QC, Canada, Amer. Meteor. Soc., 448451.

  • Liou, Y.-C., and Chang Y.-J. , 2009: A variational multiple-Doppler radar three-dimensional wind synthesis method and its impacts on thermodynamic retrieval. Mon. Wea. Rev., 137, 39924010, doi:10.1175/2009MWR2980.1.

    • Search Google Scholar
    • Export Citation
  • Marzano, F. S., Vulpiani G. , and Picciotti E. , 2004: Rain field and reflectivity vertical profile reconstruction from C-band radar volumetric data. IEEE Trans. Geosci. Remote Sens., 42, 10331046, doi:10.1109/TGRS.2003.820313.

    • Search Google Scholar
    • Export Citation
  • Park, S. G., Maki M. , Iwanami K. , Bringi V. N. , and Chandrasekar V. , 2005: Correction of radar reflectivity and differential reflectivity for rain attenuation at X-band. Part II: Evaluation and application. J. Atmos. Oceanic Technol., 22, 16331655, doi:10.1175/JTECH1804.1.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., and Zrnić D. S. , 1995: Comparison of dual-polarization radar estimators of rain. J. Atmos. Oceanic Technol., 12, 249256, doi:10.1175/1520-0426(1995)012<0249:CODPRE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., Giangrande S. E. , Melnikov V. M. , and Schuur T. J. , 2005a: Calibration issues of dual-polarization radar measurements. J. Atmos. Oceanic Technol., 22, 11381155, doi:10.1175/JTECH1772.1.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., Giangrande S. E. , and Schuur T. J. , 2005b: Rainfall estimation with a polarimetric prototype of WSR-88D. J. Appl. Meteor., 44, 502515, doi:10.1175/JAM2213.1.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., Diederich M. , Zhang P. , and Simmer C. , 2014: Potential utilization of specific attenuation for rainfall estimation, mitigation of partial beam blockage, and radar networking. J. Atmos. Oceanic Technol., 31, 599–619, doi:10.1175/JTECH-D-13-00038.1.

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  • Fig. 1.

    The locations of the C-band dual-polarization radars (marked with red squares), S-band RCCG single-polarization radars (marked with cyan squares), JWDs (marked with green asterisks), and the gauge network (marked with small white asterisks) used in the current study.

  • Fig. 2.

    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.

  • Fig. 3.

    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 are also calculated and included.

  • Fig. 4.

    Scatterplot of calculated A and KDP 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 KDP, and the coefficient dB (°)−1 was obtained through a linear least squares fit approach.

  • Fig. 5.

    (a) The model rainfall field estimated using from a horizontally uniform reflectivity field with a vertical gradient of 1.7 dB km−1. The rainfall rate estimated from the R(A) algorithm with (b) temperature-dependent and (c) fixed coefficients and .

  • Fig. 6.

    (a) The comparison results from second tilt and third tilt , where the model rainfall rate, results from 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 and on temperature T based on the simulation results.

  • Fig. 7.

    The vertical profile of the rainfall estimated from the R(A) algorithm (VPRA). Variables VPRA1 and VPRA2 are 1-h mean rain-rate estimates from the R(A) algorithm at the heights H1 and H2, respectively.

  • Fig. 8.

    Scatterplots of radar QPE vs gauge observations for typhoon precipitation. The coefficients are (a) dB (°)−1, ; (b) dB (°)−1, ; and (c) dB (°)−1, . The QPE–gauge pairs are from the plain region with the gauge’s heights are below 500 m ARL. The evaluation results in terms of MB, CC, and RMSE are also included.

  • Fig. 9.

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

  • Fig. 10.

    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.

  • Fig. 11.

    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.

  • Fig. 12.

    Scatterplots of QPE vs gauge observations using (a) R = 359A0.89, (b) R = 207Z1.45, and (c) . Two typhoon rain events, Morakot (0000–2400 UTC 8–9 Aug 2009) and Nanmadol (0000–2400 UTC 30 Aug 2011), are summarized in this example. The evaluation results in terms of MB, CC, and RMSE are also included.

  • Fig. 13.

    Scatterplots of QPE vs gauge observations using (a) R = 359A0.89, (b) R = 207Z1.45, and (c) . The 48-h (~0000–2400 UTC 17–18 Jul 2011) precipitation classified as the mixture of stratiform and convective is used in this example. The evaluation results in terms of MB, CC, and RMSE are also included.

  • Fig. 14.

    The spatial distribution of gauge observations vs radar-based QPEs from 24-h accumulation (0000–2400 UTC 18 Jul 2011). The relation of R = 359A0.89 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.

  • Fig. 15.

    Hourly accumulation comparison between gauge observations and QPE using R = 359A0.89 (red line), R = 207Z1.45 (green line), and (blue line). The gauge observation is depicted by the black line. The 24-h data from 0000 to 2400 UTC 18 Jul 2011 is used in this example.

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