Improvement of Radar Quantitative Precipitation Estimation ...

ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 29, NO. 3, 2012, 575–584

Improvement of Radar Quantitative Precipitation Estimation

Based on Real-Time Adjustments to Z–R Relationships

and Inverse Distance Weighting Correction Schemes

WANG Gaili∗ (王改利), LIU Liping (刘黎平), and DING Yuanyuan (丁媛媛)

State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Science, Beijing 100081

(Received 5 August 2011; revised 19 October 2011)

ABSTRACT

The errors in radar quantitative precipitation estimations consist not only of systematic biases causedby random noises but also spatially nonuniform biases in radar rainfall at individual rain-gauge stations.In this study, a real-time adjustment to the radar reflectivity–rainfall rates (Z–R) relationship scheme andthe gauge-corrected, radar-based, estimation scheme with inverse distance weighting interpolation was devel-oped. Based on the characteristics of the two schemes, the two-step correction technique of radar quantitativeprecipitation estimation is proposed. To minimize the errors between radar quantitative precipitation es-timations and rain gauge observations, a real-time adjustment to the Z–R relationship scheme is used toremove systematic bias on the time-domain. The gauge-corrected, radar-based, estimation scheme is thenused to eliminate non-uniform errors in space. Based on radar data and rain gauge observations near theHuaihe River, the two-step correction technique was evaluated using two heavy-precipitation events. Theresults show that the proposed scheme improved not only in the underestimation of rainfall but also reducedthe root-mean-square error and the mean relative error of radar–rain gauge pairs.

Key words: precipitation estimation, adjusted Z–R relationship, gauge correction

Citation: Wang, G. L., L. P. Liu, and Y. Y. Ding, 2012: Improvement of radar quantitative precipitationestimation based on real-time adjustments to Z–R relationships and inverse distance weighting correctionschemes. Adv. Atmos. Sci., 29(3), 575–584, doi: 10.1007/s00376-011-1139-8.

1. Introduction

A number of studies have been focused on radar-based quantitative precipitation estimation (QPE),which is crucial for timely and accurate flood and/orflash flood identification and warnings. Unfortunately,radar rainfall estimates are affected by source er-rors such as radar parameters, inappropriate radarreflectivity-rainfall rates (Z–R) relationships, rain-storm attenuations, hail, and brightband contami-nation (Wilson and Brandes, 1979; Zawadzki, 1984;Zhang et al., 2001). Based on reflectivity observa-tions, the inappropriate Z–R relation is one of themain contributors to radar rainfall underestimation(Baeck and Smith, 1998). The relationship betweenradar reflectivity and surface rainfall rate has beenstudied in the past, and the Z–R relationship has beenclearly shown to be influenced by radar parameters, re-flectivity calibration, and regional rainfall (Zawadzki,

1984; Austin, 1987; Uijlenhoet et al., 2003). One study(Tokay and Short, 1996) has shown that there is sig-nificant variability in the Z–R relationship betweenconvective and stratiform precipitation. Other stud-ies have shown improvement in QPE accuracy using aconvective or stratiform classification for rainfall anddifferent Z–R relationships (Steiner et al., 1995; Anag-nostou and Krajewski, 1999). Identification of tropicalprecipitation based on vertical profiles of reflectivity(VPRs) was developed to improve radar-based quanti-tative precipitation estimation during extreme rainfallevents (Xu et al., 2008). The real-time synchronous in-tegration of radar and rain-gauge measurements basedon quasi-same-rain-volume samples has been used toimprove quantitative precipitation estimations (Wanet al., 2010).

Rain gauges, which measure precipitation directly,are generally considered accurate. The use of raingauges in radar precipitation estimation has been uti-

∗Corresponding author: WANG Gaili, [email protected]

© China National Committee for International Association of Meteorology and Atmospheric Sciences (IAMAS), Institute of AtmosphericPhysics (IAP) and Science Press and Springer-Verlag Berlin Heidelberg 2012

576 IMPROVEMENT OF RADAR QUANTITATIVE PRECIPITATION ESTIMATION VOL. 29

lized since the 1970s. The mean field bias is calculatedby dividing the gauge amount by the radar amount(Wilson and Brandes, 1979; Smith and Krajewski,1991; Seo et al., 1999). The mean field bias representsa bias over any desired spatial domain or time scalebut does not describe biases that may occur at individ-ual rain-gauge stations. The variational method wasapplied to analyze objectively heavy rainfalls basedon radar and rain gauge measurements (Zhang et al.,1992). A Kalman filter has been used to estimateradar-rainfall field bias (Ahnert et al., 1986; Yin andZhang, 2005). Other schemes such as optimum inter-polation, kriging, and co-kriging, have been appliedto analyze radar-rainfall field bias (Bhargava and Da-nard, 1994; Seo, 1998; Li et al., 2000a). Inverse dis-tance weighting (IDW), which is the simplest methodcomputationally among three interpolation methods[i.e., IDW, multiquadric interpolation (MQ), and or-dinary kriging], had been used operationally within theNortheast Regional Climate Center (NRCC) and Na-tional Mosaic and QPE (NMQ) System (Ware, 2005;Zhang et al., 2009).

In this study, the two-step calibration techniqueof radar QPE (the AID scheme) based on a real-time-adjusted Z–R relationship (AZR) scheme and agauge-corrected, radar-based, estimation scheme withIDW interpolation was developed and evaluated. Inthis method, the real-time-adjusted Z–R relationshipscheme is used to remove the systematic bias on thetime-domain, and the gauge-corrected, radar-based,estimation scheme is then used to eliminate inconsis-tent errors in space. Based on radar data and raingauge observation near the Huaihe River, the two-stepcorrection technique was evaluated using two heavy-precipitation events.

This procedure differs from the NMQ method intwo ways. Instead of classifying precipitation regimes,a real-time-adjusted Z–R relationship (AZR) schemeis used. Rather than single hybrid fields, a regional3-D mosaic composite reflectivity field and associatedmosaic composite beam-height field are used to pro-duce a regional hybrid scan reflectivity field.

2. Data description

2.1 Mosaic of hybrid scan reflectivity

Radar data were obtained from the operationalweather radar from the China Meteorological Admin-istration (CMA). The parameters of the radar suchas data formats and detection modes were the stan-dard precipitation observation modes for the VCP21radar. In this study we aimed to produce QPE fieldsin the Huaihe River for blending satellite precipita-tion estimations, radar precipitation estimations, and

rain gauge observations. Seven S-band radars, lo-cated at Hefei, Bangbu, Nanjing, Shanghai, Hangzhou,Xuzhou, and Lianyungang were included in the regionof interest. The radar data were obtained at 6-minintervals.

The regional hybrid reflectivity field, which wasused for rainfall estimations at ground level, was pro-duced based on a regional 3-D mosaic reflectivity fieldand the associated mosaic composite beam-height field(Xiao et al., 2008a). The regional 3-D mosaic reflectiv-ity field was provided by the Doppler Weather Radar3-D Digital Mosaic System (RDMS), which was devel-oped by the State Key Laboratory of Severe Weatherof the Chinese Academy of Meteorological Science(Wang et al., 2009). The single radar reflectivity datawere quality controlled to remove non-precipitationechoes, including ground clutter, electronic interfer-ence, and anomalous propagations. The data werethen interpolated from the spherical coordinate sys-tem onto a regional 3-D mosaic reflectivity field usingRDMS. The data had a horizontal resolution of 0.01◦

latitude/longitude (∼ 1 km ×1 km), including 40 lev-els (at most) with adjustable vertical resolution anda default resolution of 500 m at low levels, 1 km atmiddle levels, and 2 km at high levels. The data werecollected at 6-min intervals, corresponding to singleradar VCP intervals (Xiao et al., 2008a, 2008b; Wanget al., 2009). Based on the regional 3-D mosaic re-flectivity field, several relevant data products were ob-tained from RDMS: composite reflectivity (CR), verti-cally integrated liquid (VIL), echo top (ET), and echoextrapolation. With the combination of the mosaiccomposite beam-height map and the regional 3-D mo-saic reflectivity field, the regional hybrid reflectivityfield was produced to be used for radar quantitativeprecipitation estimation.

Because of the different heights of the hybrid-scanreflectivity pixels, there was substantial deviation be-tween the reflectivity pixel and its adjacent pixels. Themedium filter over a region with 3 × 3 grids was per-formed to eliminate the effect of extreme reflectivity.

2.2 Rain gauge data and simple quality con-trol

The rain gauge data consists of hourly precipita-tion obtained from operational rain-gauge stations inCMA with a space interval of ∼10 km. To evaluate theQPEs, the rain gauges were divided into two groups.The group with an odd index was used for the correc-tion of the radar QPE, while the other was used forevaluating the radar QPE.

To scientifically evaluate the radar QPE, it is neces-sary to perform a quality control procedure on radar–rain gauge (R–G) pairs to eliminate unreasonable data

NO. 3 WANG ET AL. 577

(Li et al., 2009). The exclusion criteria were as follows:(1) R–G pairs with all radar QPEs of zero caused byterrain were removed; (2) R–G pairs with mean rela-tive error > 200% caused by ground clutter were re-moved; and (3) R–G pairs with an absolute error be-tween radar QPE and rain gauge measurements > 30mm h−1 caused by instrument or other factors werealso removed.

3. Algorithm description

3.1 Real-time-adjustedZ–Rrelationship (AZR)scheme

Conventionally, the Z–R relationship is used forconverting radar reflectivity to rainfall. It is wellknown, however, that the relationship is general anddoes not apply well in many cases due to asymmet-ric distribution of precipitation, even within the sameevent. The raindrop spectrum changes with time,space, and different types of precipitation. To ob-tain an optimized Z–R relationship, the standard Z–R relationship can be fitted using rain gauge data andradar reflectivity. The adjusted Z–R relationship canthen be used for radar-based QPE. This AZR schemewas applied in a rainstorm nowcasting system knownas SWIRLS (Short-range Warning of Intense Rain-storms in Localized Systems; Li et al., 2000b).

The AZR scheme is based on the Z–R relationshipof Z = ARb and the following linear formula can beobtained:

10 log Z = 10 log A + b× 10 log R, (1)

where Z is the radar reflectivity factor expressed inmm6 m−3 and R is the rain gauge rainfall expressedin mm h−1.

In this study, radar hybrid scan reflectivity (HSR)mosaic images were used for the adjustment exercise.Because raindrops of different sizes fall at differentrates and because of the delay caused by data upload-ing, the Z–R relationship was adjusted every 30 mininstead of every 5 min, as in SWIRLS. Radar reflectiv-ity was averaged for each pixel in 30 min and then wasmatched to the rain gauge observations. Due to wind,falling raindrops deviate horizontally from their start-ing positions. In this study, a search area over 3 km ×3km grids from each rain gauge position was adjustedto take this effect into account. The average inten-sity value within the search area was matched withthe rain gauge to form a potential radar–rain gauge(R–G) pair.

To eliminate incorrect R–Gs, rain gauge data wererestricted to include only data ranging from 1 mm h−1

to 120 mm h−1. The range of radar reflectivity wasrestricted to include only values from 20 dBZ to 60

dBZ.The R–G pairs underwent a linear least-squares

analysis to determine A and b in Eq. (1). Data show-ing any departure of more than 2 standard deviationunits from the best-fit line were discarded, and the cor-relation was recalculated until a correlation coefficientof r > 0.7 was reached (Li et al., 2000b). When therewere not enough R–G pairs or when the correlationcoefficient was less than a threshold (default 0.7), thestandard Z–R relationship (A = 200, b = 1.6) or theprevious Z–R relationship was used. As more R–Gpairs became available, the Z–R relationship was up-dated accordingly. Our results have proven that thisapproach is able to obtain reasonable Z–R relation-ships.

3.2 Gauge-corrected radar-derived QPEs

The local bias correction scheme used in this studywas based on the method developed by Ware (2005).The first step in the procedure is to calculate an ad-ditive radar rainfall error at each rain gauge locationaccording to the following equation:

ei = gi − ri , (2)

where ei is the error at the ith rain gauge, ri is theradar estimated rainfall at the ith rain gauge, and gi

is the gauge value at the ith rain gauge. These errorvalues are then interpolated over all of the radar hy-brid scan reflectivity (HSR) mosaic images using thefollowing equation:

Re =

n∑i=1

eiwi

n∑i=1

wi

, (3)

where Re is the estimated radar error at the pixel beinginterpolated, wi is the weight assigned to the ith raingauge, and n represents the total number of matchingR–G pairs. Each pixel of the QPE field is correctedby Re.

Ware (2005) showed that the IDW method per-forms better than kriging and similarly to MQ-basedmethods. Its calculations are also simpler than thoseof MQ. The IDW, therefore, was used to calculate cor-rection factors at each pixel of radar-based QPE fieldsin this study.

The weights were calculated using the followingequation (Ware, 2005):

wi ={

1/dbi di 6 D

0 di > D, (4)

where di is the distance (units in degrees) between theradar pixel and the ith rain gauge, b is an exponent,and n is the number of rain gauges within a specifiedradius,D,of the radar pixel. There are differentweights


Fig. 1. Scattered plots of radar-gauge analysis for a rainstorm event on 10 July 2009. The solidline represents the least-squares analysis, and the dashed line represents the general relationshipof Z = 200R1.6. The parameters obtained from the least-squares analysis are the following: (a)at 2000 UTC, A = 333, b = 0.93, correlation coefficient= 0.75, and (b) at 2300 UTC, A = 260,b = 1.15, correlation coefficient= 0.71.

for each radar pixel on each rain gauge. Two parame-ters are the specified radius D and the exponent b, inIDW. Cross-validation was used to calculate the opti-mum parameter values.

4. Case studies

Two cases were examined to assess the improve-ment of the AID scheme in comparison with the othertwo QPE schemes, the general Z–R relationship (Z =200R1.6; GZR) scheme and the AZR scheme. Threesets of QPEs were generated by GZR, AZR, and AIDschemes for each case.

The performances of the three QPE schemes wereassessed by comparing their gridded rainfall accumu-lations with corresponding rain gauge reports. Theperformance of each scheme in the rainfall estimationwas quantified based on the following statistics: (1) themean bias (Bs), (2) the R–G pairs root-mean-squareerror (RMSE), (3) the correlation coefficient (CC), and(4) the mean relative error (E). The representativeformulas are as follows:

Bs =r

g, (5)

RMSE =

√√√√√n∑

i=1

(ri − gi)2

n, (6)

CC =

n∑

i=1

(ri − r)(gi − g)

√√√√n∑

i=1

(ri − r)2(gi − g)2

, (7)

E =1n

n∑

i=1

|ri − gi|gi

× 100%, (8)

where ri and gi represent radar and gauge accumula-tions for any given R–G pair and r and g indicate av-eraging over all such pairs. A bias > 1.0 indicates thatthe radar overestimated the rainfall, and a bias < 1.0indicates that the radar underestimated the rainfall,assuming the gauge report was accurate (Xu et al.,2008). In this study, a valid R–G pair is defined asan R–G pair in which the rain gauge accumulationwas > 1 mm. Smaller accumulations were omittedto reduce errors caused by the minimum precipitationthreshold of the rain gauge. These comparisons wereused to demonstrate improvements shown by the AIDscheme over the other two schemes.

4.1 Heavy rain on 10–12 July 2009

In summer, heavy rains often appear near HuaiheRiver. The heavy rain on 10–12 July 2009 was ex-traordinary and resulted in widespread flooding with6-haccumulations > 80 mm. The focus region wasselected as 30◦–35◦N, 112◦–120◦E, considering theprecipitation mainly observed by Zhengzhou radar,Xuzhou radar and Lianyungang radar. Figure 1 showsthe scattered plots of R–G data and the parametersobtained from the least-squares analysis. This indi-cates that the Z–R relationship obtained is more rea-sonable than the general relationship of Z = 200R1.6,which could cause the underestimation of radar-basedQPE. Figure 1 also indicates that the Z–R relation-ship changes over time even through the same heavyrain case.

Figure 1 also shows that radar reflectivity can devi-ate more than 10 dBZ corresponding to the same raingauge data. In other words, there must be differencebetween radar quantitative precipitation estimationsand surface rain gauge measurements. It is necessaryto correct the radar-based quantitative precipitationestimation using local gauges.


Fig. 2. 6-h radar QPEs between 1800 UTC 10 July and 0000 UTC 11 July 2009 were ob-tained using (a) the GZR scheme, (c) the AZR scheme, and (e) the AID scheme. The scatterplots (b, d, f) show distributions of the 6-h QPEs vs. rain gauge observations.

Figure 2 presents 6-h radar QPEs and the scatterplots of R–G pairs between 1800 UTC 10 July and0000 UTC 11 July 2009. The 6-h radar QPE of theAZR scheme (Fig. 2c) was the strongest, the AIDscheme (Fig. 2e) follows in second place and the GZRscheme (Fig. 2a) was the weakest. Rainfall was under-estimated in the GZR scheme (Bs = 0.70). The under-estimation increased over precipitation strengthening(Fig. 2b). The AZR scheme significantly increased

the accumulation of rainfall, eliminating the under-estimation of rainfall (Bs = 1.01). R–G pairs weredistributed symmetrically on both sides of the diago-nal, or in other words, the accuracy of estimation hadno relation to precipitation intensity. The RMSE, E,and CC of the AZR scheme were close to those of theGZR scheme, which did not improve (Fig. 2d). Inshort, the AZR scheme could eliminate the systematicaverage bias, but it did not improve spatial error.


Fig. 3. Similar to Fig. 1, but for heavy rain on 16 May 2010. (a) 1700 UTC A = 140, b = 1.40,correlation coefficient= 0.81. (b) 2100 UTC A = 238, b = 1.10, correlation coefficient= 0.73.

The AID scheme improved not only the underesti-mation of rainfall (Bs = 0.99) but also the adjustmentof the distribution of the accumulation. The compar-ison between Figs. 2c and e shows that the precip-itation in region 1 was weaker than that in region 2in Fig. 2e after corrections with the radar QPE usingrain gauge observations with the IDW were applied.At the same time, however, the precipitation in region1 is stronger than that in region 2 (Fig. 2c). Region1 is in the radar umbrella at Zhengzhou, and region2 is in the radar umbrella at Xuzhou. By comparingreflectivity in the common observation area for bothof the radars, it can be seen that the Zhengzhou radaris hotter than Xuzhou radar. The AID scheme alsoimproved the RSME from 9.03 mm to 6.58 mm, andimproved E from 40% to 32%, and improved the CCfrom 0.78 to 0.90 (Fig. 2f). These results indicate thatthe AID scheme reduced both the systematic averagebias and the spatial error. Based on the four param-eters of evaluation, the AID scheme performed betterthan the two others for the event. If the general Z–Rrelationship of Z = 200R1.6 had been used instead ofthe adjusted Z–R relationship before using rain gaugeobservations to correct radar-based QPE, underesti-mation would have occurred in the case of heavy rain-fall. Good estimations would have been observed inthe case of general precipitation. For this reason, itshould be remembered that the Z = 200R1.6 relation-ship could significantly underestimate heavy rainfall.

4.2 Heavy rain on 16 May 2010

The overnight rainfall event in southeastern Huaiheon 16 May 2010 was very impressive, with 6-h accumu-lations approaching 100 mm. This event was located inthe region of 30◦–35◦N, 117◦–122◦E. Figure 3 displaysthe scattered plots of R–G pairs and the parametersobtained from the least-squares analysis for this event.

Accordingly, the general relationship of Z =200R1.6 must cause the underestimation of radar-based QPE, and the parameters obtained from the

least-squares analysis of R–G pairs are more reason-able.

Figure 4 presents 6-h radar QPEs and the scatterplots of R–G pairs between 1600 UTC 16 May and2200 UTC 16 May 2010. The 6-h radar QPE of theGZR scheme (Fig. 4a) was the weakest and was ob-viously underestimated, a result that is validated byFig. 3b (Bs = 0.59). The underestimation of rainfallincreased with precipitation strengthening. The AZRscheme significantly increased the accumulated rain-fall (Fig. 4c), improving the underestimation of rain-fall (Bs = 0.94). Still, the RMSE, E, and CC of theAZR scheme were not improved (Fig. 4d). In short,the AZR scheme reduced the systematic average biasbut not the spatial error. The AID scheme improvednot only in the underestimation of heavy rainfall butalso the RMSE, E, and CC (Bs = 0.96, RMSE= 4.14mm, E = 26%, CC = 0.95). The AID scheme improvedboth the systematic average bias and the spatial error.Based on the four parameters of evaluation, the AIDscheme performed better for this event than did thetwo other schemes. If the general Z–R relationship ofZ = 200R1.6 had been used instead of the adjustedZ–R relationship (before rain gauge observations wereused to correct radar-based QPE), the underestima-tion of heavy rainfall would have occurred.

Figures 2f and 4f include several large deviations insome R–G pairs. These large deviations were classifiedinto two categories. One set of rain gauge observationswere much larger than the radar estimates while theother set of rain gauge observations were much lessthan the radar estimates. To eliminate the impact ofblocking from terrain, the deviation analysis was fo-cused on the region in the radar umbrella at Lianyun-gang, where there was no terrain blocking (the radarlocated at 119.294◦N, 34.651◦E).

The R–G pairs with the bias of hourly accumula-tions < 0.5 were analyzed in 6-min intervals during theheavy rainfall periods from 2000 UTC to 2300 UTC.The radar echoes overlapping rain gauge observations


Fig. 4. Similar to Fig. 2, but for the period from 1600 UTC 16 May to 2200 UTC 16 May 2010.


Fig. 5. The radar echo data overlapped the rain gauge data on 10 July 2009 at (a) 2100 UTC and(b) 2130 UTC.

in 6-min intervals show that the R–G pairs with a bias< 0.5 were usually located at the edge of the intenseechoes (two occurrences are shown in Fig. 5). Due towind, some large raindrops deviate horizontally fromtheir starting positions to the adjacent rain gauges,resulting in rain gauge observations much larger thanradar estimates. Figure 5 also shows that in somecases rain at the gauge was marked with an ellipsewhile there was no radar echo. Therefore, the gaugemust have been inaccurate because this phenomenoncontinued for several hours.

5. Summary

The underestimation of heavy precipitation is amajor difficulty in radar QPEs. In this study, atwo-step calibration technique of radar QPE (AIDscheme) based on a real-time-adjusted Z–R relation-ship scheme and gauge-corrected, radar-based, esti-mation scheme with IDW interpolation was developed

to improve quantitative precipitation estimation. Thetechnique uses a real-time-adjusted Z–R relationshipscheme to reduce systematic bias on the time domain,then gauge-corrected, radar-based, estimation schemewith IDW interpolation is used to reduce inconsistenterrors at individual rain gauge stations.

The performance of the AID scheme was exam-ined based on two case studies of heavy precipitationevents. Table 1 summarizes the performance of radarrainfall estimates using GZR, AZR, and AID schemes.The results demonstrate substantial improvement inradar quantitative precipitation estimation using theAID technique. As shown by evaluating the case stud-ies, the AID scheme improved radar estimation of pre-cipitation in not only the underestimate of heavy pre-cipitation (Bs approaching 1) but also the RSME, CC,and E.

R–G pairs with large deviation were usually lo-cated at the edge of radar echoes. Due to wind, largeraindrops deviate horizontally from their starting po-

Table 1. Summary of gauge–radar comparisons using the three schemes.

GZR scheme AZR scheme AID scheme

Bs RMSE CC E Bs RMSE CC E Bs RMSE CC EStudy time period (mm) (mm) (mm)

1-h accumulation ending at 1900UTC 10 July 2009 0.73 3.17 0.87 0.35 0.92 2.33 0.90 0.35 1.00 1.95 0.92 0.293-h accumulation ending at 2100UTC 10 July 2009 0.70 5.63 0.85 0.42 0.87 4.90 0.85 0.40 0.96 3.80 0.91 0.306-h accumulation ending at 0000UTC 11 July 2009 0.70 11.03 0.79 0.44 1.01 9.03 0.78 0.40 0.99 6.58 0.90 0.3224-h accumulation ending at 1100UTC 11 July 2009 0.68 13.84 0.78 0.45 1.01 12.56 0.77 0.42 1.00 9.38 0.88 0.351-h accumulation ending at 2100UTC 16May 2010 0.57 2.41 0.90 0.42 1.00 3.42 0.78 0.41 0.98 2.81 0.88 0.333-h accumulation ending at 2000UTC 16May 2010 0.62 5.14 0.92 0.39 0.90 4.82 0.89 0.38 0.97 3.10 0.98 0.276-h accumulation ending at 2200UTC 16May 2010 0.59 7.73 0.89 0.42 0.94 7.01 0.85 0.38 0.96 4.14 0.95 0.2624-h accumulation ending at 0000UTC 17May 2010 0.69 10.48 0.83 0.44 0.92 10.45 0.84 0.41 0.97 7.84 0.92 0.29

Note: GZR=general Z–R relation; AZR= a real-time-adjusted Z–R relationship; AID= two-step calibration technique of radarQPE; Bs =mean bias; RMSE = root-mean-square error; CC =correlation coefficient; E =mean relative error.


sitions, which causes the deviation of R–G pairs tobecome much larger or smaller.

Various factors, including calibration, finite sam-pling, mechanical failure, funnel blockage, and signaltransmission interference can cause various types ofsystematic and random errors in rain gauge observa-tions. On the other hand, radar data may also becontaminated by ground clutter, electromagnetic in-terference, and/or calibration. Quality control mustbe improved for real-time-adjusted Z–R relationshipsand correcting radar estimates using rain gauge obser-vations. Furthermore, the method of producing the re-gional hybrid reflectivity field, which is used for radarquantitative precipitation estimation, must also be fur-ther developed.

Acknowledgements. This study was supported bythe Special Fund for Basic Research and Operation ofthe Chinese Academy of Meteorological Sciences (GrantNo. 2011Y004)，the Research and Development SpecialFund for Public Welfare Industry (Meteorology; Grant No.GYHY201006042), the National Natural Science Founda-tion of China (Grant No. 40975014), and the Open Re-search Fund for State Key Laboratory of Hydroscience andEngineering of Tsinghua University (the search of basinQPE and QPF based on new generation of weather andnumerical models). The authors also thank Dr. YangHONG at University of Oklahoma for improving the orig-inal manuscript in English. Sincere thanks also go to thetwo anonymous reviewers for their helpful comments onthe original manuscript.

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