research article attenuation correction effects in...

Research ArticleAttenuation Correction Effects in Rainfall Estimation atX-Band Dual-Polarization Radar Evaluation with a DenseRain Gauge Network

Young-A Oh1 DaeHyung Lee1 Sung-Hwa Jung2 Kyung-Yeub Nam2 and GyuWon Lee13

1Department of Astronomy and Atmospheric Sciences Research and Training Team for Future Creative Astrophysicists andCosmologists Kyungpook National University 80 Daehakro Bukgu Daegu 41566 Republic of Korea2Radar Analysis Division Weather Radar Center Korea Meteorological Administration 61 16-Gil Yeouidaebangro DongjakguSeoul 07062 Republic of Korea3Center for Atmospheric REmote Sensing (CARE) Kyungpook National University 80 Daehakro BukguDaegu 41566 Republic of Korea

Correspondence should be addressed to GyuWon Lee gyuwonknuackr

Received 25 December 2015 Accepted 24 April 2016

Academic Editor Hiroyuki Hashiguchi

Copyright copy 2016 Young-A Oh et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The effects of attenuation correction in rainfall estimation with X-band dual-polarization radar were investigated with a denserain gauge network The calibration bias in reflectivity (119885

119867) was corrected using a self-consistency principle The attenuation

correction of 119885119867and the differential reflectivity (119885DR) were performed by a path integration method After attenuation correction

119885119867and 119885DR were significantly improved and their scatter plots matched well with the theoretical relationship between 119885

119867and

119885DR The comparisons between the radar rainfall estimation and the rain gauge rainfall were investigated using the bulk statisticswith different temporal accumulations and spatial averagesThe bias significantly improves from 70 to 0 with 119877(119885

119867) However

the improvement with 119877(119885119867 119885DR) was relatively small from 3 to 1 This indicated that rainfall estimation using a polarimetric

variable was more robust at attenuation than was a single polarimetric variable method The bias did not show improvement incomparisons between the temporal accumulations or the spatial averages in either rainfall estimationmethodHowever the randomerror improved from 68 to 25 with different temporal accumulations or spatial averages This result indicates that temporalaccumulation or spatial average (aggregation) is important to reduce random error

1 Introduction

Weather radar has provided useful information abouthydrometeors for various meteorological and hydrologicalapplications since its introduction inmeteorological observa-tionsWeather radar can observe various parameters ofmete-orological phenomena with high spatiotemporal resolutionover wide observational areas However it suffers frommanyerror sources including radar calibration beam shieldingattenuation bright band contamination beam broadeningand anomalous propagation Many researchers have studiedthe characteristics of these error sources and ways to improvethe quality of radar data [1ndash3]

Recently X-band dual-polarization radar has receivedsignificant attention due to its finer resolution ease of

mobility and lower cost compared to longer wavelengthradars However the attenuation is a very important issue inX-band since it is inversely proportional to radarwavelengthThe values of the radar parameters associated with the back-scattered power such as reflectivity (119885

119867) and differential

reflectivity (119885DR) can be significantly reduced by attenuationThe attenuation is caused by absorption and scattering in

the medium along the propagation path of the radar beamThe attenuation is severe where the medium is dense and itscomposition size is largeThe attenuation by atmospheric gasmolecules is small being about 15 dB per 100 km in the C-band [3] However media such as rain drops hail andmeltedsnow particles can cause significant attenuation especiallyin shorter wavelength radar The amount of attenuation in

Hindawi Publishing CorporationAdvances in MeteorologyVolume 2016 Article ID 9716535 20 pageshttpdxdoiorg10115520169716535

2 Advances in Meteorology

the C-band can reach about 12 dB due to strong convectivecells as compared to the S-band [3] Furthermore the attenu-ation accumulates over distances as a radar beam propagatesThe power is frequently lost completely over far rangesTherefore it is not possible to monitor and analyze severeweather such as heavy rains typhoons and heavy snowswithout the proper correction of the attenuation in the C- orX-band radars

The attenuation correction has been investigated bymanyresearchers Tuttle and Rinehart [4] suggested an attenuationcorrection method using dual-wavelength (S- and X-band)radar measurements with a relationship between specificattenuation (119860

119867) and 119885

119867 Recently the specific differential

propagation phase shift (119870DP) has been used widely forattenuation correction because 119870DP is not affected by radarpower calibration attenuation and partial beam blockingIn addition 119870DP is less sensitive to the natural variability ofdrop size distributions (DSDs) in rainfall estimation Bringiet al [1] showed that both 119860

119867and the specific differential

attenuation (119860DP) are almost linearly related to 119870DP throughscattering simulations and these relationships have beenaccepted by many researchers However the coefficients ofthese relationships derived from the scattering simulationsvary significantly with temperature DSD variability and thedrop deformationmodel Park et al [5] showed that the coef-ficients of 119860

119867-119870DP and 119860DP-119860119867 relationships vary greatly

from 0139 to 0335 dB(∘)minus1 and from 0114 to 0174 dB(∘)minus1 inthe X-band respectively due to changes in temperatures andthe different drop deformation models

While 119870DP has many advantages in the attenuationcorrection as described above estimating 119870DP from themeasured total differential phase shift (ΨDP) is challengingbecause of the backscatter differential phase shift (120575) and themeasurement errors for ΨDP [1] Scarchilli et al [6] used aniterationmethod with a 120575-119885DR relationship to remove 120575 fromΨDP and corrected the attenuation using estimated 119870DP inthe C-band Anagnostou et al [7] Kalogiros et al [8] andChang et al [9] used an iteration method in the X-bandAs a different method for removing 120575 Hubbert and Bringi[10] separated 120575 and the differential propagation phase (ΦDP)from ΨDP through an iterative filtering technique (FIR) andcalculated the hail signal from 120575 Park et al [5] also usedthe same filtering technique to extractΦDP for correcting theattenuation and the differential attenuation in the X-bandRecently Mishra et al [11] investigated dual-polarimetricproducts and three types of rainfall estimation results withhigh spatiotemporal resolution data from X-band radar S-band radar and disdrometer data with an intercomparisonand T-matrix simulation method [12] Mishra et al [11] useda very similar attenuation correction process in their workwhere 119860

119867was calculated by an FIR filtered ΦDP and 119860DP

was calculated by an 119860DP-119860119867 relationship based on a self-consistency method

Two rainfall estimationmethods119877(119885119867) and119877(119885

119867 119885DR)

were used for evaluation of the attenuation correction effectThe self-consistency based correction of the attenuation andthe differential attenuation from the FIR filtered ΦDP wereused to improve the accuracy in the rainfall estimation

methods by X-band polarimetric radar The accuracy eval-uation of the rainfall estimation methods was performedby comparisons with rain gauge measurements with highspatial resolution However there were instrumental uncer-tainties and errors in the representativeness of the raingauge measurements The instrumental error has severalsources including the gauge calibration wind effects andwettingevaporation loss [13 14]The representativeness erroris linked with the spatial sampling area and the tempo-ral accumulation of the rain gauge [15] Habib et al [16]investigated sampling error of the tipping bucket gauge asfunction of accumulation times in a simulation study Ciach[17] verified local random errors in the tipping bucket gaugethrough experimental data Habib et al [18] investigatedthe correlation with separation distances in a rain gaugecluster In this study we considered the calibration effectsin the instrumental error of the rain gauge Instrumentalerror from the calibration effect was removed by laboratoryexperiments to providemore accurate and reliable referencesThe representativeness error was investigated by the temporalaccumulation and spatial average of rainfall amount

In Section 2 the radar and rain gauge data used inthis study are presented The methods for the attenuationcorrection byΦDP the rainfall estimation and its verificationand the analysis of the natural variability of rain fields usingrain gauge data are described in Section 3 The analysisresults are shown in Section 4 The results are summarizedin Section 5

2 Data

21 Radar Data The radar data from the X-band dual-polarimetric radar (NIMS-XPOL) of the National Institute ofMeteorological Sciences (NIMS) was used in this study Thegeneral characteristics of the NIMS-XPOL data are shownin Table 1 The NIMS-XPOL can be installed onto a five-tontruck bed (Figure 1(a)) and mounted on a steel tower bed(Figure 1(b))

The NIMS-XPOL was operated during June 2010 atMuan-gun Jeollanam-do which is on the southwest coastof Korea (latitude = N 350940∘ longitude = E 126285∘) forthe observation of heavy rains during the summer monsoonseason The rain estimation in Section 32 was performedwith the NIMS-X radar data collected during 55 hours from1600UTC to 2130UTC on July 10 2010 During this rainevent the NIMS-X was mounted on a steel tower bed inthe Muan-gun observation center to minimize the effect ofbeam shielding and ground clutter and a full volume scanwith 14 Plan Position Indicators (PPIs) was performed every25minThe gate spacing was 150m and the Pulse RepetitionFrequency (PRF) was 999Hz And the total rainfall amountwas over 50mm The evolution of the rain field is shown inFigure 2 The echoes moved toward the northeast and thesmall and weak rain cells near the radar site at 1601UTCwerereplaced by the strong convective cells approaching from thesouthwest

Advances in Meteorology 3

Table 1 General characteristics of the NIMS-XPOL radar [21]

X-band polarimetric mobile Doppler weather radar (ARC-X250MP) specification

Transmitter

Type MagnetronPeak power (kW) 250Frequency (MHz) 9360

PRF (MHz) 0sim2500

Antenna

Diameter (m) 244Polarization Orthogonal linear simultaneous H amp VBeamwidth (∘) 095Gain (dB) gt43

Data processingNumber of gates 30001000 PRFGate spacing 30m to 1000mRaw data 119885

119867 119881119905 119878119882 119885DR ΦDP 120588HV

(a) (b)

Figure 1 Photographs of the NIMS-XPOL radar installed onto (a) a truck bed and (b) a steel tower bed (courtesy of NIMS)

22 Rain Gauge Data The rain gauge data was collectedby ten tipping bucket (TB) rain gauges operated by theKyungpook National University (KNU) Korea The tip sizeof all of the gauges was 02mm and the diameter of thereceiving orifice was 1539 cm The time resolution was 05 sand the data was recorded based on the event (tipping) timeTo compare with the estimated rain rate (119877) from the NIMS-XPOL radar the rain accumulation from ten gauges wascollected during the month of July 2010 near Unnam-myeonwhich is located at a distance of about 16 km at 160∘ azimuthangle from the NIMS-XPOL radarThe area was only slightlyaffected by beam shielding of the NIMS-XPOL Consideringthe geographical situation and the limited locations for theinstallation all gauges were installed on the rooftops ofbuildings Figure 3 shows the location of the NIMS-XPOLand the deployment of the ten gauges (R is the radar siteand a number represents a gauge location) The total rainfallamount for the month at each gauge site is shown in Table 2At all gauge sites the total rainfall accumulation was over300mm for themonthThe rainfall amountmeasured duringthe same period with the NIMS-XPOL radar data used inthe rainfall estimation was about 50mm per 55 hours (seeTable 2)

The instrumental biases of all gauges were calculatedthrough an ideal experiment using laboratory and fieldobservations for 9 months from October 2009 to June 2010(except April 2010) at KNU The rain gauge dataset was

corrected for the instrumental bias prior to the detailedanalysis

3 Methodology

31 Attenuation Correction AlgorithmUsing Differential Prop-agation Phase Shift The attenuation correction algorithmwas performed by the procedure as shown in Figure 4 whichincluded (1) quality control of the radar data (2) estimationofΦDP (3) calculation of the attenuation amount and (4) theattenuation correction of 119885

119867and 119885DR

As a part of the quality control of the radar data 119885119867and

119885DR were corrected for instrumental biases 119885119867calibration

bias of about 37 dB was obtained by comparison with thereflectivity from the particle size velocity disdrometer (PAR-SIVEL) and from theNIMS-XPOL radarThe119885DR calibrationbias of minus15 dB was calculated from the vertical pointing data[19]The isolated point echo shows that the119885

119867values in their

surrounding pixels existed by less than 50 of the total pixelsto be removed The 120588HV threshold of 09 was applied to theentire radar measurement field

After applying the quality control measures ΦDP wasestimated from measured ΨDP by eliminating 120575 and theobservational noise through an iterative filtering techniqueIn this study the 20th FIR filter of Hubbert and Bringi [10]was used This filter preserved a monotonic increasing trendofΦDP due to the propagation medium while it removed the


1801 1816 1831

19011846

1931 1946 2001

1916

605550454030 35 65 702015100 25minus10

(dBZ)

Figure 2 PPI images of attenuation corrected 119885119867from 1801UTC July 10 2010 with an interval of 15min

Table 2 Total rainfall amount for the month and per analysis time

Gauge ID RG1 RG2 RG3 RG4 RG5 RG6 RG7 RG8 RG9 RG10Total rainfall amount for the month (mm) 3214 3717 3308 3139 3218 3426 3321 3239 3743 3245Total rainfall amount for the analysis time (mm) 476 560 510 529 552 571 544 544 513 531

smaller scale fluctuations compared to the filtering window(25 km when the gate size is 0125m) due to 120575 and theobservation noise Hubbert and Bringi [10] also found thatrepeating the filtering process 10 times produced good results

The additional problem in the estimation of ΦDP wasthe variable offset of ΦDP ΦDP observation can be noisyin near range Radar in general has ΦDP offset to avoidobserving negative value of ΦDP in near range Ideally theoffset should not change with the azimuthal angles Howeverthe offsets of measured ΨDP of the NIMS-X varied withthe azimuthal angles and ΦDP values decreased near theradar when rain cells existed above the radar Therefore

the offset was determined as the minimum value of ΦDPwithin 3 km of the radar and estimated filtered ΨDP wasadjusted accordingly

The calculation of 119860119867

and 119860DP was based on thefollowing two relationships [1 5 20]

119860119867 (119903) = 120590119870DP (119903)

119860DP (119903) = 120576119860119867 (119903) (1)

where 119860119867(119903) and 119860DP(119903) are the specific attenuation and

the specific differential attenuation at range 119903 from the radar


3510

3506

3502

3498

3494 Unnam

12628 12636 12644

1 234 96

8 75

10

R

Figure 3 Layout of NIMS-XPOL and the 10 rain gauges nearUnnam-myeon Muan-gun Jeollanam-do Korea R shows thelocation of the NIMS-XPOL the numbered points indicate theobservational sites of the 10 rain gauges

respectively119870DP(119903) is the specific differential one-way phaseshift calculated using the following equation

119870DP (119903) =ΦDP (1199032) minus ΦDP (1199031)

2 (1199032minus 1199031)

(2)

where 119903 is between 1199031and 1199032 The coefficients 120590 (= 03445)

and 120576 (= 01705) were derived from 119860119867 119860DP and 119870DP

obtained by scattering simulations with the DSDs data col-lected by the PrecipitationOccurrence Sensor System (POSS)from March to September of 2001 in Pusan Korea [21] Thetotal path integrated attenuation and differential attenuationwere calculated withΦDP by integrating the following

2int

119903

0

119860119867(1199031015840) 1198891199031015840= 120590ΦDP (119903) (3)

2int

119903

0

119860DP (1199031015840) 1198891199031015840= 120576 times 2int

119903

0

119860119867(1199031015840) 1198891199031015840 (4)

Number 2 in the equations indicates that the values are two-way values

Finally the measured reflectivity 119885119867-meas(119903) [dBZ] and

the differential reflectivity 119885DR-meas(119903) [dB] at 119903 were cor-rected with the calculated two-way path integrated attenua-tion and differential attenuation

119885119867-corr (119903) = 119885119867-meas (119903) + 2int

119903

0

119860119867(1199031015840) 1198891199031015840

119885DR-corr (119903) = 119885DR-meas (119903) + 2int119903

0

119860DP (1199031015840) 1198891199031015840

(5)

32 Radar Rain Estimation and Comparison with Rain GaugeData A comparison between estimated 119877 from the radar

Measured dual-polarization parameters(ZH ZDR ΦDP 120588HV)

Quality control

(ii) Speckling echo removal

(i) Calibration for instrumental bias of ZH ZDR

(iii) 120588HV threshold application

(ii) Adjustment of its offset(i) 20th FIR filter application to ΨDP

Estimation of ΦDP

Calculation of AH and ADP

Correction of ZH and ZDR

from DSDs120590 and 120576

Figure 4 The schematic diagram of the attenuation correctionalgorithm

parameters and the rain rate (119866) from the rain gauge data wasperformed to evaluate the attenuation correction algorithmIn addition to the rain attenuation the difference between119877 and 119866 was caused by the errors due to the instrumentaluncertainty and representativeness errors of the rain gaugedata the radar observational noise and the errors in the radarrainfall estimation The bias due to the instrumental uncer-tainty in gauge data was removed by properly calibrating thegauges through laboratory tests and a gauge intercomparisonThe representativeness errors were due to the mismatch ofthe sampling area (volume) between the gauge and the radarThe random error in the gauge data could be minimized bytime and areal integrationThe errors due to themeasurementnoise in the radar data could be reduced in a similar mannerThe time offset between the rain gauge and the radar samplingarea was ignored due to the close distance (about 16 km) andthe low elevation angle (3∘)

Therefore 119877 and 119866 were derived with two different radarsampling areas and with increasing accumulation time

(1)119877(038 km2) versus119866(0071198982)119877(038 km2)was estimated

from the average radar measurement with 9 pixels (038 km2at 16 km range) The gauge rainfall rate 119866(007m2) wasderived from the rainfall accumulation from an individualrain gauge that had a sampling area of 007m2

(2) 119877(6 1198961198982) versus 119866(6 1198961198982

) 119877(6 km2) was estimated fromthe areal averaged radar parameters at a 16 km times 31 km radar


Table 3 Two rain rate retrieval algorithms and boundary conditions [22]

119877 (119885119867) = 120572119885

120573

119867119877 (119885DR) = 120572119885

120573

1198671001120574119885DR

Z gt 35 dBZ Z lt 35 dBZ Z gt 35 dBZ 119885DR gt 03 dB Z lt 35 dBZ 119885DR gt 03 dB120572 353 times 10

minus2383 times 10

minus2103 times 10

minus2145 times 10

minus2

120573 621 times 10minus2

608 times 10minus2

985 times 10minus1

890 times 10minus1

120574 mdash mdash minus6479 minus5295

measurement resolution 119866(6 km2) was the average value of119866(007m2) from the ten gauges within the same area

Estimated 119877 from radar parameters was calculated withtwo rain estimators as shown in Table 3These rain estimatorswere derived by a least squares fit with the theoretical 119885

119867

119885DR and 119877 obtained by scattering simulations with theDSD data collected by POSS from March to Septemberof 2001 in Pusan Korea [21] To improve the estimationaccuracy each estimator was derived for two categoriesThe reflectivity threshold of 35 dBZ was used as a stan-dard stratiformconvective rain classification [22] The 119885DRthreshold of 03 dB was used to minimize the effect of the119885DR measurement noiseThePPI data with an elevation angleof 3∘ was used to suppress the beam shielding and groundclutterThe119885

119867and119885DR fields from the radar were smoothed

by the linear average of values at 3 times 3 pixels to reduce theobservational noise

The bias in 119866 from the ten rain gauges was corrected bythe laboratory test and the intercomparison with field dataThe detail is presented in Appendix To evaluate the atten-uation correction algorithm and verify the rainfall retrievalaccuracy the comparisons of119877 and119866were represented by thegeneral statistics such as normalized bias (NB) normalizedstandard deviation (NSD) root-mean square error (rmse)relative rms error (r rmse) and Spearman correlation (corr)as follows

NB119877-119866 (Δ119905) =

(1119899)sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

119866 (Δ119905)

NSD119877-119866 (Δ119905) =

radic(1119899)sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119866 (Δ119905)

rmse119877-119866 (Δ119905) =

radicsum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119899

rmse119877-119866 (Δ119905) = radic

sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

sum119899minus1

119896=0[119866119896 (Δ119905)]

2

corr119877-119866 (Δ119905)

=

sum119899minus1

119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)]

2radicsum119899minus1

119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(6)

where 119899 is the number of 119877 and 119866 pairs at a given temporalintegrationΔ119905 and the overbar indicates the temporal average

33 Spatial Correlation and Variability of the Rain FieldsRain gauges are widely used to measure rainfall amountsdue tomany advantages including easy installation mobilitylow price and ease of data processing The rain gauge datais used as a reference for the ground rainfall amount forthe evaluation of rain retrieval algorithms adjustment ofother instruments data assimilation and other hydrologicalapplications However it is affected by instrumental errorsand representativeness errors due to the variability of rainfields

In a TB rain gauge the instrumental errors are due toimproper calibration the time delay of the tips leakage dueto its measuring principle and so forthThis error is exploredin the Appendix

The representativeness errors are subdivided into spatialand temporal representativeness They are mainly caused byhaving a small sampling area and a limited sampling time dueto the gauge measuring principle The actual rain fields varywith different spatiotemporal scales that are not equivalentto the spatial and temporal resolution of the rain gaugeTherefore the rain gauge data represent the actual rain fieldsin a very limited manner

These errors should be considered and minimized priorto using rain gauge data as ground truth Furthermore thedegree of these errors has to be understood quantitativelysince there can be other error sources in various applicationsIn this section the spatial and temporal variability of the rainfields are investigated using the rain data collected by the tenrain gauges for the month of July 2010 at Muan Korea

First the Spearman correlation coefficient 119903119894119895(Δ119905)

between a pair of 119866 values from the 119894th and 119895th individualrain gauge with integration time Δ119905 was calculated fromthe following equation to obtain the Spearman correlationcoefficient of the rain fields

119903119894119895 (Δ119905)

=

sum119899minus1

119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)]


119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(7)

where 119899 is the number of gauge data pairs at given Δ119905 and theoverbar indicates the temporal average of the rainfall rate Itwas derived withΔ119905 to research the spatial and temporal scaleof the variation for the rain field

In addition the effect of the natural variability of the rainfields within two different areas (038 km2 and 6 km2) wasexplored by analyzing the bias and random error between thespatially averaged rainfall rate ⟨119866⟩ and 119866 from the individual


32km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(a)

32 km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(b)

Figure 5 PPIs of measured (a) and filtered (b) ΨDP of the NIMS-XPOL at 2101UTC July 10 2010

gauge The NB and NSD of 119866119894with ⟨119866⟩ were calculated as

follows

NB (119894) =(sum119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]) 119899

⟨119866 (Δ119905)⟩

NSD (119894) =(1119899)radic(sum

119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]

2)

⟨119866 (Δ119905)⟩

(8)

where 119894 indicates the 119894th gauge and the overbar indicates thetemporal average

This analysis provided a reasonable spatial average andtemporal accumulation resolution for the calculation ofmoreaccurate and realistic rainfall amounts from the gauge dataand a quantitative guideline regarding the errors in rainestimation due to the variability of the rain fields

4 Results

41 Attenuation Correction of Reflectivity and DifferentialReflectivity The attenuation correction algorithm in Sec-tion 31 was applied to the NIMS-XPOL radar data ΦDPwas estimated by eliminating 120575 and the observational noisefrom measured ΨDP using an iterative FIR filter The offsetof ΦDP was then adjusted Figure 5 shows the PPIs ofmeasured ΨDP and filtered ΦDP After applying the FIR filterthe small scale variation due to 120575 and observational noisein measured ΨDP was reduced and filtered ΨDP (estimatedΦDP) monotonically increased with an increase in rangeThe maximum value of estimated ΦDP reached to 140∘ Inaddition estimated ΦDP at the azimuth angles of 150∘ and200∘ sharply increased with the loss of signal beyond thesesharp gradient areas This reflected that strong convective

cells existed in these directions and that these cells caused thesevere signal attenuation EstimatedΦDP values between 250

∘

and 360∘ azimuth angle decreased after filtering since ΦDPoffsets were positive values in these directions Figure 6 showsthe range profile of measured and filtered ΨDP for estimationof ΦDP at 71

∘ 160∘ and 334∘ azimuth angles The unexpectedlarge values near the radarwere removed by the120588HV threshold(red line)The small fluctuation inmeasuredΨDP due to 120575 andthe observational noise was effectively removed after filteringThe value of estimated ΦDP was adjusted to 0 by the offset(blue line)

Estimated ΦDP was used to calculate the path integrated119860119867 and the measured119885

119867values were corrected as shown in

Figure 7 Figure 7(a) represents measured-attenuated119885119867and

relatively small values of 119885119867at far ranges This may indicate

that the 119885119867values at far ranges were affected by the strong

attenuation due to strong convective cells near the radarThisspatial pattern of 119885

119867was the typical feature of the attenuated

radar signal due to the rain After correcting the attenuationthe value of the 119885

119867field became larger over the entire area

and the radially attenuated 119885119867

was corrected by showinga typical rain cell pattern in 119885

119867(Figure 7(b)) The largest

difference between the uncorrected and the corrected 119885119867at

2101UTCwas over 50 dB However the white area behind thestrong echoes was not detected as there was a complete loss ofthe signal powerThese regions could not be corrected by thisalgorithmThe circle pattern of119885

119867fields within about a 4 km

range from theNIMS-XPOL could not present the actual rainechoes due to the instrumental issues (the same was true for119885DR) These results are also presented in the range profiles inFigure 8

Similarly measured 119885DR were corrected with the pathintegrated 119860DP derived from the path integrated 119860

119867using

(4) (see Figure 9) Before applying attenuation correction


Measured dataPreprocessed dataCorrected data

10 20 30 40 50 600Slant range (km)

0

50

100

150

200

ΦDP (∘) azimuth angle = 71∘

(a)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(b)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(c)

Figure 6 Range profiles of measured (black) 120588HV threshold isolated point removing (red) and FIR filter and offset adjusted (blue) ΨDP forestimation of ΦDP at 71

∘ (a) 160∘ (b) and 334∘ (c) azimuth angles of NIMS-XPOL for the case in Figure 5

32km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(a)

32 km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(b)

Figure 7 PPIs of measured (a) and attenuation corrected (b) 119885119867of the NIMS-XPOL for the case in Figure 5



10 20 30 40 50 600Slant range (km)

ZH (dBZ) azimuth angle = 71∘

minus20

0

20

40

60

80

(a)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(b)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(c)

Figure 8 Range profiles of measured (line) calibration bias 120588HV threshold and isolated point removing (dot) and attenuation corrected(dash) 119885

119867at 71∘ (a) 160∘ (b) and 334∘ (c) azimuth angles of NIMS-XPOL for the case in Figure 5

the attenuation signature in119885DR was determined Ideally the119885DR value for rain should be positive since rain drops areoblate due to aerodynamic force However themeasured119885DRfield in Figure 9 showed a negative value over wide areasAfter correcting the attenuation the119885DR field was larger than0 dB and showed a realistic rain patternThis is also presentedin the range profile of Figure 10The largest difference of119885DRbetween before and after attenuation correction at 2101UTCwas about 8 dB The 119885DR values around the 220∘ azimuthangle beyond 40 km were the largest They did not matchwith the area of the largest 119885DR values (around the 210∘azimuth angle with a range of 20 km and 40 km) This wasan unexpected result because 119885DR is proportional to 119885

119867in

theory This mismatch between 119885119867

and 119885DR at far rangemay be due to contamination due to beam broadening andaccumulated errors due to uncertainty in the attenuationcorrection with different ranges

Figures 11 and 12 show the time series of 119885119867

and119885DR at the ten gauge sites before and after applying theattenuation correction The differences between uncorrectedand corrected values existed after 1800UTC and were at amaximumaround 2100UTCThis attenuation correctionwas

evaluated through comparison with the theoretical values of119885119867and 119885DR In Figure 13 the uncorrected 119885

119867-119885DR scatter

plots are apart from the theoretical119885119867-119885DR values [23] After

attenuation correction the119885119867-119885DR scatter plots were close to

the calculated valuesThis indicated that119885119867and119885DR over the

gauge sites were corrected with reliable values

42 Variability of the Rain Fields The Spearman correlationcoefficient of the rainfall rate from the 10 spatially dis-tributed rain gauges was calculated with accumulation timeand separation distance (Figure 14) The overall Spearmancorrelation coefficient decreased with increasing separationdistance at all accumulation timesThis tendency was similarto the result from Habib and Krajewski [24] However thecorrelation value was higher in this study Note that the gaugetip resolution in Habib and Krajewski [24] was 0254mmwhile it was 02mm in this study In addition the rainfall ratesfrom the gauge data used in this study mainly consisted ofmoderate rainfall rates while Habib and Krajewski [24] useddata containing heavy rainfall rates

For accumulation times of less than 10min the corre-lation at the same distance was dramatically increased with


32km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(a)

32 km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(b)

Figure 9 PPIs of measured (a) and attenuation corrected (b) 119885DR of NIMS-XPOL for the case in Figure 5

increasing accumulation time and the slope of the correlationfunction was steep This was due to the reduction of theinstrumental errors of the gauge data by time accumulationThis indicated that rainfall accumulated for less than 10minfrom single gauge data cannot represent the rainfall over itssurrounding area due to instrumental errors For accumula-tion times longer than 10min the slope became less steepThis reflected the remaining variability of the rain field Inaddition the accumulated rainfall rate of about 10min wassuitable for minimizing the instrumental uncertainty whilepreserving the variation in the rain field The correlationreached about 098 at 05 km in 10min of accumulationand this approached 098 at 10 km at 60min accumulationTherefore a single rain gauge mostly represented the rainfallrate within 05 km and 10 km with 10min and 60minaccumulation respectively

The NB between an areal averaged rainfall rate ⟨119866⟩ anda single gauge rainfall rate 119866 is shown with accumulationtime in Figures 15(a) and 16(a) Where the average area was038 km2 (corresponding to 9 pixels of NIMS-XPOL radarat 16 km range) the NB reached a 6ndash8 maximum Wherethe averaged area is 6 km2 (corresponding to the coverage forall of the gauges) the NB reached about a 10 maximumFurthermore the NB hardly changed with accumulationtime Note that this statistic was derived after removinginstrumental bias This indicated that the rainfall rate froma single gauge was biased due to the spatial variability of therain fields and this bias was maintained with accumulationtime

The NSD of a single gauge for a mean area of 038 km2was over 40 and it reached about 70ndash90 for a mean areaof 6 km2 at an accumulation time of 1min (see Figures 15(b)and 16(b)) This statistic included instrumental errors (about

40ndash60 at 16mmhminus1 and 60ndash80 at 10mmhminus1 as shownin the Appendix) as well as the spatial variability of the rainfields This indicated that the variance between the point andarea values from the gauge data at short accumulation timeswas similar to the errors due to the instrumental uncertaintyof the rain gaugeTheNSD in 60min accumulation decreasedto over 10 and about 15ndash45 with a mean area of 038 km2and 6 km2 respectively including the NSD of 6ndash10 due toinstrumental uncertainty This indicated that the rainfall ratefrom single gauges may differ significantly from the actualrainfall rate due to the variability of the rain fields and theinstrumental uncertainty in short accumulation times

43 Verification of Rainfall Retrieval The rainfall rate fromthe NIMS-XPOL radar measurements was retrieved withtwo rainfall rate estimators 119877(119885

119867) and 119877(119885

119867 119885DR) The

estimated rainfall rate was verified through comparison withthe rainfall rate (119866) from the rain gauge data These twoestimators were applied before and after the attenuation cor-rection First 119877(038 km2) was compared with 119877(007 km2)at 10min accumulation (Figure 17) Using 119877(119885

119867) the NB

NSD rmse and r rmse without the attenuation correctionwere significantly large at 70 127 127 (mmhr) and78 respectively However they were reduced to minus152 521 (mmhr) and 32 respectively after applying theattenuation correction Using 119877(119885

119867 119885DR) the NB was just

3 NSD was 49 rmse was 496 (mmhr) and r rmsewas 31 before applying attenuation correction This wassimilar to the result from 119877(119885

119867) after attenuation correction

However there was no significant change in119877(119885119867 119885DR)with

attenuation correction This means that 119877(119885119867 119885DR) was less

sensitive to rain attenuation than was 119877(119885119867) because 119885

119867is

proportional to 119877 and 119885DR is inversely proportional to 119877



10 20 30 40 50 600Slant range (km)

ZDR (dB) azimuth angle = 71∘

minus10

minus5

0

5

10

(a)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(b)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(c)

Figure 10 Range profiles of measured (line) calibration bias 120588HV threshold and isolated point removing (dot) and attenuation corrected(dash) 119885DR at 71∘ (a) 160∘ (b) and 334∘ (c) azimuth angles of NIMS-XPOL for the case in Figure 5

in this rain estimator (see Table 3) Furthermore comparingthe analysis of variance results between areal (038 km2) andpoint (007m2) values from the gauge data (Section 42)half of the errors after attenuation correction were producedby the small scale variability of the rain fields and theinstrumental uncertainty of the rain gauge

A similar comparison is shown in Figure 18 for a 60minaccumulation Using 119877(119885

119867) the NB NSD rmse and r rmse

were decreased from minus65 86 71 (mmhr) and 70to minus5 34 28 (mmhr) and 28 by the attenuationcorrection respectively Using 119877(119885

119867 119885DR) the NB NSD

rmse and r rmse were only slightly decreased after theattenuation correction However the NSD rmse and r rmsewere reduced when compared at 10min accumulation In thesame accumulation time the errors in the gauge data reachedto over 15

This comparison was affected by different sampling areasof the gauges and the radar Therefore the areal averagevalues were compared (Figure 19) Using119877(119885

119867)with the areal

averaged radar measurements the NB was reduced fromminus69 to 7 NSD was reduced from 122 to 42 rmsewas reduced from 39 (mmhr) to 13 (mmhr) and r rmse

was reduced from 77 to 26 at an accumulation time of10min Using 119877(119885

119867 119885DR) the NB NSD rmse and r rmse

were decreased fromminus24 67 21 (mmhr) and 42 to 539 12 (mmhr) and 24 respectively

TheNB and r rmsewithmatched sampling areas betweenthe gauge and the radar are shown in Figures 20 and 21 Thereduction of NB due to temporal accumulation was smallin both of the rain estimators The NB was reduced to lessthan 7 by attenuation correction for all accumulation timeswith both119877(119885

119867) and119877(119885

119867 119885DR)The attenuation correction

effect was significantly greater in119877(119885119867) Similarly the r rmse

was reduced significantly in 119877(119885119867) by attenuation correction

(from 68 to 25 at a 60min accumulation) The reductionof the r rmse due to temporal accumulation was larger in119877(119885119867 119885DR) because the significant observational noise of

119885DR was smoothed The r rmse was decreased from 18to 15 in 119877(119885

119867 119885DR) at a 60min accumulation time after

attenuation correction

5 Conclusions

In this study an attenuation correction algorithm based onΦDP was developed to improve the accuracy of the rainfall


1st gauge site 2nd gauge site

3rd gauge site 4th gauge site

5th gauge site 6th gauge site



17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

UncorrectedCorrected


Figure 11 Time series of measured (red circle) and attenuation corrected (blue circle) 119885119867at the 10 rain gauge sites




17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

Figure 12 Time series of measured (red circle) and attenuation corrected (blue circle) 119885DR at the 10 rain gauge sites


minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Corrected Simulated from DSD(b)

Figure 13 Scatter plots of 119885119867and 119885DR before (a) and after (b) attenuation correction at the 10 rain gauge sites DSD observation results (dot

[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41

Range between two rain gauges (km)

0 2 3 41

Range between two rain gauges (km)0 2 3 41


0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min

Figure 14 The Spearman correlation coefficient 119903 between data from two rain gauges at different accumulation times

estimation using X-band radar This algorithm was evalu-ated with radar measurements from NIMS-XPOL Howevermeasured ΨDP contained 120575 and observation noise as wellas ΦDP Furthermore the ΨDP offset varied with azimuthangles and decreased near the radar when rain cells were

above the radar In this study ΦDP was estimated by aniterative filtering technique and by adjusting with an offsetdetermined as the minimum value ofΦDP within 3 km of theradar As a result estimated ΦDP monotonically increasedThe path integrated value of119860

119867and119860DP was calculated from


2nd 6th 9th gaugesMean NB

10 1001

Accumulation time (min)

minus20

minus10

0

10

20

NB

()

⟨G⟩(038km2) versus G

(a) Normalized bias


2nd 6th 9th gaugesMean NSD

Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001


(b) Normalized standard deviation

Figure 15 (a) The NB and (b) NSD between ⟨119866⟩(038 km2) and 119866 from three rain gauges with accumulation time ⟨119866⟩ is the temporallyaveraged rainfall rate of ⟨119866⟩

All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001



Figure 16 (a) The NB and (b) NSD between ⟨119866⟩(6 km2) and 119866 from 10 rain gauges with accumulation time ⟨119866⟩ is the temporally averaged⟨119866⟩ with accumulation time

estimated ΦDP using 119860119867-ΦDP and 119860DP-ΦDP relationships

derived from the DSDs data Measured 119885119867

and 119885DR werecorrected with the calculated path integrated 119860

119867and 119860DP

by each gate The attenuated signal patterns of 119885119867and 119885DR

were restored to a typical rain echo pattern However theattenuation corrected 119885

119867and 119885DR fields were not matched

at distant ranges This was likely because of contaminationdue to beam broadening and the accumulation of errorswith increasing range Comparing the 119885

119867-119885DR scatter plots

over the 10 rain gauge sites with the results obtained froma scattering simulation with the DSD data the attenuation

corrected 119885119867-119885DR scatter plots are in good agreement with

the 119885119867-119885DR scatter plots from the DSDs

The validation for the improvement of accuracy in therainfall estimation through attenuation correction was per-formed by comparing with dense rain gauge network data119877(119885119867) from the attenuated (observed)119885

119867produced a severe

underestimation with an NB NSD rmse and r rmse of70 127 127 (mmhr) and 78 at 10min accumulationrespectively while 119877(119885

119867) from the attenuation corrected 119885

119867

showed better agreement with the gauge measurements withan NB NSD rmse and r rmse of minus1 52 521 (mmhr)


R(m

mh

)

CorrectedUncorrected

0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh

)CorrectedUncorrected

20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)

Figure 17 The scatter plots of 119877(038 km2 10min) versus 119866(007m2 10min) (a) using 119885119867and (b) using 119885

119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR

and 32 at 10min accumulation respectively At 60minaccumulation theNBNSD rmse and r rmsewere decreasedfrom minus65 86 71 (mmhr) and 70 to minus5 3428 (mmhr) and 28 respectively Using 119877(119885

119867 119885DR) the

NB NSD rmse and r rmse were only slightly reduced even if

attenuation was corrected but were smaller than when using119877(119885119867) This indicated that 119877(119885

119867 119885DR) was less sensitive to

the attenuation than 119877(119885119867) In addition half of the errors

that remained after attenuation correction were caused by thesmall scale variability of the rain fields and the instrumental


R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)

Figure 19 The scatter plots of 119877(6 km2 10min) versus 119866(6 km2 10min) (a) using 119885119867and (b) using 119885

119867and 119885DR

R(ZH)

20 40 60 80 1000Accumulation time (min)

minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)

Figure 20 The normalized bias of 119877(6 km2) versus 119866(6 km2) with an accumulation time (a) using 119885119867and (b) using 119885

119867and 119885DR The red

point-line and the blue point-line indicate without and with the attenuation correction respectively

uncertainty of the rain gauges Using an areal averagedvalue the NB was reduced to less than 7 with attenua-tion correction using either rainfall estimator regardless ofaccumulation timeThe r rmse were significantly reduced byattenuation correction in 119877(119885

119867) and the reduction of r rmse

with 119877(119885119867 119885DR) was even more dramatic

As summarized above the rain attenuation for 119885119867

and 119885DR in the X-band was corrected by ΦDP and theresults showed a good agreement with the value obtainedby scattering simulations with the DSD datasets The resultsof comparison with rain gauge data also showed a signifi-cant improvement in the accuracy of rainfall estimation by


CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)

Figure 21 The relative root-mean square error of 119877(6 km2) versus 119866(6 km2) with an accumulation time (a) using 119885119867and (b) using 119885

119867and

119885DR The red point-line and the blue point-line indicate without and with the attenuation correction respectively

attenuation correction which supports the quantitative useof the X-band radar in rain data retrieval

Appendix

A Instrumental Uncertainty of the Rain Gauge

The instrumental uncertainty of the TB rain gauge is asso-ciated with improper calibration leakage and precipitationmissing the gauge due to the measurement principle andwetting and evaporation losses In addition external sourcessuch as wind turbulence and installed position also con-tribute to the instrumental uncertainty Ciach [17] reportedthat the TB gauge data suffers a significant uncertainty asso-ciated with random differences between closely collocatedTB gauges through the analysis of the error as a functionof the rainfall intensity for three timescales In addition theimproper calibration induces a bias in the rainfall measure-ment and this bias cannot be removed by increasing accu-mulation timeTherefore the proper correction or processingof TB gauge data is necessary to obtain accurate and reliablereading of the rainfall amount

In this appendix instrumental biases were calculatedto reduce the instrumental uncertainty through an idealexperiment in the laboratory and a field intercomparisonwith 10 TB rain gauges In addition the random errors werequantitatively calculated as a function of rainfall rate andaccumulation time

A1 Correction of Instrumental Bias The instrumental bias119861119868(119894) of the 119894th gauge was defined as a combination

of the absolute bias 119861119860(ref) of the reference gauge and

the relative bias 119861119877(119894) of the 119894th gauge according to the

following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)

119861119860(ref) signified the ratio of the calculated value from

the instrumental resolution of the reference gauge to the truevalue measured by other instruments

119861119860 (ref) =

rainfalltruthrainfallgauge (ref)

(A2)

In this study 119861119860(ref) was derived by an ideal experiment

using an electronic scale First the reference gauge was puton the scale and the scale was initialized The water dropsflowed out into the receiving orifice of the reference gaugeuntil the tipping number became 60Themeasured weight of60 tips was 2144 g while the theoretical (or expected) valuewas 2244 g for the reference gauge (receiving orifice size of1545 cm 60 tips and 02mm tip resolution) Therefore theabsolute bias of the reference gauge from (A2) was about0955 This indicates that the rainfall amount measured bythis reference gauge was overestimated by about 45 andthis bias should be corrected prior to any interpretation

119861119877(119894) represented the ratio of the observed (recorded)

value from the 119894th gauge to the observed (recorded) valuefrom the reference gauge

119861119877 (119894) =

rainfallgauge (ref)rainfallgauge (119894)

(A3)

119861119877(119894) was calculated from ten collocated rain gauges

including the reference gauge located at an observation field


Table 4 The instrumental and relative biases of the 10 tipping bucket rain gauges

Gauge ID RG1 RG2 RG3 RG4 RG5 RG6 RG7 RG8 RG9 RG10Instrumental bias 094 108 099 100 096 104 098 102 108 098Relative bias 098 113 103 105 100 109 102 107 113 102

013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()

Figure 22 Two-dimensional normalized standard deviationbetween the standard rainfall and each rain gauge

at KNUKoreaThe observational period for intercomparisonwas from October 2009 to June 2010 (14 rainy days) andthe total accumulated rainfall for this period was about300mm The results are presented in Table 4 All relativebiases were mainly larger than 10 This indicated that themost of gauges underestimated the rainfall amount comparedto the reference rain gauge The relative bias of the referencegauge (119894 = 5) was 10

Finally 119861119860(119894) was calculated from (A1) (see Table 4) All

instrumental biases were between 090 and 11 and the meanvalue of the biases was nearly 10 This indicated that therainfall rate from a single gauge data had a maximum 10bias These biases were corrected for each gauge to removeexisting instrumental errors

A2 Quantification of Random Errors To quantify the ran-dom error due to instrumental uncertainty the NSD of theten gauges was calculated with accumulation time and rainrate using data from an intercomparison The NSD of the 119894thgauge compared to the reference gauge was derived for 20rain rate classes (Δ119877) and 17 accumulation time classes (Δ119905)as follows

NSD119894 (Δ119905 Δ119877)

=

(1119899)radicsum119899minus1

119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)

where 1198661015840 and 119866 indicate the reference and individual gaugesrespectively The overbar means the temporal average ofthe rainfall rate The NSDs of nine different gauges (exceptthe reference gauge) were averaged to obtain the two-dimensional average NSD (Figure 22) The average NSD

tended to decrease with increasing accumulation time andwith increasing rain rate The NSD was about 10ndash15when accumulation time was 10min and the rain rate was10mmhminus1 The instrumental errors were quite significant forlonger accumulation times and higher rainfall rates Theseerrors should be used as a guideline when a single gauge isused as a reference for any validation study

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This paper has been revised and extended fromMs Young-AOhrsquos MS thesis [25] of Kyungpook National University Thisresearch is supported by Development and Application ofCross Governmental Dual-Pol Radar Harmonization (WRC-2013-A-1) project of theWeather Radar Center KoreaMeteo-rological AdministrationThis work was funded by the KoreaMeteorological Administration Research and DevelopmentProgram under Grant KMIPA2015-1010

References

[1] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onradar measurements at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[2] A Huggel W Schmid and AWaldvogel ldquoRaindrop size distri-butions and the radar bright bandrdquo Journal of AppliedMeteorol-ogy vol 35 no 10 pp 1688ndash1701 1996

[3] G W Lee Errors in rain measurement by radar effect of vari-ability of drop size distributions [PhD thesis]McGill University2003

[4] J D Tuttle and R E Rinehart ldquoAttenuation correction in dual-wavelength analysesrdquo Journal of ClimateampAppliedMeteorologyvol 22 no 11 pp 1914ndash1921 1983

[5] S-G Park V N Bringi V Chandrasekar M Maki andK Iwanami ldquoCorrection of radar reflectivity and differentialreflectivity for rain attenuation at X band Part I theoretical andempirical basisrdquo Journal of Atmospheric and Oceanic Technol-ogy vol 22 no 11 pp 1621ndash1632 2005

[6] G Scarchilli E Gorgucci V Chandrasekar and T A SeligaldquoRainfall estimation using polarimetric techniques at C-bandfrequenciesrdquo Journal of Applied Meteorology vol 32 no 6 pp1150ndash1160 1993

[7] M N Anagnostou E N Anagnostou and J VivekanandanldquoCorrection for rain path specific and differential attenuation ofX-band dual-polarization observationsrdquo IEEE Transactions onGeoscience and Remote Sensing vol 44 no 9 pp 2470ndash24802006


[8] J Kalogiros M N Anagnostou E N Anagnostou M Mon-topoli E Picciotti and F S Marzano ldquoEvaluation of a newpolarimetric algorithm for rain-path attenuation correction ofX-band radar observations against disdrometerrdquo IEEE Transac-tions on Geoscience and Remote Sensing vol 52 no 2 pp 1369ndash1380 2014

[9] W-Y Chang J Vivekanandan and T-C C Wang ldquoEstimationof X-band polarimetric radar attenuation and measurementuncertainty using a variational methodrdquo Journal of AppliedMeteorology and Climatology vol 53 no 4 pp 1099ndash1119 2014

[10] J Hubbert and V N Bringi ldquoAn iterative filtering technique forthe analysis of copolar differential phase and dual-frequencyradar measurementsrdquo Journal of Atmospheric and OceanicTechnology vol 12 no 3 pp 643ndash648 1995

[11] K V Mishra W F Krajewski R Goska et al ldquoDeploy-ment and performance analyses of high-resolution iowa XPOLradar system during the NASA IFloodS campaignrdquo Journal ofHydrometeorology vol 17 no 2 pp 455ndash479 2016

[12] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[13] M D Humphrey J D Istok J Y Lee J A Hevesi and AL Flint ldquoA new method for automated dynamic calibration oftipping-bucket rain gaugesrdquo Journal of Atmospheric andOceanicTechnology vol 14 no 6 pp 1513ndash1519 1997

[14] E HabibW F Krajewski V Nespor andA Kruger ldquoNumericalsimulation studies of rain gage data correction due to windeffectrdquo Journal of Geophysical ResearchAtmospheres vol 104 no16 Article ID 1999JD900228 pp 19723ndash19733 1999

[15] G J Ciach and W F Krajewski ldquoOn the estimation of radarrainfall error variancerdquoAdvances inWater Resources vol 22 no6 pp 585ndash595 1999

[16] E Habib W F Krajewski and A Kruger ldquoSampling errors oftipping-bucket rain gaugemeasurementsrdquo Journal of HydrologicEngineering vol 6 no 2 pp 159ndash166 2001

[17] G J Ciach ldquoLocal random errors in tipping-bucket rain gaugemeasurementsrdquo Journal of Atmospheric andOceanic Technologyvol 20 no 5 pp 752ndash759 2003

[18] EHabibW F Krajewski andG J Ciach ldquoEstimation of rainfallinterstation correlationrdquo Journal ofHydrometeorology vol 2 no6 pp 621ndash629 2001

[19] NIMS ldquoStudy on estimation of rainfall amount and classifi-cation of hydrometeor species using dual-polarimetric radar(III)rdquo pp 1ndash20 2010

[20] E Gorgucci V Chandrasekar and L Baldini ldquoCorrection ofX-band radar observation for propagation effects based on theself-consistency principlerdquo Journal of Atmospheric and OceanicTechnology vol 23 pp 1668ndash1681 2006

[21] NIMS ldquoStudy on estimating raindrop size distribution forquantitative estimation of radar rainfall amountrdquo pp 1ndash55 2009

[22] NIMS ldquoQuantitative precipitation estimation and hydrometeoridentification using dual-polarization radar-Phase IIrdquo pp 1ndash742009

[23] S-G Park M Maki K Iwanami V N Bringi and V Chan-drasekar ldquoCorrection of radar reflectivity and differential reflec-tivity for rain attenuation at X band Part II Evaluation andapplicationrdquo Journal of Atmospheric and Oceanic Technologyvol 22 no 11 pp 1633ndash1655 2005

[24] E Habib and W F Krajewski ldquoUncertainty analysis of theTRMM ground-validation radar-rainfall products applicationto the TEFLUN-B field campaignrdquo Journal of Applied Meteorol-ogy vol 41 no 5 pp 558ndash572 2002

[25] Y-A Oh Rainfall estimation from X-band dual-polarizationradar measurements effects of attenuation correction and evalu-ation with a dense rain gauge network [MS thesis] KyungpookNational University 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of


EarthquakesJournal of


Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining


Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of


Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering


GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

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OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in


MineralogyInternational Journal of


MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Geological ResearchJournal of


Geology Advances in


the C-band can reach about 12 dB due to strong convectivecells as compared to the S-band [3] Furthermore the attenu-ation accumulates over distances as a radar beam propagatesThe power is frequently lost completely over far rangesTherefore it is not possible to monitor and analyze severeweather such as heavy rains typhoons and heavy snowswithout the proper correction of the attenuation in the C- orX-band radars

The attenuation correction has been investigated bymanyresearchers Tuttle and Rinehart [4] suggested an attenuationcorrection method using dual-wavelength (S- and X-band)radar measurements with a relationship between specificattenuation (119860

119867) and 119885

119867 Recently the specific differential

propagation phase shift (119870DP) has been used widely forattenuation correction because 119870DP is not affected by radarpower calibration attenuation and partial beam blockingIn addition 119870DP is less sensitive to the natural variability ofdrop size distributions (DSDs) in rainfall estimation Bringiet al [1] showed that both 119860

119867and the specific differential

attenuation (119860DP) are almost linearly related to 119870DP throughscattering simulations and these relationships have beenaccepted by many researchers However the coefficients ofthese relationships derived from the scattering simulationsvary significantly with temperature DSD variability and thedrop deformationmodel Park et al [5] showed that the coef-ficients of 119860

119867-119870DP and 119860DP-119860119867 relationships vary greatly

from 0139 to 0335 dB(∘)minus1 and from 0114 to 0174 dB(∘)minus1 inthe X-band respectively due to changes in temperatures andthe different drop deformation models

While 119870DP has many advantages in the attenuationcorrection as described above estimating 119870DP from themeasured total differential phase shift (ΨDP) is challengingbecause of the backscatter differential phase shift (120575) and themeasurement errors for ΨDP [1] Scarchilli et al [6] used aniterationmethod with a 120575-119885DR relationship to remove 120575 fromΨDP and corrected the attenuation using estimated 119870DP inthe C-band Anagnostou et al [7] Kalogiros et al [8] andChang et al [9] used an iteration method in the X-bandAs a different method for removing 120575 Hubbert and Bringi[10] separated 120575 and the differential propagation phase (ΦDP)from ΨDP through an iterative filtering technique (FIR) andcalculated the hail signal from 120575 Park et al [5] also usedthe same filtering technique to extractΦDP for correcting theattenuation and the differential attenuation in the X-bandRecently Mishra et al [11] investigated dual-polarimetricproducts and three types of rainfall estimation results withhigh spatiotemporal resolution data from X-band radar S-band radar and disdrometer data with an intercomparisonand T-matrix simulation method [12] Mishra et al [11] useda very similar attenuation correction process in their workwhere 119860

119867was calculated by an FIR filtered ΦDP and 119860DP

was calculated by an 119860DP-119860119867 relationship based on a self-consistency method

Two rainfall estimationmethods119877(119885119867) and119877(119885

119867 119885DR)

were used for evaluation of the attenuation correction effectThe self-consistency based correction of the attenuation andthe differential attenuation from the FIR filtered ΦDP wereused to improve the accuracy in the rainfall estimation

methods by X-band polarimetric radar The accuracy eval-uation of the rainfall estimation methods was performedby comparisons with rain gauge measurements with highspatial resolution However there were instrumental uncer-tainties and errors in the representativeness of the raingauge measurements The instrumental error has severalsources including the gauge calibration wind effects andwettingevaporation loss [13 14]The representativeness erroris linked with the spatial sampling area and the tempo-ral accumulation of the rain gauge [15] Habib et al [16]investigated sampling error of the tipping bucket gauge asfunction of accumulation times in a simulation study Ciach[17] verified local random errors in the tipping bucket gaugethrough experimental data Habib et al [18] investigatedthe correlation with separation distances in a rain gaugecluster In this study we considered the calibration effectsin the instrumental error of the rain gauge Instrumentalerror from the calibration effect was removed by laboratoryexperiments to providemore accurate and reliable referencesThe representativeness error was investigated by the temporalaccumulation and spatial average of rainfall amount

In Section 2 the radar and rain gauge data used inthis study are presented The methods for the attenuationcorrection byΦDP the rainfall estimation and its verificationand the analysis of the natural variability of rain fields usingrain gauge data are described in Section 3 The analysisresults are shown in Section 4 The results are summarizedin Section 5

2 Data

21 Radar Data The radar data from the X-band dual-polarimetric radar (NIMS-XPOL) of the National Institute ofMeteorological Sciences (NIMS) was used in this study Thegeneral characteristics of the NIMS-XPOL data are shownin Table 1 The NIMS-XPOL can be installed onto a five-tontruck bed (Figure 1(a)) and mounted on a steel tower bed(Figure 1(b))

The NIMS-XPOL was operated during June 2010 atMuan-gun Jeollanam-do which is on the southwest coastof Korea (latitude = N 350940∘ longitude = E 126285∘) forthe observation of heavy rains during the summer monsoonseason The rain estimation in Section 32 was performedwith the NIMS-X radar data collected during 55 hours from1600UTC to 2130UTC on July 10 2010 During this rainevent the NIMS-X was mounted on a steel tower bed inthe Muan-gun observation center to minimize the effect ofbeam shielding and ground clutter and a full volume scanwith 14 Plan Position Indicators (PPIs) was performed every25minThe gate spacing was 150m and the Pulse RepetitionFrequency (PRF) was 999Hz And the total rainfall amountwas over 50mm The evolution of the rain field is shown inFigure 2 The echoes moved toward the northeast and thesmall and weak rain cells near the radar site at 1601UTCwerereplaced by the strong convective cells approaching from thesouthwest




Transmitter


PRF (MHz) 0sim2500

Antenna



119867 119881119905 119878119882 119885DR ΦDP 120588HV

(a) (b)





3 Methodology


119867and 119885DR








1801 1816 1831

19011846

1931 1946 2001

1916

605550454030 35 65 702015100 25minus10

(dBZ)









119860119867 (119903) = 120590119870DP (119903)

119860DP (119903) = 120576119860119867 (119903) (1)




3510

3506

3502

3498

3494 Unnam

12628 12636 12644

1 234 96

8 75

10

R



119870DP (119903) =ΦDP (1199032) minus ΦDP (1199031)

2 (1199032minus 1199031)

(2)




2int

119903

0

119860119867(1199031015840) 1198891199031015840= 120590ΦDP (119903) (3)

2int

119903

0

119860DP (1199031015840) 1198891199031015840= 120576 times 2int

119903

0

119860119867(1199031015840) 1198891199031015840 (4)




119885119867-corr (119903) = 119885119867-meas (119903) + 2int

119903

0

119860119867(1199031015840) 1198891199031015840


0

119860DP (1199031015840) 1198891199031015840

(5)



Quality control





Estimation of ΦDP









(2) 119877(6 1198961198982) versus 119866(6 1198961198982




119877 (119885119867) = 120572119885

120573

119867119877 (119885DR) = 120572119885

120573

1198671001120574119885DR


minus2383 times 10

minus2103 times 10

minus2145 times 10

minus2


608 times 10minus2

985 times 10minus1

890 times 10minus1




119867





NB119877-119866 (Δ119905) =

(1119899)sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

119866 (Δ119905)

NSD119877-119866 (Δ119905) =


119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119866 (Δ119905)

rmse119877-119866 (Δ119905) =


119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119899

rmse119877-119866 (Δ119905) = radic

sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

sum119899minus1

119896=0[119866119896 (Δ119905)]

2

corr119877-119866 (Δ119905)

=

sum119899minus1

119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)]


119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(6)








119903119894119895 (Δ119905)

=

sum119899minus1

119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)]


119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(7)




32km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(a)

32 km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(b)



follows

NB (119894) =(sum119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]) 119899

⟨119866 (Δ119905)⟩

NSD (119894) =(1119899)radic(sum

119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]

2)

⟨119866 (Δ119905)⟩

(8)



4 Results



∘




















119867using




10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(a)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(b)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(c)



32km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(a)

32 km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(b)




10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(a)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(b)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(c)




119867in






119867-119885DR scatter








32km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(a)

32 km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(b)







119867) and 119877(119885

119867 119885DR) The


119867) the NB








119867is




10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(a)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(b)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(c)






119867 119885DR) the NB NSD









119867) and119877(119885








5 Conclusions








17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




Transmitter


PRF (MHz) 0sim2500

Antenna



119867 119881119905 119878119882 119885DR ΦDP 120588HV

(a) (b)





3 Methodology


119867and 119885DR








1801 1816 1831

19011846

1931 1946 2001

1916

605550454030 35 65 702015100 25minus10

(dBZ)









119860119867 (119903) = 120590119870DP (119903)

119860DP (119903) = 120576119860119867 (119903) (1)




3510

3506

3502

3498

3494 Unnam

12628 12636 12644

1 234 96

8 75

10

R



119870DP (119903) =ΦDP (1199032) minus ΦDP (1199031)

2 (1199032minus 1199031)

(2)




2int

119903

0

119860119867(1199031015840) 1198891199031015840= 120590ΦDP (119903) (3)

2int

119903

0

119860DP (1199031015840) 1198891199031015840= 120576 times 2int

119903

0

119860119867(1199031015840) 1198891199031015840 (4)




119885119867-corr (119903) = 119885119867-meas (119903) + 2int

119903

0

119860119867(1199031015840) 1198891199031015840


0

119860DP (1199031015840) 1198891199031015840

(5)



Quality control





Estimation of ΦDP









(2) 119877(6 1198961198982) versus 119866(6 1198961198982




119877 (119885119867) = 120572119885

120573

119867119877 (119885DR) = 120572119885

120573

1198671001120574119885DR


minus2383 times 10

minus2103 times 10

minus2145 times 10

minus2


608 times 10minus2

985 times 10minus1

890 times 10minus1




119867





NB119877-119866 (Δ119905) =

(1119899)sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

119866 (Δ119905)

NSD119877-119866 (Δ119905) =


119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119866 (Δ119905)

rmse119877-119866 (Δ119905) =


119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119899

rmse119877-119866 (Δ119905) = radic

sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

sum119899minus1

119896=0[119866119896 (Δ119905)]

2

corr119877-119866 (Δ119905)

=

sum119899minus1

119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)]


119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(6)








119903119894119895 (Δ119905)

=

sum119899minus1

119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)]


119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(7)




32km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(a)

32 km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(b)



follows

NB (119894) =(sum119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]) 119899

⟨119866 (Δ119905)⟩

NSD (119894) =(1119899)radic(sum

119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]

2)

⟨119866 (Δ119905)⟩

(8)



4 Results



∘




















119867using




10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(a)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(b)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(c)



32km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(a)

32 km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(b)




10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(a)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(b)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(c)




119867in






119867-119885DR scatter








32km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(a)

32 km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(b)







119867) and 119877(119885

119867 119885DR) The


119867) the NB








119867is




10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(a)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(b)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(c)






119867 119885DR) the NB NSD









119867) and119877(119885








5 Conclusions








17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


1801 1816 1831

19011846

1931 1946 2001

1916

605550454030 35 65 702015100 25minus10

(dBZ)









119860119867 (119903) = 120590119870DP (119903)

119860DP (119903) = 120576119860119867 (119903) (1)




3510

3506

3502

3498

3494 Unnam

12628 12636 12644

1 234 96

8 75

10

R



119870DP (119903) =ΦDP (1199032) minus ΦDP (1199031)

2 (1199032minus 1199031)

(2)




2int

119903

0

119860119867(1199031015840) 1198891199031015840= 120590ΦDP (119903) (3)

2int

119903

0

119860DP (1199031015840) 1198891199031015840= 120576 times 2int

119903

0

119860119867(1199031015840) 1198891199031015840 (4)




119885119867-corr (119903) = 119885119867-meas (119903) + 2int

119903

0

119860119867(1199031015840) 1198891199031015840


0

119860DP (1199031015840) 1198891199031015840

(5)



Quality control





Estimation of ΦDP









(2) 119877(6 1198961198982) versus 119866(6 1198961198982




119877 (119885119867) = 120572119885

120573

119867119877 (119885DR) = 120572119885

120573

1198671001120574119885DR


minus2383 times 10

minus2103 times 10

minus2145 times 10

minus2


608 times 10minus2

985 times 10minus1

890 times 10minus1




119867





NB119877-119866 (Δ119905) =

(1119899)sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

119866 (Δ119905)

NSD119877-119866 (Δ119905) =


119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119866 (Δ119905)

rmse119877-119866 (Δ119905) =


119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119899

rmse119877-119866 (Δ119905) = radic

sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

sum119899minus1

119896=0[119866119896 (Δ119905)]

2

corr119877-119866 (Δ119905)

=

sum119899minus1

119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)]


119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(6)








119903119894119895 (Δ119905)

=

sum119899minus1

119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)]


119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(7)




32km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(a)

32 km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(b)



follows

NB (119894) =(sum119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]) 119899

⟨119866 (Δ119905)⟩

NSD (119894) =(1119899)radic(sum

119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]

2)

⟨119866 (Δ119905)⟩

(8)



4 Results



∘




















119867using




10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(a)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(b)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(c)



32km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(a)

32 km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(b)




10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(a)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(b)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(c)




119867in






119867-119885DR scatter








32km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(a)

32 km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(b)







119867) and 119877(119885

119867 119885DR) The


119867) the NB








119867is




10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(a)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(b)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(c)






119867 119885DR) the NB NSD









119867) and119877(119885








5 Conclusions








17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


3510

3506

3502

3498

3494 Unnam

12628 12636 12644

1 234 96

8 75

10

R



119870DP (119903) =ΦDP (1199032) minus ΦDP (1199031)

2 (1199032minus 1199031)

(2)




2int

119903

0

119860119867(1199031015840) 1198891199031015840= 120590ΦDP (119903) (3)

2int

119903

0

119860DP (1199031015840) 1198891199031015840= 120576 times 2int

119903

0

119860119867(1199031015840) 1198891199031015840 (4)




119885119867-corr (119903) = 119885119867-meas (119903) + 2int

119903

0

119860119867(1199031015840) 1198891199031015840


0

119860DP (1199031015840) 1198891199031015840

(5)



Quality control





Estimation of ΦDP









(2) 119877(6 1198961198982) versus 119866(6 1198961198982




119877 (119885119867) = 120572119885

120573

119867119877 (119885DR) = 120572119885

120573

1198671001120574119885DR


minus2383 times 10

minus2103 times 10

minus2145 times 10

minus2


608 times 10minus2

985 times 10minus1

890 times 10minus1




119867





NB119877-119866 (Δ119905) =

(1119899)sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

119866 (Δ119905)

NSD119877-119866 (Δ119905) =


119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119866 (Δ119905)

rmse119877-119866 (Δ119905) =


119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119899

rmse119877-119866 (Δ119905) = radic

sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

sum119899minus1

119896=0[119866119896 (Δ119905)]

2

corr119877-119866 (Δ119905)

=

sum119899minus1

119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)]


119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(6)








119903119894119895 (Δ119905)

=

sum119899minus1

119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)]


119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(7)




32km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(a)

32 km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(b)



follows

NB (119894) =(sum119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]) 119899

⟨119866 (Δ119905)⟩

NSD (119894) =(1119899)radic(sum

119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]

2)

⟨119866 (Δ119905)⟩

(8)



4 Results



∘




















119867using




10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(a)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(b)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(c)



32km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(a)

32 km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(b)




10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(a)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(b)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(c)




119867in






119867-119885DR scatter








32km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(a)

32 km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(b)







119867) and 119877(119885

119867 119885DR) The


119867) the NB








119867is




10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(a)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(b)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(c)






119867 119885DR) the NB NSD









119867) and119877(119885








5 Conclusions








17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



119877 (119885119867) = 120572119885

120573

119867119877 (119885DR) = 120572119885

120573

1198671001120574119885DR


minus2383 times 10

minus2103 times 10

minus2145 times 10

minus2


608 times 10minus2

985 times 10minus1

890 times 10minus1




119867





NB119877-119866 (Δ119905) =

(1119899)sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

119866 (Δ119905)

NSD119877-119866 (Δ119905) =


119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119866 (Δ119905)

rmse119877-119866 (Δ119905) =


119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

119899

rmse119877-119866 (Δ119905) = radic

sum119899minus1

119896=0[119877119896 (Δ119905) minus 119866119896 (Δ119905)]

2

sum119899minus1

119896=0[119866119896 (Δ119905)]

2

corr119877-119866 (Δ119905)

=

sum119899minus1

119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119877119894119896 (Δ119905) minus 119877119894 (Δ119905)]


119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(6)








119903119894119895 (Δ119905)

=

sum119899minus1

119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)] [119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]


119896=0[119866119894119896 (Δ119905) minus 119866119894 (Δ119905)]


119896=0[119866119895119896 (Δ119905) minus 119866119895 (Δ119905)]

2

(7)




32km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(a)

32 km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(b)



follows

NB (119894) =(sum119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]) 119899

⟨119866 (Δ119905)⟩

NSD (119894) =(1119899)radic(sum

119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]

2)

⟨119866 (Δ119905)⟩

(8)



4 Results



∘




















119867using




10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(a)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(b)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(c)



32km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(a)

32 km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(b)




10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(a)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(b)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(c)




119867in






119867-119885DR scatter








32km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(a)

32 km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(b)







119867) and 119877(119885

119867 119885DR) The


119867) the NB








119867is




10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(a)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(b)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(c)






119867 119885DR) the NB NSD









119867) and119877(119885








5 Conclusions








17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


32km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(a)

32 km

21 km

11 km

20km40km60km

minus180 18020 30 40 50 60 70 80 90 100120140160100(b)



follows

NB (119894) =(sum119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]) 119899

⟨119866 (Δ119905)⟩

NSD (119894) =(1119899)radic(sum

119899minus1

119896=0[119866119894119896 (Δ119905) minus ⟨119866119896 (Δ119905)⟩]

2)

⟨119866 (Δ119905)⟩

(8)



4 Results



∘




















119867using




10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(a)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(b)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(c)



32km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(a)

32 km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(b)




10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(a)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(b)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(c)




119867in






119867-119885DR scatter








32km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(a)

32 km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(b)







119867) and 119877(119885

119867 119885DR) The


119867) the NB








119867is




10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(a)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(b)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(c)






119867 119885DR) the NB NSD









119867) and119877(119885








5 Conclusions








17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(a)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(b)


10 20 30 40 50 600Slant range (km)

0

50

100

150

200


(c)



32km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(a)

32 km

21 km

11 km

20km40km60km

minus10 10 15 20 25 30 35 40 45 50 55 60 65 700(b)




10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(a)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(b)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(c)




119867in






119867-119885DR scatter








32km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(a)

32 km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(b)







119867) and 119877(119885

119867 119885DR) The


119867) the NB








119867is




10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(a)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(b)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(c)






119867 119885DR) the NB NSD









119867) and119877(119885








5 Conclusions








17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(a)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(b)


10 20 30 40 50 600Slant range (km)


minus20

0

20

40

60

80

(c)




119867in






119867-119885DR scatter








32km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(a)

32 km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(b)







119867) and 119877(119885

119867 119885DR) The


119867) the NB








119867is




10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(a)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(b)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(c)






119867 119885DR) the NB NSD









119867) and119877(119885








5 Conclusions








17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


32km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(a)

32 km

21 km

11 km

20km40km60km

18

14

00

02

04

06

26

40

minus10

22

minus20

30

10

50

minus30

(b)







119867) and 119877(119885

119867 119885DR) The


119867) the NB








119867is




10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(a)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(b)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(c)






119867 119885DR) the NB NSD









119867) and119877(119885








5 Conclusions








17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(a)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(b)


10 20 30 40 50 600Slant range (km)


minus10

minus5

0

5

10

(c)






119867 119885DR) the NB NSD









119867) and119877(119885








5 Conclusions








17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)

minus20

0

20

40

60

ZH

(dBZ

)







17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




17 18 19 20 2116Time (h)

17 18 19 20 2116Time (h)






minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)

minus6

minus4

minus2

0

2

4

6

ZD

R(d

B)



minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)

Uncorrected(a)

minus6

minus4

minus2

0

2

4

ZD

R(d

B)

0 10 20 30 40 50 60 70minus10

ZH (dBZ)



[21])

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41



0 2 3 41


04

05

06

07

08

09

10

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

04

05

06

07

08

09

10

Cor

relat

ion

coeffi

cien

tr

0 2 3 41


0 2 3 41


Accum time = 1min

Accum time = 10min

Accum time = 2min

Accum time = 20min

Accum time = 5min

Accum time = 60min







10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias



Mean R

0

20

40

60

80

100

NSD

()

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

10 1001




All gaugesMean NB

10 1001


minus20

minus10

0

10

20

NB

()


(a) Normalized bias

0

5

10

15

20

Mea

n ra

in ra

te (m

mh

)

0

20

40

60

80

100

NSD

()

All gaugesMean NSD

Mean R


10 1001







119867and 119860DP













119867



R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus070

NSD = 127

rmse = 1279

corr = 0858

Corrected

NB = minus001

NSD = 052

rmse = 521

corr = 0927

r_rmse = 0786 r_rmse = 0320

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = 003

NSD = 049

rmse = 496

r_rmse = 0305

corr = 0936

Corrected

NB = 001

NSD = 050

rmse = 502

r_rmse = 0308

corr = 0936

(b) 119877(119885119867119885DR)


119867and 119885DR


R(m

mh

)

0

10

20

30

40

10 20 30 400G (mmh)

Uncorrected

NB = minus065

NSD = 086

rmse = 706

r_rmse = 0702

corr = 0878

Corrected

NB = minus005

NSD = 034

rmse = 281

r_rmse = 0279

corr = 0866

(a) 119877(119885119867)


R(m

mh

)

10 20 30 400G (mmh)

0

10

20

30

40

Uncorrected

NB = 008

NSD = 023

rmse = 189

r_rmse = 0188

corr = 0942

Corrected

NB = 007

NSD = 025

rmse = 205

r_rmse = 0203

corr = 0940

(b) 119877(119885119867119885DR)


119867and 119885DR


119867 119885DR) the







R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


R(m

mh

)


0

20

40

60

80

20 40 60 800G (mmh)

Uncorrected

NB = minus069

NSD = 122

rmse = 391

r_rmse = 0770

corr = 0893

Corrected

NB = 007

NSD = 042

rmse = 133

r_rmse = 0262

corr = 0960

(a) 119877(119885119867)

R(m

mh


20 40 60 800G (mmh)

0

20

40

60

80

Uncorrected

NB = minus024

NSD = 067

rmse = 215

r_rmse = 0424

corr = 0718

Corrected

NB = 005

NSD = 039

rmse = 124

r_rmse = 0245

corr = 0891

(b) 119877(119885119867119885DR)


119867and 119885DR

R(ZH)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(a) 119877(119885119867)

R(ZH ZDR)


minus10

minus08

minus06

minus04

minus02

00

02

04

NB


(b) 119877(119885119867119885DR)










CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


CorrectedMean R

Uncorrected


00

02

04

06

08

10r_

rmse

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH)

(a) 119877(119885119867)

CorrectedMean R

Uncorrected


00

02

04

06

08

10

r_rm

se

6

7

8

9

10

11

Mea

n ra

in ra

te (m

mh

)

R(ZH ZDR)

(b) 119877(119885119867119885DR)


119867and



Appendix







following equation

119861119868 (119894) = 119861119860 (ref) times 119861119877 (119894) (A1)



119861119860 (ref) =


(A2)





119861119877 (119894) =


(A3)






013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




013610152230406080120150200250300400

()

Rain

rate

(mm

h)

100101


10

100NSD ()






NSD119894 (Δ119905 Δ119877)

=


119896=0[1198661015840

119870(Δ119905 Δ119877) minus 119866119894119896 (Δ119905 Δ119877)]

2

1198661015840

(A4)



Competing Interests


Acknowledgments


References




































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in





























Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

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