• ADVANCES IN ATMOSPHERIC SCIENCES, 2019, 36(1): 41-54
doi: 10.1007/s00376-018-8032-7
Evaluating the Algorithm for Correction of the Bright Band Effects in QPEs with S-, C- and X-Band Dual-Polarized Radars
Yang CAO1,2,3, Debin SU2,5, Xingang FAN2,4, Hongbin CHEN*,1,

Abstract:

The bright band, a layer of enhanced radar reflectivity associated with melting ice particles, is a major source of significant overestimation in quantitative precipitation estimation (QPE) based on the Z-R (reflectivity factor-rain rate) relationship. The effects of the bright band on radar-based QPE can be eliminated by vertical profile of reflectivity (VPR) correction. In this study, we applied bright-band correction algorithms to evaluate three different bands (S-, C- and X-band) of dual-polarized radars and to reduce overestimation errors in Z-R relationship-based QPEs. After the reflectivity was corrected by the algorithms using average VPR (AVPR) alone and a combination of average VPR and the vertical profile of the copolar correlation coefficient (AVPR+CC), the QPEs were derived. The bright-band correction and resulting QPEs were evaluated in eight precipitation events by comparing to the uncorrected reflectivity and rain-gauge observations, separately. The overestimation of Z-R relationship-based QPEs associated with the bright band was reduced after correction by the two schemes for which hourly rainfall was less than 5 mm. For the verification metrics of RMSE (root-mean-square error), RMAE (relative mean absolute error) and RMB (relative mean bias) of QPEs, averaged over all eight cases, the AVPR method improved from 2.28, 0.94 and 0.78 to 1.55, 0.60 and 0.40, respectively, while the AVPR+CC method improved to 1.44, 0.55 and 0.30, respectively. The QPEs after AVPR+CC correction had less overestimation than those after AVPR correction, and similar conclusions were drawn for all three different bands of dual-polarized radars.

Key words: dual-polarized radar; bright band; QPE; vertical profile of reflectivity;
摘要: 零度层亮带是指融化的冰晶粒子造成反射率因子增大的带区，其存在会引起基于Z-R关系的定量估测降水（QPE）明显高估。采用反射率因子垂直廓线（VPR）进行零度层亮带订正可以减弱QPE高估。本文将此订正方法应用于三个不同波段（S、C、X）的双线偏振雷达上，以减小QPE高估误差。采用平均反射率因子垂直廓线法（AVPR）和平均反射率因子垂直廓线与平均相关系数垂直廓线相结合的方法（AVPR+CC）分别对反射率因子进行订正，采用8次降水过程比较订正前后反射率因子反演的降水，并与地面雨量站实测降水比较。结果表明，当小时降雨量小于5mm时，两种订正方法均能有效减弱零度层亮带存在引起的QPE高估。采用均方根误差、相对平均绝对误差和相对平均偏差三个参数进行误差分析，平均来看，AVPR法分别从2.28，0.94和0.78提高到1.55，0.60和0.40，AVPR+CC法分别提高到1.44，0.55和0.30。AVPR+CC法订正后的反射率因子反演的QPE误差小于AVPR法，三个波段雷达具有相似的结果。
关键词: 双偏振雷达 ; 零度层亮带 ; 定量估测降水 ; 反射率因子垂直廓线

1. Introduction

In radar observation of cloud and precipitation, quantitative precipitation estimation (QPE) based on the Z-R (reflectivity factor-rain rate) relationship is a widely used method proven to be efficient for stratiform and light rainfall events, even when the dual-polarized radars have improved QPE for moderate to heavy rainfall events (Cifelli et al., 2011). However, the bright band, which is a layer of high reflectivity often observed due to the melting of snowflakes falling below the freezing level, has been found to be a major source of significant overestimation in Z-R relationship-based QPE (Smith, 1986; Xiao et al., 2010; Zhang and Qi, 2010; Zhang et al., 2012; Kalogiros et al., 2013; Qi et al., 2013b, 2013c; Qi and Zhang, 2013; Yang et al., 2013; Zhuang et al., 2013; Hall et al., 2015). A real-time vertical profile of reflectivity (VPR) correction algorithm has been developed to correct the contamination from the bright band using the WSR-88D (Weather Surveillance Radar-1988 Doppler) volumetric reflectivity data (SÁnchez-Diezma et al., 2000; Zhang et al., 2008; Zhang and Qi, 2010; Zhang et al., 2012; Qi et al., 2013b, 2013c; Qi and Zhang, 2013; Hall et al., 2015). Bright bands are most often associated with stratiform precipitation, although not all stratiform precipitation systems contain one (Fabry and Zawadzki, 1995; White et al., 2003; Zhang et al., 2008; Wang et al., 2017). Normally, it is necessary to segregate convective and stratiform precipitation for bright-band correction (Zhang et al., 2008; Zhang and Qi, 2010). (Zhang et al., 2008) proposed a segregation method using radar reflectivity and air temperature profiles in the native radar coordinates. Another segregation method using the vertically integrated liquid water (VIL) field was developed by (Zhang and Qi, 2010), and an average VPR (AVPR) correction scheme was developed for bright bands. The AVPR is the vertical profile of azimuthally averaged reflectivities in the bright-band area at a given tilt. This correction method has been proven to be effective in various weather processes of different regions (Zhang et al., 2012; Qi et al., 2013c).

A correctly identified bright-band bottom is critical for effective correction, but is not always easy to find with AVPR (Qi et al., 2013b; Qi and Zhang, 2013). Fortunately, dual-polarized radar provides variables that are sensitive to melting hydrometeors found in the bright-band area. For example, the linear depolarization ratio and differential reflectivity peak, while the copolar correlation coefficient reduces, in the bright-band area (Giangrande et al., 2005; Giangrande et al., 2008; Park et al., 2009; Boodoo et al., 2010; Qi et al., 2013b; Wu et al., 2018). The copolar correlation coefficient, especially, can provide a much better depiction than reflectivity of the vertical structure of the bright band (Shusse et al., 2011; Kalogiros et al., 2013; Qi et al., 2013b). (Qi et al., 2013b) developed a correction scheme that combined the AVPR and the average vertical profile of the copolar correlation coefficient (AVPCC) for the bright-band area (hereafter the AVPR+CC correction scheme). The AVPCC is the vertical profile of the azimuthally averaged copolar correlation coefficient within the same area where the AVPR was calculated for each tilt. Combining the AVPR and AVPCC to detect the bright-band top and bottom, respectively, has been proven to provide significant improvements in radar-based QPE over AVPR alone (Qi et al., 2013b).

Different types of weather radar of various wavelengths, such as S-, C- and X-bands, have been used in weather monitoring applications in China. In recent years, dual-polarized radar has started to become widely adopted in operational weather services. It is therefore important to evaluate the applicability of various bright-band correction algorithms with different types of radars for evaluating their observational capabilities. In this study, the AVPR and AVPR+CC correction algorithms were applied with three dual-polarized radar systems (S-, C- and X-band). The corrected reflectivity from the AVPR and AVPR+CC schemes were used in Z-R relationship-based QPE. Finally, the resulting QPEs were verified against rain-gauge observations. The data and associated preprocessing methods are presented in section 2. Section 3 describes the methods and algorithms, including freezing-level height estimation, attenuation correction of radar reflectivity, convective and stratiform precipitation segregation, the bright-band correction algorithm, and the Z-R relationship-based QPE calculation. Results and analysis are illustrated in section 4. Section 5 summarizes with conclusions and discussion.

2. Data

In this study, reflectivity and copolar correlation coefficients observed from three dual-polarized radars (one each in the S-, C- and X-bands) were used to validate the bright-band correction algorithm for QPE estimation during eight stratiform precipitation events (Table 1). The three radars had higher range resolutions (250 m for S-band and 150 m for C- and X-band) than operational radars in China (1000 m). Radiosonde data and ERA-Interim data (Dee et al., 2011) were used in estimating the freezing-level height. The resulting QPEs were verified against rain-gauge observations.

Table 1. Radars in operation during selected precipitation events with a detected bright band (BB).

The three operational dual-polarized radars included one S-band radar located in Xiamen, China (24.5067°N, 118.0036°E), one C-band radar located in Beijing, China (39.945°N, 116.290°E), and one X-band radar located in Beijing, China (39.9768°N, 116.3912°E). Multiple variables, including reflectivity at the horizontal polarization, Doppler velocity, spectrum width, differential reflectivity, total differential phase, and the copolar correlation coefficient, were acquired. The S- and C-band radars operated in simultaneously transmitting and receiving horizontally (H) and vertically (V) polarized waves (SHV). The X-band radar operated in fast alternating H and V transmission mode (AHV) (Hubbert et al., 2010). The detailed radar parameters are given in Table 2. The radar observations were preprocessed by the median filtering algorithm in order to eliminate random fluctuations, and by a 5× 5 point window filtering to remove the isolated point echoes.

Table 2. Radar parameters of operation.

The radiosonde data were acquired from sounding stations at Beijing (39.8°N, 116.47°E) and Xiamen (24.47°N, 118.07°E), China. The air temperature profiles were used to derive the freezing-level height with a temporal resolution of 12 h. For times when no sounding data were available, the geopotential height and air temperature from the ERA-Interim data were used to derive the freezing-level height (http://apps.ecmwf.int/datasets/data/interim_full_daily/). The ERA-Interim data had a spatial resolution of 0.125°× 0.125° and temporal resolution of 6 h (Dee et al., 2011). The hourly rainfall data were acquired from rain gauges operated by the Beijing Meteorological Bureau and Fujian Meteorological Bureau. The precision of the rainfall rate data was 0.1 mm h-1.

3. Methods

The algorithms in Z-R relationship-based QPE calculation include four components: (2) estimation of freezing-level height; (3) correction of radar reflectivity for rain attenuation at the C- and X-band wavelengths; (4) segregation of convective and stratiform precipitation based on reflectivity, air temperature profile, and VIL; (5) correction of the bright band based on the AVPR and AVPR+CC schemes; and (6) calculation of QPE based on the Z-R relationship.

3.1. Estimation of freezing-level height

The freezing-level height (h f) represents the altitude where the temperature is at 0°C in the free atmosphere. The freezing-level height can be obtained from radiosonde data. Due to the limited spatial and temporal resolutions of radiosonde data, however, ERA-Interim data, which includes assimilated ground-based and upper-air observations and satellite remote sensing data, may be used as a supplement (Mooney et al., 2011; Haimberger et al., 2012; Hall et al., 2015; Kumar and Naseef, 2015).

The freezing-level height was determined by the linear interpolation of air temperature profiles from radiosonde observation or ERA-Interim data. In order to evaluate the differences in the heights from the two data sources, freezing-level heights were estimated for a 10-yr (2005-14) period and three statistical metrics, including the correlation coefficient (CC), mean error (ME), and mean absolute error (MAE) were calculated (Kumar and Naseef, 2015), as follows: $${\rm CC}=\frac{\sum_{i=1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^n(x_i-\bar{x})^2}\sum_{i=1}^n(y_i-\bar{y})^2} , \ \ (1)$$ where n is the sample size, x is the height from ERA-Interim data, y is the height from radiosonde data, $\bar{x}$ and $\bar{y}$ are the averages of x and y; \begin{eqnarray} {\rm ME}&=&\frac{\sum_{i=1}^n(x_i-y_i)}{n} ;\ \ (1)\\ {\rm MAE}&=&\frac{\sum_{i=1}^n|x_i-y_i|}{n} . \ \ (2)\end{eqnarray}

3.2. Attenuation correction

Radars with shorter wavelengths, such as C- and X-band radars, are affected by attenuation resulting from moderate to heavy rain, which causes a significant decrease in radar reflectivity. Therefore, errors in reflectivity due to attenuation should be corrected before calculating Z-R relationship-based QPE (Bringi et al., 2001; Park et al., 2005a, 2005b). With dual-polarized radar, the attenuation of reflectivity can be corrected using the differential propagation phase DP) or the specific differential phase (K DP), which are immune to radar attenuation and miscalibration. The K DP is estimated as the derivative of range profiles of the Φ DP (Wang et al., 2009). The attenuation correction algorithm used herein was adopted from the studies of (Bringi et al., 1990) and (Jameson, 1992). The specific attenuation (A H) is nearly linear with the K DP (A H=aK DP, where a is the attenuation coefficient in dB (°)-1, A H is in dB km-1, and K DP is in ° km-1) from scattering simulations. For C- and X-band radars, a is 0.08 and 0.275, respectively, from scattering simulations based on drop spectra measured by a disdrometer (Bringi et al., 2001; Park et al., 2005a, 2005b).

Fig. 1 Average vertical profile of reflectivity (AVPR, dark blue dots) and average vertical profile of copolar correlation coefficient (AVPCC, orange dots), averaged azimuthally in the bright-band area: (a) at 2.4° tilt from the C-band radar at 1229 UTC 4 August 2013; (b) at 3° tilt from the X-band radar at 0550 UTC 27 October 2016; and (c) at 2.4° tilt from the S-band radar at 1644 UTC 31 March 2017.

3.3. Convective and stratiform precipitation segregation

The segregation of convective and stratiform precipitation is based on reflectivity, air temperature profiles, and VIL in the native radar coordinates (Qi et al., 2013a). The air temperature profile was obtained from either radiosonde or ERA-Interim data. The VIL was calculated from a volume scan of reflectivity data using the method described in (Zhang and Qi, 2010). By adopting the method and decision tree of Qi et al. (2013a, Fig. 2), the radar bins were classified as either convective or stratiform.

Fig. 2 Time series of the bright-band top, bottom, α and β obtained from the AVPR and AVPR+CC schemes for the three events from the (a) C-band radar at 2.4° tilt at 1200-1300 UTC 4 August 2013, (b) X-band radar at 3° tilt at 0500-1100 UTC 27 October 2016, and (c) S-band radar at 2.4° tilt at 1400-1800 UTC 31 March 2017.

3.4. Bright-band correction

Two methods——namely, the AVPR and AVPR+CC methods——were adopted for bright-band correction (Zhang and Qi, 2010; Qi et al., 2013b). The stratiform precipitation was further divided into areas of existence or nonexistence of a bright band. The initial criteria for the existence of a bright band were when the reflectivity was greater than 15 dBZ and composite reflectivity was greater than 30 dBZ within a first-guess range of the bright band top (h f+D1) and bottom (h f-D1-5 km). D1 is defined as half of the vertical range at the point where the center of the lowest beam intersects the freezing level. The AVPR was calculated by averaging the reflectivity azimuthally across the bright-band area at a given tilt (Zhang and Qi, 2010). The height of the maximum reflectivity in the AVPR (h peak) was found by searching from 500 m above the freezing-level downward. A 500-m buffer zone was used to reduce the influence of any uncertainties in freezing-level height estimation (Zhang et al., 2008). The first inflection point in the AVPR above and below h peak was defined as the bright-band top (h top; green dotted line in Fig. 1) and bottom (h bottom; pink dotted line in Fig. 1), respectively. The h bottom was further constrained by the reflectivity at the bright-band bottom being greater than 28 dBZ (Zhang and Qi, 2010). The inflection point was determined following the method of (Sun et al., 2015).

The AVPR+CC method was developed by (Qi et al., 2013b) to improve the accuracy in bright-band bottom estimation, taking advantage of the high sensitivity of the copolar correlation coefficient to melting hydrometeors. The AVPCC is the vertical profile of the azimuthally averaged copolar correlation coefficient in the area where the AVPR is calculated at the given tilt. The new h bottom (light blue dotted line in Fig. 1) was updated by searching for the first inflection point in the AVPCC below the h peak, where the copolar correlation coefficient was greater than or equal to 0.92 (Qi et al., 2013b).

The reflectivity higher than a given threshold [default value of 30 dBZ, consistent with the eight precipitation events presented in Table 1 and (Zhang and Qi, 2010)] in the bright-band area can be corrected for radar-based QPEs according to the following equations, as given in (Zhang and Qi, 2010): \begin{eqnarray} Z_{\rm a}(e,m,n)&\!\!=\!\!\!&\left\{\!\! \begin{array}{l} \alpha[h_{\rm b}(e,m,n)\!-\!h_{\rm peak}(e)]\!+\!\beta[h_{\rm peak}(e)\!-\!h_{\rm bottom}(e)],\\ \qquad h_{\rm b}(e,m,n)>h_{\rm peak}(e)\\ \beta[h_{\rm b}(e,m,n)-h_{\rm bottom}(e)],\\ \qquad h_{\rm b}(e,m,n)\le h_{\rm peak}(e) \end{array} \right.\!;\ \ (4)\\\\ Z_{\rm c}(e,m,n)&\!\!=\!\!\!&Z_0(e,m,n)-Z_{\rm a}(e,m,n) . \ \ (5)\end{eqnarray} Here, e, m and n are the tilt number, azimuth and gate, respectively; h b is the height of the beam axis at a given bin; Z0 and Z c are the reflectivities before and after correction, respectively; Z a is the reflectivity-correction value; α is the slope of the AVPR between the h top and h peak obtained by least-squares line fitting; and β is the same as α but for the AVPR between the h peak and h bottom. Figure 2 shows the time series of h top, h bottom, α and β obtained from the AVPR and AVPR+CC schemes for the three events from C-band radar at 2.4° tilt at 1200-1300 UTC 4 August 2013, X-band radar at 3° tilt at 0500-1100 UTC 27 October 2016, and S-band radar at 2.4° tilt at 1400-1800 UTC 31 March 2017. Most of the bottom identified from the AVPR scheme was higher than the new bottom derived from the AVPR+CC scheme.

3.5. QPE

For Z-R relationship-based QPE calculation, two Z-R relationships were utilized. The first was Z=237R1.57 for the C- and X-band radars in Beijing, which was derived from various types of raindrop data for Beijing in 1982, and by the microwave remote sensing group of the Institute of Atmospheric Physics, Chinese Academy of Sciences. The other was Z=200R1.6 for the S-band radar in Xiamen (Liu et al., 2010; Zhang and Qi, 2010; Qi et al., 2013b). The rain rate R was then aggregated into hourly rainfall for verification against the rain-gauge observations.

In this study, QPEs were calculated for both before and after bright-band correction in order to compare and evaluate the AVPR and AVPR+CC correction schemes. The performances of the AVPR and AVPR+CC correction schemes were further evaluated using three statistical scores (Zhang and Qi, 2010; Qi et al., 2013b).

(1) Root-mean-square error (RMSE): $${\rm RMSE}=\left[\frac{1}{p}\sum_{t=1}^p(r_t-g_t)^2\right]^{1/2} , \ \ (6)$$ where rt and gt are the tth matching pairs of the radar-based and rain-gauge observed hourly rainfall, and p is the total number of matching pairs in the bright-band area. A matching pair was found when both the radar and rain gauge indicated hourly rainfall.

(2) Relative mean absolute error (RMAE): \begin{eqnarray} {\rm RMAE}&=&\frac{\frac{1}{p}\sum_{t=1}^p|r_t-g_t|}{\bar{g}} ;\ \ (7)\\ \bar{g}&=&\frac{1}{p}\sum_{t=1}^p{g_t} . \ \ (8)\end{eqnarray} Here, $\bar{g}$ is the average of hourly rain-gauge observations.

(3) Relative mean bias (RMB): $${\rm RMB}=\frac{\frac{1}{p}\sum_{t=1}^p(r_t-g_t)}{\bar{g}} . \ \ (9)$$

4. Case study results
4.1. Estimation of freezing-level height

Figure 3 shows the time series and a scatterplot for the freezing-level heights obtained from radiosonde data and ERA-Interim data for a 10-yr (2005-14) period in Beijing, China. The freezing-level heights were mostly between 0 and 6 km above mean sea level. The high density of the scattered points along the diagonal indicates high correlation between the heights of the two data sources. The sample size, CC, ME, MAE, and significance test p-value are also labeled in the figure. The statistics show that the differences in the freezing-level heights from the two data sources were insignificant. In addition, the negative ME values show that the freezing level from ERA-Interim was slightly lower than that from the radiosonde data. In conclusion, both the radiosonde data and ERA-Interim data can be used to obtain the freezing-level height.

Fig. 3 (a) Time series and (b) scatterplot of freezing-level height above mean sea level (MSL) obtained from radiosonde data and ERA-Interim data for a 10-yr (2005-14) period in Beijing, China. The solid line is the scatter fitting line; the colored bar indicates the probability density of the scattered points. The sample size (n), correlation coefficient (CC), mean error (ME), mean absolute error (MAE) and p-value (P) of the significance test between the radiosonde and ERA-Interim data are labeled.

4.2. Attenuation correction

Figure 4 shows range profiles of measured and attenuation-corrected reflectivity at 354° azimuth and 2.4° tilt from the C-band radar at 1229 UTC 4 August 2013, and at 20° azimuth and 3° tilt from the X-band radar at 0550 UTC 27 October 2016, as well as the corresponding measured reflectivity from the S-band radar in Beijing, which can ignore the effect of attenuation. The difference in attenuation-corrected reflectivity and reflectivity from the S-band radar could be attributed to the difference in sampling time and sampling resolution (range, elevation, etc.) of the three radars. As shown in the figure, the amount of attenuation correction in reflectivity increased with range, especially for the X-band radar, which had a large correction at far range. The maximum correction in the bright-band areas for the C- and X-band radars was about 3 and 4.5 dB, respectively——equivalent to an underestimation of 1.0 and 1.5 mm h-1, respectively, in QPEs using the conventional Z-R relationship (Z=200R1.6 for stratiform precipitation). In this study, the impacts of the attenuation correction for Z-R relationship-based QPE are a necessary consideration for the C- and X-band radars.

Fig. 4 Range profiles of reflectivity at (a) 354° azimuth and 2.4° tilt from the C-band radar at 1229 UTC 4 August 2013, (b) at 20° azimuth and 3° tilt from the X-band radar at 0550 UTC 27 October 2016. The "uncorrected" (solid black line) denotes the original measured reflectivity of the C- and X-band radar, while the "corrected" (dashed gray line) indicates attenuation-corrected values. The difference between the measured and attenuation-corrected reflectivity is shown by the dash-dotted line. "SA-radar" indicates the measured reflectivity of the S-band radar in Beijing.

4.3. Convective and stratiform precipitation segregation

Fig. 5 The (a, c, e) reflectivity field and (b, d, f) segregated precipitation type (a) at 2.4° tilt from the C-band radar at 1229 UTC 4 August 2013, (b) at 3° tilt from the X-band radar at 0550 UTC 27 October 2016, and (c) at 2.4° tilt from the S-band radar at 0008 UTC 22 February 2017.

Figure 5 shows examples of the reflectivity field and precipitation type segregation for the C-band radar at 2.4° tilt at 1229 UTC 4 August 2013, X-band radar at 3° tilt at 0550 UTC 27 October 2016, and S-band radar at 2.4° tilt at 0008 UTC 22 February 2017. There was a large area of enhanced reflectivity in the stratiform precipitation region, resulting from the melting of ice crystal aggregates. The algorithm for convective and stratiform precipitation segregation successfully identified the convective and stratiform areas for all three different bands of dual-polarized radars.

Figure 6 shows the averaged VPRs derived from stratiform and convective precipitation based on the radar volumetric reflectivity data for the event shown in Table 1. The averaged VPRs were calculated by averaging reflectivity azimuthally across the stratiform and convective precipitation areas, respectively, at a given height using the method described in (Zhang et al., 2008). Dashed lines indicate the freezing level. The averaged stratiform VPR (Fig. 6a) showed an apparent bright-band feature, which is a layer of enhanced reflectivity near the freezing level, while no such feature existed in the averaged convective VPR (Fig. 6b).

Fig. 6 Average VPR profiles of (a) stratiform and (b) convective precipitation for the eight events shown in Table 1, averaged azimuthally across the stratiform and convective precipitation areas, respectively, from the radar volumetric data. Dashed lines indicate the freezing level.

4.4. Impact of bright-band correction on radar-based QPEs

Figure 7 shows the reflectivity fields before and after bright-band correction using the AVPR and AVPR+CC schemes for the events shown in Fig. 1. The raw reflectivity fields in the stratiform areas (Figs. 7a, d and g) show the bright bands clearly (between two dotted circles). The large reflectivity in the bright-band areas was reduced from 40 dBZ to below 35 dBZ by AVPR correction (Figs. 7b, e and h), and further down to below 30 dBZ by the AVPR+CC correction (Figs. 7c, f and i). The reflectivity in the bright-band areas was then consistent with their surrounding areas.

Fig. 7 Reflectivity fields (a, d, g) before correction, and after correction using the (b, e, h) AVPR and (c, f, i) AVPR+CC methods for the events shown in Fig. 1. Dashed circles indicate the bright-band bottom and top, respectively.

The radar-derived hourly rainfall was compared with rain-gauge observations (Fig. 8) for the three events from the C-band radar at 3.4° tilt at 1200-1300 UTC 4 August 2013, X-band radar at 2° tilt at 0500-1100 UTC 27 October 2016, and S-band radar at 2.4° tilt at 1400-1800 UTC 31 March 2017. The radar-based QPEs from the uncorrected reflectivity significantly overestimated the rainfall in the bright-band areas (Figs. 8a, d and g). The QPE overestimations in the bright-band areas were reduced after the reflectivity fields were corrected by the AVPR (Figs. 8b, e and h) and AVPR+CC (Figs. 8c, f and j) schemes. Figure 8 also shows the scatter points of rainfall data that had no contamination of bright bands. The corrected bright-band area rainfall shows a similar distribution as those of no contamination. Three statistics (RMSE, RMAE and RMB) were calculated and listed in Table 3 for the radar-derived hourly rainfall with respect to the surface rain-gauge observations, focusing only on the bright-band affected areas. Figure 9 shows the scatter points of rainfall data that had contamination of bright bands at different tilts. The rainfall from the uncorrected and corrected reflectivity shows a similar distribution. In general, reflectivity corrections based on the AVPR and AVPR+CC schemes had positive impacts in reducing the overestimation of Z-R relationship-based QPEs in the bright-band areas. Furthermore, the AVPR+CC correction scheme eliminated more overestimation of QPE than the AVPR correction scheme, as the reflectivity in the bright-band areas was further reduced by the AVPR+CC scheme (Figs. 7c, f and i versus Figs. 7b, e and h).

Fig. 8 Scatterplots of radar-based hourly rainfall versus surface rain-gauge observations for the three events from the (a-c) C-band radar at 3.4° tilt at 1200-1300 UTC 4 August 2013, (d-f) X-band radar at 2° tilt at 0500-1100 UTC 27 October 2016, and (g-i) S-band radar at 2.4° tilt at 1400-1800 UTC 31 March 2017. The radar-based rainfall is from (a, d, g) before correction, and after correction using (b, e, h) AVPR and (c, f, i) AVPR+CC. The comparisons are separated for bright-band areas (red) and non-bright-band areas (blue).

Fig. 9 Scatterplots of radar-based hourly rainfall versus surface rain-gauge observations for the three events shown in Fig. 8. Radar-based rainfall are from (a, d, g) before correction, and after correction using (b, e, h) AVPR and (c, f, i) AVPR+CC. The comparisons are for bright-band areas at different tilts.

Table 3. The RMSE, RMAE and RMB scores for radar-derived hourly rainfall before and after correction using the AVPR and AVPR+CC schemes with respect to the surface rain-gauge observations for the events shown in Fig. 8. The comparisons were for bright-band affected areas only. Values in bold font indicate the additional improvement of AVPR+CC compared to AVPR.

Fig. 11 The (a) RMSE, (b) RMAE and (c) RMB scores calculated for different rainfall intensities using the 1538 radar-gauge data pairs in bright-band areas at lower tilt from the eight events of the three different bands of dual-polarized radars.

In addition to the above detailed case studies, the overall performance of the bright-band correction schemes was further tested in the eight events shown in Table 1. The three statistics of RMSE, RMAE and RMB were calculated. The comparisons were focused only on the bright-band affected areas, and the results are shown in Fig. 10. The AVPR and AVPR+CC correction schemes consistently reduced the radar-based QPE errors for all of the events. The reduction of radar-based QPE errors was bigger for four events (including 20130804 from the C-band radar, 20130811 and 20161027 from the X-band radar, and 20170331 from the S-band radar), which had large-scale continuous and homogeneous stratiform precipitation, than the other four events (20120424 and 20130811 from the C-band radar, and 20161122 and 20170222 from the S-band radar), due to the unsuitability of the Z-R relationship-based QPEs for relatively large rainfall events (maximum hourly rainfall >11 mm; Table 1). For relatively lighter rainfall events (maximum hourly rainfall <5 mm), the AVPR+CC correction yielded smaller RMSEs and RMAEs than the AVPR correction for three events (20130804 from the C-band radar, 20161027 from the X-band radar, and 20170331 from the S-band radar), because Z-R relationship-based QPE is efficient for stratiform and lighter rainfall events. Furthermore, the underestimation of QPEs in non-bright-band areas indicated that the errors in corrected QPEs were partially from the Z-R relationship-based QPE estimation, not totally from the reflectivity correction.

Fig. 10 The (a) RMSE, (b) RMAE and (c) RMB scores for radar-derived hourly rainfall at lower tilt before (black bars) and after correction using the AVPR (dark grey bars) and AVPR+CC (light gray bars) schemes with respect to the surface rain-gauge observations. The comparisons are for bright-band affected areas only.

Table 4. The RMSE, RMAE and RMB scores for different rainfall intensities before and after correction using the AVPR and AVPR+CC schemes from three dual-polarized radar systems (S-, C- and X-bands). The rainfall was divided into light rain (hourly rainfall <2 mm), moderate rain (2 mm hourly rainfall <5 mm), and heavy rain (hourly rainfall 5 mm).

According to the previous analysis, the improvement in QPE relates to the intensity of the rainfall events. The RMSE, RMAE and RMB were further calculated for different rainfall intensities using the 1538 radar-gauge data pairs in the bright-band areas from the eight events including all three radars (Table 1). The results are shown in Fig. 11 along a spectrum of rainfall intensity. It was found that the radar-based QPEs were improved by the two correction schemes when hourly rainfall was less than 5 mm. The negative RMB when hourly rainfall was greater than or equal to 5 mm indicated an underestimation of the QPEs, which was also reflected by the increased RMSE and RMAE. For the three statistical scores averaged over all eight cases, the AVPR scheme improved from 2.28, 0.94 and 0.78 to 1.55, 0.60 and 0.40, respectively, while the AVPR+CC scheme improved to 1.44, 0.55 and 0.30, respectively; the AVPR+CC scheme performed better than the AVPR scheme. Accordingly, the rainfall was divided into light rain (hourly rainfall <2 mm), moderate rain (2 mm hourly rainfall <5 mm), and heavy rain (hourly rainfall 5 mm) for all three different bands of dual-polarized radars; the three statistical scores are presented in Table 4. The three statistical scores showed a similar distribution for the three radars; the QPEs were improved by the two correction schemes when hourly rainfall was less than 5 mm, and after AVPR+CC correction had less overestimation than that after AVPR correction. For heavy rain, the three radars also had a similar impact from the underestimation of Z-R relationship-based QPE. Overall, the Z-R relationship-based QPE was suitable for events in which hourly rainfall was less than 5 mm, because Z-R relationship-based QPE was efficient for lighter rainfall events. The AVPR+CC scheme was more efficient in reducing the overestimation of Z-R relationship-based QPEs, and the results were similar for all three different bands of dual-polarized radars, because the increased accuracy of the bright-band bottoms were identified by AVPCC.

5. Summary

The bright band is a major source of significant overestimation in Z-R relationship-based QPE if it is not be corrected. VPR correction can be used to eliminate the effects of bright bands in radar-based QPE. In this study, the AVPR and AVPR+CC correction algorithms were applied to reflectivity from three dual-polarized radar systems (S-, C- and X-bands). The corrected reflectivity from the AVPR and AVPR+CC schemes were used in Z-R relationship-based QPE. Finally, the resulting QPEs were verified against rain-gauge observations.

Bright bands are most often associated with stratiform precipitation, and can be corrected based on VPR and freezing-level height. The freezing-level height could be derived from either radiosonde data or ERA-Interim data, and their difference was found to be negligible. Z-R relationship-based QPE is sensitive to the attenuation of reflectivity resulting from rain at shorter-wavelength radars (here, C- and X-bands). The attenuation can be corrected by using K DP, which is immune to radar attenuation and miscalibration, and nearly linear with specific attenuation (A H). The convective and stratiform precipitation segregation algorithm is based on reflectivity, air temperature profiles and VIL in the native radar coordinates, which worked well for three dual-polarized radars. After the reflectivity fields were corrected by the AVPR and AVPR+CC correction schemes, the Z-R relationship-based QPEs were derived and compared with those from uncorrected reflectivity, as well as verified against rain-gauge observations. The overestimation errors in radar-based QPEs associated with the bright band were reduced after either AVPR or AVPR+CC correction when hourly rainfall from the surface rain-gauge observation was less than 5 mm. For the verification metrics of the RMSE, RMAE and RMB of QPEs, averaged over all eight cases, the AVPR scheme improved from 2.28, 0.94 and 0.78 to 1.55, 0.60 and 0.40, respectively, while the AVPR+CC scheme improved to 1.44, 0.55 and 0.30, respectively. The QPEs after AVPR+CC correction had less overestimation than those after AVPR correction, and the results were similar for all three different bands of dual-polarized radars. In general, Z-R relationship-based QPE is suitable for events in which hourly rainfall is less than 5 mm, and VPR correction based on either the AVPR or AVPR+CC schemes will have positive impacts in reducing the overestimation errors of Z-R relationship-based QPE associated with a bright band. In future work, more precipitation events with a detected bright band need to be collected to further verify these results.

This research was funded by a China National 973 Program on Key Basic Research project (Grant No. 2014CB441401), the Beijing Municipal Natural Science Foundation (Grant No. 8141002), and the Public Welfare Industry (Meteorology) of China (Grant No. GYHY201106046). The authors greatly appreciate the immense assistance provided by the other participants at the Institute of Atmospheric Physics and the Meteorological Bureau of Beijing and Xiamen, China.

Acknowledgements. This research was funded by a China National 973 Program on Key Basic Research project (Grant No. 2014CB441401), the Beijing Municipal Natural Science Foundation (Grant No. 8141002), and the Public Welfare Industry (Meteorology) of China (Grant No. GYHY201106046). The authors greatly appreciate the immense assistance provided by the other participants at the Institute of Atmospheric Physics and the Meteorological Bureau of Beijing and Xiamen, China.

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Key words
dual-polarized radar
bright band
QPE
vertical profile of reflectivity

Authors
Yang CAO
Debin SU
Xingang FAN
Hongbin CHEN