A Dynamical Z-R Relationship for Precipitation Estimation Based on Radar Echo-Top Height Classification
A Dynamical Z-R Relationship for Precipitation Estimation Based on Radar Echo-Top Height...
Wu, Wenxin;Zou, Haibo;Shan, Jiusheng;Wu, Shanshan
2018-08-19 00:00:00
Hindawi Advances in Meteorology Volume 2018, Article ID 8202031, 11 pages https://doi.org/10.1155/2018/8202031 Research Article A Dynamical Z-R Relationship for Precipitation Estimation Based on Radar Echo-Top Height Classification 1,2 1 1 3 Wenxin Wu , Haibo Zou , Jiusheng Shan , and Shanshan Wu Meteorological Disaster Emergency Warning Centre of Jiangxi, Nanchang 330096, China Shangrao Meteorological Bureaus, Shangrao 334000, China Jiangxi Climate Centre, Nanchang 330096, China Correspondence should be addressed to Haibo Zou; zouhaibobo@sohu.com Received 7 April 2018; Revised 25 June 2018; Accepted 12 July 2018; Published 19 August 2018 Academic Editor: Hisayuki Kubota Copyright © 2018 Wenxin Wu et al. +is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Using echo-top height and hourly rainfall datasets, a new reflectivity-rainfall (Z-R) relationship is established in the present study for the radar-based quantitative precipitation estimation (RQPE), taking into account both the temporal evolution (dynamical) and the types of echoes (i.e., based on echo-top height classification). +e new Z-R relationship is then applied to derive the RQPE over the middle and lower reaches of Yangtze River for two short-time intense rainfall cases in summer (2200 UTC 1 June 2016 and 2200 UTC 18 June 2016) and one stratiform rainfall case in winter (0000 UTC 15 December 2017), and then the comparative analyses between the RQPE and the RQPEs derived by the other two methods (the fixed Z-R relationship and the dynamical Z-R relationship based on radar reflectivity classification) are accomplished. +e results show that the RQPE from the new Z-R relationship is much closer to the observation than those from the other two methods because the new method simultaneously considers the echo intensity (reflecting the size and concentration of hydrometers to a certain extent) and the echo-top height (reflecting the updraft to a certain extent). Two statistics of 720 rainfall events in summer (April to June 2017) and 50 rainfall events in winter (December 2017) over the same region show that the correlation coefficient (root-mean-squared error and relative error) between RQPE derived by the new Z-R relationship and observation is significantly increased (decreased) compared to the other two Z-R relationships. Besides, the new Z-R relationship is also good at estimating rainfall with different intensities as compared to the other two methods, especially for the intense rainfall. to the quantitative estimate of precipitation. Different re- 1. Introduction gions usually yield quite different parameters [10, 11]. +e Radar quantitative precipitation estimation (RQPE) has RQPE obtained from the U.S. WSR-88D radar system obeys 1.4 finer temporal and spatial resolutions than those of tradi- the relationship of Z � 300R in extratropical regions, 1.2 tional gauge-based station rainfall observations and can while obeys Z � 250R in the tropical regions [12]. In accurately reflect the nonuniformness of the precipitation China mainland, the RQPE obtained from China New over a large area [1–3]. +erefore, RQPE is of great im- Generation Weather Radar (CINRAD) system follows the 1.4 portance to severe weather monitoring, industrial and ag- fixed relationship of Z � 300R . In fact, there is consid- ricultural production, natural disasters prediction and erable variation in the coefficients a and b, and they are preventing, and even weather modification [4–6]. In prac- significantly affected by the characteristics of raindrop-sized tice, the value of RQPE is computed through a nonlinear spectra [7, 13]. +erefore, the parameters a and b in the Z-R empirical relationship between radar reflectivity (Z) and relationship are affected by synoptic weather situations, precipitation rate (R), Z � aR , where a and b are two hydrology, geography, and so on and thus vary with time parameters to be determined [7–9]. and space. Such a fact could produce different values of these In early studies, a simple Z-R relationship can be ob- parameters in different climates and even different rainfall tained statistically over a climatic timescale and then applied events [14–17]. Rosenfeld and Ulbrich [18] also discuss the 2 Advances in Meteorology rainfall threshold (HART) method to estimate the mean differences in the Z-R relationship between maritime and continental, convective, transition and stratiform, and convective rainfall over an area (i.e., an averaged value over an area) and show better results. +erefore, using ET height orographic precipitation. +erefore, a fixed Z-R relationship may not be accurate for a rainfall event with different instead of radar reflectivity to categorize observational intensities. precipitation and reflectivity into different groups is ex- From then on, in order to obtain a more complex and pected to further improve the accuracy of RQPE because the accurate Z-R relationship, precipitation is categorized into new method simultaneously considers the content of hy- different types (or radar reflectivity is classified into different drometers (radar reflectivity) and the updraft (ET height) of intensities). +en, a set of Z-R relationships in different types a storm to a certain extent. Section 2 introduces the study area and data processing procedure. Section 3 describes the of precipitation are derived. +is method is well known as the classification Z-R relationship and has been a great dynamical Z-R relationship based on reflectivity classifica- tion, and Section 4 depicts the new constructed Z-R re- improvement in accuracy [19, 20]. Besides, Alfieri et al. [21] assumed that the Z-R relationship changes with time and lationship based on ET height classification. Section 5 shows the performance of the new Z-R relationship to derive pointed out that the Z-R relationship within a specific time should be determined by the reflectivity and rainfall during RQPE. Conclusions are given in the final section. that time (i.e., dynamical Z-R relationship). +e method of the dynamical Z-R relationship also improves the accuracy 2. Data Source and Processing of RQPE. Although the above two methods (classification Z-R +e area of interest in the present study is over the middle and ° ° relationship and dynamical Z-R relationship) improve the lower reaches of Yangtze River (113–119 E, 27.5–31 N), where accuracy of RQPE, they both have obvious shortcomings. short-time intense precipitation (rain intensity more than −1 +e classification Z-R relationship (i.e., the method in [19] 10 mm·h ) occurs very frequently in the summer time and [20]) does not take into account the possible temporal (April–August). +is area includes six provinces of Jiangxi, variation of the relationship, while the dynamical Z-R re- Anhui, Zhejiang, Hunan, Hubei, and Fujian in China, con- lationship (i.e., the method in [21]) does not take into ac- taining 3468 automatic rainfall observational stations and 12 count different types of precipitation. With the advantages of CINRAD Doppler radars (Figure 1). +e observed radar and the classification Z-R relationship and dynamical Z-R re- rain gauge data are provided by the Meteorological In- lationship, Wang et al. [22] proposed a dynamical Z-R re- formation Center of the Jiangxi (in China) Meteorological lationship based on radar reflectivity classification. a and b in Administration (JMA) and can be accessed from the CMISS this Z-R relationship vary with the time and echo strength. interface (http://10.116.89.55/cimissapiweb/) at the Intranet +is method is shown to have both advantages of the of JMA. previous two methods and thus further improves the ac- When estimating the rainfall using the reflectivity of the curacy of RQPE [22]. Doppler radar, it is common to use the echoes on the Previous works mainly focused on the spatial or tem- constant-altitude plan position indicator [28] at 1.5 km from poral variation of the empirical coefficients a and b in the the sea level or echoes at low elevation angles [29]. However, Z-R relationship, while Wang et al. [22] simultaneously in the area of interest here, there are some blind regions in consider their spatial and temporal variation. +ey cate- the radar CAPPI at 2 km due to the uneven distribution and gorize observational precipitation and reflectivity into dif- different altitudes of radar stations. Besides, there are also ferent groups based on the radar reflectivity and then mountains (elevation larger than 600 m) within 30 km for dynamically (in different times) calculate the coefficients several radar stations (Shangrao, Yichun, and Quzhou) that a and b in the Z-R relationship in different groups. Although prevent the detection of radar beams at small elevation the radar reflectivity value (echo strength) is closely related angles (i.e., some radar beams at small elevation angles may to the size and concentration of hydrometeors in a sampled be blocked by surrounding mountains). +erefore, in this area [18] and can directly reflect the rain rate of a storm to area, the radar mosaic of composite reflectivity (CR) is used a certain extent, the echo-top (ET) height is also a good for RQPE instead of using 1.5 km CAPPI and small-angle indicator of rain rate. Adler and Mack [23] and Atlas et al. echoes. CR is accomplished through four steps. Firstly, radar [24] noted that the rain rate in a storm is determined by the reflectivity data in polar coordinates are processed to remove updraft and the vertical gradient of saturation vapor density isolated nonmeteorological echoes and ground clutters using (which can change the content of hydrometeors), and the the improved quality control method in [30]. +en, the storm height (i.e., the echo-top height) is also determined horizontal interpolation with the nearest neighbor on the essentially by the updraft velocity. Adler and Mack [23] and range-azimuth plane [31] is selected to convert radar data in Rosenfeld et al. [25] have shown that the echo-top (ET) polar coordinates into a regular latitude/longitude grid of height is well correlated with rain rate. Bedka et al. [26] also 0.01 resolution. +irdly, the maximum value of CR in implied that the ET height is more representative to the different radars is used as the value of the radar mosaic for development of a storm and rainfall system. Also, ET height overlapping regions. Finally, a 9-point smooth operator is can be used to identify the ground clutters based on the applied to yield the final mosaic for each time. +e processes different features between meteorological echoes and of the mosaic in ET height are similar to those in CR. Here, ground clutters [27]. Owing to the advantages of ET height, the ET height is calculated using the improved method of Rosenfeld et al. [25] utilized it to develop the height-area [32]. +e algorithm is as follows. Advances in Meteorology 3 30.9°N 30.6°N An Qing Wu Han 30.3°N 30°N 29.7°N 29.4°N Jiu jiang Kingt Ekchen Yue Yang 29.1°N Qu Zhou 28.8°N 28.5°N Nan Chang Chang Sha Shang Rao 28.2°N 27.9°N Fu Zhou Yi Chun 27.6°N Jian Yang 113°E 113.5°E 114°E 114.5°E 115.5°E 116°E 116.5°E 117°E 117.5°E 118°E 118.5°E 119°E 115°E 200 400 600 800 1000 1200 1400 1600 Figure 1: Doppler radar stations (cross point) and automatic rainfall observation stations (dot) over the middle and lower reaches of Yangtze River. Circles indicate the range of CAPPI at 2 km height and shaded portions indicate altitude (unit: m). into account the spatial variation (i.e., classification of θ − θ b a θ � Z − Z + θ , (1) T T a b precipitation) and Alfieri et al. [21] consider the temporal Z − Z b a variation (i.e., dynamical fitting of a and b using observa- tional rainfall and reflectivity in a given time) to construct where θ is the maximum elevation angle where the the Z-R relationship. Wang et al. [22] proposed a Z-R re- reflectivity value Z exceeds the echo-top reflectivity threshold Z (e.g., 18 dBZ). θ and Z are the elevation angle lationship which has simultaneously taken into account the T a a spatial variation (classification based on radar reflectivity) and reflectivity value at the next higher elevation angle of θ . θ obtained by (1) is an elevation angle rather than a height and temporal variation (dynamical fitting) of a and b (e.g., dynamical Z-R relationship based on echo intensity classi- over the radar site. +e radar beam height (i.e., the ET fication). +is method significantly improves the accuracy of height) of θ can be calculated by the method of [33]: RQPE compared to that of [19] and [21]. 1/2 2 2 (2) +e dynamical Z-R relationship based on echo intensity R + R + 2R · R · sin θ − R � 4.5. W W classification is designed as follows [22]: Firstly, getting the +e improved method for obtaining ET height (e.g., (1)) CR mosaic using the maximum-value-based composite is proposed that echo tops be computed by interpolating method introduced in Section 2. Secondly, averaging the CR between elevation scans that bracket the echo-top threshold mosaic over a specific time (one hour in the present study), and results in smaller errors when higher-elevation scans are as well as obtaining the accumulated amount of observa- available [32]. tional precipitation in different sites over the same time. +irdly, classifying the averaged CR into different groups according to the interval of 5 dBZ (i.e., 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, and 75 dBZ). Fourthly, the 3. Dynamical Z-R Relationship Based on Echo accumulated precipitations are also classified into different Intensity Classification groups according to the groups of CR. Fifthly, the Z-R re- +e parameters a and b in the Z-R relationship are affected lationships in different groups (e.g., the CR group of 30 dBZ by local weather, hydrology, geography, and so on. +ere- and the corresponding precipitation group) are determined fore, different regions in a given time or different times in by fitting the CR to the precipitation using the optimizing a given region usually correspond to different parameters method developed in [34]. A set of a and b corresponding to a and b. In other words, the parameters a and b vary with different groups are obtained in the given time, yielding time and space. Liu et al. [20] and Chumchean et al. [19] take a “best-fit” Z-R relationship for the time. +e optimizing 4 Advances in Meteorology method proposed in [34] is to obtain the minimum values of Table 1: +e correlation coefficients between reflectivity/ET height a criterion function (CTF) which is expressed as follows: and observational rainfall. ⎧ ⎨ ⎫ ⎬ Time Composite reflectivity ET height CTF � min H − G + H − G , (3) i,j,k i i,j,k i ⎩ ⎭ April 2017 0.508 0.522 i�1 May 2017 0.505 0.510 where G is the observed precipitation at station i and n is the number of stations. +e estimated precipitation H is i,j,k calculated by the Z-R relationship at station i as log Z −log a / b /100 i j k (4) H � 10 , i,j,k where a � 1, 2, . . . , 1200, b � 100, 101, . . . , 300, and Z is j k i the reflectivity value at station i. +e best value of a and b (i.e., the most suitable Z-R relationship) is obtained through iteratively computing CTF to get the minimum Storm 1 Storm 2 value. Ciach et al. [35] and Chumchean et al. [19] used a very similar method to get the Z-R relationships. Finally, re- Figure 2: Schematic illustrations of two storms with the same echo peatedly performing the above 1–5 steps in different times intensity and different ET heights. (i.e., dynamical) can induce the coefficients a and b in the Z-R relationship to vary with the reflectivity intensity and depicted in Section 3, except for echo classification using ET time, finally forming the dynamical Z-R relationship based height instead of reflectivity intensity. +e specific steps are on echo intensity classification. as follows: firstly, getting the CR mosaic and ET height mosaic using the maximum-value-based method introduced in Section 2. Secondly, averaging the CR mosaic and ET 4. Dynamical Z-R Relationship Based on height mosaic over a specific time (one hour in the present ET Classification study), as well as obtaining the accumulated amount of observational precipitation over the same time. +irdly, the Radar ET height is defined as the radar beam height at the averaged CR is classified into different groups based on the highest elevation angle where the detected reflectivity value ET height with 1 km interval (i.e., 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, is not less than a threshold of 18 dBZ. ET height not only can 12, 13, 14, and 15 km). +e 4–6 steps are the same as those of reflect the storm development stage and precipitation system the dynamical Z-R relationship based on echo intensity intensity [26] but also can identify ground clutters since they which has been depicted in Section 3. have a relatively low ET height [27]. +erefore, it has been widely used in weather forecasting and synoptic diagnostics 5. Results [36, 37] (Evens, 2004). Table 1 shows the mean correlation coefficients between echo intensity or ET height and ob- +e study [26] and the correlation analysis in Section 4 have servational rainfall in the region of Figure 1 during April and shown that ET height can reflect preferably the develop- May 2017. It is clear that the correlation coefficients between ment of storm. +erefore, the dynamical Z-R relationship both of them are greater than 0.5, and the correlation based on ET height classification is expected further to coefficient between observational precipitation and ET improve the accuracy of RQPE. To verify this, three height is slightly large in both April and May 2017. +is methods (Z-R relationships) are used to derive RQPE and further confirms that ET height can be an indicator of then compared to observational precipitation. +e three rainfall intensity very well. Besides, although two storms methods are the fixed-parameter algorithm (SM), dy- with the same reflectivity and different ET heights in the namical Z-R relationship based on echo intensity classifi- conical surface may have a similar amount of hydrometeors cation (EIDM) developed in [22], and dynamical Z-R (Figure 2), they may yield different precipitation rates relationship based on ET height classification (ETDM) because the rain rate is well related to the updraft and the developed in this paper. ET height is the embodiment of the updraft (Adler and Mack, 1984) [24]. +erefore, if the two storms are grouped by ET height, they may have different precipitation rainfall 5.1. Case Study. We choose two short-time intense rainfall because they are classified into different groups. But if they events (occurred, resp., at 2200 UTC 1 June 2016 and 2200 are grouped by echo intensity, they belong to a same group UTC 18 June 2016) over the middle and lower reaches of and yield the same precipitation. +erefore, the Z-R re- Yangtze River to test the ETDM. For the case happened at lationship based on ET height classification (rather than 2200 UTC 18 June 2016, precipitation was mainly located at reflectivity classification) may further improve the accuracy the northern part of Jiangxi Province and the border regions of RQPE. of provinces of Jiangxi, Hubei, and Anhui, with maximum −1 +e procedure of the dynamical Z-R relationship based values exceeding 40 mm·h (Figure 3(a)). +e main rainfall −1 on ET height classification is similar to that of the dynamical belt (with precipitation more than 10 mm·h ) is northwest- Z-R relationship based on echo intensity which has been southeast distributed. +e three methods that derived RQPE Advances in Meteorology 5 32°N 32°N 40 40 31°N 31°N 30 30 30°N 20 20 30°N 10 10 29°N 29°N 5 5 28°N 28°N 112°E 113°E 114°E 115°E 116°E 117°E 118°E 119°E 112°E 113°E 114°E 115°E 116°E 117°E 118°E 119°E (a) (b) 32°N 32°N 40 40 31°N 31°N 30 30 20 20 30°N 30°N 10 10 29°N 29°N 28°N 28°N 112°E 113°E 114°E 115°E 116°E 117°E 118°E 119°E 112°E 113°E 114°E 115°E 116°E 117°E 118°E 119E (c) (d) Figure 3: Precipitations (mm) obtained from (a) observation, (b) SM method, (c) EIDM method, and (d) ETDM method at 2200 UTC 18 June 2016. have been produced with reasonable rainfall distribution consistently smaller than observations over the areas with −1 (Figure 3(a)). However, it can be seen that the RQPE de- rainfall exceeding 15 mm·h , as shown in Figure 4(a). By termined by the SM method (Figure 3(b)) was obviously comparison, the EIDM improves the accuracy of RQPE, with underestimated, and the area of RQPE exceeding 10 or an obvious increase in precipitation (with the maximum −1 −1 30 mm·h was significantly decreased. +e distribution and rainfall exceeding 30 mm·h ). But the rainfall intensity is still value of RQPE derived by EIDM (Figure 3(c)) are very similar smaller than that of observation. More importantly, the to those of SM (Figure 3(b)), except for that the SM over- ETDM (Figure 4(d)) conspicuous improved RQPE quality estimates the RQPE in the red circle region in Figure 3. By which is more close to the observation (Figure 4(a)). +e comparison, the ETDM obtains the best RQPE (Figure 3(d)) spatial correlation coefficients between RQPEs determined by in both magnitude and region as compared to the observation the three methods and observational precipitation (more than −1 (Figure 3(a)). +e spatial correlation coefficients between 0.1 mm·h ) are 0.68 (SM), 0.72 (EIDM), and 0.74 (ETDM), RQPEs estimated by the three methods and observational respectively. +e ETDM has still the largest correlation co- −1 precipitation (≥0.1 mm·h ) are 0.76 (SM), 0.80 (EIDM), and efficient in the three methods. 0.88 (ETDM), respectively. +is further implies that the +e above two short-time intense rainfall cases (2200 ETDM to obtain RQPE is best in the three methods. UTC 1 June 2016 and 2200 UTC 18 June 2016) have shown In the case of 2200 UTC 1 June 2016, the precipitation the well performance of ETDM to derive RQPE. Why ETDM was mainly distributed at the northwestern part of Jiangxi has better performance than EIDM? In fact, the EIDM −1 Province, with maximum values exceeding 30 mm·h (ETDM) is constructed by classifying CR and precipitation (Figure 4(a)). +e main rainfall belt (with precipitation into different groups based on echo intensity (ET height), and −1 more than 10 mm·h ) is also northwest-southeast orien- the parameters a and b in the Z-R relationship are fitted by the tated. Like the case of 2200 UTC 18 June 2016, all three CR values and the observed precipitations for a specific group. methods (SM, EIDM, and ETDM) have successfully de- If there are more samples with intense (weak) precipitation in rived the distribution of precipitation (Figures 4(b)–4(d)). the group, the fitted Z-R relationships will derive intense But the RQPE determined (Figure 4(b)) by the SM method is (weak) RQPE. +e distributions of CR, ET height, and 6 Advances in Meteorology 32°N 32N 31°N 31N 30°N 30N 29°N 29N 28°N 28N 112°E 113°E 114°E 115°E 116°E 117°E 118°E 119°E 112E 113E 114E 115E 116E 117E 118E 119E (a) (b) 32°N 32°N 30 30 31°N 31°N 25 25 30°N 20 30°N 20 15 15 29°N 29°N 10 10 28°N 28°N 5 112°E 113°E 114°E 115°E 116°E 117°E 118°E 119°E 112°E 113°E 114°E 115°E 116°E 117°E 118°E 119°E (c) (d) FIGURE 4: Precipitations (mm) obtained from (a) observation, (b) SM method, (c) EIDM method, and (d) ETDM method at 2200 UTC 1 June −1 precipitation in the rectangular region in Figure 4 are shown maximum values less than 4 mm·h (Figure 6(a)). All three in Figure 5. As shown in Figure 5, the strong precipitation methods (SM, EIDM, and ETDM) have successfully derived occurs in the areas of strong radar echo (≥35 dBZ) and high the precipitation near the maximum precipitation center ET height (≥9 km). But the high ET height corresponds better (i.e., the black square in Figure 6). But precipitations ob- to the intense precipitation than the large CR. For example, tained by the three methods are less than the observation. −1 a region with relatively weak precipitation (6 mm·h ), strong +e SM method throws away many areas with precipitation, echoes (exceeding 40 dBZ), and relatively low ET height (less leading to many scattered precipitation points appeared at than 9 km) appears at the black circle area in Figure 5. +is the domain (Figure 6(b)). +is induces that the correlation coefficient between observation and RQPE derived by SM indicates that when constructing the Z-R relationships using EIDM, the group (especially for the group that included most is only 0.32 which is significantly less than those of the intense precipitation samples) may contain more weak pre- above two convective cases. By comparison, the EIDM cipitation samples than using the ETDM. +e more weak estimates more areas with precipitation (Figure 6(c)), precipitation samples will result in that the EIDM un- increasing the correlation coefficient to 0.55. More im- derestimates the RQPE than the ETDM (e.g., Figures 3(c), portantly, the ETDM not only increases the areas of 3(d), 4(c), and 4(d)). precipitation but also enlarges the intensity of precipitation Although the new method based on ET classification to (Figure 6(d); the maximum precipitation is more than −1 derive RQPE performs better than the other two methods, 2.5 mm·h ), further increasing the correlation coefficient the two cases used to test belong to convective storms. to 0.58. As shown in Figure 6, all three methods cannot Rosenfeld et al. [25] also indicated that a deeper convective derive the precipitation in the area encircled by the red storm can more easily produce heavy rain, and a better rectangle which is in fact the mountainous region (Figure 1). correlation can be obtained using the classification statistics +is may be induced by the blockage of mountains to the based on ET height. +erefore, how does the new method radar beam in lower elevation angles. Zou et al. [30] in- performs in nonconvective storm (i.e., stratiform pre- dicated that this area is also a blind region of the Nanchang cipitation system)? To answer this question, a stratiform radar in 0.5 tilt. It is clear that although the RQPE derived precipitation case that occurred at 0000 UTC 15 December from the stratiform precipitation system is less accurate than 2017 is selected to further test the new method. At 0000 UTC that from the convective storm, the ETDM to derive RQPE 15 December 2017, the precipitation mainly fell in the still has a significant advantage compared with the other middle and northeastern parts of Jiangxi Province, with methods. Advances in Meteorology 7 17 6 17 6 8 4 4 29.4°N 10 8 29.4°N 10 3 19 3 194 4 4 45 4 5 5 18 18 4 4 5 5 16 5 16 6 5 12 27 6 4 12 27 6 4 31 4 3 4 3 6 6 6 10 23 10 23 8 28 7 6 7 24 24 6 8 6 10 277 8 6 27 7 12 8 8 12 8 8 3 4 3 4 16 10 10 25 25 16 29.2°N 40 29.2°N 5 12 10 6 12 10 6 12 12 12 12 12 3 12 3 19 19 8 8 47 47 10 10 47 47 4 30 26 12 35 4 30 212 6 5 25 4 5 25 4 21 21 9 11 11 25 29°N 25 29°N 38 38 28 2828 28 14 14 5 5 6 6 3 3 20 20 11 11 9 9 30 22 12 5 12 5 28 28 25 3 21 25 3 5 21 16 5 16 13 9 13 13 9 13 28 28 7 12 12 22 22 14 14 7 15 14 7 14 28.8°N 8 17 11 17 28.8°N 8 17 11 17 6 6 6 8 8 6 914 5 9 14 5 25 3 6 4 25 4 8 16 8 16 12 5 17 137 12 5 17 137 4 18 6 18 4 18 8 10 9 13 338 8 10 9 2 35 5 2 213 5 382163 37 37 12 34 4 12 34 4 4 6 3 4 6 4936 8 39 8 39 17 26 17 26 4 24 4 24 15 23 15 23 6 6 8 20 17 20 8 20 17 4 4 28.6°N 6 16 14 28.6°N 6 16 14 3 3 5 5 10 10 4 4 8 8 10 3 10 6 3 6 8 8 9 9 13 17 13 28.4°N 4 28.4°N 4 20 20 10 10 11 11 8 4 4 19 19 8 33 33 5 5 6 6 28.2°N 28.2°N 114.8°E 115.2°E 115.6°E 116°E 116.4°E 114.8°E 115.2°E 115.6°E 116°E 116.4°E (a) (b) Figure 5: (a) CR (unit: dBZ) and (b) ET (unit: km) in the black rectangle in Figure 4 at 2200 UTC 1 June 2016. Digits show the 1-hour precipitation (mm) observed by rain gauges. 5.2. Statistical Analysis. It has been shown in the above three coe‡cient R reŒects the similarity of the spatial patterns cases that the ETDM proposed in the present study results in between RQPE and observational precipitation, with the a more accurate RQPE than the traditional SM and EIDM bigger the R, the higher the accuracy of RQPE. †e RMSE do. Is this viewpoint universality? To address this problem, shows the overall deviation of RQPE from the observation, in the following section, 720 rainfall cases in the summer with the smaller the RMSE, the higher the accuracy of RQPE. season (April to June 2017) and 50 rainfall cases in the winter †e RE reŒects the overall relative error of RQPE related to season (December 2017) over the middle and lower reaches observation, with the smaller the RE, the higher the accuracy of Yangtze River were collected to further compare SM, of RQPE. EIDM, and ETDM methods. †e precipitations over the Table 2 shows all these statistics in (5)–(7) which are region in the summer time comprise convective rainfall and averaged from April to June 2017 (i.e., in the summer season, stratiform precipitation (with a high ET height), while the with a total of 720 rainfall cases) over the middle and lower precipitations occurring in the winter time system are reaches of Yangtze River. It can be seen from Table 2 that the mainly induced by the stratiform system (with a lower ET RQPE derived by the SM is able to preferably reproduce the height). †ree statistics, correlation coe‡cient (R), root- spatial pattern and amount of observational precipitation, mean-squared error (RMSE), and relative error (RE), be- with a correlation coe‡cient of 0.59, an RMSE of 3.0 mm, tween RQPEs derived by the three methods and observed and an RE of 69.1%. However, there is a signi–cant im- precipitation are used to evaluate the performance of each provement for the EIDM to derive RQPE, with a signi–cant method: increase of correlation coe‡cient to 0.64, a reduction of RMSE to 2.5 mm, and a decrease of RE to 59%. More im- H − H Q − Q i1 i i i i portantly, there is also a further improvement for the ETDM (5) 2 2 n n to derive RQPE (relative to EIDM), with R increasing to 0.69 H − H · Q − Q i i i i i1 i1 (it is 0.1 or 0.05 larger than that of the SM or EIDM, resp.), RMSE reducing to 2.3 mm, and RE decreasing to 56.2%. †erefore, it is shown that there are continuous improve- RMSE H − Q , (6) i i ments from SM to EIDM and then to ETDM, which results i1 in more and more accurate RQPE. To further assess the performances of the three methods H − Q to derive RQPE in the winter season (small precipitation and i1 i i (7) RE . lower ET height), these statistics in (5)–(7) during December i1 i 2017 (with a total of 50 rainfall cases) are shown in Table 3. where H is the estimated precipitation (according to (4)), Q †e correlation coe‡cient between RQPE derived by SM i i is the observed precipitation at station i, and n is the number and observation is only 0.44, decreasing by 0.15 compared of stations with valid rainfall in a given time. †e correlation to that of the summer season (Table 2). Correspondingly, 64 8 Advances in Meteorology 32°N 32°N 3 3 31°N 31°N 2.5 2.5 2 30°N 30°N 1.5 1.5 29°N 29°N 0.5 28°N 0.5 28°N 112°E 113°E 114°E 115°E 116°E 117°E 118°E 119°E 112°E 113°E 114°E 115°E 116°E 117°E 118°E 119°E (a) (b) 32°N 32°N 31°N 31°N 2.5 2.5 30°N 30°N 1.5 1.5 29°N 29°N 0.5 0.5 28°N 28°N 112°E 113°E 114°E 115°E 116°E 117°E 118°E 119°E 112°E 113°E 114°E 115°E 116°E 117°E 118°E 119°E (c) (d) FIGURE 6: Precipitations (mm) obtained from (a) observation, (b) SM method, (c) EIDM method, and (d) ETDM method at 0000 UTC 15 December 2017. Table 2: Statistics of correlation coefficient (R), root-mean-squared the relative error RE (70.5%) is more than that of the error (RMSE), and relative error (RE) that evaluate the perfor- summer season. Note that the smaller RMSE in the winter mance of the three methods to derive RQPE during April to June season (Table 2) does not reflect the higher accuracy. +is is mainly induced by a small amount of precipitation in the winter season. Clearly, the performance of SM in the Method R RMSE (mm) RE (%) summer season is better than that in the winter season. SM 0.59 3.0 69.1 Similarly, the EIDM improves the accuracy of RQPE in the EIDM 0.64 2.5 59.0 winter season on the basis of SM. +e correlation co- ETDM 0.69 2.3 56.2 efficient increases to 0.49 accompanied by a reduction of RMSE to 0.63 mm and a decrease of RE to 70.4%. More importantly, the ETDM further improves the accuracy of 10 mm. However, with the increase in rainfall, the RE of RQPE on the basis of EIDM so that the correlation co- both SM and EIDM decreases significantly. When the efficient increases to 0.51 followed by a slight decrease in rainfall amount is larger than or equal to 50 mm, the RE of RMSE and RE. It is clear that although the accuracy of the SM and EIDM decreases to about 55% and 40%, re- RQPE in the winter season is worse than that in the spectively. It is also shown in Figure 7 that the RE of ETDM summer season, the ETDM still can improve the accuracy is the smallest one at the intensity level of 0.1–10 mm, and of RQPE derived by EIDM and SM. then it decreases more rapidly than those of SM and EIDM. +us, the RE of ETDM is the smallest one at different +e above analysis evaluates the performance of the SM, EIDM, and ETDM to derive RQPE in an overall perspective. rainfall intensities, and the RE difference between the It is also interesting to evaluate their performance in de- ETDM and SM increases with the increase of rainfall in- riving RQPE at different rainfall intensities. Here, four tensity. +erefore, it is obvious that the ETDM constructed intensity levels of 0.1–10 mm, 10–25 mm, 25–50 mm, and in the paper is a better choice to derive RQPE at different above 50 mm are chosen to evaluate the three methods (SM, rainfall intensities, especially for precipitation more than EIDM, and ETDM). Figure 7 shows the RE (relative error; 50 mm which has the smallest RE (∼30%). Besides, among i.e., (7)) between observed precipitation and the RQPEs the three methods to derive RQPE, the reduction speed of obtained by the three methods at different rainfall in- RE of SM is the slowest with the increase of rainfall in- tensities. It is clear that the RE of the SM (∼75%) is close to tensity. +is implies that the SM has the worst performance that of the EIDM when the rainfall amount is less than in the three methods to obtain the precipitation rate. Advances in Meteorology 9 Table 3: Statistics of correlation coefficient (R), root-mean-squared the correlation coefficient and reduces the root-mean- error (RMSE), and relative error (RE) that evaluate the perfor- squared error and relative error between the RQPE and mance of the three methods to derive RQPE during December the observed precipitation regardless of summer or winter. Besides, the new ETDM yields a more accurate RQPE in different intensity rainfalls as compared to the SM and Method R RMSE (mm) RE (%) EIDM methods. It is clear that the ETDM-based ET clas- SM 0.44 0.66 70.5 sification further improves the accuracy of derived RQPE EIDM 0.49 0.63 70.4 compared with the EIDM-based echo intensity ETDM 0.51 0.62 70.3 classification. A new dynamical Z-R relationship is established based on ET height classification in this paper. +e tests of the 0.8 three cases (two in summer and one in winter) and two 0.7 statistics (one in summer and the other one in winter) show that the new Z-R relationship has well performed to derive 0.6 RQPE. However, the merging results of multiple sources of 0.5 rainfall rates can provide a better quantity than any single source [38]. Although satellite QPE is limited by a lack of 0.4 robust correlation between cloud-top brightness tempera- 0.3 ture and surface rainfall, it is more spatially coherent than radar QPE and is not subject to terrain-based blockages or 0.2 discontinuities due to lack of data and instrumentation 0.1 differences [38]. +erefore, future work will focus on the 0.0 blending of RQPE developed in this paper, satellite rainfall 0–10 10.1–25 25.1–50 50.1–100 QPE, and rain gauge estimate. Measured value of precipitation (mm) SM Data Availability EIDM ETDM +e data used to support the findings of this study are Figure 7: Relative error (%) of RQPE determined from the SM, available from the corresponding author upon request. EIDM, and ETDM methods. Conflicts of Interest 6. Conclusions +e authors declare that they have no conflicts of interest. In the present study, a new dynamical reflectivity-rainfall Acknowledgments (Z-R) relationship is established for the operational RQPE, based on the echo-top (ET) height which can preferably +is study was jointly supported by the Jiangxi Provincial reflect the development of the rainfall storm. +en, it is Department of Science and Technology Project (Grant no. applied to derive the RQPE over the middle and lower 20171BBG70004) and the National Natural Science Foun- reaches of Yangtze River for three cases (two cases are short- dation of China (Grant no. 41765001). time intense rainfall cases, resp., at 2200 UTC 1 June 2016 and 2200 UTC 18 June 2016, and one is a stratiform rainfall References case). +e results show that the RQPEs derived from two summer cases are more accurate compared to that from the [1] R. A. Scofield and R. J. Kuligowski, “Status and outlook of winter case. 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