Journal of Hydrology 517 (2014) 1035–1048

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Journal of Hydrology

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Improving the flood prediction capability of the Xinanjiang model inungauged nested catchments by coupling it with the geomorphologicinstantaneous unit hydrograph

http://dx.doi.org/10.1016/j.jhydrol.2014.06.0370022-1694/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +86 (025) 8378 7478.E-mail address: yaocheng@hhu.edu.cn (C. Yao).

Cheng Yao a,⇑, Ke Zhang b,c, Zhongbo Yu a, Zhijia Li a, Qiaoling Li a

a State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Hydrology and Water Resources, Hohai University, Nanjing 210098, PR Chinab Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USAc Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, OK, USA

a r t i c l e i n f o

Article history:Received 3 August 2013Received in revised form 12 June 2014Accepted 22 June 2014Available online 1 July 2014This manuscript was handled by AndrasBardossy, Editor-in-Chief, with theassistance of Ezio Todini, Associate Editor

Keywords:Xinanjiang modelGIUHUngauged catchmentsRegionalizationParameter transpositionFlood simulation

s u m m a r y

Improving the predictive capabilities of rainfall-runoff models in ungauged catchments is a challengingtask but has important theoretical and practical significance. In this study, we investigated the predictivecapabilities of the conceptual Xinanjiang model (XAJ), which is widely used for flood forecasting and sim-ulation in China, in ungauged catchments. We further produced a hybrid rainfall-runoff model (namedXAJ-GIUH) by coupling the XAJ model with the geomorphologic instantaneous unit hydrograph (GIUH)to achieve improved flood predictions in ungauged catchments. The flood prediction capabilities of theoriginal XAJ model and the XAJ-GIUH model were investigated and compared at an hourly time scalein a mountainous catchment with six nested catchments located in the south of Anhui province, China.The two models were first calibrated for each individual catchment by comparing with the observedstreamflows. Then, the nested catchments were treated as ungauged and modeled using the parametervalues regionalized by transposition from the downstream catchments. The results show that the perfor-mance of both models is comparable and satisfactory on different catchment scales in the case that modelparameters are calibrated in each catchment. However, the models perform differently in the case thatmodel parameters are transposed from the downstream catchments. The XAJ-GIUH model producedmarkedly improved estimates of peak discharge and peak time as compared to the original XAJ modelin the latter case, indicating that the runoff routing is a major uncertainty source for the application ofthe XAJ model in this case. Coupling XAJ with topography-based GIUH has the potential to substantiallyimprove the flood prediction capability of the XAJ model in ungauged catchments. Our analysis furtherreveals that the models do not necessarily perform better when the parameter values are transposedfrom closer donor catchment. Instead, adopting the parameter values from the catchment with more sim-ilar topographic characteristics is more likely to produce better model performance. This study implicatesthe necessity of including remotely sensed geomorphologic characteristics of ungauged catchments toimprove flood predictions in these regions.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Floods are one of the most significant water-related naturaldisasters, causing serious property damage and loss of lives(WMO, 2011). To reduce the impact of flooding, operational floodforecasting systems have been developed around the world(Todini, 2005). The growing necessity of these operational systemspromotes the development of rainfall-runoff models, which arecommonly used in the existing systems (Todini, 2005; WMO,

2011). With the rapid development of computational technologies,a large number of studies on rainfall-runoff models for flood simu-lation and forecasting have been carried out over the past severaldecades (e.g. Beven and Kirkby, 1979; Zhao, 1992; Garrote andBras, 1995; Singh, 1995; Todini, 1996; De Roo et al., 2000; Korenet al., 2004; Smith et al., 2004; Manfreda et al., 2005; Moore,2007; Yao et al., 2009; Beven, 2012).

With the growing need to forecast floods at any location wherethere is a risk of disastrous flood events, hydrologists are widelyinterested in applying the rainfall-runoff models to ungauged catch-ments (Blöschl, 2005; Moore et al., 2006; Cole and Moore, 2009).However, it is one of the most challenging tasks in theoretical and

1036 C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048

operational hydrology due to the lack of hydrologic observationsthat could be used for model calibration. Since 2003, an initiative,decade-long plan of Predictions in Ungauged Basins (PUB) has beenlaunched by the International Association of Hydrological Sciences(IAHS) (e.g. Sivapalan et al., 2003; Montanari and Toth, 2007;Moore et al., 2007; Wagener and Montanari, 2011; Blöschl et al.,2013; Hrachowitz et al., 2013). The decade plan has stimulatedthe extensive research activities in addressing the ungauged basinproblem associated with considerable uncertainties and continuedto push PUB to the forefront of hydrology research. Regionalizationapproaches, such as regression, spatial proximity and physical sim-ilarity, involving the transfer of parameter values from a donorgauged catchment to the receptor ungauged catchment, have beendesigned and typically used to handle the issue of PUB (e.g.Sivapalan, 2003; Wagener et al., 2004, 2007; Merz and Blöschl,2004; Wagener and Wheater, 2006; Young, 2006; Bárdossy, 2007;Götzinger and Bárdossy, 2007; Reed et al., 2007; Norbiato et al.,2008; Seibert and Beven, 2009; Javelle et al., 2010; He et al., 2011;Beven, 2012; Yao et al., 2012; Singh et al., 2012; Yang et al., 2008,2010, 2013).

The Xinanjiang model, which is the most popular conceptualrainfall-runoff model in China, has been extensively used for floodsimulation and operational forecasting in gauged catchments sincefirst developed in the 1970s (Zhao, 1977, 1992; Zhao et al., 1980;Zhao and Liu, 1995; Todini, 2005) and already deployed in theChina National Flood Forecasting System (WMO, 2011). Althoughsome insensitive parameters of the Xinanjiang model can be pre-set or estimated in terms of the implementation experience, thesensitive parameters must be calibrated based on historicalstreamflow data using either a trial-and-error approach and/oran automatic optimization algorithm (Lü et al., 2013). This makesit difficult to apply the Xinanjiang model to the ungauged catch-ments to achieve good results. Some recent studies have claimedto address the relevant issue using the regionalization approaches,but these studies mainly focused on the application of Xinanjiangmodel at daily time scale (Li et al., 2009; Zhang and Chiew,2009). Since the Xinanjiang model parameters related to runoffseparation and routing are sensitive to time scale, their values,which cannot be obtained in a theoretically based way of takingaccount of change of time-step (e.g. Moore et al., 1999), shouldalways be adjusted through recalibration when using the modelfor flood simulation and forecasting at a shorter time interval.Therefore, this raises the questions whether the regionalizationapproaches can be successfully used in the application of theXinanjiang model at a sub-daily time scale (e.g., commonly usedtime interval of 1-h with respect to flood simulation and forecast-ing), and how the performance of the Xinanjiang model can beimproved in ungauged catchments. Unfortunately, there is littleguidance in the modeling literature on these two questions.

The first objective of this paper is therefore to assess the floodprediction capability of the Xinanjiang model using the regionaliza-tion approaches at an hourly time scale. A nested region containinginterior stream gauging (hypothetical ungauged for regionalization)stations was selected as the study region according to the recom-mendations of IH (1999), Smith et al. (2004, 2012) and Beven(2012). It has been shown by Merz and Blöschl (2004) that strongregional similarities exist for nested catchments and better perfor-mance can be achieved by using the parameters transposed fromnested neighbors. In this study, the model parameters for theinterior locations were regionalized by transposition from thedownstream catchments. Results derived in this way are consid-ered indicative of expected model performance at upstreamungauged locations, under the conditions that the model calibra-tion may be carried out at larger spatial scales and that thecalibrated parameters may be transposed to smaller spatial scales(Norbiato et al., 2008). The scale problems caused by transposing

the parameters from large gauged catchments to small ungaugedcatchments can also be investigated in a nested catchment system(McNamara et al., 1998; Mendiondo et al., 2007; Lee et al., 2009).

Secondly, we intend to address how to improve the flood pre-diction capability of the Xinanjiang model in ungauged catchmentsusing the regionalized parameters. It has been widely recognizedthat the simulated flood events by the Xinanjiang model are extre-mely sensitive to the parameters of the ‘‘lag-and-route’’ runoffrouting method. In spite of its easy implementation, this methodis not theoretically strong. Moreover, its parameters are purelyempirical according to Zhao (1992) and Zhao and Liu (1995). Thequantitative link between these parameters and the catchmentcharacteristics has not been well studied for PUB. Hence, we thinkthat it is a good starting point to use a more physically meaningfulrouting technique in place of the lag-and-route method. The geo-morphologic instantaneous unit hydrograph (GIUH) approachbased on the linearity assumption was chosen here to replace thelag-and-route component of the Xinanjiang model. The GIUHapproach was first introduced by Rodriguez-Iturbe and Valdes(1979) and later generalized by Gupta et al. (1980). It has theadvantage of requiring a limited number of parameters whereasthe necessary geomorphologic data can be obtained from topo-graphic maps or digital elevation model (DEM) (Ros and Borga,1997). This approach has been reported as a powerful tool for link-ing the hydrologic response of catchments to their geomorphologiccharacteristics, which can provide an insight to the hydrologicbehavior of ungauged catchments (Kumar et al., 2007). Theefficiency and robustness of the GIUH approach in ungauged catch-ments have been tested and verified by many studies (e.g. Ros andBorga, 1997; Yen and Lee, 1997; Al-Wagdany and Rao, 1998; Rui,2003; Fleurant et al., 2006; Kumar et al., 2007; Bhadra et al.,2008; Grimaldi et al., 2012; Hrachowitz et al., 2013).

We have noticed that there are also other physically based rout-ing methods contributing to PUB. For example, the Horton–Izzardnonlinear storage approach (Moore and Bell, 2002; Moore, 2007),which has been used to represent network flow paths in a grid-based distributed model (Ciarapica and Todini, 2002; Mooreet al., 2007; Bell et al., 2009), can be linked to the physical proper-ties of a channel network to address the ungauged problem.Because the GIUH approach is a source-to-sink routing formulation(Moore et al., 2006), we think it is more appropriate to the semi-distributed formulation of the Xinanjiang model. Thus, we coupledthe Xinanjiang model with the GIUH approach (hereinafter,referred to as XAJ-GIUH) in this study to simulate flood events.The performance of the XAJ-GIUH model was investigated to deter-mine whether improved simulations can be obtained when usingthe parameters transposed from the donor catchments.

2. Study area and data

The Tunxi (TX) catchment located in the southern mountainousregion of Anhui province, China is chosen as our study area (Fig. 1).It is a meso-scale catchment and has a drainage area of 2692 km2.The long-term average annual rainfall, runoff and pan evaporationfrom 1982 to 2003 are 1922 mm/yr, 1279 mm/yr and 646 mm/yr,respectively. Because of the dominance of a monsoon climate,more than 60% of annual rainfall occurs during the flood season(May to August). Apart from the river gauging station at the outletof TX, there are six interior nested stations within the Tunxi catch-ment, including Yuetan (YT), Wanan (WA), Chengcun (CC), Xinting(XT), Liukou (LK) and Yucun (YC) (Fig. 1). The landscape character-istics of all seven catchments are summarized in Table 1 and werederived from a DEM with a spatial resolution of 90 m (300) providedby International Scientific and Technical Data Mirror Site, Com-puter Network Information Center, Chinese Academy of Sciences(http://datamirror.csdb.cn). Station observations of rainfall,

Fig. 1. Map for the study catchments and locations of the river gauging stations.

Table 1Physical and meteorological characteristics, data records and relationships of the study catchments.

Station name Downstreamdonor catchment(s)

Drainage area(km2)

Elevationrange (m)

Meanelevation (m)

Mean slope (�) Length of thelongestflow path (km)

Number offlood events

Period forflood events

Tunxi (TX) – 2692 136–1619 380 14.2 143.9 35 1982–2003Yuetan (YT) TX 952 157–1619 428 16.1 109.8 51 1982–2003Wanan (WA) TX 865 152–1406 364 13.6 56.1 33 1988–2003Chengcun (CC) TX, YT 290 251–1619 583 20.2 36.3 32 1986–1999Xinting (XT) TX, WA 184 181–1406 520 20.2 41.1 48 1986–2000Liukou (LK) TX, YT, CC 107 278–1423 556 19.5 22.6 22 1969–1980Yucun (YC) TX 96 141–1237 453 18.8 22.1 39 1987–1999

C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048 1037

discharge and E-601 pan evaporation data for these catchmentswere used to assess the performance of both the Xinanjiang andXAJ-GIUH models. The number of flood events and relevant periodwith data available for each catchment are listed in Table 1.

3. Methodology

Two rainfall-runoff models including the original Xinanjiangmodel and the developed XAJ-GIUH model were applied at anhourly time-step for flood simulation using the calibrated andtransposed parameters, respectively. Although the flood predictioncapability of the Xinanjiang model has been well demonstrated ingauged catchments, there is a particular requirement to evaluate itfor ungauged conditions (WMO, 2011). Therefore, it is necessary toexamine how the Xinanjiang model performs when using theregionalization approaches to simulate floods. The XAJ-GIUHmodel is developed by replacing the empirical lag-and-route com-ponent of the Xinanjiang model with the geomorphology-basedrouting method GIUH. It is anticipated that the developed modelwill produce better regionalization results than the original modelthrough the use of GIUH to better account for the effect of geomor-phologic characteristics on the parameter transfer.

3.1. The Xinanjiang model

The Xinanjiang model, developed in the 1970s, is a semi-distrib-uted conceptual rainfall-runoff model. It uses sub-catchments asprimary hydrologic units, allowing the spatial patterns of inputsto be taken into account at the sub-catchment level. In the floodforecasting and management practice in China, historical stream-flow observations are usually reported on the sub-daily time scalefor the flooding periods and on the daily time scale for the otherperiods (MWR, 2009). According to the availability of observed

streamflow data, the Xinanjiang model is usually operated in prac-tice at two time scales: daily continuous simulation and hourly forflood events forecasting. In the operational use, daily simulationsare implemented to compute the soil moisture states that are usedas antecedent conditions for the flood events. The main feature ofthe model is the concept of runoff formation on the repletion ofstorage capacity, which implies that runoff is not produced untilthe soil water content of the aeration zone reaches its field capac-ity, and thereafter the excess rainfall becomes the runoff withoutfurther loss. For each sub-catchment, the outflow is calculated byfour major modules:

(1) Evapotranspiration module: The actual evapotranspiration iscomputed from potential evapotranspiration while soil stor-age deficit is calculated in three layers, i.e., upper, lower anddeep soil layers.

(2) Runoff generation module: The runoff is generated accordingto rainfall and soil storage deficit; and the tension watercapacity distribution curve is utilized to provide for a non-uniform distribution of tension water capacity throughoutthe sub-catchment.

(3) Runoff separation module: The total runoff is subdivided intothree components, including surface runoff, interflow andgroundwater runoff, based upon the free water capacity dis-tribution curve.

(4) Runoff routing module: The surface runoff is routed directlyto the outlet of each sub-catchment in a source-to-sink form(Moore et al., 2006) by means of the lag-and-route method,while the interflow and groundwater runoff are routedthrough linear reservoirs.

The outflow from each sub-catchment is finally routed by theMuskingum successive-reaches model to produce the flow at the

1038 C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048

outlet of the whole catchment. The river reach is normally subdi-vided into sub-reaches in this successive routing scheme. Thereare two parameters to be determined for each sub-reach, includingthe Muskingum time constant and weighting factor.

The Xinanjiang model involves a total of 17 parameters, whichare listed in Table 2. In principle, these parameters are spatiallyuniform, meaning that they represent integrated effects of catch-ment properties. The schematic diagram and more details aboutthe Xinanjiang model can be found in Zhao (1992) and Zhao andLiu (1995).

3.2. The XAJ-GIUH model

Based on the original Xinanjiang model, the XAJ-GIUH model isdeveloped by using the GIUH approach instead of the lag-and-route method for runoff routing within the sub-catchment. TheGIUH, under the assumption of linearity, can be easily derived fromthe probability density functions of flow path length and slope interms of the DEM analysis. The following is a brief description ofthe derivation of the GIUH based on Rodriguez-Iturbe and Valdes(1979), Gupta et al. (1980), Maidment et al. (1996), Rui (2003)and Fleurant et al. (2006).

Assuming that identical raindrops are instantaneous, weaklyinteracting (statistically independent) and spatially uniform overa region, the following equivalence can be obtained from the lawof large numbers and water balance (Gupta et al., 1980):

uð0; tÞ ¼ f ðtÞ ð1Þ

i.e.

SðtÞ ¼ FðtÞ ð2Þ

where u(0, t) is the instantaneous unit hydrograph, f(t) is the prob-ability density function (pdf) of holding times or arrival times at theoutlet of randomly placed raindrops, S(t) is the S-hydrograph, andF(t) is the distribution function of holding times.

Let a random variable T denote the flow time to the outlet, then:

T ¼ LV

ð3Þ

where L is the flow length of the path of a raindrop from the fallinglocation to the outlet, and V is the velocity along the flow path.

Table 2List of parameters of the Xinanjiang model and the calibrated values for the study catchm

Module Parameter Description

Evapotranspiration K* Ratio of potential evapotranspiration to pan evapWum Tension water capacity of upper layer (mm)Wlm Tension water capacity of lower layer (mm)C Evapotranspiration coefficient of deeper layer

Runoff generation Wm Tension water capacity (mm)B Exponent of distribution of tension water capaciIm Ratio of impervious area to the total area of the

Runoff separation Sm* Free water capacity (mm)

Ex Exponent of distribution of free water capacityKg

* Outflow coefficient of free water storage to grouKi

a Outflow coefficient of free water storage to inter

Routing Cg* Recession constant of groundwater storage

Ci* Recession constant of interflow storage

Cs*,b Recession constant in the lag-and-route method

Lag*,b Lag time (h)

Kec Muskingum time constant for each sub-reach (h)

Xe* Muskingum weighting factor for each sub-reach

* We focused on the calibration of these parameters.a The sum Ki + Kg was kept as 0.7 based on the suggestion of Zhao and Liu (1995).b The parameters Cs and Lag of the lag-and-route method are not included in the XAJ-c The Ke value was set to be equal to the computational time interval (1-h in our applica

the Muskingum successive-reaches model in China.

According to the GIUH concept, L and V are independent ran-dom variables. Consequently, on the basis of probability theory,f(t) and F(t) can be formulated as (Rui, 2003):

f ðtÞ ¼Z vmax

0vgðlÞuðvÞdv ð4Þ

and

FðtÞ ¼Z 1

0GðlÞdWðvÞ ð5Þ

where vmax is the maximum flow velocity of raindrops, g(l) and u(v)are the pdfs of L and V, respectively, G(l) and W(v) are the distribu-tion functions of L and V, respectively. The pdf of L is equivalent inform to the width function since it gives the probability of having agiven flow distance between a definite location and the outlet.

Eqs. (4) and (5) indicate that the GIUH can be derived if the pdfsor distribution functions of flow length and velocity are obtained inadvance. The flow length can be readily extracted from the DEMdata; however, it is difficult to directly determine the flow velocity.A simplification of the Manning formula presented by the US SoilConservation Service is employed to estimate the velocity(Maidment et al., 1996; Grimaldi et al., 2012):

V ¼ affiffiffiSp

ð6Þ

where a is a coefficient related to Manning’s roughness, and S is theland slope, which can also be extracted from the DEM data. Therelation of Eq. (6) to Manning’s equation has been discussed byRui et al. (2008).

As the coefficient a is a constant, the distribution function W(v)is equivalent to the distribution function of S, denoted by H(s). Inthis case, based on Eqs. (3) and (6), the discrete expression of Eq.(5) is given by:

FðtÞ ¼Xm

i¼1

GðtaffiffiffiffisipÞ½HðsiÞ �Hðsi�1Þ� ð7Þ

where m is the number of discrete slopes.Eq. (7) indicates that the distribution function F(t) can be

derived from the distribution functions of flow length and slope,both of which can be easily obtained from the DEM analysis. Then,the Dt-period unit hydrograph for each subcatchment is imple-mented by:

ents.

TX YT WA CC XT LK YC

oration 0.907 0.955 1.000 0.812 1.126 1.127 1.26320 20 20 20 20 20 2060 60 60 60 60 60 600.18 0.18 0.18 0.18 0.18 0.18 0.18

120 120 120 120 120 120 120ty 0.4 0.3 0.3 0.3 0.2 0.2 0.2basin 0.01 0.01 0.01 0.01 0.01 0.01 0.01

47.517 32.444 36.233 59.483 50.574 56.785 52.1661.5 1.5 1.5 1.5 1.5 1.5 1.5

ndwater 0.173 0.148 0.249 0.074 0.209 0.012 0.161flow 0.527 0.552 0.451 0.626 0.491 0.688 0.539

0.980 0.990 0.980 0.989 0.997 0.992 0.9800.265 0.437 0.349 0.011 0.021 0.076 0.0550.846 0.888 0.830 0.612 0.630 0.526 0.4352 4 2 1 1 0 11 1 1 1 1 1 10.305 0.151 0.105 0.305 0.349 0.185 0.118

GIUH model.tions) based on the suggestion of Zhao et al. (1980) and operational experience with

Tabl

e3

Acc

urac

yst

atis

tics

ofth

eX

inan

jiang

mod

elsi

mul

atio

nsw

ith

calib

rate

dpa

ram

eter

sfo

rbo

thca

libra

tion

and

valid

atio

nsev

ents

.

Cat

chm

ent

Qu

alifi

edra

tio

(%)

Abs

olu

tem

ean

Ave

rage

RR

ER

PEPT

ER

RE

(%)

RPE

(%)

PTE

(h)

NSE

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

TX95

.890

.991

.790

.991

.710

0.0

5.2

8.0

10.4

9.7

1.1

1.0

0.94

0.95

YT

100.

087

.580

.081

.388

.687

.57.

78.

813

.012

.51.

22.

30.

910.

89W

A95

.790

.082

.610

0.0

100.

010

0.0

7.6

8.8

9.0

8.6

0.4

0.5

0.94

0.92

CC

100.

010

0.0

90.9

90.0

95.5

90.0

5.7

4.9

7.3

9.7

0.7

1.0

0.91

0.95

XT

97.0

93.3

93.9

93.3

97.0

93.3

7.2

8.2

8.8

11.3

0.9

1.3

0.91

0.92

LK93

.310

0.0

93.3

100.

086

.710

0.0

6.5

6.7

9.3

9.5

2.4

0.4

0.89

0.94

YC

100.

091

.792

.691

.796

.310

0.0

6.0

6.9

8.0

9.1

0.8

0.3

0.92

0.89

C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048 1039

uðDt; tÞ ¼ SðtÞ � Sðt � DtÞ ¼ FðtÞ � Fðt � DtÞ ð8Þ

where Dt is the time interval, and u(Dt, t) is the derived unithydrograph.

The XAJ-GIUH shares 15 of the 17 Xinanjiang model parameters.The Cs and Lag parameters of empirical lag-and-route method in theoriginal Xinanjiang model are not needed in the XAJ-GIUH model.Instead, a velocity parameter a is introduced in the XAJ-GIUHmodel. Therefore, there are a total of 16 parameters in the XAJ-GIUH model.

3.3. Model calibration and parameter transposition

To compare the performance of the original Xinanjiang modeland the XAJ-GIUH model, two sets of simulations were imple-mented at the hourly time scale: (1) simulations using parameterscalibrated at each of the seven catchments (hereinafter, calibratedsimulations); and (2) simulations from a simple downstream-to-upstream transposition method, i.e., simulations using parametersets transposed from the downstream donor catchments (hereinaf-ter, simulations using parameter transposition).

3.3.1. Calibrated simulationsIn the calibrated simulations, the two models were applied to

each of the seven study catchments and calibrated separately ineach individual catchment. Approximately two thirds of hourlyflood events for each catchment were used for calibration, whilethe remaining events were used for validation. It is believed thatthe efficiency of model calibration could clearly be enhanced byconcentrating the effort on the parameters with high sensitivity(Freer et al., 1996; Beven and Freer, 2001; Beven, 2012). Hence,for the Xinanjiang model, we focused on the calibration of 8 keyparameters (marked by asterisk in Table 2) that significantly affectthe model simulation results. All the other parameters were fixedand set to their ‘typical’ values based on the literature and/or expe-rience with the model implementation (e.g., Zhao, 1992; Zhao andLiu, 1995). It should be noted that the Muskingum time constantfor each sub-reach, i.e. Ke listed in Table 2, is also a sensitiveparameter. The value of Ke can be set to be equal to the time inter-val based on the discussion by Zhao et al. (1980) and operationalexperience with the Muskingum successive-reaches model inChina, to satisfy the linearity assumption of the Muskingummethod and avoid the negative outflow. For the XAJ-GIUH model,additional calibration was performed only for the velocity param-eter a, while the other parameter values were directly adoptedfrom the calibrated Xinanjiang model.

The shuffled complex evolution (SCE-UA) global optimizationalgorithm (Duan et al., 1992) was adopted for the calibration ofthe model parameters. The objective function for optimizing theparameters consists of four terms, involving relative runoff volumeerror (RRE, %), relative peak discharge error (RPE, %), peak timeerror (PTE, h) and Nash–Sutcliffe efficiency (NSE) (Nash andSutcliffe, 1970):

Fo ¼ 1� 1Ne

XNe

j¼1

ðwrEr;j þwpEp;j þwtEt;j þwcEc;jÞ ð9Þ

where Ne is the total number of calibration events, wr, wp wt and wc

are the weights associated with RRE, RPE, PTE and NSE, respectively,and Er,j, Ep,j, Et,j and Ec,j are the error indices for the event j. Here,equal weight (i.e. 0.25) was given to the four terms. If the calibra-tion efficiency for the event j (NSEj) is less than 0.5, then Ec,j is equalto 0; otherwise, it is equal to NSEj. In accordance with the accuracystandard established by the MWR (2008), the simulation resultqualifies relative to total runoff volume, peak discharge, and peaktime if the absolute value of RRE is less than 20%, if the absolute

1040 C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048

value of RPE is less than 20%, and if the difference in peak time iswithin a routing period or 3 h, respectively (Yao et al., 2012). There-fore, the indices Er,j, Ep,j, and Et,j are defined as:

Er;j ¼1� jRREj j

20 jRREjj < 20%

0 jRREjjP 20%

(ð10Þ

Ep;j ¼1� jRPEj j

20 jRPEjj < 20%

0 jRPEjjP 20%

(ð11Þ

Et;j ¼1� jPTEj j

4 jPTEjj < 4 h0 jPTEjjP 4 h

(ð12Þ

where RREj, RPEj and PTEj are the statistical metrics computed forthe event j.

Clearly, the values of the objective function can range from 0 to1. A smaller Fo value (close to 0) corresponds to a better match ofthe simulated streamflow to the observed data. Thus, the parame-ters were calibrated by minimizing the objective function.

3.3.2. Simulations using parameter transpositionIn the simulations using parameter transposition, the upstream

catchments were treated as ungauged while their downstreamcatchments were regarded as the donor catchments. In otherwords, the upstream hypothetical ungauged catchments are mod-eled using the calibrated parameter sets from the downstreamdonor catchments, within which the receptor catchments arenested. The rationale behind this transposition is that one wouldexpect the parameter values to be similar since these are nestedcatchments (Merz and Blöschl, 2004; Blöschl, 2005).

The donor catchments for the interior receptor catchmentslisted in Table 1 were selected according to their locations fromdownstream to upstream (see Fig. 1). For YT, WA and YC, modelparameters were transposed from a single donor catchment, i.e.TX, while multiple donor catchments were used for CC, XT andLK. In the latter case, the calibrated parameter set from each donorcatchment were individually utilized to model the flood events toassess whether better performance could be achieved by adoptingthe parameters from closer donor catchment.

4. Results and discussion

4.1. Results of calibrated simulations

The calibrated parameter values of the Xinanjiang model foreach catchment are listed in Table 2. The accuracy statistics ofthe model performance are summarized in Table 3, which reportsthe percentages of qualified simulations, the absolute means withrespect to RRE, RPE and PTE, and the average NSE values for the

Fig. 2. Box plots of the (a) RRE, (b) RPE and (c) NSE statistics of all hourly simulatio

separate calibration and validation flood events. Fig. 2 shows thedistributions of RRE, RPE and NSE statistics for all simulations(both calibration and validation events). The top and bottom linesof these box plots represent the maximum and minimum values,respectively, while the top, middle, and bottom of the box repre-sent the 75th percentile, median and 25th percentile, respectively.For all calibration and validation events, the ratios of qualified RRE,RPE and PTE simulations for the seven study catchments rangefrom 93.9% to 100.0%, 80.4% to 95.5% and 88.2% to 100.0%, respec-tively, while the absolute means of RRE, RPE and PTE range from5.4% to 8.0%, 8.1% to 12.8%, 0.5 to 1.8 h, respectively. The averageNSE varies between 0.90 and 0.94. These results indicate that theXinanjiang model is capable of reproducing both the magnitudeand dynamics of observed flood events at different catchmentscales once its 8 key parameters are calibrated.

For the XAJ-GIUH model, the calibrated values of the velocityparameter a are 1.755, 1.031, 1.644, 1.127, 1.160, 1.485 and1.603 m/s for TX, YT, WA, CC, XT, LK and YC, respectively. The other15 parameters are directly adopted from the calibrated Xinanjiangmodel parameters that are listed in Table 2. The accuracy statisticsof the simulation results for the separate calibration and validationevents (Table 4) are comparable to those using the calibratedXinanjiang model (Table 3). Additionally, the overall distributionsof the three metrics for all flood events (Fig. 3) are also similar tothose from the simulations by calibrated Xinanjiang model(Fig. 2). The results suggest that the performance of the calibratedXAJ-GIUH and Xinanjiang models are generally comparable at dif-ferent catchment scales.

4.2. Results of simulations using parameter transposition

Table 5 provides the accuracy statistics of the Xinanjiang andXAJ-GIUH model results for the hypothetical ungauged catchmentsby using parameters transposed from their downstream donors.There are ten cases listed in Table 5 based on the combination ofdifferent receptor and donor catchments. The simulations by theXinanjiang model show higher qualified ratio for the RRE statisticsthan the RPE and PTE metrics. The qualified ratios in terms of RREare larger than 90.0% for all the ten cases, while the absolute meansof RRE are all less than 10.0% (Table 5). This suggests that theXinanjiang model has a high capability to simulate the total runoffvolume in these ungauged catchments by directly transposingparameters from the downstream donor catchments. However,the original Xinanjiang model shows relatively poor performancein simulating the peak values of discharges in these ‘‘ungauged’’cases. For seven out of the ten cases, the percentages of qualifiedsimulations in terms of peak discharge are lower than 60.0% andthe absolute means of RPE are larger than 20.0% (Table 5). Theseresults cannot even meet the lowest level standard required forflood simulation or forecasting according to MWR (2008). This sug-

ns, including both calibration and validation events, by the Xinanjiang model.

Tabl

e4

Acc

urac

yst

atis

tics

ofth

eX

AJ-

GIU

Hm

odel

sim

ulat

ions

wit

hca

libra

ted

para

met

ers

for

both

calib

rati

onan

dva

lidat

ions

even

ts.

Cat

chm

ent

Qu

alifi

edra

tio

(%)

Abs

olu

tem

ean

Ave

rage

RR

ER

PEPT

ER

RE

(%)

RPE

(%)

PTE

(h)

NSE

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

Cal

ibra

tion

Val

idat

ion

TX95

.890

.991

.790

.995

.890

.95.

27.

810

.59.

61.

11.

50.

940.

95Y

T10

0.0

87.5

80.0

81.3

88.6

100.

08.

18.

612

.611

.22.

02.

20.

910.

91W

A95

.790

.082

.610

0.0

100.

010

0.0

7.4

8.7

9.0

7.8

0.7

0.5

0.93

0.91

CC

100.

010

0.0

90.9

90.0

95.5

100.

05.

75.

27.

59.

50.

70.

20.

910.

95X

T97

.093

.393

.910

0.0

97.0

93.3

7.2

8.2

9.7

10.7

0.8

1.3

0.89

0.90

LK93

.310

0.0

93.3

100.

086

.710

0.0

6.5

6.6

9.6

9.7

2.5

0.4

0.89

0.95

YC

100.

091

.796

.391

.710

0.0

100.

06.

06.

98.

39.

10.

40.

30.

910.

88

C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048 1041

gests that the major source of uncertainty in the application of theXinanjiang model in these ungauged catchments lies in the modelprocess of runoff routing. The average NSE values range from 0.58to 0.91 for the ten cases with a mean of 0.79, indicating that theXinanjiang model can reasonably predict the general shapes ofthe storm hydrographs when using the downstream-to-upstreamtransposition method. Gray box plots in Fig. 4 illustrate the distri-butions of the RPE and NSE statistics for all ungauged catchmentsimulations by the Xinanjiang model. According to Fig. 4, theXinanjiang model using the transposed downstream parametersshows relatively poor performance in simulating the peak dis-charges and tends to underestimate these values.

It is not surprise that both the Xinanjiang and XAJ-GIUH modelshave the same values for the qualified ratios in terms of RREbecause the two models use the same runoff generation modules(Table 5). As compared to the Xinanjiang model, the XAJ-GIUHmodel shows a remarkable improvement on the simulations ofpeak discharge and its timing in these ‘‘ungauged’’ cases (Table5). For the XAJ-GIUH model, the percentage of qualified peak sim-ulations is higher than 60.0% for all but one of the ten cases, whilethe absolute means of RRE are lower than 20.0% for all but two ofthe ten cases. The most marked improvement in peak simulationsis found in the case in which the YC catchment is treated as anungauged catchment. The YC catchment has the smallest drainagearea and is geographically closest to its donor catchment TX. Thequalified ratio relative to RPE for the YC case is increased from2.6% by the Xinanjiang model to 87.2% by the XAJ-GIUH model,whereas the absolute mean of RRE is reduced from 35.5% by theXinanjiang model to 12.5% by the XAJ-GIUH model (Table 5). Interms of the PTE metric, the qualified ratio and absolute meanfor the ten cases using the XAJ-GIUH model range from 78.4% to100% and 0.7 to 3.1 h, respectively. These results are also generallybetter than the simulations of the Xinanjiang model. The averageNSE values for these XAJ-GIUH simulations range from 0.71 to0.92 with a mean of 0.82, which also demonstrates an improve-ment relative to the simulations of the Xinanjiang model. Blackbox plots in Fig. 4 illustrate the distributions of the RPE and NSEstatistics for all ungauged catchment simulations by the XAJ-GIUHmodel. By looking collectively at the simulation results shown inTable 5 and Fig. 4, it is clear that the XAJ-GIUH model outperformsthe Xinanjiang model in most of these ‘‘ungauged’’ cases wheremodel parameters for these ungauged catchments are transposedfrom their downstream donor catchments.

4.3. Discussion

As one might expect, the simulations using the regionalizationapproach based on the parameter transfer (see Table 5 andFig. 4) are poorer than the calibrated simulations (see Tables 3, 4and Figs. 2, 3) for both Xinanjiang and XAJ-GIUH models. Oncethe parameters are calibrated by the local observations, the twomodels present fairly comparable results. However, their perfor-mance diverges in the six interior nested catchments once thesecatchments are treated as ungauged and model parameter trans-position is applied. The main difference between the two modelsis the method for runoff routing within the sub-catchment. Inother words, the empirical lag-and-route method is used by theoriginal Xinanjiang model, while the geomorphology-based GIUHmethod is used by the XAJ-GIUH model. All but one of the param-eters of the XAJ-GIUH model is identical to these of the Xinanjiangmodel (Table 2). In addition, two routing parameters (i.e. Cs andLag) in the original Xinanjiang model are not used by the XAJ-GIUHmodel any more since the routing method is replaced by the GIUHmodel. Therefore, the difference in the simulations of the two mod-els results from the runoff routing method.

Fig. 3. Box plots of the (a) RRE, (b) RPE and (c) NSE statistics of all hourly simulations including both calibration and validation events, by the XAJ-GIUH model.

Fig. 4. Box plots of (a) RPE and (b) NSE statistics of the Xinanjiang model (gray box plots) and the XAJ-GIUH model (black box plots) results by transposing the parametersfrom the downstream donor catchments (after the slash) to the upstream receptor catchments (before the slash).

Table 5Comparison of the Xinanjiang (XAJ) and XAJ-GIUH model results for all flood events based on the downstream-to-upstream transfer approach.

Receptorcatchment

Downstream donorcatchment

Qualified ratio (%) Absolute mean Average

RRE RPE PTE RRE (%) RPE (%) PTE (h) NSE

XAJ XAJ-GIUH

XAJ XAJ-GIUH

XAJ XAJ-GIUH

XAJ XAJ-GIUH

XAJ XAJ-GIUH

XAJ XAJ-GIUH

XAJ XAJ-GIUH

YT TX 96.1 96.1 78.4 72.5 80.4 78.4 7.9 8.2 13.3 15.6 3.0 3.1 0.90 0.89WA TX 90.9 90.9 84.8 87.9 100 100 9.7 9.5 11.2 9.8 0.8 0.7 0.91 0.92CC TX 96.9 100 21.9 75 87.5 93.8 8.4 8.1 23.8 13.6 2.6 1.6 0.85 0.78

YT 100 100 18.8 68.8 15.6 93.8 7.1 6.6 25.9 14.5 4.9 1.5 0.69 0.80XT TX 97.9 97.9 12.5 81.3 89.6 93.8 7.6 7.5 32.6 12.1 2.3 1.3 0.75 0.77

WA 95.8 95.8 33.3 75.0 93.8 93.8 8.0 8.0 24.3 14.7 2.1 1.4 0.83 0.71LK TX 100 100 40.9 63.6 54.5 86.4 7.3 7.5 21.8 20.4 4.4 1.8 0.78 0.79

YT 100 100 36.4 45.5 4.5 90.9 6.1 6.3 23.2 22.6 6.7 2.0 0.58 0.76CC 95.5 95.5 77.3 77.3 90.9 90.9 6.9 6.9 12.0 12.4 2.5 2.2 0.91 0.91

YC TX 97.4 97.4 2.6 87.2 79.5 97.4 5.9 5.8 35.5 12.5 3.3 0.7 0.69 0.83

1042 C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048

C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048 1043

As seen from the aforementioned accuracy assessment, thecapability of the Xinanjiang model for peak simulation in theseparameter transposition cases was substantially downgraded atthe hourly time scale relative to the calibrated simulations. It isknown that the parameter Cs has a significant impact on the perfor-mance of the Xinanjiang model at hourly time-step (Zhao, 1992;Zhao and Liu, 1995). This parameter represents the retentioncapacity of the catchment and contributes to the flood peak atten-uation. Generally, the value of Cs ranges from 0 to 1 and has a largervalue for a larger catchment. Therefore, it is a scale-dependentparameter. Direct transposition of Cs from a larger catchment toa smaller catchment would correspondingly cause an underesti-mation of the flood peak discharge, just as the results shown inFig. 4a. In addition, the values of Cs commonly tend to decreasefrom downstream to upstream areas due to the influence ofincreasing slope on flow velocity. However, this difference isignored in the process of parameter transfer. Therefore, we suggestthat the effects of drainage area and slope on Cs values should betaken into account in order to improve the flood prediction capa-bility of the original Xinanjiang model in its application utilizingparameter transposition. The concept of topographic index(Beven and Kirkby, 1979) can be used here to quantify the effects.As an example, Fig. 5 shows the regressed relationships betweenthe Cs values individually calibrated in each of these catchments(see Table 2) and the corresponding drainage areas (Ad), meanslopes (b) and catchment-average topographic indices (CTIs)defined as ln(Ad/tanb) (the values of Ad and b are listed in Table1). Fig. 5a and c indicate that the study catchments with largerdrainage areas or CTI values tend to have higher Cs values, whileFig. 5b shows that Cs has an inverse relationship with slope. Itcan be seen that the relationship between Cs and CTI is strongerthan the relationships of Cs with area and slope. This resultsuggests that the Cs parameter in the original model should beregionalized on the basis of catchment geomorphologic character-istics (e.g. drainage area, slope and CTI) rather than a simpleparameter transposition, since direct adoption of parameter valuefrom the donor catchment may result in poor performance dueto the likely geomorphologic difference between the donor andreceptor catchments. The capability of the Xinanjiang model forflood prediction at ungauged catchments may be improved byderiving the Cs value from its regressed relationship with catch-ment geomorphologic characteristics.

Besides the Cs parameter, the Lag parameter is another impor-tant parameter that controls the runoff routing in the Xinanjiangmodel. It contributes to the translation of the hydrograph andhence affects the simulated timing of the peak discharge. The sta-tistical values in Table 5 indicate that the simulated peak time bythe Xinanjiang model are acceptable using the transposed Lag

values for the donor catchment TX. However, in the CC and LKungauged cases, the results for peak discharge time estimates areconsiderably worse by transposing the Lag parameter from the YT

Fig. 5. Relationships between the recession parameter Cs and the (a) drainage

catchment than the results by transposing the parameter fromthe TX catchment. This is because the Lag parameter is quite differ-ent between the CC and LK catchments and the YT catchment. Thecalibrated value of the Lag parameter is 4 h for the donor catchmentYT, but the calibrated values are 1 and 0 h for the receptor catch-ments CC and LK, respectively. Therefore, the Xinanjiang model isunable to give satisfactory prediction of time to peak under thiscondition. Consequently, it is necessary to find better ways ofregionalizing the parameter Lag. It is also notable that the Lag valuefor YT is even larger than the value of its donor catchment TX. Onepossible explanation is that the hydrograph response at TX is influ-enced more by contributions of outflow from the WA catchment(see Fig. 1), since both of them have the same lag time. This findingsuggests that the lag time for the upstream catchment is not nec-essarily shorter than that for the downstream one. The catchmentattributes such as topographic characteristics, soil texture and veg-etation types that have big influence on the lag time should be alsoconsidered in the process of regionalizing the Lag parameter forflood predictions in ungauged catchments.

Relative to the original Xinanjiang model, the XAJ-GIUH modelgenerally produces improved simulations of the peak discharge,peak time and hydrograph. Fig. 6 shows some of the simulatedhydrographs based on the regionalized parameters by the twomodels. Overall, the XAJ-GIUH model yields better results thanthe Xinanjiang model. As shown in Fig. 6c–f, there is a tendencyfor the Xinanjiang model to underestimate the flood peaks in thecases of transposing the parameters from larger donor catchmentsto smaller receptor catchments. The better performance exhibitedby the coupled XAJ-GIUH model can be attributed to the use of theGIUH approach accounting for the impacts of flow length and landslope on the routing process. When the two properties are differentbetween the receptor and donor catchments, the GIUH derived byusing the same a value can still be able to capture the unique rout-ing behavior within each individual catchment to some extent.Fig. 7 illustrates the distribution functions of flow length and slope(i.e. G(l) and H(s) in Eq. (7)), and their corresponding pdfs (g(l) andh(s)) for the study catchments. To derive Fig. 7, the DEM was firstused to calculate the flow length and slope for each grid cell withinthe catchment. Then, the distribution functions can be derived byanalyzing the range and areal extent of the length and slope values.The empirical forms of these functions were used directly in theconstruction of the GIUHs. As seen from Fig. 7, the probability dis-tributions show large differences among the seven catchments;however, their effects on the routing process cannot be addressedby the lag-and-route method. The geomorphology-based GIUHapproach is more physically based than the empirical lag-and-route method although they are both source-to-sink routingformulations. Hence, the XAJ-GIUH model has a higher potentialof producing better flood predictions in ungauged catchments.

There is no obvious evidence that the two models performbetter by taking advantage of the parameters transposed from

area, (b) mean slope and (c) catchment-average topographic index CTI.

Fig. 6. Examples of hourly hydrographs from the observations and simulations of the Xinanjiang model and the XAJ-GIUH model results in the (a) YT, (b) WA, (c) CC, (d) XT,(e) LK, and (f) YC catchments; the model simulations are based on the parameter transposition from the donor catchments (shown after the slash).

1044 C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048

the closer donor catchment. For instance, both models producedegraded results for the CC and LK catchments by transposingparameters from the nearer YT catchment as compared to theresults by transposing parameters from the farther TX catchment.As discussed before, this degradation is mainly due to the spatialheterogeneity of the routing parameters. One suggestion forimprovement is to take into account the effects of catchment attri-butes, especially for the Xinanjiang model. Although the XAJ-GIUHmodel can yield improved results using the catchment-specificflow length and slope characteristics derived from the DEM data,it is still worthwhile to consider more catchment-specific attri-butes such as soil and vegetation information for the process ofderiving or regionalizing model parameters. These spatial datacan be easily gained through remote sensing.

Our results also show that the accuracy of simulations for runoffvolume is always better than the accuracy of simulations for peakdischarge when parameter transposition is applied in the TXcatchment and six nested catchments. However, this does not nec-essarily mean that parameter transposition in the other nestedcatchments will also achieve better runoff simulations than peakdischarge simulations. The relative good performance of thesemodels on the simulations of runoff volume within the TX catch-ment is at least partially due to the similarity of runoff generationprocesses within the TX catchment and six nested catchments.The distribution functions of respective topographic index andGIUH can be regarded as indicators of the similarities of runoffgeneration and routing processes (Wood and Hebson, 1986;Sivapalan et al., 1987, 1990; Beven et al., 1988; Wagener et al.,

Fig. 7. Comparisons of the distribution functions of flow length and slope, i.e. (a) G(l) and (b) H(s), and their corresponding pdfs, (c) g(l) and (d) h(s), for the study catchments.

C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048 1045

2007). For the purpose of comparison, the two indicators werederived from the DEM at the catchment scale and shown in Fig. 8.As seen from Fig. 8a, the distributions of topographic index showstrong similarities among the seven catchments, implying that sim-ilar runoff generation behaviors can be expected in these catch-ments. This is actually confirmed by this study because ourresults show that the use of parameter transposition within theTX catchment does not substantially degrade the accuracy of runoffsimulations. In contrast, the GIUHs show strong discrepanciesamong these catchments (see Fig. 8b), indicating that largedifference may exist in the routing processes among these catch-ments. This largely explains why relatively poor peak simulations

Fig. 8. Comparisons of (a) the probability distribution functions of t

were obtained when the downstream routing parameters wereused. Moreover, the results from the two models based on param-eter transposition also suggest that spatial similarity and local geo-morphologic characteristics should be considered in the process ofparameter transfer.

The above discussion is based on the results obtained from asimple downstream-to-upstream transfer approach. We presentan additional discussion here about the model performancederived from a diverse approach of parameter transfer for betterassessing the flood prediction capabilities of the two models atungauged locations. In this approach, the catchment characteristicCTI is used as a similarity index on the basis of the analysis of Fig. 5,

opographic index and (b) the GIUHs for the study catchments.

Fig. 9. Box plots of (a) RPE and (b) NSE statistics of the Xinanjiang model (gray boxplots) and the XAJ-GIUH model (black box plots) results by transposing theparameters from the donor catchments (after the slash) to the receptor catchments(before the slash) based on using the catchment characteristic CTI as a similarityindex.

1046 C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048

namely that the parameter set is transposed from a catchmentwith the closest CTI value. Hence, the donor catchments for YT,WA, CC, XT, LK and YC, chosen by the similarity index (see Fig. 5for the catchment CTI values), are WA, YT, XT, CC, YC and LK,respectively. Fig. 9 illustrates the distributions of the RPE andNSE statistics for all ‘‘ungauged’’ catchment simulations obtainedwhen considering the CTI as a similarity measure. It can be seenfrom the comparison of Figs. 4 and 9 that the similarity transferapproach in terms of the catchment characteristic CTI generallyperforms better than the downstream-to-upstream transferapproach for both models. Furthermore, the results in Fig. 9 revealthat the XAJ-GIUH model still outperforms the Xinanjiang modelwhen using the parameter set transposed from the catchment withthe closest value of CTI. Again it indicates that, compared to theempirical lag-and-route method, the topography-based GIUHmethod is more able to yield better flood predictions in ungaugedcatchments. According to the results presented here and aforemen-tioned similarity analysis of runoff generation and routingprocesses (Fig. 8), it is suggested that the similarity approachesbased on the catchment characteristics are more likely suitablefor the transfer of parameter sets of both models. The XAJ-GIUHmodel has the potential to produce substantially improved floodpredictions in ungauged catchments.

5. Conclusions

In this study, we evaluated the flood prediction capability of theXinanjiang model at the hourly time scale for the purpose of floodforecasting in ungauged catchments, where the parameters cannotbe calibrated but can be transposed from one or more donor

catchments. In view of the deficiencies of the lag-and-routemethod in the original Xinanjiang model, we proposed to replaceit with the GIUH and to produce a coupled XAJ-GIUH model. TheGIUH method has an advantage of taking the local geomorphologiccharacteristics into account and is less impacted by uncertaintyresulted from the parameter transposition for the ungauged catch-ments. Both the Xinanjiang model and the XAJ-GIUH model wereapplied to a meso-scale catchment (2692 km2), which containssix interior nested catchments with available streamflow observa-tions, and evaluated for the cases that model parameters wereseparately calibrated in each of these catchments and that modelparameters were directly transposed from the downstream donorcatchments. The first case roughly identify the potentially largestpredictive capabilities of these models and also approximate the‘‘true’’ values of these parameters for each of the catchments, whilethe latter case provides an opportunity to test the practical floodprediction capabilities of these models and further helps us iden-tify the direction on how to improve the model performance inungauged catchments.

Our results show that both models are capable of providing sat-isfactory and comparative simulations of runoff volume, peak dis-charge, peak time and flood hydrograph at different catchmentscales once they are well calibrated. Unsurprisingly, the perfor-mance of both models is degraded to some extent once theirparameters are transposed from the downstream catchments.However, the degradation is much smaller for the XAJ-GIUH modelrelative to the original Xinanjiang model. The original model tendsto underestimate the peak discharge when the recession parame-ter Cs is transposed from the downstream larger donor catchmentto the smaller receptor catchment, because Cs a scale-dependentparameter and is also affected by the catchment slope. Our resultsshow that Cs has stronger relationship with catchment-averagetopographic index (CTI) than with drainage area and catchment-average slope in the study region. This is because that CTI takesboth drainage area and slope into account; therefore, CTI is sug-gested to be used for the regionalization of Cs.

The accuracy of peak time simulation by the Xinanjiang modelis limited to the transposition of the Lag parameter, which contrib-utes to the translation of the hydrograph. Our results indicate thenecessity to find new topography-based approaches for the region-alization of the parameter Lag. Using the GIUH method in place ofthe original lag-and-route method presents a good way to improvethe predictive capability of the Xinanjiang model for flood predic-tions in our ungauged case. This indicates that the runoff routing isa major uncertainty source when the original Xinanjiang modelwas applied to the study catchments at the hourly time scale forflood simulation by using parameters transposed from their down-stream donors. Additionally, our results highlight that regionalgeomorphologic characteristics of a given catchment play a largerole in controlling the physical processes of runoff routing. Besidesthese geomorphologic characteristics, the other physical and bio-logical characteristics such as topography, soil properties andland-use/land-cover, which can be obtained from spaceborne orairborne remote sensing techniques, should be taken into accountin the process of deriving or regionalizing model parameters.

We also found that the two models do not necessarily performbetter by transposing parameters from closer donor catchment.This finding indicates that the closer gauge may not be the bettergauge to use, even though they are located in a nested region.Furthermore, we found that the similarity of the hydrologicresponses among the study catchments can be quantified by thedistribution functions of topographic index and GIUH. The resultsshow that, in our case, the distribution functions of topographicindex and GIUH can be regarded as indicators of the similarity ofrunoff generation and routing processes, respectively. For the appli-cation of the Xinanjiang model to simulate flood events at the

C. Yao et al. / Journal of Hydrology 517 (2014) 1035–1048 1047

hourly time scale, transposing parameters from the catchment withmore similar topographic index distribution function is more likelyto produce better runoff simulations. However, poor peak simula-tions may be obtained when using model parameters transposedfrom the catchment with quite different GIUH characteristics.

It can be seen from the analysis that the transfer of parameter setsof the two models should be based on the similarity of catchmentcharacteristics. This point has been further discussed by consideringthe catchment CTI as a similarity measure for the parameter trans-fer. The discussion indicates that generally improved regionalizationresults can be obtained for both models through the use of the CTImeasure. Thus it may be a good strategy to take the similarityapproaches, looking at the catchment characteristics, to the transferof parameter sets of the two models. Meanwhile, the results suggestthat the XAJ-GIUH model is still able to outperform the Xinanjiangmodel for the similarity transfer case. In addition, we think it is nec-essary to apply more regionalization methods, including regressionequations and a priori parameter estimates, to achieve operationalimplementation of both the Xinanjiang model and the XAJ-GIUHmodel in ungauged catchments.

Acknowledgements

This work was supported by the National Natural Science Foun-dation of China (Grant Nos. 41101017, 41130639, 51179045 and41201028) and the National Basic Research Program of China(2010CB951101). The hydrologic data were kindly provided bythe Hydrology Bureau of Anhui province. The authors gratefullyacknowledge Ezio Todini, Robert J. Moore and an anonymousreviewer for their valuable comments on this manuscript.

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