Journal of Hydrology 369 (2009) 44–54

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Journal of Hydrology

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Development and testing of a new storm runoff routing approach basedon time variant spatially distributed travel time method

Jinkang Du a, Hua Xie a, Yujun Hu a, Youpeng Xu a, Chong-Yu Xu b,c,*

a School of Geographic and Oceanographic Sciences, Nanjing University, Nanjing 210093, PR Chinab Department of Geosciences, University of Oslo, P.O. Box 1047 Blindern, N-0316 Oslo, Norwayc Department of Earth Sciences, Uppsala University, Villavgen 16, 75236 Uppsala, Sweden

a r t i c l e i n f o s u m m a r y

Article history:Received 4 January 2008Received in revised form 24 July 2008Accepted 9 February 2009

This manuscript was handled by K.Georgakakos, Editor-in-Chief, with theassistance of Christa D. Peters-Lidard,Associate Editor

Keywords:Storm runoffSpatially distributed routingGeographic information systems, China

0022-1694/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.jhydrol.2009.02.033

* Corresponding author. Address: Department of GeP.O. Box 1047 Blindern, N-0316 Oslo, Norway. Tel.:854215.

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

In this study, a GIS based simple and easily performed runoff routing approach based on travel time wasdeveloped to simulate storm runoff response process with consideration of spatial and temporal variabil-ity of runoff generation and flow routing through hillslope and river network. The watershed was discret-ized into grid cells, which were then classified into overland cells and channel cells through river networkdelineation from the DEM by use of GIS. The overland flow travel time of each overland cell was esti-mated by combining a steady state kinematic wave approximation with Manning’s equation, the channelflow travel time of each channel cell was estimated using Manning’s equation and the steady state con-tinuity equation. The travel time from each grid cell to the watershed outlet is the sum of travel times ofcells along the flow path. The direct runoff flow was determined by the sum of the volumetric flow ratesfrom all contributing cells at each respective travel time for all time intervals. The approach was cali-brated and verified to simulate eight storm runoff processes of Jiaokou Reservoir watershed, a sub-catch-ment of the Yongjiang River basin in southeast China using available topography, soil and land use datafor the catchment. An average efficiency of 0.88 was obtained for the verification storms. Sensitivity anal-ysis was conducted to investigate the effect of the area threshold of delineating river networks andparameter K relating channel velocity calculation on the predicted hydrograph at the basin outlet. Theeffects of different levels of grid size on the results were also studied, which showed that good resultscould be attained with a grid size of less than 200 m in this study.

� 2009 Elsevier B.V. All rights reserved.

Introduction relates the geomorphologic structure of a basin to the IUH obtained

In flood prediction and estimation of catchment response torainfall input, runoff routing is vital. The unit hydrograph theoryhas played a prominent role in runoff routing computation for sev-eral decades since its development. This system response theoryassumes that the basin response to rainfall input is linear and timeinvariant. The discharge at the basin outlet is given by the convo-lution of excess rainfall and the instantaneous unit hydrograph(IUH, Dooge, 1959). In engineering practice, the unit hydrographis often determined by numerical de-convolution techniques(Chow et al., 1988) using observed stream flow and rainfall data.Many efforts have been made in linking the basin hydrological re-sponse to basin geomorphological features. Rodriguez-Iturbe andValdes (1979) introduced the concept of geomorphologic instanta-neous unit hydrograph (GIUH), which was later generalized byGupta et al. (1980) and Gupta and Waymire (1983). The concept

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from the surface-water travel time probability density function,which is defined in terms of watershed’s geomorphologic proper-ties (Horton’s empirical laws) and by the probability density func-tions for travel times through channels. Mesa and Mifflin (1986)and Gupta et al. (1980) obtained their GIUH by means of the widthfunction and the inverse Gaussian probability density function(PDF). Similar methodologies were presented by Naden (1992)and Troch et al. (1994). Sivapalan et al. (1990) incorporated the ef-fect of partial contributing areas in the basic formulation of GIUH.Rodriguez-Iturbe and Gonzalez-Sanabria (1982) proposed a geo-morphoclimatic theory of the instantaneous unit hydrograph as alink between climate, geomorphologic structure and hydrologic re-sponse of a basin based on GIUH. The probability density functionsof the peak flow and time to peak of the IUH can be derived asfunctions of the rainfall characteristics and the basin geomorpho-logical parameters. The geomorphoclimatic or geomorphologicaltheories of the instantaneous unit hydrograph offer a simple meth-od of deriving a watershed’s unit hydrograph without the need forobserved rainfall and runoff data.

In recent years, the use of the geographic information system(GIS) to facilitate the estimation of runoff from watersheds has

J. Du et al. / Journal of Hydrology 369 (2009) 44–54 45

gained increasing attention. Maidment (1993) presented a gridbased methodology for deriving a spatially distributed unit hydro-graph, which assumes a time invariant flow velocity field. It usesGIS to describe the connectivity of each grid cell and the watershedflow network. The travel time from each cell to the watershed out-let is calculated by dividing each flow length by a constant velocity.Subsequently, isochronal curves and the time–area diagram aredetermined, and the unit hydrograph is obtained as the incremen-tal areas of the time–area diagram. The spatially distributed hydro-graph can in fact be classified as a type of geomorphoclimatic unithydrograph, since its derivation depends on watershed geomor-phology, rainfall and hydraulics. Maidment et al. (1996) presenteda more elaborate flow model than that by Maidment (1993), whichaccounts for both translation and storage effects in grid cells. Intheir paper, the watershed response is calculated as the sum ofthe responses of individual sub-watersheds, which is determinedas a combined process of channel flow followed by a linear reser-voir routing. Muzik (1996a) and Ajward (1996) applied Maid-ment’s procedure to watersheds and obtained good results. Eventhough the unit hydrograph is derived in a distributed way, itsuse is still lumped.

In natural conditions, the precipitation, the generation of runoff,and the flow of water over the watershed are spatially distributedprocesses, which limit the use of the unit hydrograph model. Intrying to relax the unit hydrograph assumptions of uniform andconstant rainfall, considerable research about distributed IUH hasbeen conducted in recent years.

Olivera and Maidment (1999) proposed a method for routingspatially distributed excess precipitation over a watershed. A rout-ing response function is defined for each grid cell by the first pas-sage–time response function, which is derived from the advection–dispersion equation of flow routing. Water movement from cell tocell can be convolved to yield a response function along a flowpath; parameters of the flow path response function are relatedto the flow velocity and the dispersion coefficient. The watershedresponse is obtained as the sum of the flow path response to spa-tially distributed precipitation excess.

Liu et al. (2003) presented a diffusive transport approach forflow routing. A response function is determined for each grid celldepending upon two parameters, the average flow time and thevariance of the flow time. The flow time and its variance are deter-mined by the local slope, surface roughness and the hydraulic ra-dius. The flow path response function at the catchment outlet orany other downstream convergence point is calculated by convo-luting the responses of all cells located within the drainage areain the form of the probability density function (PDF) of the firstpassage time distribution. This routing response serves as aninstantaneous unit hydrograph and the total discharge is obtainedby convolution of the flow response from all spatially distributedprecipitation excess.

De Smedt et al. (2000) proposed a flow routing method in whichrunoff is routed through the basin along flow paths determined bythe topography using a diffusive wave transfer model that enablesto calculate response functions between any start and end pointsdepending upon slope, flow velocity and dissipation characteristicsalong the flow lines. All the calculations are performed with stan-dard GIS tools.

Even though the distributed IUH method could route the vari-ant spatially distributed rainfall to the watershed outlet, such amethod is a lumped linear model of watershed response. Sincemany watersheds may display a nonlinear behavior over a widerrange of net rainfall and discharge, to minimize errors resultingfrom the assumption of linearity, Pilgrim and Cordery (1993) sug-gested that unit hydrographs should be derived from floods ofmagnitudes as close as possible to those that will be calculatedusing the derived unit hydrographs. Muzik (1996b) stated that a

family of unit hydrographs should be derived for a considered wa-tershed, each unit hydrograph being applicable within a certainrange of excess rainfall.

Another category of runoff routing is the distributed hydraulicmethod, where the watershed is discretized into a number of com-putational elements, and one or two dimensional approximation(kinematic wave or diffusive wave) to the St. Venant equations isused to estimate overland flow or channel flow for each element.This method is often found in physically-based distributed hydro-logical models, such as the SHE model (Abbott et al., 1986a,b), theIHDM model (Institute of Hydrology Distributed Model; e.g., Calverand Wood, 1995), the CSIRO TOPOG model (e.g., Vertessy et al.,1993), and HILLFLOW (Bronstert and Plate, 1997). The advantageof such methods is the full consideration of rainfall and flow prop-erties in time and space, while the disadvantages are the low com-putation efficiency, complicated computational techniques, andlarge data and computer power demands (Beven, 2001). The appli-cation of these methods is therefore limited.

Melesse and Graham (2004) proposed a routing model based ontravel time. The overland flow travel time of each overland cell wasestimated by combining a steady state kinematic wave approxima-tion with Manning’s equation; the channel flow travel time of eachchannel cell was estimated using Manning’s equation and the stea-dy state continuity equation; the travel time from each grid cell tothe watershed outlet is the sum of travel times of cells along a flowpath; and the direct runoff flow was determined by the sum of thevolumetric flow rates from all contributing cells at each respectivetravel time. Unlike previous approaches (e.g., Maidment, 1993;Muzik, 1995, 1996a,b; Ajward, 1996), this method can develop adirect hydrograph for each spatially distributed rainfall event with-out relying on developing a spatially lumped unit hydrograph. Thedisadvantage of this model is that the travel time field variationduring the storm is not considered, and it cannot be used for floodforecasting since it can only be calculated after the whole stormprocess has finished.

In this paper, a GIS based simple and easily performed routingapproach has been put forward to simulate the storm runoff pro-cess with consideration of spatial and temporal variability of runoffgeneration and flow routing through hillslope and river network.The approach proposed here is based on the model developed byMelesse and Graham (2004), and an improvement was made byconsidering travel time field variation due to rainfall variation intime. The model is based on raster data structures; grids are usedto describe spatially distributed terrain parameters (i.e., elevation,land use, soil type, etc.), and hydrologic features of each grid (i.e.,slope, flow direction, flow accumulation, flow length, stream net-work, etc.) can be determined using standard functions includedin GIS. The model is described and applied to simulate eight stormrunoff processes for Jiaokou Reservoir watershed, a sub-basin ofYongjiang River in southeast China with available topography, soiland land use data for the watershed. Finally sensitivity analysiswas conducted to study the effect of the area threshold of delineat-ing river networks and parameter K relating channel velocity cal-culation on the predicted hydrograph at the basin outlet.

Study area and data

The study area, Jiaokou Reservoir watershed (259 km2) withelevation ranges from 59 m to 976 m, is a sub-basin of YongjiangRiver basin located in Zhejiang province, southeastern part of Chi-na. The land use of the watershed consists of forest (78.3%), agri-culture (14.5%), grassland (2.5%), water surface (2.7%), andresidential areas (1.9%). The dominant soil is poorly drained claywith high runoff potential, falling into D hydrologic soil groupaccording to the SCS classification. The region has a typical

46 J. Du et al. / Journal of Hydrology 369 (2009) 44–54

subtropical monsoon climate. The average annual temperature is16.3 �C with the minimum and maximum temperatures of�11.1 �C and 39.5 �C occurring in January and July, respectively.The mean annual precipitation is about 2000 mm with most ofthe rainfall occurring between March and September.

There are three rain gauging stations and one river flow gaugingstation. The watershed location, elevation, distribution of rainfalland flow gauging stations, and streams are seen in Fig. 1.

The data collected for this study include land cover processedfrom Landsat TM images, hydrologic soil group (HSG) from the soilmaps (Fig. 2), 50 m resolution DEMs produced from digital topo-graphic map, GIS point coverage of rain gauge locations and riverflow gauge station site, and hourly rainfall and discharge data atthe Jiaokou Reservoir watershed.

A total of eight isolated storms with observed runoff responseswere selected to calibrate and verify the approach. The direct run-off hydrographs were obtained using a straight line base flow sep-aration method, and the spatial distribution of rainfall for eachstorm was calculated by constructing Thiessen polygons with threerainfall gauges using ArcView. The summary of eight rainfall anddischarge events is given in Table 1.

The digitized contour maps (1:50,000 scale) are used to gener-ate DEM by using the Kriging interpolation method; to avoid pro-ducing a large number of pixels for the catchment, 50 m wasselected as the size of each grid, even so, the total grid cells reach103,600. The DEM was then used to derive hydrologic parametersof the watershed, such as slope, flow direction, flow accumulation,and stream network. A threshold number of cells (minimum sup-port area) is selected when the delineated channel network wascoincided with the digitized river network from contour maps.

The spatial distribution of Manning’s coefficient was deter-mined for each storm based on the values published in the litera-

Fig. 1. Location of the stations and the

ture for the appropriate land cover (Brater and King, 1976;Montes, 1998). The land cover information of the area was derivedfrom Landsat TM image on 18 May 1987; the classification proce-dure was performed by using a Maximum–Likelihood–Classifier,which results in four land use classes. Furthermore, from soil typemaps (1:300,000 scale), three hydrological soil types and their dis-tributions were obtained.

Methodology

As discussed in the introduction section, the spatially distrib-uted direct hydrograph travel time method (SDDH) developed byMelesse and Graham (2004) takes the excess rainfall intensity asa constant for calculating the travel time field for the whole rainfallprocess, and does not take into account the temporal variation ofsurface runoff leading to the change of travel time field. In thepresent study, a new approach, named time variant SDDH method,has been developed to route spatially–temporally distributed sur-face runoff to the watershed outlet.

The developed approach is a distributed runoff routing tech-nique based on GIS, the flow path and network are needed forthe model which can be derived from the digital elevation model(DEM). A single downstream cell, in the direction of the steepestdescent, can be defined for each DEM cell by the use of flow direc-tion GIS function, so that a unique connection from each cell to thewatershed outlet can be determined. This process produces a cellnetwork presenting the paths of the watershed flow system. Fordefining the hillslope and channel network, a threshold numberof cells (minimum support area) is set to delineate the channel net-work for the watershed. Any cell with a number of cells upstreamequal to or greater than the threshold value is considered to be a

catchment in the map of PR China.

Fig. 2. Hydrologic soil group of the study area.

Table 1Summary of rainfall and discharge events.

Storm no. Storm date Rainfalla Direct runoff

Depth (mm) Duration (h) Average intensity (mm/h) Peak (m3/s) Time to peak (h)

1 August 23, 1979 377.7 60 6.3 828 422 August 30, 1981 458.6 96 4.8 1591 453 September 9, 1987 304.1 73 4.2 841 494 July 29, 1988 222.7 19 11.7 1483 155 August 30, 1990 386.0 43 9.0 1128 336 August 28, 1992 504.4 89 5.7 1481 807 September 13, 2000 262.8 53 5.0 693 308 June 23, 2001 153.6 85 1.8 249 29

a Values represent weighed average from the three rain gauges.

J. Du et al. / Journal of Hydrology 369 (2009) 44–54 47

channel cell; others are hillslope cells. The routing parameters ofeach cell can be described from the flow path network, and thekey point of the approach is the travel time estimation.

Overland flow travel time estimation

Overland flow travel time in a grid cell can be estimated bycombining the kinematic wave approximation with Manning’sequation (Singh and Aravamuthan, 1996).

For overland flow, the continuity equation and momentumequation can be written as:

Continuity equation :@h@tþ @q@l¼ ie ð1Þ

Momentum equation : Sf ¼ S0 ð2Þ

where h is the depth of water on the surface (m); q is the unit-width discharge (m2/s); ie is the vertical net incoming flux (m/s);

l is the length of the slope (m), if the cell has horizontal or ver-tical flow directions, l is equal to grid size; if the cell has diagonalflow directions, l is equal to the grid size multiplied by

ffiffiffi2p

; t isthe time (s); Sf is the friction slope; and So is the slope of thesurface.

The surface flow rate is calculated by Manning’s equation(Chow et al., 1988):

V ¼ S1=2f h2=3

=n ð3Þ

where n is Manning’s roughness coefficient of the surface.For steady state overland flow, q can be written as:

q ¼ iel ð4Þ

For overland flow, q can also be written as:

q ¼ hV ð5Þ

48 J. Du et al. / Journal of Hydrology 369 (2009) 44–54

From Eqs. (4) and (5), h can be obtained

h ¼ iel=V ð6Þ

Substituting Eq. (6) into Eq. (3), and solving for V

V ¼ S3=100 l2=5i2=5

e n�3=5 ð7Þ

The travel time, to, for each overland cell is computed from the cellvelocity and the travel distance of the cell as

to ¼ l=V ð8Þ

Channel flow travel time estimation

The calculation of travel time for channel cell to the watershedoutlet requires computation of flow velocity. Channel flow velocity,V, is computed using Manning’s equation and the continuity equa-tion for a wide channel following the procedure described below(Muzik, 1996a,b; Melesse, 2002):

For channel flow with no lateral inflow, the continuity equationis given by

@Q@lþ @A@t¼ 0 ð9Þ

where A is flow section area of channel (m2); l is flow length (m); Qis the cumulative discharge (m3/s) through the cell that is deter-mined by summing up the upstream flow contributions and thecontribution from precipitation excess for that cell.

If the flow is steady, @A@t ¼ 0, thus @Q

@l ¼ 0 indicating Q is constantIn this case the continuity equation reduces to

Q ¼ VA ¼ VBh ð10Þh ¼ Q=VB ð11Þ

where B is the channel effective width (m).Channel flow velocity V is calculated by Manning’s equation

(Chow et al., 1988) as

V ¼ S1=2f R2=3=n ð12Þ

where R is the hydraulic radius (area of flow section divided by thewetted perimeter), n is Manning’s roughness coefficient, and Sf isthe friction slope.

Using Manning equation for a wide channel (R = h), and com-bining the kinematic wave approximation Sf = S0 yields

V ¼ V�2=3B�2=3Q 2=3S1=2o =n ð13Þ

Solving for V yields

V ¼ S3=10o Q 2=5B�2=5n�2=5 ð14Þ

where S0 is the slope of the cell that can be obtained from DEM. Eq.(14) is the travel velocity method used by Muzik (1996a,b); Melesse(2002) and Melesse and Graham (2004).

Due to the difficulty in obtaining the river width, the Manningequation (12) was approximated as (Kouwen et al., 1993; Aroraet al., 2001):

V ¼ S1=2f A1=3=n ð15Þ

where A is the channel cross-sectional area. Replacing Sf by So, theformula for the outflow Q is obtained as:

Q ¼ S1=2o A4=3

=n ð16Þ

Solving Eq. (16) for A yields

A ¼ S�3=8o Q 3=4n3=4 ð17Þ

Replacing A in Eq. (15) with Eq. (17) yields

V ¼ S3=8o Q 1=4n�3=4 ð18Þ

To account for the estimation error for n and So, parameter K isadded to Eq. (18), which will be determined by calibration. So Eq.(18) can be written as

V ¼ KS3=8o Q 1=4n�3=4 ð19Þ

The travel time, tc, for each channel cell is computed from the cellvelocity and the travel distance of the cell as

tc ¼ l=V ð20Þwhere l is travel distance (if the cell has horizontal or vertical flowdirections, l is equal to grid size; if the cell has diagonal flow direc-tions, l is equal to grid size multiplied by

ffiffiffi2p

); V is the channelvelocity estimated by Eq. (19).

Cumulative travel time and runoff estimation

In the SDDH method, the cumulative travel timeP

ti of surfacerunoff for each grid cell to the watershed outlet is computed bysumming up travel times along the respective flow paths from eachcell following the flow direction. Once the cumulative travel timeof each cell to the outlet is computed, the volumetric flow rate con-tributed by that cell (excess rainfall intensity of each cell multi-plied by the cell area) at that time is noted. The direct runoff isdetermined by the sum of the volumetric flow rate at each respec-tive travel time from all contributing cells. This method takes tra-vel time of surface runoff for each grid cell invariant for a stormevent and ignores the variation of travel time due to the variationof surface runoff in time.

In our method, named time variant SDDH, the variation of surfacerunoff and rainfall is considered by dividing the rainfall process intoseveral time intervals, and for each time interval the excess rainfallintensity of each cell was calculated, the travel time, and cumulativetravel time for each cell were calculated according to Eqs. (8) and(20). Therefore, the cumulative travel time for each cell at each timestep may be different due to variant surface runoff. Once the cumu-lative travel time

Pti of each cell to the outlet at time interval t is

computed, the volumetric flow rate at time step t (excess rainfallintensity of each cell at that time interval multiplied by the cell area)is noted by arriving time ta computed as ta ¼

Pti þ ðt � 1ÞDt. The

direct runoff at each respective arriving time is determined by thesum of the volumetric flow rates with the same arriving time forall time intervals from all contributing cells.

Runoff generation

To test the developed time variant SDDH approach, the SoilConservation Service (SCS) curve number (CN) method (as citedby Chow et al. (1988)) was used to calculate runoff products. Ding-man (2001) stated that the SCS–CN method will continue to beused since (a) it is computationally simple, (b) it uses readily avail-able watershed information, (c) it appears to give reasonable re-sults under many conditions, and (d) there are a few otherpracticable methodologies for obtaining a priori estimates of runoffthat are known to be better. In our approach, the curve numbermethod in its differential form (Mancini and Rosso, 1989) is usedto compute spatially distributed excess rainfall.

In the differential form of the SCS-CN method, the excess rain-fall depth Qt (mm) of each element cell at the time step t is com-puted as

Qt ¼ðPt � 0:2SÞ2

ðpt þ 0:8SÞ If ðPt > 0:2SÞ ð21Þ

where Pt (mm) is the cumulative depth of precipitation at time stept, computed as

Pt ¼Xt

j¼1

pjDt ð22Þ

J. Du et al. / Journal of Hydrology 369 (2009) 44–54 49

where pj is the rainfall intensity at the time step j (mm/s), Dt is timestep length (s), S is the maximum soil potential retentions (mm), gi-ven by S ¼ 25400

CN � 254 where CN (1–100) is runoff curve number,which is determined from hydrologic soil group (HSG), land use,hydrologic conditions as well as antecedent soil moisture condition(AMC) (Mishra and Singh, 1999). CNs for each storm were deter-mined from both land cover and HSGs based on the CN tables ofthe US Department of Agriculture, Soil Conservation Service (Chowet al., 1988). The soil antecedent moisture condition can be classi-fied into three levels according proceeding 5 days accumulatedrainfall: AMC-I for dry, AMC- II for normal, and AMC-I for wet con-ditions. Fig. 3 shows one of the CNs with AMC-II. When Pt 6 0.2S, therainfall is completely absorbed by soils, no overland flow generatesand the runoff depth is zero.

The surface runoff rate it (mm/s) from each grid cell at the timestep t is

it ¼ ðQt � Qt�1Þ=Dt ð23Þ

Model evaluation criteria

The model efficiency coefficient (EF), volume conservation in-dex (VCI), absolute error of the time to peak (DN) and relative errorof peak flow rate (dPmax) were used in this study to evaluate theperformance of the approach. EF and VCI were calculated fromEqs. (24) and (25), respectively.

EF ¼ 1�PN

i¼1ðOi � ZiÞ2PNi¼1ðOi � OÞ2

ð24Þ

VCI ¼XN

i¼1

Zi

,XN

i¼1

Oi ð25Þ

Fig. 3. Distribution of

where Oi is the observed system response at discrete times i, Zi isthe predicted system response at discrete times i, and O is the meanof the observed values over all times. Obviously, a bigger EF valuemeans a better efficiency of the model performance, and if the VCIis close to 1, the simulation quality is higher.

Results and discussion

AMC determination

AMC is an important factor in determining surface runoff in theSCS-CN method, because of the lack of data in preceding rainfallstorms, VCI was employed here to determine the AMC levels, i.e.,one of the three AMC levels (AMC-I, AMC-II and AMC-III) was se-lected if it made VCI close to 1. For the eight storms, the most suit-able antecedent soil moisture condition was selected (Table 2). It isseen from Table 2 that AMC has a significant effect on runoffvolume.

Model calibration

Storm 1 with a single peak was selected for model calibration. Apreliminary sensitivity analysis of parameters showed that thechannel threshold and parameter K have a great influence on thesimulation accuracy, and they need to be calibrated. Five levelsof channel threshold (1, 5, 10, 50 and 100 cells), and six values ofK (1, 5, 7.5, 10, 20 and 30) were set to simulate the storm, andthe results (parts of them are listed in Table 3) indicated that whenchannel threshold was equal to 10, a minimum relative peak ratiocould be obtained, and when channel threshold was equal to 1, amaximum efficiency could be obtained, making this multiobjective

curve numbers.

Table 2Volume conversation indexes under different antecedent soil moisture conditions.

No. Flood date VCI Selected AMC level

AMC-I AMC-II AMC-III

1 August 23, 1979 0.79 1.11 1.29 II2 August 30, 1981 0.75 0.92 1.04 III3 September 9, 1987 0.80 1.15 1.37 II4 July 29, 1988 0.71 1.10 1.46 II5 August 30, 1990 0.77 1.06 1.24 II6 August 28, 1992 0.85 1.08 1.22 II7 September 13, 2000 0.63 0.86 1.04 III8 June 23, 2001 0.65 1.15 1.56 II

Table 4Simulation results for seven storms.

Storm no. Peak (m3/s) Time to peak (h) dPmax |DN| (h) EF VCI

2 1289 43 �0.25 �1 0.93 1.043 782 49 �0.09 0 0.97 1.154 1602 14 0.03 �1 0.93 1.105 1161 27 �0.02 �6 0.93 1.056 1555 80 �0.04 0 0.96 1.087 658 28 �0.07 1 0.97 1.048 384 28 0.26 �1 0.48 1.14

50 J. Du et al. / Journal of Hydrology 369 (2009) 44–54

problem have no optimal solution, but Poreto solutions. Consider-ing all the evaluation criteria, i.e., relative peak ratio, time to peakerror, efficiency, and time to peak, a compromised solution is ob-tained with the K = 7.5, and channel threshold = 5 as the valuesof calibrated parameters.

Model verification

Simulations for other seven storms were performed with thisapproach using the parameter values calibrated by storm 1. Table4 summarizes the results of model simulation and error statistics.It is seen that six out of seven storms have efficiencies greater than0.90, five out of seven storms have a relative error of peak flow rateless than 10%, and only one storm has time to peak error with 6hours.

Observed and predicted hydrographs for all seven storms areshown in Fig. 4. The model predicted runoffs for storms 2, 3, 4, 5,6, and 7 very well. The peak flow rate, time to peak and total runoffvolume were all simulated with good accuracy, and a few sub-peaks of these storms were also reproduced. Storm 8 with doublepeaks was not simulated well. In general, the simulation resultsshowed that the observed and predicted hydrographs agreed welland the error statistics are acceptable for practical purposes.

Sensitivity analysis

Sensitivity analysis was conducted to assess the change in fourcriteria for changes in model parameters. In our study, sensitivityanalysis was carried out for the threshold value for stream networkdelineation (i.e., classification of overland versus channel cells) andparameter K.

Sensitivity analysis was performed for combinations of the twoparameters, i.e., channel threshold A and parameter K. The resultsfor twenty five parameter combinations, i.e., five channel thresholdvalues (1, 3, 5, 7, and 10 cells) and five K values (1, 3, 5, 7.5, and 10)are shown in Figs. 5 and 6. It is indicated that (1) larger channelthreshold A values (more overland cells and shorter channel dis-tance) when K keeps unchanged resulted in slower travel timesthat delayed the time to peak and also lower peak discharge com-pared to the observed data (Fig. 5a and b). (2) Larger K values in-creased the channel flow velocity resulting in shorter travel

Table 3The statistic results of runoff simulation for storm no.1 at different values of K and chann

k Channel threshold = 1 Channel threshold =

dPmax DN EF VCI dPmax dN

1 �0.05 9 0.07 1.11 �0.09 95 0.41 0 0.92 1.11 0.16 07.5 0.39 �1 0.93 1.11 0.15 0

10 0.44 �1 0.92 1.11 0.17 �1

times and higher peak flows when A keeps unchanged (Fig. 6aand b). (3) Both Figs. 5c and 6c showed when either channelthreshold A or parameter K takes values smaller than or equal to3, the model efficiency value became either low or unstable. Fur-thermore, as the channel threshold increases, the K value that cor-responding to the highest efficiency also increases (Fig. 5c); theefficiency increases steeply with the increase of K value from 1to 3, and decreases smoothly with the increase of K value afterthe highest efficiency value has been reached except with A = 1(Fig. 6c). (4) In general, the model efficiency, peak flow, and timeto peak are more sensitive when A = 1 and 3 and/or K = 1 and 3than other A and K values (Figs. 5 and 6). (5) The threshold valuesA and parameter K had little effect on VCI (Figure is not shown), be-cause they have no effect on the calculation of rainfall excess.

Comparison with SDDH simulation

For comparative purposes, the SDDH method was also used tosimulate the eight storms, the best results were found when chan-nel threshold was 1 cell and K = 5. The results of the two methodswere shown in Table 5. It can be seen that, in the test catchment,the modified SDDH method improved the results of the SDDHmethod in more cases than not meaning that it is of importanceto consider the temporal variation of travel time field during rain-fall in flow simulation. It is anticipated that the improvementwould be larger for large catchments.

Effects of grid size on simulation

Changes in spatial resolution of the model will lead to differentvalues of the GIS derived slope, flow direction, and spatial distribu-tion of flow paths, which, in turn, affect the model simulation. Inthis paper, three types of DEMs with grid sizes of 100 m, 200 m,and 300 m were used to simulate the eight storm runoffs. Witheach type of DEMs the best channel threshold and parameter Kwere selected, and the results were shown in Table 6.

It can be seen that, low-resolution of DEMs with a grid size of100 m leads to a little change in efficiency, relative peak ratioand time to peak, which may be caused by several reasons. Onone hand, lower resolution leads to a decrease of derived sloperesulting in longer travel times and lower peak flows; on the otherhand, lower resolution also leads to a decrease of flow path result-ing in shorter travel times and high peak flows, and these two

el threshold with Grid size = 50 m.

5 Channel threshold = 10

EF VCI dPmax DN EF VCI

�0.09 1.11 �0.14 12 �0.19 1.100.85 1.11 0.03 1 0.77 1.100.89 1.11 0.03 0 0.83 1.100.91 1.11 0.03 �1 0.85 1.10

storm No.1

0

200

400

600

800

1000

0 20 40 60

Time (h)

Dis

char

ge(m

3 s-1)

storm No.2

0

400

800

1200

1600

2000

0 20 40 60 80

Time (h)

Dis

char

ge(m

3 s-1)

storm No.3

0

200

400

600

800

1000

0 20 40 60

Time (h)

Dis

char

ge(m

3 s-1)

storm No.4

0

400

800

1200

1600

0 10 20 30 40

Time (h)

Dis

char

ge(m

3 s-1)

storm No.5

0

200

400

600

800

1000

1200

0 10 20 30 40

Time (h)

Dis

char

ge(m

3 s-1)

storm No.6

0

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800

1200

1600

0 20 40 60 80 100

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Time (h)

Dis

char

ge(m

3 s-1)

storm No.7

0

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400

600

800

0 20 40 60

Time (h)

Dis

char

ge(m

3 s-1)

storm No.8

0

100

200

300

400

0 20 40 60 80 100

Dis

char

ge(m

3 s-1)

Fig. 4. Comparison of the observed (solid line) and simulated (dashed line) discharges for the eight storms.

J. Du et al. / Journal of Hydrology 369 (2009) 44–54 51

effects compensate for each other resulting in a small change intravel time and peak flow. Another effect of lower resolution ofDEM is the change in optimal channel threshold values, pertainingrelatively the channel length. Just as pointed out by Horritt andBates (2001), predictions with a low-resolution may also give anessentially correct result in many cases.

The effect of accumulated runoff excess on lower grid cells isvery small; as can be seen from Table 6 that the VCI (which canshow accumulated runoff excess) have a small decreasing changewith increasing grid size.

However, this study also showed that when grid size is equal to200m and 300m the results were poor, meaning that good results

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

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1 3 5 7 10channel threshold A

rela

tive

peak

flow

err

or

k=1k=3k=5k=7.5k=10

-4

0

4

8

12

16

1 3 5 7 10channel threshold A

time

to p

eak

erro

r

k=1k=3k=5k=7.5k=10

0

0.2

0.4

0.6

0.8

1

1 3 5 7 10channel threshold A

effic

ienc

y k=1k=3k=5k=7.5k=10

a

b

c

Fig. 5. Sensitivity analysis results – change of model performs with the channelthreshold A.

-0.4-0.3

-0.2-0.1

00.1

0.20.3

0.4

1 3 5 7.5 10parameter K

parameter K

rela

tive

peak

flow

err

or

A=1A=3A=5A=7A=10

-4

0

4

8

12

1 3 5 7.5 10tim

e to

pea

k er

ror A=1

A=3A=5A=7A=10

0

0.2

0.4

0.6

0.8

1

1 3 5 7.5 10parameter K

effic

ienc

y

A=1A=3A=5A=7A=10

a

b

c

Fig. 6. Sensitivity analysis results – change of model performs with the parameter Kvalues.

52 J. Du et al. / Journal of Hydrology 369 (2009) 44–54

could be attained with a grid size of less than 200 m in the studycase.

Conclusions

This study has developed a new approach to simulate stormrunoff with consideration of spatial and temporal variability ofrunoff generation and routing. The runoff production was esti-mated using the SCS-CN method, and runoff routing at each timestep was performed by the use of a time variant SDDH. The ap-proach was applied to the Jiaokou watershed in southeast Chinaand produced acceptable results. When reliable spatially distrib-uted geographic and climatic data are available, the time variantSDDH approach is preferable to the SDDH approach and time–areamethod, since it can directly use time variant spatially distributedexcess rainfall. The SDDH method uses the average excess rainfallintensity of a flood event to estimate travel time, ignoring thechanges of travel time due to variant surface runoff caused by

changing excess rainfall. However, in reality the average excessrainfall intensity will never be known before the whole storm pro-cess has finished, and such a method can only be used for stormrunoff simulation rather than forecasting. The time–area method(Maidment, 1993; Muzik, 1996a; Maidment et al., 1996) is a unithydrograph approach, which requires spatially constant excessrainfall, ignoring the spatial variation of precipitation. Moreover,the unit hydrograph derived is also invariant for a storm eventand ignores changes of travel time.

The approach developed in this study has a simple structureand can easily be performed in a GIS environment. It uses onlyDEMs, land cover, soil type, and rainfall data which are becomingmore and more available. Most parameters needed for this ap-proach can be derived from these data, and only channel thresholdand parameter K need to be determined by calibration. With onlytwo parameters needed to be calibrated, and taking spatial andtemporal variations of rainfall into account for runoff productionand runoff routing, the method has promising application potentialin storm runoff simulation.

It should be noted that in this approach, although the calcula-tion of overland and channel travel time uses the physically-based

Table 5The comparison of two methods.

Storm no. SDDH Method in this paper Improved

dPmax DN EF VCI dPmax DN EF VCI dPmax DN EF VCI

1 0.25 1 0.90 1.11 0.15 0 0.89 1.11 0.10 1 �0.01 02 �0.20 1 0.95 1.04 �0.25 �1 0.93 1.04 �0.05 0 �0.02 03 �0.07 1 0.96 1.15 �0.09 0 0.97 1.14 �0.02 1 0.01 0.014 0.09 0 0.86 1.10 0.03 �1 0.93 1.10 0.06 �1 0.07 05 0.01 �4 0.88 1.09 �0.02 �6 0.93 1.04 �0.01 �2 0.05 0.056 �0.09 3 0.91 1.08 �0.04 0 0.96 1.08 0.05 3 0.05 07 0 �1 0.94 1.04 �0.07 1 0.97 1.03 �0.07 0 0.03 0.018 0.28 52 0.59 1.15 0.26 �1 0.48 1.14 0.02 51 �0.11 0.01

Table 6The statistic results of storm runoff simulation with different Grid size.

Storm no. Grid size = 50 m, channelthreshold = 5, K = 7.5

Grid size = 100 m, channelthreshold = 1, K = 7.5

Grid Size = 200 m, channelthreshold = 1, K = 15

Grid Size = 300 m, channelthreshold = 1, K = 15

dPmax DN EF VCI dPmax DN EF VCI dPmax DN EF VCI dPmax DN EF VCI

1 0.15 0 0.89 1.11 0.13 0 0.93 1.04 0.05 �1 0.72 1.03 �0.25 �1 0.48 1.022 �0.25 �1 0.93 1.04 �0.22 �1 0.92 0.98 �0.43 6 0.76 0.97 �0.60 �1 0.56 0.963 �0.09 0 0.97 1.14 �0.05 0 0.97 1.07 �0.32 �1 0.84 1.06 �0.47 0 0.63 1.064 0.03 �1 0.93 1.10 0.14 �1 0.89 1.03 �0.25 �1 0.70 1.02 �0.36 �1 0.58 0.995 �0.02 �6 0.93 1.04 0 �6 0.88 1.01 �0.19 �1 0.82 0.90 �0.44 �6 0.54 0.666 �0.04 0 0.96 1.08 0.01 0 0.97 1.03 �0.19 0 0.80 1.02 �0.30 0 0.68 1.017 �0.07 1 0.97 1.03 �0.03 �1 0.94 1.00 �0.17 4 0.86 0.98 �0.48 �2 0.58 0.948 0.26 �1 0.48 1.14 0.54 �1 0.18 1.05 0.37 �1 0.03 1.04 0.11 47 0.14 1.00Average 0 �1 0.88 1.09 0.07 �1.25 0.84 1.03 �0.14 0.63 0.69 1.00 �0.35 4.5 0.52 0.96

J. Du et al. / Journal of Hydrology 369 (2009) 44–54 53

methods, as Melesse and Graham (2004) pointed out that calibra-tion of parameter K and cell threshold casts some doubt on thephysical basis for these parameters. Nevertheless, it is suggestedthat these parameters shall be calibrated and verified when apply-ing the method to other watersheds.

Acknowledgments

The study is financially supported by the National Natural Sci-ence Foundation of China (Nos. 40171015 and 40371020). Theauthors would like to thank the reviewers for their valuable com-ments and suggestions which significantly improved the quality ofthe paper.

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