Sensitivity and uncertainty analysis of mesoscale model downscaled hydro-meteorological variables...

HYDROLOGICAL PROCESSESHydrol. Process. (2013)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.9946

Sensitivity and uncertainty analysis of mesoscale modeldownscaled hydro-meteorological variables for discharge

prediction

Prashant K. Srivastava,1* Dawei Han,1 Miguel A. Rico-Ramirez1 and Tanvir Islam1,2

1 WEMRC, Department of Civil Engineering, University of Bristol, Bristol, UK2 National Oceanic and Atmospheric Administration (NOAA), College Park, MD, USA

*CMaUnE-m

Co

Abstract:

Precipitation and Reference Evapotranspiration (ETo) are the most important variables for rainfall–runoff modelling. However, itis not always possible to get access to them from ground-based measurements, particularly in ungauged catchments. This studyexplores the performance of rainfall and ETo data from the global European Centre for Medium Range Weather Forecasts(ECMWF) ERA interim reanalysis data for the discharge prediction. The Weather Research and Forecasting (WRF) mesoscalemodel coupled with the NOAH Land Surface Model is used for the retrieval of hydro-meteorological variables by downscalingECMWF datasets. The conceptual Probability Distribution Model (PDM) is chosen for this study for the discharge prediction.The input data and model parameter sensitivity analysis and uncertainty estimations are taken into account for the PDMcalibration and prediction in the case study catchment in England following the Generalized Likelihood Uncertainty Estimationapproach. The goodness of calibration and prediction uncertainty is judged on the basis of the p-factor (observations bracketed bythe prediction uncertainty) and the r-factor (achievement of small uncertainty band). The overall analysis suggests that theuncertainty estimates using WRF downscaled ETo have slightly smaller p and r values ( p= 0.65; r= 0.58) as compared toground-based observation datasets ( p= 0.71; r= 0.65) during the validation and hence promising for discharge prediction. On thecontrary, WRF precipitation has the worst performance, and further research is needed for its improvement ( p= 0.04; r= 0.10).Copyright © 2013 John Wiley & Sons, Ltd.

KEY WORDS evapotranspiration; precipitation; WRF-NOAH LSM; global datasets; sensitivity analysis; uncertainty estimation;discharge prediction

Received 22 March 2013; Accepted 18 June 2013

INTRODUCTION

From a long time, ungauged basins pose a challenge tohydro-meteorological studies due to unavailability ofdatasets for proper calibration and validation. ThePrediction in Ungauged Basin (well knows as PUBS)(Sivapalan et al., 2003; Sivapalan, 2006) is under practicefor more than a decade to come up with some major ideasto solve this problem. One of the major suggestions whichcome out during the last PUBS symposium meeting(http://www.iahs-pub.org/) is to stress on the use ofremote sensing or mesoscale model-based datasets as apossible solution for ungauged basins. For rainfall–runoffmodelling and hydro-meteorological applications, theprecipitation and Reference Evapotranspiration (ETo)

orrespondence to: Prashant K. Srivastava, Water and Environmentnagement Research Centre, Department of Civil Engineering,iversity of Bristol, Bristol - BS8 1TR, UK.ail: [email protected]; [email protected]

pyright © 2013 John Wiley & Sons, Ltd.

considered as the two important key variables (Shuklaand Mintz, 1982; Nemani and Running, 1989; Srivastavaet al., 2013a, b, c). Both have significant effects on flowover spatial and temporal scales, which in turn signifi-cantly affect the catchment water balance, water yield andgroundwater recharge (Zhang et al., 2001; Al Shrafanyet al., 2013; Srivastava et al., 2013a, b, c). Their reliableestimates from terrestrial surfaces are very much requiredfor efficient flood, drought and irrigation management(Thakur et al., 2011; Srivastava et al., 2012a). Hence,monitoring these two important variables at local, regionalor global scales is an essential task for assessing climate andhuman-induced effects on natural and agricultural ecosys-tems and flood forecasting (Kustas and Norman, 1996;Al-Shrafany et al., 2012; Thakur et al., 2012). Estimation ofprecipitation is now possible from satellites such as TRMMand newmissions likeGPM and downscaling via mesoscaleweather models like MM5 and Weather Research andForecasting (WRF) (Bromwich et al., 2009; Gupta et al.,2012; Islam et al., 2012). The global terrestrial ETo can beobtained by using the satellite remote sensing data (Running

P. K. SRIVASTAVA ET AL.

et al., 2011) and mesoscale models like MM5/WRF (Ishaket al., 2013). However, to reduce the input data uncertainty,appropriate meteorological data selection is important if thedata are derived from a mesoscale model (Evans et al.,2011) or satellite data like MODIS. In this study, theMODIS ETo is not taken into account because of its nonsub-daily availability.Traditionally, estimates of ETo and precipitation are

obtained through the use of ground-based observations(Novák, 2012). But these ground-based observations cancover only small areas, and large areas require a largenumber of observation sites because of the heterogeneityof landscapes and very high variations in energy transferprocesses (Caylor et al., 2006). As a result, the ground-based approaches are very expensive, labour intensiveand very tough to maintain for very long time periods,so alternative approaches are required to estimate EToand precipitation at large scales. Recently, efforts havebeen made to determine the spatial and temporalvariability of ETo (Niyogi et al., 2009; Ishak et al.,2010) and precipitation through mesoscale model likeMM5/WRF. Srivastava et al. (2013b) reported thatEuropean Centre for Medium Range Weather Forecasts(ECMWF) datasets are promising for hydro-meteorologicaldata retrieval in comparison to National Centres forEnvironmental Prediction (NCEP) data. Due to lack ofdetailed studies, utilities of these datasets are still in theirearly stage especially for the hydrological applicationssuch as for discharge prediction. Therefore, there is aneed to know the performances of ECMWF global dataproducts as compared with ground-based measurementand whether it is possible to use this data for ungaugedcatchment runoff prediction. This is especially aproblem in developing countries due to lack of gaugenetworks.Sensitivity analysis (SA) and uncertainty analysis (UA)

are considered to be an important tool in hydrologicalpredictions (Zheng and Keller, 2007; Blasone et al.,2008). It has gained popularity in day-to-day sciencessuch as in water quality (Beck, 1987), biosciences(Blower and Dowlatabadi, 1994), atmospheric sciences(Derwent and Hov, 1988), structural sciences (Adelmanand Haftka, 2012) and discharge prediction (Beven andBinley, 2006; Yatheendradas et al., 2008) to explore thehigh-dimensional parameter spaces, parameteridentifiability, structural uncertainty and also to under-stand the sources of uncertainty. The SA and UA incatchment-based modelling can be achieved with variousmethods, of which formal Bayesian that is the General-ized Likelihood Uncertainty Estimation (GLUE) is themost popular (Beven and Freer, 2001) and used by manyresearchers in hydrology (Ratto et al., 2007; Wagener andKollat, 2007; Hassan et al., 2008; Yang et al., 2008) andhence used in this study as well. Some limitations of

Copyright © 2013 John Wiley & Sons, Ltd.

GLUE are well discussed in the past works (Mantovanand Todini, 2006; Stedinger et al., 2008).Hence, the foremost objective of the study is focused

on to assess the hydro-meteorological derived ETo andprecipitation products downscaled using the WRF modelcentred over the Brue catchment in the UK andinvestigation of the sensitivity and uncertainty estimatesof the mesoscale model-based products (ETo and rainfall)for discharge prediction following the GLUE approach.The remainder of this paper is structured as follows: Inthe second section, we introduce the materials andmethodologies used for the comparison, give a briefoverview of the datasets, selected techniques, and then listthe criteria for the assessment. In Section “Results anddiscussion”, the results are presented and discussed. Thelast section contains the conclusions.

MATERIALS AND METHODOLOGY

Study area and datasets

The Brue catchment (135.5 Km2) is chosen as the studyarea which is located in the south-west of England, 51.11°Nand 2.47°W. The major land use is pasture land on clay soilwith some patches of woodland in the higher easterncatchment. The land use/land cover of Brue is illustrated inFigure 1 with the Digital Elevation Model (DEM) and landuse. The DEM of this area is obtained from EDINA, UK(http://digimap.edina.ac.uk/digimap/home) with 50m spa-tial resolution. The satellite image of this area is classifiedusing ANN technique for estimating the land use(Srivastava et al., 2012b). The flow data is obtained fromEnvironment Agency, UK. All meteorological datasets areprovided by the British Atmospheric Data Centre (BADC),UK. Despite the increasing computing power from desktopPCs, downscaling usingWRF at a high spatial and temporalresolution is still quite time consuming. Hence, in this workonly one and half year hourly datasets are taken into accountstarting from August 2010 to January 2012. For thecalibration of the Probability Distribution Model (PDM)model, one year hourly datasets (August 1, 2010 to July 31,2011) are used, while for the validation, 6months (August 1,2011 to January 31, 2012) datasets are taken into account.The data provided by BADC are used for evaluating thehourly precipitation and ETo data from the WRF. Theglobal ECMWF ERA interim reanalysis data used in thisstudy are downloaded from http://www.ecmwf.int/.

WRF-NOAH LSM model

The latest WRF mesoscale model coupled with NOAHLand Surface Model (LSM) is used in this study with theAdvanced Research WRF dynamic core version 3.1(Powers, 2007; Schwartz et al., 2009). WRF-NOAH

Hydrol. Process. (2013)

Figure 1. Study area with digital elevation model, land use and WRF domains

UNCERTAINTY IN MESOSCALE MODEL VARIABLES FOR DISCHARGE PREDICTION

LSM is adopted in this study because many researchersand weather modeller show that its results are veryefficient (Skamarock et al., 2005) and second it is anoperational model in use by NCEP. It is a next-generationnon-hydrostatic model with terrain following eta-coordinate modelling system intended to serve bothoperational forecasting and atmospheric research require-ments (Skamarock et al., 2001; Skamarock and Klemp,2008). The original LSM was developed at the OregonState University by Pan and Mahrt (1987) and modifiedby Chen et al. (1997), which included an explicit canopyresistance formulation used by Jacquemin and Noilhan(1990) and a surface runoff scheme given by Schaakeet al. (1996). The soil water movement and flow in theNOAH LSM is governed by the mass conservation lawand the diffusivity form of Richards' equation (Chen andDudhia, 2001):

∂θ∂t

¼ ∂∂z

D∂θ∂z

� �þ ∂K

∂zþ Fθ (1)

where θ is the volumetric soil water content, D is the soilwater diffusivity (m2 s�1) and K is the hydraulicconductivity (m s�1) and both are functions of θ; t istime (s) and z is the soil layer depth (m); and Fθ representssources and sinks for soil water (i.e. precipitation,evaporation and runoff). A more detailed description ofthe WRF-NOAH LSM can be found in (Chen andDudhia, 2001).


The WRF-NOAH LSM model is centred over the Bruecatchment with three nested domains (D1, D2 and D3)with horizontal grid resolutions of 81 km, 27 km and9 km, in which the innermost domain (D3) is the area ofinterest. The smallest domain is taken into considerationto avoid any spatial mismatch problem as it is closest tothe catchment under study. The three domains consist of18×18, 19×19, and 22×22 horizontal grids points fordomain D1, D2 and D3, respectively. A two-way nestingscheme is used allowing information from the childdomain to be fed back to the parent domain. Imposedboundary conditions are updated every 6 h with theECMWF datasets. The WRF model is used to downscalethe ECMWF global data to derive wind, solar radiation,surface temperature, dew point, temperature and precip-itation. The main physical options include WRF Dudhiashortwave radiation (Dudhia, 1989) and Rapid RadiativeTransfer Model (RRTM) long wave radiation (Mlaweret al., 1997) with Lin microphysical parameterization. ABetts–Miller–Janjic Cumulus parameterization scheme isused because it is well tested for regional application andprecipitation forecasting (Vaidya and Singh, 2000).Gilliland and Rowe (2007) found that it considerssophisticated cloud mixing scheme in order to determineentrainment/detrainment which is found to be moresuitable for non-tropical convection. The Yonsei University(YSU) planetary boundary layer (PBL) scheme (Hu et al.,2010). The third-order Runge–Kutta is used for thetime integration as it is stable without any damping



(Zhong,1996), while for the spatial differencing scheme, thesixth-order centred differencing scheme is used. The reasonbehind using this differencing scheme is its high numericalstability. The brief analysis byChu and Fan (1997) indicatedthat the sixth-order scheme has error reductions by factors of5 compared to the fourth-order difference scheme, and byfactors of 50 compared to the second-order differencescheme. The Arakawa C-grid is used for the horizontal griddistribution. The thermal diffusion scheme is used for thesurface layer parameterization. The top and bottomboundary conditions chosen for the study are gravity waveabsorbing (diffusion or Rayleigh damping) and physical orfree-slip, respectively. The Lambert conformal conicprojection is used as the model horizontal coordinates.The WRF model configuration is shown in Table Iand well tested over the Brue catchment by Srivastavaet al. (2013b).

PROBABILITY DISTRIBUTED MODEL

There are many hydrological models available around theworld, and in this study, a typical rainfall–runoff modelcalled PDM is used. The PDM model is a fairly generalconceptual rainfall–runoff model which transforms rain-fall and evaporation data to flow at the catchment outletand is well tested (Moore, 2007; Liu and Han, 2010). The

Table I. WRF model configuration used in this study

Initial conditions Three-dimensional real data(1°×1° FNL)

Map projection LambertCentral point of domain Central latitude: 51.11° N;

Central longitude: 2.47° WDomain Three domainHorizontal grid distribution Arakawa C-gridHorizontal grid distance Domain 3 (9 km)NCEP time interval 6 hModel output HourlyNesting 2 wayTime integration Third-order Runge–KuttaSpatial differencing scheme Sixth-order centred differencingLateral boundary condition Specified options for real dataTop boundary condition Gravity wave absorbing

(diffusion or Rayleigh damping)Bottom boundary condition physical or free-slipMicrophysics LinRadiation scheme Dudhia's short wave radiation/

RRTM long waveSurface layer parameterization Thermal diffusion schemeCumulus parameterizationschemes

Betts–Miller–Janjic

PBL parameterization YSU schemeVertical coordinate Terrain following hydrostatic

pressure coordinate(28 sigma levels up to 1 hPa)


PDM has been widely applied throughout the world, bothfor operational and design purposes (Bell and Moore,1998). It has evolved as a toolkit of model functions thattogether constitute a lumped rainfall–runoff modelcapable of representing a variety of catchment-scalehydrological behaviours (Srivastava et al., 2013d). Themodel formulations are well suited for automaticparameter estimations. In the PDM, the main inputs arerainfall and ETo, and the river flow is the model output.For real-time flow forecasting applications, the PDMmodel is complemented by updating methods based onerror prediction and state-correction approaches (Belland Moore, 2000). In this study, five PDM parametersare used such as Cmax (maximum store capacity), b(exponent of pareto distribution), g (groundwaterrecharge time constant), Kf (fast flow component) andKs (slow flow component) for the whole hydrologic year.

Model structure identification and GLUE

GLUE is a UA technique based on importancesampling and regional SA (Beven and Beven, 2001;Yang et al., 2008). The model identification processinvolves estimation of a suitable parameter set, i.e. theactual calibration of the model structure (Gupta et al.,2005). The parameters of each model structure needadjustment until the observed system output and themodel output show acceptable levels of agreement(Wagener et al., 2003). The main advantage with theGLUE parameter uncertainty is that it takes into accountall sources of uncertainty either explicitly or implicitly(Beven and Binley, 2006; Zheng and Keller, 2007). It isconceptually simple and requires no restricted errorassumptions if a goodness-of-fit measure is used as itslikelihood function and hence makes it less vulnerable tomodel discontinuity (Yang et al., 2008). For multi-objective approaches GLUE's uncertainty bounds aremore likely to reflect the real magnitude of uncertainty(Choi and Beven, 2007). In GLUE, the parameteruncertainty is described by a set of discrete ‘behavioural’parameter sets with their corresponding ‘likelihoodweights’ (Beven and Freer, 2001):

wi ¼ L θið Þ∑N

k¼1L θkð Þ (2)

where N is the number of behavioural parameter sets andL(θ)is generalized likelihood measure. In the literature,the most frequently used likelihood measure for GLUE isthe Nash–Sutcliffe coefficient (NSE) (Beven and Beven,2001; Beven and Freer, 2001; Montanari, 2005) which isalso used in this study. ‘R’-based programming language(Team, 2008) is used for GLUE implementation; the moredetailed information is well described at http://www.uncertain-future.org.uk/RSoftware.htm.



ETo estimation

The ETo from WRF downscaled meteorological andobservation stations variables are calculated using the PMmethod proposed and developed by (Penman, 1956;Monteith, 1965) as given in FAO56 report (Allen et al.,1998). The ETo (in mm) according to the PM equation isas follows:

ETo ¼0:408Δ Rn � Gð Þ þ γ 37

Tþ273U2 es � eað ÞΔþ γ 1þ rc

ra

� � (3)

where Δ = slope of the saturated vapour pressure curve(kPa/°C); Rn = net radiation at the crop surface (MJ/m2/h);G = soil heat flux density (MJ/m2/h); γ = psychrometricconstant (kPa/°C); T = mean air temperature at 2m height(°C); es = saturation vapour pressure (kPa); ea= actualvapour pressure (kPa); es� ea=saturation vapour pres-sure deficit (kPa); U2= wind speed at 2 m height (m/s);ra (aerodynamic resistance)=208/U2 s m�1; andrc (canopy resistance)=70 s m�1.

Performance analysis

The performance analysis is divided into two parts:first, the performances of WRF downscaling is comparedfor the three domains used in this study, and then the SAand uncertainty estimations of discharge prediction forvarious combinations are used in this study. To judge theperformances of input data, i.e. precipitation and ETodownscaled using WRF, Taylor diagrams (Taylor, 2001)are employed. It provides a way of graphically summa-rizing how closely a pattern matches observations. Thesimilarities between two patterns are quantified in termsof their correlation, their centred root-mean-squaredifference and the amplitude of their variations (repre-sented by their standard deviations (SDs)). The threeperformance statistics: the NSE (Nash and Sutcliffe,1970), p-factor and r-factor are taken into account forevaluating the sensitivity and uncertainty of various inputdata and PDM model for discharge prediction. The NSEis used as a likelihood measure for rainfall–runoff model(PDM) following the GLUE approach (Nash andSutcliffe, 1970). The NSE is calculated using:

NSE ¼ 1�∑n

i¼1yi � xi½ �2

∑n

i¼1xi � x½ �2

(4)

where xi is the ground-based measurements and yi is theestimated measurements; x is the mean of ground-basedmeasurements.For comparison of the uncertainty bounds two statistical

indices are taken into account, i.e. the p-factor (observations


bracketed by the 95% prediction uncertainty (95UB)) andthe r-factor (achievement of small uncertainty band). The95% uncertainty boundary (95UB) is generated through theGLUE analysis. The goodness of calibration and predictionuncertainty is judged on the basis of the nearness of thep-factor to 100 and the r-factor to 1. The r-factor canbe represented by (Yang et al., 2008):

r � factor ¼1n∑

nti¼1 yMti;97:5% � yMti;2:5%

� �σobs

(5)

where yMti;97:5% and yMti;2:5%represent the upper and lowerboundary of the 95UB, and σobs stands for the SD ofthe observed data.

RESULTS AND DISCUSSION

Assessment of WRF downscaled datasets

The Taylor diagram (Figure 2 (a–b)) are used to showthe ability of the output of downscaled variables with theobserved data. The circle mark in the x-axis, calledreference point, represents the perfect fit between modelresults and data. The position of the labels, representingthe results of the different runs, is determined by thevalues of the correlation R and of the SD of the modelleddata. The graph clearly indicates a high performance ofdomain 3 datasets as compared to the other domains asdomain 3 data point is found closer to the reference pointrepresenting a better performance of the WRF simulationfor this domain. The observation indicates a comparableroot mean square centred error E for all the domains incase of ETo, but there exists a significant differencebetween the precipitation datasets. The tendency to over/under estimate the observed values can be observed bythe Taylor diagram. The data indicates that the SD of thedomain 1 is much higher than the SD for domain 2 and 3.This indicates that domain 1 precipitation data is higherthan that of the observed values and hence showing ahigher overestimation. The SD analysis for all the threedomains indicates a marginal outperformance of domain 3.Further, a low correlation is observed in between the WRFand observed rainfall for all the domains, with slightimprovement in domain 3 datasets. However, for hydro-meteorological variables, a high correlation is observedbetween observed and downscaled datasets. The overallperformance indicates that the WRF is relatively skilful indownscaling the variability of the hydro-meteorologicalvariables. This performance is very high for the ETo butnot very effective for the rainfall.

Evaluation of hydro-meteorological datasets

The analysis of downscaled data indicates a highperformance of domain 3 datasets as compared to other


Figure 2. Taylor diagrams for the domains performances

Figure 3. Scatter plots between WRF downscaled ECMWF with observeddatasets (a) hourly precipitation with observed and (b) hourly ETo with

observed


domains under study. Henceforth, only domain 3 datasetsare taken into consideration for all the examination usingthe PDM model. The scatter plots between the WRFderived precipitation and ETo for the domain 3 with theobserved datasets are shown in Figure 3. The uniquefeatures can be seen from these figures that ECMWF ETofollows the ground observed datasets more closely and avery poor performance of the ECMWF precipitation. Thesimulated and ground-based observations indicate thatduring the year, the ETo increases significantly during thesummer months and then decreases during the winterseason exhibiting a bell-shape response in the complete


datasets during the calibration and validation. Althoughthe ETo increases gradually from January to July, thissurge is found to be more rapid during the April–Maymonths than during winter months, which can beattributed to high solar radiation and temperatureobserved during those months (graph not shown). Asimilar trend can be observed with validation datasets. Bycontrast, there is a significant difference existed betweenthe ECMWF downscaled precipitation for all the monthsunder consideration as compared to the observed datasets.The bias statistics shows that the simulated products, ingeneral, are quite promising with the ground-based ETo(NSE = 0.76; RMSE = 0.06 & Bias = 0.00). On the otherhand, the downscaled precipitation has a poor perfor-mance with very high underestimation (Bias = �0.03)and poor RMSE = 0.46 and NSE = �0.17. The reason forthe poor goodness of fit with the precipitation datasetsmay be ascribed to the insufficiency of the parameteri-zation scheme. In this study, the best available cumulusparameterization scheme is used as proposed by several



past studies (Ishak et al., 2011), indicating that there is aneed of further development for a new parameterizationscheme especially for the maritime climate. Thesuitability of data for ETo estimations suggests thatECMWF could be used for hydro-meteorologicalapplications.The time series plots for all the input datasets are

shown in Figure 4. The comparisons between ETo andflow time series exhibit a similar variability for the wholehydrologic year and follow a strong seasonal cycle,peaking normally in January and February; this may bebecause of a very high wet soil profile and low EToduring the period of December–February. Similar inter-pretation can be observed from ETo and flow time series,as the increasing temperatures and high evaporationthrough the period April–May to August–September leadto a progressive drying of the soil. The soil wetnessincreases after a rain event, and it follows an exponentialdecay as expected during the drying period. When ETodecreases in November–December, rainfall wets up thesoil profile, and that's the reason for a surging graph inFigure 4. The rainfall pattern shows that November–December is the relatively wettest periods during thewhole hydrologic year. On the contrary, March to May isslightly drier than other months. Generally, maximumrainfall intensities are also higher in June and areassociated with moderately short-duration storms. ETo

Figure 4. Time series plot for (a) measu


is low over winter, and soils are near to the field capacityuntil mid April in most of the year. There is a significantlag time behaviour occurred between the rainfall andflow, which can be used to underline the influence ofrainfall on non linear runoff generation processes.Interestingly, the ETo values during the period of Aprilto mid August is very high, revealing the strong influenceexerted by net radiation and temperature conditions onboth surface and subsurface response. The higher rainfallin this period could be a possible reason that regardless ofsome high ETo events, the flow did not change veryeffectively. It is observed that during the very wetconditions, ETo and rainfall on average started to rise atapproximately the same time.

Sensitivity analysis and uncertainty estimation

The multiple Monte Carlo model simulations followingthe GLUE approach is used in this study for the SA andUA. To evaluate the performances, the three combina-tions are used in this study. The first combination(Combination 1) is based on measured rainfall using raingauge and observed ETo, while the second (Combination 2)and third (Combination 3) are formed by using rain gaugeand WRF downscaled ECMWF ETo and both WRFdownscaled products that is rainfall and ETo, respectively.An SA is performed on locally conditioned model

red flow (b) precipitation and (c) ETo



performance measures of the PDM such as Cmax (maximumstore capacity), b (exponent of pareto distribution),g (groundwater recharge time constant), Kf (fast flowcomponent) and Ks (slow flow component) for the wholehydrologic year. The uncertainty in model calibration andvalidation has been estimated, and the plots are derived withNSE as a likelihood measure under the natural flowconditions. In this study, the threshold value of GLUEapplication is chosen to be 0.60, i.e. the simulations withNSE values larger than 0.60 are behavioural otherwise non-behavioural. At the start, the analyses are performed to testhow sensitive the GLUE results are to the threshold valuesof retained solutions. As suggested, the starting initial valuechosen for the threshold is zero, and then increasedgradually (http://www.uncertain-future.org.uk/RSoftware.htm). At 0.6, the maximum behavioural parameters areobtained along with an acceptable NSE. All the GLUEsimulations are performed with 4000 iterations. However,for the ECMWF rainfall and precipitation, the GLUEsimulation is performed with 0.1 thresholds as above thisvalue, all the points becomes non-behavioural. This showsthat even at 0.1 thresholds, ECMWF downscaled rainfall isnot very good enough to produce a convincing discharge.The calibration procedure in particular focuses on theestimation of storage time constants, the optimal separation

Figure 5. Dotty plots retrieved fromall the three combinations (i.e. Combinationand Combination 3- (EC


of slow and fast runoff and the good agreement betweensimulated and observed discharge. The measured andsimulated flow time series are compared over the completemonitoring period. The overall analysis indicates an NSEvalue of 0.85 during the calibration and 0.82 for thevalidation (Combination 1), while for the Combination 2(NSE calibration = 0.82; NSE validation 0.80) andCombination 3 (NSE calibration = 0.58; NSE validation0.06) are obtained. The overall analysis of the likelihoodmeasure obtained with all the combination shows thatCombination 2 is slightly lower but comparable toCombination 1 and indicates a possibility of WRF ETofor rainfall–runoff modelling. While Combination 3suggests that WRF precipitation needs more improvements,if it is used for discharge prediction. For each simulation,the dotty plot, cumulative posterior distribution and 95%Uncertainty Bounds (95UB) are analysed. Figures 5 and 6illustrates the information content for the model param-eters derived using a window size of hourly time steps. Itcan clearly be seen that the main information about themodel parameters emerges during the wetting up periods.The information values during the remaining periodsespecially the dry periods are relatively small. Theperformance statistics with best PDM estimate are shownin Table II.

1- (Raingauge + observedETo), Combination 2- (Raingauge +ECMWFETo)MWF rainfall + ETo)


Table II. Performance indices

Criterion best estimateCombination 1

(Raingauge + observed ETo)Combination 2

(Raingauge + ECMWF ETo)Combination 3

(ECMWF rainfall + ETo)

Cmax 160.10 180.42 137.89B 0.17 0.14 0.15G 0.47 0.47 0.55Kf 0.16 0.15 0.16Ks 0.00 0.00 0.00NSE calibration 0.85 0.82 0.58NSE validation 0.82 0.80 0.06p-factor for calibration 0.84 0.76 0.37p-factor for validation 0.71 0.65 0.04r-factor for calibration 0.68 0.62 0.38r-factor for validation 0.65 0.58 0.10


The dotty plots of the information measure areplotted and shown in Figure 5. Parameter sensitivitycan be evaluated by estimating the spread of thecumulative parameter distributions and clear peak (seeblue dots). For example, in the case of Kf, a smallvariation is linked with the highest likelihood as asharp and clear peak is observed with this parameter.This indicates that Kf is highly sensitive. Similarly, theinsensitive parameters are obtained by diffused peakrepresented by cumulative distributions. The dotty plotdemonstrates that for each parameter, solutions withsimilarly good values of the NSE can be found withinthe complete prior range. The SA of model parametersshows that in Combination 1 Kf is the most sensitiveparameter for discharge prediction followed by Ks,Cmax, b and g. It is clear from Figure 5 that ‘g’parameter is less skilled in retrieving information todistinguish between the performances of differentvalues of g and may be identifiable during distinctiveperiods of recession or caused by structural inadequa-cies of this component. Nearly similar performance isobtained with Combination 2 used in this study;however, the poorest performance is observed withCombination 3, which is mainly because of very poorprecipitation estimated from WRF.The cumulative distributions estimated for every time

step is used to derive prediction limits for the discharge(Figure 6). A wider confidence boundary suggests thatparameter values associated with equally good perfor-mance are distributed widely over the parameter space(Yang et al., 2008), whereas narrow boundary limitsreveal that the best performing parameters are concen-trated in a smaller area. The analysis reveals that themodel tends to match the observed hydrographs quitewell while some low performance can be seen with low-flow conditions. The plot obtained from the 95UB basedon the parameter uncertainty from Combination 1 is quitenarrow (r-factor calibration = 0.68; and validation = 0.65)


and parameter uncertainty and uncertainty sourcesrepresented by the GLUE model bracket more than84% of the observed points (p-factor) for calibration and71% for the validation periods (Table II). For Combina-tion 2, a slightly smaller p-factor (76%) and r-factor(0.62) are obtained, while during the validation (p-factor(65%) and r-factor (0.58)), comparable results areobtained indicating that WRF ETo may be used fordischarge prediction in the absence of ground-basedmeasurements. In Combination 3, the poorest perfor-mance is obtained in terms of NSE, p-factor (calibration=37%; validation=4%) and r-factor (calibration =0.38;validation=0.10), which shows that the WRF precipitationis poor for discharge prediction. However, summarizingthe values of p-factor and r-factor for all the threecombinations suggests that there is a large uncertainty ininput, output and model structure in addition to parameteruncertainty as changing input datasets reveals a signifi-cant difference in the discharge prediction. As can also beseen, there is a slight overestimation of predictionuncertainty during the dry season, and this suggests moreattention should be paid to the dry season whenconstructing the likelihood function or seems that itmay be because of subjective element in the initialfeasible parameter space by the model, and similarobservations are also observed by Zheng and Keller(2007). The information contained in Figures 5 and 6 maybe used to find the combinations of parameters respon-sible for the model's behaviour during specific responseperiods and thus could be utilized for input data selection(Wheater et al., 1986; Jaafar et al., 2011; Wan Jaafar andHan, 2012). However, no such attempts are taken in thisstudy, and future studies may include the data fusion and/or bias correction techniques for the improvement ofinput datasets, i.e. precipitation and ETo for rainfall–runoff modelling.The overall analysis indicates that ETo products

from the global reanalysis data could be suitable for


Figure 6. 95UB (grey shaded) produced by GLUE during the calibration period and validation period for the Combination 1- (Raingauge + observed ETo),Combination 2- (Raingauge + ECMWF ETo) and Combination 3- (ECMWF rainfall + ETo) obtained by GLUE. The black line corresponds to the observed

discharge at the basin outlet


hydro-meteorological applications and for dischargePUBS. In contrary, the downscaled precipitation is unfitfor stream flow prediction. The main limitation of thisstudy is the computational power of the WRF simulatingmachines. Despite increasing computing powers, down-scaling by the WRF at a high spatial and temporalresolution is still time consuming. Similarly with GLUE,the main drawback of this approach is its prohibitivecomputational burden imposed by its random samplingstrategy. On the other hand, it is also observed thatincreasing iteration and decreasing time step in the GLUEimprove its efficiency.


CONCLUSIONS

WRF-NOAH LSM may be used to downscale the globaldata into much finer resolutions in space and time forhydro-meteorological applications. Despite the impor-tance of these valuable data sources, there is a lack ofstudies in technical literature domain about the quality ofsuch data for rainfall–runoff modelling. The studyindicates that ECMWF ETo could be suitable forhydrological applications. The suitability of data forrainfall–runoff modelling suggests that ECMWF ETo hasa comparable performance to the observed datasets in


Figure 6. (Continued)


combination with rain gauges. On the other hand,ECMWF downscaled precipitation and ETo together givea poor performance, indicating that there is a need formore work on parameterization schemes to improve theprecipitation estimates as well as the need for dataassimilation. The SA and uncertainty estimation revealthe importance of more rigorous model calibration andthus facilitate a good modelling practice for hydrologicalpredictions. This is not only useful for planner anddisaster management but also important for qualitycontrol in the estimation of underlying uncertainty andrelated assumptions. The rigorous analysis tools likeGLUE up to some extent address these aspects in detailand thus are very beneficial in communicating theanalysis results to the end-users and obtaining convincing


model predictions. Hence, it's recommended to apply andinclude the detailed consideration and estimation ofuncertainty in the modelling of hydrological systemsdriven by global datasets. This study provides hydrolo-gists with valuable information on downscaled weathervariables from global datasets and its applicability torainfall–runoff model, and further exploration of thispotentially valuable data source by the hydrological andmeteorological community is recommended so that usefulexperience and knowledge could be accumulated in thetechnical literature domain for other geographical andclimatic conditions. The pattern obtained by precipitationwith observed measurements indicates a possibility ofimprovement with implication of bias correction schemesor data fusion techniques. Hence, future research will


Figure 6. (Continued)


focus on parameterization schemes and correction ofprecipitation using above mentioned techniques for animproved forecasting.

ACKNOWLEDGEMENTS

The authors would like to thank the CommonwealthScholarship Commission, British Council, UnitedKingdom and Ministry of Human Resource Develop-ment, Government of India for providing the necessarysupport and funding for this research. The authors wouldlike to acknowledge the British Atmospheric Data Centre,United Kingdom for providing the ground datasets. Theauthor also acknowledges the Advanced ComputingResearch Centre at University of Bristol for providing


the access to supercomputer facility (The Blue Crystal)for R language support and recent PUBS symposium forsome useful information on uncertainty and sensitivityanalysis. Authors would like to thank hydro-communityDepartment of Geography and Civil Engineering,University of Bristol for their useful and constructingcomments over the work.

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