Journal of Hydrology 542 (2016) 343–356

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Journal of Hydrology

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Research papers

Similarity and difference of global reanalysis datasets (WFD andAPHRODITE) in driving lumped and distributed hydrological modelsin a humid region of China

http://dx.doi.org/10.1016/j.jhydrol.2016.09.0110022-1694/� 2016 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: State Key Laboratory of Water Resources andHydropower Engineering Science, Wuhan University, Wuhan 430072, PR China.

E-mail address: c.y.xu@geo.uio.no (C.-Y. Xu).

Hongliang Xu a,d, Chong-Yu Xu b,c,⇑, Sidian Chen a, Hua Chen b

a School of Environment and Energy, Peking University Shenzhen Graduate School, Shenzhen, PR Chinab State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, PR ChinacDepartment of Geosciences, University of Oslo, PO Box 1047 Blindern, N-0316 Oslo, NorwaydDepartment of Land Resources and Tourism, Nanjing University, 163 Xianlin Road, Qixia District, Nanjing, Jiangsu 210023, PR China

a r t i c l e i n f o

Article history:Received 1 April 2016Received in revised form 5 July 2016Accepted 2 September 2016Available online 4 September 2016This manuscript was handled by K.Georgakakos, Editor-in-Chief, with theassistance of Carlos Jimenez, AssociateEditor

Keywords:Xiangjiang River basinReanalysisWFDAPHRODITEXinanjiang ModelSWAT Model

a b s t r a c t

Different conclusions have been drawn in literature as using reanalysis rainfall products to drive hydro-logical models for the simulation of streamflow, which warrant a need of further investigation before ageneralised conclusion can be drawn. This paper assesses the utility of two widely used reanalysis rainfalldatasets (WFD (developed by the WATCH project) and APHRODITE (Asian Precipitation–Highly-ResolvedObservational Data Integration Towards Evaluation of the water resources)) against the gauged rainfall interms of flood simulation in lumped (Xinanjiang Model) and distributed (SWAT Model) hydrologicalmodels in a tributary basin of Yangtze River with 94,660 km2 drainage area in humid region of southernChina. Differences in terms of rainfall accumulation, number of rainy days, spatial patterns of the rainfallamount and frequency distribution of the rain rates are evaluated. The APHRODITE product shows highconsistency with the gauged rainfall while WFD data gives large errors in various statistical indices in thestudy region. Simulated discharges from the gauged and reanalysis rainfall data, respectively, are anal-ysed and compared with the observed discharge in basin outlet over the period 1991–2005. TheAPHRODITE data show relatively high ability in modelling hydrological responses while the WFD databased models give large error in simulating the discharge. For the assessment of the high flows, bothdatasets exhibit some skills in flood prediction, however, APHRODITE data perform better than theWFD data when forcing into the lumped Xinanjiang Model than into the distributed SWAT Model interms of flood duration, Probability of Detection, False Alarm Rate, regressions of annual peaks and partialduration series.

� 2016 Elsevier B.V. All rights reserved.

1. Introduction weather systems and climate variability (Bosilovich et al., 2009).

Understanding the spatial and temporal variations of precipita-tion is vital for studying hydrologic cycle and water resources onglobal and regional scales. Accurate precipitation informationplays an important role in both scientific studies and applicationfields such as fresh water assessment and management, and riskreduction of flood and drought. Traditionally, precipitation volumeis measured by pluviometers over basin scales. However, due tothe limitation of economic and topographic conditions, many areasare poorly gauged or ungauged. In recent decades, the global scalereanalysis precipitation datasets which are based on data assimila-tion systems have become a valuable source of data for studying

Precipitation estimates from atmospheric reanalysis products withspatial and temporal continuity provide a potential alternative inregions where there is a lack of conventional in situ precipitationmeasurements (Tong et al., 2014).

With technological advancements, many global reanalysismeteorological datasets are available in recent decades (e.g. theGlobal Precipitation Climatology Project (GPCP), the Global Precip-itation Climatology Centre (GPCC), theWATCH Forcing Data (WFD),the ERA Interim Reanalysis, the Climatic Research Unit (CRU) pre-cipitation database, etc.). In general, a typical reanalysis dataset iscomposed of two main components: the data assimilation andforecast systems. The role of the data assimilation system is merg-ing available observational data into a mathematical model to getan objective estimate of the state which can be propagated throughthe model to obtain a prediction (McDougall, 2012). Globalretrospective analyses (reanalysis) products provide long-term

344 H. Xu et al. / Journal of Hydrology 542 (2016) 343–356

hydrologic datasets that can support global frequency analyses ofhydrologic extremes (Seyyedi et al., 2015). Many studies show thatthe reanalysis datasets which yield long-term records of atmo-spheric and surface fields have great potential in hydrologicalresearches (e.g. Serreze and Hurst, 2000; Marengo, 2004;Frauenfeld et al., 2005; Betts, 2009; Silva et al., 2011; Sushamaet al., 2014; etc.). However, although the reanalysis precipitationproducts generally agree in their temporal trends and spatial distri-bution, remarkable differences at basin scales can be observed(Adler et al., 2000; Li et al., 2013). Maidment et al. (2013) evaluatedthree satellite based products and two reanalysis rainfall productsin Uganda, East Africa by the help of a network including 27 raingauges in 2001–2005. The study showed that the reanalysis prod-ucts tended to misestimate the rainfall in rainy season whereasall three satellite products showed similar characteristics comparedwith the gauged data. Bosilovich et al. (2009) compared five reanal-ysis precipitation datasets with two observed data products toassess the strengths and weaknesses of the reanalysis datasetsand indicated that spatial patterns of the NCEP–NCAR (NationalCentres for Environmental Prediction—National Centre for Atmo-spheric Research) reanalysis data were closer to observed precipita-tion than NCEP–Department of Energy in some ocean regions, andthe 40-yr ECMWF (European Centre for Medium-Range WeatherForecasts) reanalysis data produced reasonable comparisons overNorthern Hemisphere continents, but less so in the tropical oceans.Diro et al. (2009) evaluated two reanalysis rainfall estimates overEthiopia at seasonal and inter-annual scales. The study revealedthat the spatial pattern of the rainfall is captured well by bothproducts but they tend to overestimate the mean rainfall innorth-western, western and central regions and underestimate inthe south and east, meanwhile, the inter-annual variability is lesswell captured than the spatial and seasonal variability. Jury(2010) examined the spatial variability of mean annual rainfall inthe Caribbean by the intercomparison of gridded rainfall fields fromrain gauges, satellite estimators, reanalysis products, and coupledgeneral circulation models (CGCMs). The study showed statisticalconsensus among the data products in general, but no single pro-duct is without discrepancy. Meanwhile, most of the precipitationdatasets poorly handled the high rainfall over southern Cuba andthe rain shadow region in western Hispanola. Tong et al. (2014)studied the precipitation in Tibetan Plateau using eight reanalysisand satellite based datasets at both basin and plateau scales andsuggested that the use of precipitation derived from reanalysisdatasets is less preferable for hydrological analysis than the gaugeddata at basin scales but still holds a great potential for providinghigh-resolution precipitation information in remote regions.Shepherd et al. (2014) examined the biases of daily satellite andreanalysis rainfall products in the Savannah River basin in south-eastern United States. It is found that the biases occur seasonally.Furthermore, the satellite-based data tended to overestimate lightprecipitation relative to the multi-gauge average.

Currently, with more and more global precipitation datasetsdeveloped, the application of reanalysis products in hydrologicalmodelling arouse study interests (e.g. Fekete et al., 2004; Pianiet al., 2010; Seyyedi et al., 2014; Adjei et al., 2015; etc.). As a hotresearch field, many studies focus on the application of indirectlymeasured precipitation data on flood risk evaluation at basin scales(e.g. Bitew and Gebremichael, 2011a,b; Yong et al., 2012;Praskievicz and Bartlein, 2014; Seyyedi et al., 2015; etc.) and dis-cuss their potential utility for the hydrological prediction ofungauged/poorly gauged basins (e.g. Artan et al., 2007; Thiemiget al., 2013; Casse et al., 2015; etc.). Findings on the statistical anal-ysis and hydrological modelling using the indirect precipitationmeasurements showed that these reanalysis precipitation prod-ucts are able to reveal long term characteristics of rainfall overbasins in general but lack of the ability to accurately estimate

the rainfall volume and variation in short periods (Looper andVieux, 2012a,b). Furthermore, the errors in precipitation estima-tions are easily transformed to the errors in discharge simulations.For example, the studies over the river basins in West Africa fromThiemig et al. (2013) and Gosset et al. (2013) indicated that theglobal rainfall datasets, regardless of bias correction, are not freeof errors and distort the spatial and frequency distributions of rainrate when compared to gauged precipitation. Therefore, the useful-ness of reanalysis precipitation datasets in driving hydrologicalmodels at basin scale needs to be further evaluated (Cheema andBastiaanssen, 2012) due to the indirect nature of precipitationmeasurements and relative coarser spatial resolution (e.g. on lati-tude and longitude of 2.5� � 2.5�, 5� � 5�).

From the foregoing studies, it is clear that: (1) many studiescompared the reanalysis datasets on/at regional/basin scales basedon the sparsely distributed rain gauges, and thus the spatial char-acteristics of precipitation cannot be reflected by the gauged dataaccurately and may result in the explanation of the biases of thereanalysis products on spatial patterns with deviations. (2) Reanal-ysis products are available for estimating the temporal rainfallcharacteristics in long periods. However, due to lack of consecutivelong period of gauged data, the long term temporal biases inreanalysis products are not well evaluated. (3) Many literaturesfocused on the statistical analysis of the reanalysis datasets, butstudies aiming at the evaluation of the performances of hydrolog-ical models derived by reanalysis products have not yet conductedin many basins at different time and spatial resolutions. (4) Manystudies focused on analysing the hydrological process in general;however, the ability of reanalysis datasets in modelling flood arenot paid enough attention and not well discussed yet.

The above considerations form the basis of this study, and themain objectives of this study are therefore designed to: (1) Inves-tigating the temporal and spatial characteristics of two widelyused long period reanalysis precipitation products (WFD and APH-RODITE) on a humid climate basin in southern China with denselydistributed and long period rain gauge data as reference. (2) Eval-uating the performance of the reanalysis precipitation products indriving lumped and distributed hydrological models in simulatingthe daily runoff in the catchment. And (3) assessing the applicabil-ity of reanalysis datasets in modelling flood events. This study con-tributes to the improvement of understanding the differencesbetween the reanalysis precipitation datasets and gauged rainfallin long term and in simulating flood events at basin scale and willbe useful to enhance the knowledge regarding the utility of thehydrological models driven by varying data sources. Furthermore,this study will provide some insights into the applicability of globalmeteorological datasets for research in basins that are poorlygauged.

2. Precipitation products and hydrological context

2.1. Precipitation products

Two state-of-the-art reanalysis precipitation products thatcover long periods are used in this study: (1) the APHRODITEV1101 is a gridded daily precipitation products (Yatagai et al.,2012) covering the monsoon Asia, Middle East and Russia, and isavailable on 0.5� � 0.5� and 0.25� � 0.25� grids during the periodof 1951–2007 (http://www.chikyu.ac.jp/precip/). The dataset wascreated by collecting rain gauge observation data across Asiathrough the APHRODITE project. The number of valid stations wasbetween 5000 and 12,000, representing 2.3–4.5 times the dataavailable through the Global Telecommunication System (GTS) net-work for precipitation products (Sohn et al., 2012). (2) TheWFD glo-bal reanalysis product was developed by the WATCH project

H. Xu et al. / Journal of Hydrology 542 (2016) 343–356 345

(Weedon et al., 2011) as input for large-scale land-surface andhydrological models. WFD dataset is combined with two sub-datasets: WATCH Forcing Data 20th Century (WFD 20C) for landsurface and hydrological models (1901–2001) and WATCH-Forcing-Data-ERA-Interim (WFDEI) which produced post-WATCHusing WFD methodology extending into early 21st Century(1979–2012). TheWFD dataset consists of meteorological variablesneeded to run hydrological models (2 m air temperature, dew pointtemperature andwind speed, 10 m air pressure and specific humid-ity, downward long wave and shortwave radiation, rainfall andsnowfall rates) (Uppala et al., 2005). The WFD dataset used in thisstudy is processed by connecting the WFD 20C (1901–1978) withWFDEI (1979–2012). These two reanalysis rainfall products areavailable with consistent temporal resolution of one day and spatialresolution of 0.5 degree in the study area. The two reanalysis data-sets used in this study have been tested in many basins over theworld and showed great potentials in hydrologic studies (e.g. Döllet al., 2009; Stahl et al., 2010; Javanmard et al., 2010; Vliet et al.,2011; Kamiguchi et al., 2011; etc.). However, due to the limitedobservations in China used in constructing the assimilation systemsin the two reanalysis products (Weedon et al., 2011; Yatagai et al.,2012), the accuracy and potential applicability of WFD and APHRO-DITE data in modelling hydrological responses have not beenvalidated in many basins in China and therefore the WFD andAPHRODITE datasets are evaluated in this study.

As reference, the gauged precipitation dataset derived from adensely distributed observation network that consists of 181 raingauges (Fig. 1) from 1st January 1963 to 31st December 2005was provided by the Hydrology and Water Resources Bureau ofHunan Province, China. To make the reanalysis precipitation prod-ucts comparable with the gauged data, the common period 1963–2005 is adopted and the gauged data were interpolated into0.5� � 0.5� grid during statistical analysis.

Fig. 1. Study area: the location of Xiangjiang Riv

2.2. Hydrological context

Xiangjiang River (Fig. 1) is one of the seven major tributaries ofthe Yangtze River. It is located in 24�300-29�300N and 110�300-114�E with 94,660 km2 drainage area and 670 km long mainstreamin central-south China. The basin is surrounded by mountains in itsheadwaters while hills and plains are the two main landscapes inthe middle and lower reaches. The basin is dominated by the EastAsian summer monsoon that brings heavy rainfall from the IndianOcean and Pacific Ocean. The multi-year mean precipitation isapproximately 1600 mm, of which nearly two thirds of the rainfalloccur in the main wet season from April to September. As the riverbasin is located in humid area, good relationship between precip-itation and runoff holds. The multi-year mean depth of streamflowat Xiangtan gauge (basin outlet) is 910 mm, and the runoff changesaccordingly with the rainfall and nearly half of the annual floodevents occur in June and July. There is a remarkable inter-annualdifference in precipitation and the resulting discharge. The AnnualMean Precipitation in wet years is 19.3% and 32.3% higher thannormal and dry years, respectively. Meanwhile, the annual meandischarge in wet years is 28.3% and 33.4% higher than normaland dry years, respectively.

3. Methodology

3.1. Statistical analysis methods

To compare the performances of hydrological models driven byreanalysis datasets and gauged precipitation, it is necessary to firstanalyse the differences between the datasets. Hence, the observeddifferences between the three products which included precipita-tion accumulation, inter-annual variability, and intensity distribu-

er basin and the distribution of rain gauges.

346 H. Xu et al. / Journal of Hydrology 542 (2016) 343–356

tions are tested. To quantify the differences and assess how theymay influence flood simulation, three parts of comparison aremade: (1) basic statistical indices which include Annual Mean Pre-cipitation (MA), Relative Error (RE), Standard Deviation (STDE),Coefficient of Determination (R2), Max Dry Spell (MDS) and MaxFive-day Precipitation (M5P) (a brief description of these indicesis shown in Appendix A), (2) accumulation, inter-annual variabilityand intensity distributions are analysed in the first and secondpart. Then (3) the spatial differences between monthly precipita-tion of reanalysis and gauged datasets are discussed. It should benoted that the WFD 20C and WFDEI datasets have the commonperiod of 1979–2001, therefore, it is necessary to validate theirconsistency by testing the mean, variance and distribution patternsgrid by grid before connecting the two datasets.

3.2. Hydrological models

Xinanjiang Model (Zhao, 1992; Zhao and Liu, 1995; Yan et al.,2016; Jie et al., 2016; Zeng et al., 2016) is a widely used conceptualrainfall–runoff hydrological model in humid area in China for floodforecasting, reservoir operation, water resources management, etc.(e.g. Hu et al., 2005; Yao et al., 2009; Bao et al., 2011; Yao et al.,2012; Lü et al., 2013; Yao et al., 2014; Lin et al., 2014). It was devel-oped in 1973 and the English version was first published in 1980(Zhao et al., 1980). Based on the concept that runoff is not pro-duced until the soil moisture content of the aeration zone reachesfield capacity, and thereafter runoff equals to the rainfall excesswithout further loss, the model consists of a runoff generatingcomponent and a runoff routing component (Ren et al., 2006).Daily areal precipitation and measured daily pan evaporation arethe input of the model and observed discharge is used for modelcalibration.

SWAT (Soil and Water Assessment Tool) Model is a physically-based distributed-parameter model designed to predict the effectsof land management practices on the hydrology, sediment, andcontaminant transport in agricultural watersheds under varyingsoils, land use, and management conditions (Arnold et al., 1998;Tamm et al., 2016; Awan et al., 2016; Singh et al., 2016). Basedon the concept of Hydrologic Response Units (HRUs), the modeluses a modified Soil Conservation Service-Curve Number (SCS-CN) method to calculate runoff. SWAT Model simulates the hydro-logic cycle using the water balance equation (Neitsch et al., 2002)as below:

SWt ¼ SW0 þXti¼1

ðRday � Qsurf � Ea �Wseep � QgwÞ ð1Þ

where SWt is the final soil water content, SW0 is the initial soil watercontent on day i, t is the time (days), Rday is the amount of precipi-tation on day i, Qsurf is the amount of surface runoff on day i, Ea is theamount of evapotranspiration on day i,Wseep is the amount of waterentering the vadose zone from the soil profile on day i, and Qgw isthe amount of return flow on day i.

3.3. Model calibration

For the limitation of the common time duration of the tworeanalysis datasets and the meteorological data available (severalmeteorological stations changed their locations in 2006 whichcould result in data inconsistencies) and the main purpose of thisstudy is to investigate the usability of the reanalysis products inmodelling hydrological responses, the period of 1991–2005 is cho-sen to test the hydrological models using both reanalysis andgauged precipitation, in which, data of 1991–2000 are used asthe calibration period (including the warming-up period of 1991)while data of 2001–2005 are used as the validation period.

The basin is delineated into 55 sub-basins and 555 HRUsdepending on river channels, elevation, soil types and land-usetypes in SWAT Model. By setting the Nash-Sutcliffe efficiency coef-ficient as objective function, the Genetic Algorithm and SUFI2(Sequential Uncertainty Fitting version 2) Algorithms provided bySWAT CUP (SWAT Calibration and Uncertainty Procedures) areused for calibrating the Xinanjiang Model and SWAT Model,respectively. Unlike physical process based models (e.g. SWATModel), some parameters in conceptual models (e.g. XinanjiangModel) cannot be directly estimated from physically measurabledata. Therefore, the initial values and variation range of the param-eters in Xinanjiang Model are set empirically. Meanwhile, the sameinitial values and ranges of parameters are used in calibrating thehydrologic models driven by reanalysis and gauged precipitation.

Furthermore, it should be noted that Xinanjiang Model andSWAT Model are deterministic models; therefore, the same out-puts will be produced by every successive model run that usesthe same inputs (both hydro-meteorological data and initialparameter values) and calibration method. These types of modelsare preferred for isolating hydrologic response to a single variableallowing the impact of any change to be isolated and analysed forits effect on discharge simulations.

4. Results and discussion

4.1. Observed differences between the precipitation products

The results of statistical analyses show that the WFD 20C andWFDEI datasets have the same mean value (using Student t test),same variance (using F test) and same distribution pattern (usingK-S test) under the significance level of 0.05 in all of the 28 gridsin the common period. It demonstrates that it is statistically feasi-ble to connect the WFD 20C and WFDEI datasets to compose theWFD precipitation.

4.1.1. Basic statistical indices of areal reanalysis and gaugedprecipitation

Table 1 shows the comparison ofMA, RE ofMA, STDE, R2,MDS andM5P computed between areal mean reanalysis and gauged data. Itis seen that the MA of gauged precipitation and WFD dataset aresimilar, but the MA of APHRODITE data is 3.9% less than that ofgauged data. A comparison of STDE computed from the three data-sets showed that the difference of STDE between WFD and APHRO-DITE precipitation is smaller than the difference between WFD/APHRODITE and gauged rainfall. The values of R2 of monthly pre-cipitation between WFD/APHRODITE and gauged precipitationare similar and higher than 0.95 revealing that the two reanalysisdatasets correlate well with the gauged data in monthly scale. Thedifferences in MDS days reveal that the WFD dataset monitorsmore non-rainy days than the gauged data whereas the APHRO-DITE dataset suggests less non-rainy days compared with thegauged data. Considering the differences in the extreme rainfallwhich are reflected by the M5P (Dankers and Hiederer, 2008), bothWFD and APHRODITE datasets record less precipitation than thegauged data in storms while the WFD data are more similar tothe gauged storm than that of APHRODITE data.

4.1.2. Spatial characteristics of reanalysis and gauged datasetsFig. 2 shows the spatial distribution of long-term average of RE

of MA between gauged and WFD/APHRODITE datasets. It is seenthat the spatial patterns of RE computed from the two reanalysisdatasets are similar to the gauged data. Compared with the gaugedprecipitation, both the WFD and APHRODITE data underestimatethe precipitation in the mountain areas in the upstream and over-estimate the precipitation in the plain areas in the downstreams.

Table 1Comparison of statistical indices among Gauged, APHRODITE and WFD areal meanprecipitation from 1963 to 2005.

MA (mm) RE STDE (mm)*

Gauged 1521 / 288.8WFD 1517 �0.3% 209.6APHRODITE 1462 �3.9% 232.1

R2** MDS (day) M5P (mm/5-day)

Gauged / 51 180WFD 0.95 64 168APHRODITE 0.97 46 146

* The Standard Deviation (STDE) is computed by using annual precipitation.** The Coefficient of Determination (R2) is computed by using monthly

precipitation.

H. Xu et al. / Journal of Hydrology 542 (2016) 343–356 347

Meanwhile, the absolute values of RE gradually decreased from thenorth/south of the basin to the central part of the basin. But thearea and the grade of overestimation of precipitation from WFDdata are larger and higher than that from APHRODITE data.

The Nash–Sutcliffe model efficiency coefficient (NSE) is a widelyused index for evaluating the performances of hydrological models.Therefore, if regards the daily reanalysis precipitation as the ‘‘sim-ulation” of the daily gauged precipitation, NSE can be used to eval-uate the quality of reanalysis datasets in comparing with gaugeddata. Fig. 3 shows that the APHRODITE precipitation ‘‘simulates”the gauged rainfall much better than the WFD data during 1963–

Fig. 2. The spatial distribution of long-term average of RE of MA computed (a) between gby using Kriging interpolation method.

Fig. 3. The spatial distribution of NSE between gauged and reanalysis datasets mapped bWFD datasets and (b) is the NSE computed by daily gauged and APHRODITE datasets.

2005. The APHRODITE data match the gauged data best in themountain areas (southeast and southwest of the basin) with NSEvalues reaching 0.42. However, the WFD data match the gaugedprecipitation poorly over the basin with the highest value of NSElower than 0.3 in the upstreams of the basin.

4.1.3. Rainfall accumulation, Inter-annual variability and intensitydistributions between gauged and reanalysis datasets

Fig. 4 highlights the differences among precipitation products interms of annual accumulation (Fig. 4(a) and (b)), number of rainydays (Fig. 4(c) and (d)) and spatial extension of the daily rain pat-terns which indicates the percentage of pixels with at least 0.1 mmon days when the mean areal precipitation over the domain isabove 0.1 mm (Fig. 4(e) and (f)) over the period 1963–2005. Unlikethe annual total precipitation (Fig. 4(a) and (b)), the temporal andspatial distributions of precipitation vary substantially betweenthe two reanalysis datasets indicating that the two reanalysis pre-cipitation (especially the WFD data) have large uncertainty in esti-mating the characteristics of precipitation. The APHRODITE dataestimate the rainy days closer to the gauged data but the WFD datatend to spread the precipitation in fewer rainy days (Fig. 4(c) and (d)). Furthermore, rainfall events cover about 75%–85% ofthe study area of interest for APHRODITE data, and less (60%–85%) for WFD data as shown in Fig. 4(e) and (f). For the distributedSWAT model, simulation of streamflow is computed in each HRUfirstly, then converges the streamflow to the basin trunk stream

auged and WFD datasets and (b) between gauged and APHRODITE datasets mapped

y using Kriging interpolation method: (a) is the NSE computed by daily gauged and

Fig. 4. Scatter plots of the inter-annual (1963–2005) precipitation series computed by the three tested datasets: (a) and (b) mean areal annual precipitation; (c) and (d)number of rainy days; and (e) and (f) Mean Percentage of rain extension Area (M.P.A) over the study area.

348 H. Xu et al. / Journal of Hydrology 542 (2016) 343–356

and routes the output to the control station by using Muskingummethod; the differences in spatial extension of the rain patternsis expected to impact the hydrological modelling in SWAT Modelmore obvious.

The consideration of the distribution of precipitation by inten-sity classes is important for hydrological modelling. Vischel andLebel (2007) reported a strong sensitivity of the modelled dis-charge to the proportion of heavy rainfall. Fig. 5 presents (a) thefrequency distribution of the daily rainfall and (b) the contributionof rain rate classes to the annual accumulation computed for theregion of interest for the period of 1963–2005. It is seen that therainfall estimated with APHRODITE data is similar with the gaugedprecipitation data in most of the rainfall classes except in rainfallclass of 1–5 mm. However, the WFD data tend to obviously overes-timate the rainfall in the rainfall classes of 1–5 mm and 5–10 mm,and underestimate it in the rainfall classes of 0.1–0.5 mm and 0.5–1 mm. From Fig. 5(b) it is seen that the APHRODITE data show sim-ilar results to those using the gauged data in general, while differ-ences in the total rainfall among the products mostly occurred inthe rainfall classes of 5–10 mm and 20–40 mm. The WFD data tendto project more rainfall in the rainfall class of 5–10 mm, in contrast,the gauged data record more precipitation in storm rainfall above40 mm.

The comparison of the differences between the gauged andreanalysis precipitation indicates that the APHRODITE data resem-

Fig. 5. The distribution of precipitation in the three tested datasets: (a) Frequencyaccumulation.

ble the gauged closer than the WFD data do. This is mainly due tothe data sources and assimilation methods of the two reanalysisdatasets are different: (1) The WFD dataset is derived from theERA-40 reanalysis product which is directly assimilated the satel-lite radiation data and has the main limitations of larger tropicalmoisture estimation and precipitation greatly exceeds evaporation(National Centre for Atmospheric Research Staff (Eds), 2016).Meanwhile, in constructing the WFD precipitation data, the precip-itation rates estimated from ERA-40 were corrected on globalaspect for the number of wet days, bias, precipitation gauge under-catch (Adam and Lettenmaier, 2003), etc. While (2) the APHRODITEprecipitation dataset is created by collecting and analysing raingauge observation data across Asia. Many methods were appliedfor checking, maintaining and improving the quality of gauged dataused in making APHRODITE dataset (Hamada et al., 2011; Yatagaiet al., 2012) especially in Asian region.

4.2. Performances of hydrologic models driven by reanalysis andgauged precipitation

4.2.1. Evaluation of the streamflow in daily step simulationStatistical results of the performances of the hydrological mod-

els driven by reanalysis and gauged precipitation are shown inTable 2. It is seen that the two hydrological models show reason-able model performances when driving by the three precipitation

distribution of daily rainfall. (b) Contribution of rain rate classes to the annual

Table 2The daily step hydrological modelling results in Xinanjiang Model and SWAT Model forced by gauged, WFD and APHRODITE rainfall.

Xinanjiang Model SWAT Model

Gauged WFD APHRODITE Gauged WFD APHRODITE

NSE Calibration 0.95 0.76 0.92 0.89 0.71 0.82Validation 0.94 0.75 0.88 0.88 0.69 0.79

RE Calibration �0.6% �1.1% �0.2% �3.7% 6.7% �2.5%Validation �2.2% 4.6% �0.3% 3.5% 7.8% �2%

H. Xu et al. / Journal of Hydrology 542 (2016) 343–356 349

datasets in general. The gauged precipitation based XinanjiangModel and SWAT Model (abbreviated as G_X.M and G_S.M) per-form best while the WFD data based models perform worst (theWFD data based Xinanjiang Model and SWAT Model are abbrevi-ated as W_X.M and W_S.M, and the APHRODITE data based Xinan-jiang Model and SWAT Model are abbreviated as A_X.M and A_S.Mbelow).

In case of the Xinanjiang Model, it is seen that the NSE valuescomputed from the model driven by gauged and APHRODITE pre-cipitation are higher than 0.9 in calibration period, while in valida-tion period, the NSE values achieve 0.94 and 0.88 when the gaugedprecipitation forced into the Xinanjiang and SWAT model, respec-tively. However, the NSE values computed from W_X.M are low(0.76 and 0.75 for the calibration and validation periods, respec-tively). Meanwhile, the water balance reflected by RE is good whendriving by the three precipitation datasets; the RE values are allsmaller than 5% both in calibration and validation periods.

The SWATModel driven by the reanalysis and gauged precipita-tion performs worse than that of Xinanjiang Model in general. TheNSE values computed from the G_S.M are close to 0.9 both in cali-bration (NSE = 0.89) and validation (NSE = 0.88) periods, and theNSE values computed from A_S.M are 0.82 and 0.79 in calibrationand validation period, respectively. However, W_S.M gives some-how lower NSE values (0.71 and 0.69 in calibration and validationperiod respectively). Similarly, the RE values computed from themodel driven by gauged and APHRODITE precipitation are lessgood (all |RE| > 5% in calibration and validation periods), whereas,W_S.M tends to estimate more discharge (RE > 6%). In summary,without considering the gauged precipitation, the APHRODITE dataperform better results than that of WFD data both in calibrationand validation periods at daily time step.

The low NSE values (smaller than 0.5) observed from Fig. 3 indi-cate the two reanalysis datasets do not agree with the gauged pre-cipitation well at daily step over the basin. However, the impacts ofthe relatively unsatisfactory ‘‘simulation” of the precipitation onthe performances of lumped and distributed hydrological modelsare obviously different. This is due to that the input in lumpedXinanjiang Model is Areal Mean Daily Precipitation (AMDP), inwhich errors can be weakened when calculating the AMDP usingevery single point precipitation. While the distributed SWATModel uses only the single rain gauge nearest to the sub-basin’scentroid as rainfall input for each sub-basin (Galván et al., 2014),and each sub-basin in the SWAT Model can be regarded as a‘‘lumped hydrological model”, the errors existed in the reanalysisprecipitation are directly substituted into each ‘‘lumped hydrolog-ical model”. Therefore, the SWAT Model is very sensitive to theerrors in reanalysis precipitation when analysing the modelledrunoff. Meanwhile, this also explains that the differences in spatialrain patterns (e.g. Fig. 4(e) and (f)) of the two reanalysis dataimpact the performances of the distributed SWAT Model moreobvious than that of the lumped Xinanjiang Model.

For illustrative purpose, Fig. 6 shows the graphical comparisonof the difference between observed and simulated daily stream-flow of 1999–2000 in Xiangtan gauge by the Xinanjiang Modeland SWAT Model. It is seen that the streamflow produced by

G_X.M and G_S.M match the observed discharge best (Fig. 6(a) and (d)), and the W_X.M shows lager errors in low flow thanthe A_X.M (Fig. 6(b) and (c)). However, it is also seen that theW_S.M gives lager errors in simulating the flood events than theA_S.M (Fig. 6(e) and (f)).

4.2.2. Comparison of the difference of parameters calibrated in thehydrological models

As the errors in modelling results derived from the errors ofinputs can be reduced to some extent by optimizing the models’parameters, it is important to investigate the change of the param-eters in models forced by different precipitation datasets toimprove the model efficiency. Table 3 compares the most sensitiveparameters calibrated in the gauged and reanalysis precipitationbased models (not all the parameters calibrated in the models). Itis seen that the parameters calibrated in the APHRODITE databased models are close to the parameters calibrated in the gaugeddata based models than that of WFD data based models in general.

In case of Xinanjiang Model: (1) Um, Lm and K relate to thecomputation of evapotranspiration. Um + Lm is the areal mean ten-sion water capacity that reflects the drought degree of the basin.The higher value of Um + Lm is calibrated, the smaller evapotran-spiration volume is computed in wet season and more runoff isproduced (e.g. in Fig. 6(b)); (2) Sm and KG mainly impact the totalrunoff of flood events. The higher values of Sm and KG are cali-brated, the greater of the ratio of underground runoff to total run-off, and the smaller flood volumes are estimated. To reduce theoverestimation of flood runoff caused by the errors in precipitationand other parameters (e.g. Um and Lm), greater values of Sm andKG are calibrated in W_X.M and A_X.M, respectively; and (3) CImainly impacts the shape of the hydrograph. By adjusting the val-ues of CI, the two reanalysis data based models make the simulatedhydrographs close to the observed ones to the greatest extent.

In case of SWAT Model: (1) a_BF impacts the time length of therecession of base flow, the greater value that a_BF calibrated, thelarger underground flow is modelled and the more stable of baseflow recession can be observed. The a_BF values are higher inW_S.M and A_S.M than in G_S.M in order to simulate the stream-flow in dry seasons more accurately to reduce the impact of under-estimation of light rain in the reanalysis data (e.g. the precipitationclass of 0.1–0.5 mm and 0.5–1 mm in Fig. 5); (2) CN2 reflects thesynthetic characteristics of the basin before rainfall events andESCO adjusts the evaporation in deep soil layer. The runoff volumeproduction increases with the increase of the CN2 and ESCO valuesaccordingly. Compare with the CN2 value in G_S.M, it is seen thatthe W_S.M and A_S.M give lower and higher CN2 values, respec-tively, to lighten the errors transferred from reanalysis datasetsto the modelled runoff. Meanwhile the higher ESCO values cali-brated in the models forced by reanalysis datasets reduce theerrors that caused by the CN2 values to some extent; and (3) SUR-LAG impacts the water volume that enter to the river channels, andrunoff increases with the decrease of the SURLAG value. As demon-strate by Fig. 6(e) and (f), higher and lower SURLAG values are cal-ibrated from the W_S.M and A_S.M to produce the simulatedrunoff with the smallest possible errors.

Fig. 6. Comparison of the observed and simulated daily hydrographs at Xiangtan station: (a), (b) and (c) are hydrographs of Xinanjiang Model driven by gauged, WFD andAPHRODITE precipitation respectively; (d), (e) and (f) are hydrographs of SWAT Model driven by gauged, WFD and APHRODITE precipitation respectively.

Table 3Comparison of the main sensitive parameters’ values calibrated in the two models forced by gauged and reanalysis data.

Parametername

Description Parameter value

Gaugedrainfall

WFDrainfall

APHRODITErainfall

XinanjiangModel

Um Averaged soil moisture storage capacity of the upper layer (mm) 16.34 25.22 26.56Lm Averaged soil moisture storage capacity of the lower layer (mm) 99.15 137.09 80.62K Ratio of potential evapotranspiration to the pan evaporation 0.956 1.159 0.882Sm Areal mean free water capacity of the surface soil layer (mm) 31.848 35.308 30.21KG Outflow coefficients of the free water storage to groundwater

relationships0.902 0.905 0.992

CI Recession constants of the lower interflow storage 0.697 0.377 0.89SWAT Model a_BF Base flow recession factor (days) 0.048 0.063 0.051

CN2* Curve number 78.1 71.5 88.6ESCO Soil evaporation compensation factor 0.3 0.39 0.34SURLAG Surface runoff lag coefficient (days) 15 19 13CH_N Manning’s ‘‘n” value for the main channel 0.25 0.21 0.26

* In SWAT Model, based on the infiltration characteristics of the soil, the soil is classified into four hydrologic groups. Different soil types are calibrated with different CN2values in the model and here shows the mean CN2 values.

350 H. Xu et al. / Journal of Hydrology 542 (2016) 343–356

This section only discusses the impact of some of the most sen-sitive parameters calibrated in the two hydrological models forcedby gauged and reanalysis data on the modelled runoff. It should benoted that hydrological models are the simplifications of highlynonlinear natural water cycle, the nonlinear functions and complex

structures make the parameters in the models independent andinteract with each other to some extent, therefore, quantitativeanalysis of the influences of parameters on model performancesis difficult. Meanwhile, the parameter sets calibrated with differentvalues in the hydrological models may give equivalent model per-

Table 4The comparison of rainfall in the maximum flood event.

WFD - gauged APHRODITE - gauged

AAE 9443 mm 7748 mmAAE of storm rainfall (SR) 4054 mm 3175 mmAAE of SR in mountain areas 2718 mm 1980 mm

H. Xu et al. / Journal of Hydrology 542 (2016) 343–356 351

formances (known as equifinality in the literature) making the dis-cussion even more difficult.

4.2.3. A closer view of flood events dynamics

(1) The evolution of the rainfall and modelled runoff in a typicalflood event

Fig. 7 illustrates the genesis of one typical flood process in 1994that includes the maximum flood peak during the modelling per-iod and the rainfall that caused it by using gauged and reanalysisdata in Xinanjiang Model and SWAT Model, respectively. This rain-fall process is selected using the rainy days with the highest rain-fall of the period by the gauged precipitation data (the 99thpercentile is reached). However, the absolute rain intensities ofthe flood event derived from WFD and APHRODITE data are differ-ent from that of gauged data.

The WFD and APHRODITE data have similar values of cumula-tive rainfall over this flood process (398 mm and 392 mm respec-tively), but less than the gauged rainfall (431 mm), and thepositive bias in reanalysis products propagates as a positive biasin modelled runoff (Fig. 7(b), (d) and (f)). Further examination ofthe distribution panels of rainfall over the domain in Fig. 7(c) and (e) reveals the differences in the way the precipitation isdistributed both spatially and temporally.

Table 4 explains the reasons that the A_X.M and A_S.M performbetter than W_X.M and W_S.M: (1) The Accumulative AbsoluteError (AAE) which is computed by the summation of the valuesof absolute error between APHRODITE and gauged rainfall in eachgrid at each time step is 7748 mm, evidently smaller than the AAEcomputed between WFD and gauged rainfall (9443 mm); (2) thecomparison of storm rainfall (>25 mm/day) that is vital for induc-ing severe flood events shows that the AAE of storm rainfall esti-mated between gauged and APHRODITE data (3175 mm) isobviously smaller than that of between gauged and WFD data(4054 mm). And (3) as demonstrated by Xu et al. (2015), thegauged precipitation in mountain areas contributes more weightin modelling discharge, thus, the analysis of storm rainfall esti-mated by the 16 grids which cover the mountain area in thedomain is necessary. The AAE values of storm rainfall in mountain

Fig. 7. Time evolution of the rainfall over the region (i.e., the 28 pixels) and the observedcolour represents the amount of rainfall for each pixel daily. Bottom: Time evolutiondischarge; (a) and (b), gauged rainfall and its performance in the two models; (c) and (d),and its performance in the two models.

areas estimated between gauged and WFD/APHRODITE data are2718 mm and 1980 mm respectively, which contribute approxi-mately two thirds of the AAE of storm rainfall in the whole basinindicating that the WFD data have limited ability to correctly esti-mate the heavy rainfall in mountain areas compared with the APH-RODITE data.

(2) The ability of the models in simulating flood events

As expected from the previous sections, the simulations basedon the reanalysis products generate a lot of spurious floods in bothmodels because of the excess of rainfall. To further quantify themissed and spuriously simulated floods, the skill of the simulationsis analysed in terms of Probability of Detection (PoD, Table 5) andFalse Alarm Rate (FAR, Table 6) for individual flood days (the top10% largest discharge during the modelling period (P4940 m3/s,as threshold). The equations of computing PoD and FAR are shownin Appendix B). In addition, a temporal tolerance is allowed incomputing the classical PoD/FAR by comparing each observedflood with the simulated flood on the same day. The detection isconsidered valid if one flood day is predicted within a time windowD (D = 1, 3 and 5 days) of plus/minus N (N = 0, 1 and 2) days. Due tothe relatively coarse spatial resolution of the reanalysis productsand that the hydrological models are a simplification of the rain-fall–runoff processes; the models may cause slight shifts in thetiming of the hydrological response.

The modelled runoff from G_X.M is in good agreement withobserved streamflow. The PoD is 66.3% and rises to 90.6% for a timetolerance of 2 days, while the FAR of this simulation is initially 1.8%and drops to 0.6% for the tolerance of 2 days. With the simulationsbased on reanalysis products, for the differences between thegauged and WFD/APHRODITE data in terms of number, intensity

and simulated discharge in 1994. Top: y axis: pixel number (1–28); x axis: time; theof the daily areal mean rainfall over the domain, the observed and the simulatedWFD rainfall and its performance in the two models; (e) and (f), APHRODITE rainfall

Table 5The Probability of Detection (PoD) and PoD with different temporal tolerance windows for the models forced by the three rainfall datasets.

Window (day(s)) Xinanjiang Model SWAT Model

Gauged WFD APHRODITE Gauged WFD APHRODITE

1 (N = 0) 0.663 0.4 0.593 0.53 0.487 0.4573 (N = 1) 0.888 0.549 0.838 0.709 0.647 0.6185 (N = 2) 0.906 0.603 0.875 0.744 0.703 0.678

Table 6The False Alarm Rate (FAR) and FAR with different temporal tolerance windows for the models forced by the three rainfall datasets.

Window (day(s)) Xinanjiang Model SWAT Model

Gauged WFD APHRODITE Gauged WFD APHRODITE

1 (N = 0) 0.018 0.042 0.025 0.028 0.034 0.0293 (N = 1) 0.016 0.018 0.02 0.02 0.023 0.0185 (N = 2) 0.006 0.013 0.011 0.01 0.016 0.01

352 H. Xu et al. / Journal of Hydrology 542 (2016) 343–356

and spatial extension of the rainy days (Figs. 4 and 5), the twomodels forced by reanalysis data produce smaller PoD but largerFAR. In accordance with the evaluation of the models which indi-cates the SWAT model has lower ability to accurately representthe discharge, the scores of PoD/FAR are substantially lower/higherfor the reanalysis products forced SWAT model in comparing withthe Xinanjiang Model in general. The PoD and FAR obtained withthe WFD and APHRODITE products are worse in SWAT Model thanin Xinanjiang Model, which agrees with their tendency to misesti-mate the number of rainy days as represented in Fig. 4. Further-

Fig. 8. Scatter plots of the standardized simulated peak discharge versus the standardizeWFD and APHRODITE rainfall respectively; (d), (e) and (f) are SWAT Model forced by ga

more, a tolerance window of three days is needed to reach a PoDhigher than 60% and FAR below 2% in the two models forced bythe reanalysis data.

(3) The variability of inter-annual high streamflow

The previous discussion shows that the APHRODITE data basedmodels have better skills in predicting floods than the modelsforced by WFD rainfall, even though the reanalysis rainfall prod-ucts have biases in comparing with the gauged rainfall. Besides,

d observed peak discharge: (a), (b) and (c) are Xinanjiang Model forced by gauged,uged, WFD and APHRODITE rainfall respectively.

Fig. 9. The partial duration series and their corresponding cumulative frequency derived from (a) Xinanjiang Model and (b) SWAT Model forced by gauged and reanalysisprecipitation.

H. Xu et al. / Journal of Hydrology 542 (2016) 343–356 353

the inter-annual stability of the reanalysis products performed inthe models should be considered due to that the dramatic variationof the biases in reanalysis rainfall from one year to another maycause an erroneous flood simulation. Therefore, the inter-annualvariability of the peak discharge and the consistency between thesimulations and the observations are analysed and shown inFig. 8 by using the standardized (i.e. subtraction of the inter-annual mean and division by the Standard Deviation) observedAnnual Maximum Flows (AMF) as well as the modelled flows atthe same time. Meanwhile, the Coefficient of Determination (R2),Pearson’s linear correlation coefficient (Rp, Pearson, 1896) andthe Spearman’s rank correlation coefficient (Rsp, Spearman, 1904)are also computed between the standardized series of simulatedand observed peak discharge iteratively by using all the data andby omitting each year in turn to verify the significance of the agree-ment and differences between series.

The agreement between the standardized simulated andobserved discharge peak is consistent with the previous discus-sions, the APHRODITE data based models as well as the lumpedXinanjiang Model give the generally good results compared tothe gauged data based models while the WFD data give unsatisfiedpeak discharge in simulations, this is in direct relation with theyear to year variability of the bias of the reanalysis products men-tioned in Section 4.1. The values of R2, Rp and Rsp (only mean valuesare showed in Fig. 8) indicate that the correlations calculated fromA_X.M are stable and similar with the G_X.M. While the W_S.M,A_S.M and W_X.M exhibit lower ability in modelling the peakstreamflow as seen in Fig. 8(b), (d), (e) and (f), in which, the dotsdispersed in the quadrants but not concentrated on the both sidesof the regression lines.

For the hydrological modelling period is relatively short (tenyears for calibration and five years for validation), the processesof high flows represented by the AMF series derived from theobserved and simulated discharge series are not all-inclusive. Thisis due to the AMF series ignore the significant high flows which arenot the highest in a year but higher than the other chosen highestflows of other years (Mohssen, 2009). Therefore, the Partial Dura-tion Series (PDS, see Appendix C) analysis which consists of all sig-nificant flood events above a pre-defined threshold (Birikundavyiand Rousselle, 1997) is needed to analyse the difference betweenthe observed and modelled high flow process.

Fig. 9 shows the PDS selected using threshold daily dischargeQ0 = 9231.5 m3/s and h = 15 days. It is seen that: (1) in case of

Xinanjiang Model, PDS derived from W_X.M and A_X.M fit theobserved PDS relatively well in the Cumulative Frequency (C.F.)interval of (0.1, 0.2) and (0.7, 1), while modelled PDS using WFDdata show large differences in the C.F. interval of (0.2, 0.7). (2) Incase of SWAT Model, PDS from W_S.M and A_S.M fit the observedPDS well in the C.F. interval of (0.2, 1), but tend to overestimate theextreme high flows (i.e. PDS belongs to C.F. interval (0, 0.2)). And(3) corresponding to Fig. 8(b) and (e), the differences betweenobserved and modelled PDS (especially in the WFD data basedmodels) can be explained by the low values of R2, Rp and Rsp. Forthe PDS are usually applied for design flood calculation and riskassessment, it should be prudent on the errors from modelled highflows when using the reanalysis data based hydrological models.

The various discussions in Section 4 suggest that the APHRO-DITE data and lumped Xinanjiang Model show generally bettercapacity in modelling long term hydrological process as well asin simulating flood events. However, it should be noted that theseresults are area and model dependent. Many studies pointed outthat the accuracy of the reanalysis products varies by regions(e.g. Adam and Lettenmaier, 2003; Li et al., 2013; Mochida et al.,2014; etc.). Meanwhile, a hydrological model with different con-ceptualization and representation of the rainfall-runoff processmay result in different conclusions.

5. Conclusions

This paper compared the differences of two widely used globalreanalysis precipitation datasets, WFD and APHRODITE, withgauged precipitation and forced the three datasets in lumpedXinanjiang Model and distributed SWAT Model for discharge sim-ulations at daily step in Xiangjiang River basin with an area of94,660 km2, south China to demonstrate the utility of the reanaly-sis rainfall datasets in simulating the hydrological process and theoccurrence of flood events.

The following conclusions can be drawn from the results of thisstudy:

(1) In comparing with the precipitation datasets in mean arealscale, the WFD precipitation data show better values in theindices of Relative Error and Max Five-day Precipitation thanthe APHRODITE data do, while the APHRODITE precipitationdata give better values in the indices of Standard Deviation,Coefficient of Determination and Max Dry Spell.

354 H. Xu et al. / Journal of Hydrology 542 (2016) 343–356

(2) The APHRODITE and WFD datasets show similar spatial pat-tern in the index of Relative Error, while the APHRODITEdata show obviously higher values of Nash-Sutcliffe coeffi-cient over the basin than that of WFD data.

(3) The discharge modelling results show that the gauged pre-cipitation based Xinanjiang Model and SWAT Model givethe best model performances. Meanwhile, in consistent withthe statistical analysis of the differences of the two reanaly-sis rainfall products, the simulation of daily hydrologicalprocesses shows that the two models using APHRODITE dataproduce a relatively overall good fit, while the WFD databased two models are in less good agreement with the gaugesimulations at daily time step, the values of NSE are lowerthan 0.8 in both models in calibration and validation periodsand the RE values are larger than 5% in SWAT Model in bothcalibration and validation periods.

(4) The simulated flood discharges from the two models revealthat APHRODITE precipitation data have the potential tomodel the flood events in both hydrological models in termsof flood evolution dynamics, Probability of Detection andFalse Alarm Rate, whereas the WFD dataset is less capablein simulating the flood process.

This study highlights the capability and uncertainty associatedwith two coarse spatial resolution reanalysis datasets for the pur-pose of streamflow simulation. In general, the APHRODITE precip-itation dataset shows better consistency with the gaugedprecipitation data than the WFD and has good potential in mod-elling streamflows at daily step and in revealing the flood events,especially in driving the lumped hydrological model. However, itshould be noted that several shortcomings, such as the reanalysisdatasets cannot accurately reveal the temporal variation of therainfall in short time steps compared with the gauged data andthe relatively low spatial resolution of the reanalysis datasets,etc., may limit the applications of the reanalysis datasets in hydro-logical studies in small river basins.

Acknowledgement

This research was supported by the Project of Technology& Innovation Commission of Shenzhen Municipality(ZDSYS20140509094114169).

Appendix A

Before computing the basic statistical indices mentioned in Sec-tion 3.1, the following items are defined at first:

GPi,j: Gauged precipitation at day j that associated with a Thies-sen polygon i (Thiessen, 1911), which is equivalent to the pointprecipitation of the station located at the centroid of the poly-gon i;RPi,j: Reanalysis precipitation at day j that associated with grid i;K: Total number of grids that the reanalysis data cover thewatershed;Ai: Area defined by the Thiessen polygon alone (if the polygonlies completely within the watershed boundary), or by theintersection of the Thiessen polygon and the watershedboundary;AT: Total area of the watershed;

The Mean Area Gauged Precipitation at day j (MAGPj) which isestimated by using Thiessen polygons over a watershed as below:

MAGPj ¼Xi

Ai

ATGPi;j

The Mean Area Reanalysis Precipitation at day j (MARPj) over awatershed is computed as below:

MARPj ¼ 1K

XKi¼1

RPi;j

The Relative Error (RE), Standard Deviation (STDE), Coefficient ofDetermination (R2) are computed as below:

RE ¼ RMA � GMA

GMA

STDE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

XNi¼1

xi � 1N

XNi¼1

xi

!" #2vuut

R2 ¼ 1�XMi¼1

e2i

! XMi¼1

yi �1M

XMi¼1

yi

!224

35,

where GMA and RMA are the gauged and reanalysis Annual MeanPrecipitation computed by MAGPj and MARPj respectively; xj andyi are the annual and monthly precipitation calculated by MAGPjor MARPj, respectively; ei is the residuals defined as: ei ¼ yi � yi; yiis the predicted (or modelled) value associated with yi; N and Mare the total number of years and months used in the computation.

The Max Dry Spell (MDS) is computed by the longest period ofconsecutive days with less than 0.1 mm precipitation based onMAGPj and MARPj; the Max 5-day Precipitation (M5P) is the maxi-mum precipitation volume in a consecutive five rainy days calcu-lated from MAGPj and MARPj.

Appendix B

Before computing the Probability of Detection and False AlarmRate, the following items are defined at first:

D: time window, see Section 4.2.3;Fobs: observed discharge which is larger than 4940 m3/s, and theday with Fobs is defined as flood day;

Detected flood: in one flood day, if at least one simulated dis-charge is larger than 0.9Fobs in the time window D, this flood dayis regarded as detected;

Nf: total number of flood days;Ndf: total number of detected flood days;NFobs: observed discharge which is smaller than 4940 m3/s, andthe day with NFobs is defined as non-flood day;

False detected flood: in one non-flood day, if at least one simu-lated discharge is larger than 4940 m3/s (when the NFobs of this dayis smaller than 4940 m3/s � 0.9 = 4446 m3/s) or larger than4940 m3/s � 1.1 = 5434 m3/s (when the NFobs of this day is largerthan 4446 m3/s) in the time windowD, this day is regarded as falsedetected flood day;

Nfdf: total number of false detected flood days;Nnf: total number of non-flood days;

The Probability of Detection is computed as below:

PoD ¼ Ndf

Nf

The False Alarm Rate is computed as below:

FAR ¼ Nfdf

Nnf

H. Xu et al. / Journal of Hydrology 542 (2016) 343–356 355

Appendix C

In AMF series, the magnitudes of flood events are denoted as Xi,where the subscript i = 1, 2, . . ., N indicates year. It is assumed thatthe flood events Xi are independent and identically distributed. InPDS, flood event exceedances over the threshold discharge Q0 aredenoted as wðtiÞ, where ti indicates the time when the flood peakwðtiÞ occurs. Meanwhile, the PDS elements wðtiÞ are assumed inde-pendent and drawn from the same Cumulative DistributionFunction.

In order to guarantee that the flood peaks are independent inthe PDS, the consecutive flood events are separated using the equa-tions below (USWRC, 1976):

Qmin > 34 min½Qi;Qiþ1�

h < 5þ lnðAÞ

(

where Qi is the peak discharge of flood event i, Qmin is the minimumdischarge between the two consecutive flood events i and i + 1, h isthe time lag between two consecutive flood peaks, A is the drainagearea. When the two equations above are satisfied simultaneously,the smaller flood peak in (Qi, Qi+1) should not be included in the PDS.

The threshold Q0 is defined by using (Rosbjerg et al., 1992):

Q0 ¼ EðQÞ þ 3ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVarðQÞ

pwhere E(Q) and Var(Q) are the expectation and variance of theobserved daily discharge Q, respectively.

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