Jun Li*,Chang-ming Liu

aKey Laboratory of Mountain Hazards and Earth Surface Processes,Institute of Mountain Hazards and Environment, Chinese Academy of Sciences,Chengdu 610041,China

bKey Laboratory of Water Cycle and Related Land Surface Processes,Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences,Beijing 100101,China

Improvement of LCM model and determination of model parameters at watershed scale for flood events in Hongde Basin of China

Jun Lia,*,Chang-ming Liub

aKey Laboratory of Mountain Hazards and Earth Surface Processes,Institute of Mountain Hazards and Environment, Chinese Academy of Sciences,Chengdu 610041,China

bKey Laboratory of Water Cycle and Related Land Surface Processes,Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences,Beijing 100101,China

Considering the fact that the original two-parameter LCM model can only be used to investigate rainfall losses during the runoff period because the initial abstraction is not included,the LCM model was redefined as a three-parameter model,including the initial abstraction coefficient λ,the initial abstractionIa,and the rainfall loss coefficientR.The improved LCM model is superior to the original two-parameter model,which only includesrandR,whereris the initial rainfall loss index and can be calculated with λ using the Soil Conservation Service curve number(SCS-CN)method,withr=1/（1+λ）.The trial method was used to determine the parameter values of the improved LCM model at the watershed scale for 15 flood events in the Hongde Basin in China.The results show that largerrvalues are associated with smallerRvalues,and the parameterRranges widely from 0.5 to 2.0.In order to improve the practicability of the LCM model,r=0.833 with λ=0.2 is reasonable for simplifying calculation.When the LCM model is applied to arid and semi-arid regions,rainfall without yielding runoff should be deducted from the total rainfall for more accurate estimation of rainfall-runoff.

LCM model;SCS-CN method;Rainfall-runoff;Initial abstraction;Partial-area runoff;Determination of parameter;Loess Plateau

1.Introduction

Rainfall-runoff calculation is one of the difficulties of hydrological research,especially in arid and semi-arid regions. The Soil Conservation Service curve number(SCS-CN) method has been widely used to estimate the runoff generated from a rainfall event(Ponce and Hawkins,1996;Patil et al., 2008;Mishra and Singh,2003).This method was developed by Soil Conservation Service of the U.S.Department of Agriculture and has undergone several updates(USDA-SCS, 1964,1971,1985,1993,2004).The use of the SCS-CN method as a soil and water assessment tool(SWAT)has made the method popular(Arnold et al.,1996;Grassman et al.,2007).As a simple and practical method for estimating the runoff generated from a storm rainfall event,the SCS-CN method has been used in many regions in China(e.g., Gao et al.,2006;Huang et al.,2007;Wang and Huang,2008; Shi et al.,2009;Zhou and Lei,2011).However,the range of the initial abstraction coefficient and the theoretical rationality of the SCS-CN method are still not clear.A relationship between the initial abstractionIaand the initial abstraction coefficient λ,i.e.,Ia=λS,has been derived from the study of many small experimental watersheds,whereSis the maximumpotential retention,and many studies have indicated that λ ranges from 0 to 0.3(Ponce and Hawkins,1996).Aron et al. (1977)found that the simulated runoff is usually underestimated if λ=0.2,especially for medium and small flood events,so they proposed a value of 0.1 or even smaller values for λ.Some studies have indicated that a value of 0.05 might lead to accurate results of runoff simulation(Lim et al.,2006). Mishra and Singh(2002,2004)considered that λ could be a variable,which might be 0.05 or even smaller,close to 0.

During the period of 1958-1978,in order to predict the flood peak discharge in ungauged watersheds,Liu et al. (1965),Liu and Zhong(1978),and Liu and Wang(1980) established and improved an empirical equation,which was called the LCM model,to calculate rainfall-runoff based on analysis of the storm runoff in small watersheds and arti ficial rainfall experiments.The LCM model and the SCS-CN method were developed during a similar period.The LCM model parameters can be easily obtained from field experiments,while,the parameters of the SCS-CN method are dif ficult to measure.Liu et al.(2008,2010,2013,2014)subsequently developed a distributed hydrological model based on the LCM model and other hydrological processes(Wang et al.,2004,2005),which has been called the hydroinformatics modeling system(HIMS).With the HIMS,the rainfall loss coef ficientRand initial rainfall loss indexrof the LCM model,with possible ranges of 0.83-1.27 and 0.56-0.92,respectively,have been obtained from arti ficial rainfall experiments in small experimental watersheds (Table 1).

Although the LCM model is a simple and effective rainfallrunoff model,its physical basis and the determination of its parameters have been dif ficult problems to solve at the watershed scale.Moreover,the original two-parameter LCM model can only be used to investigate rainfall losses during the runoff period because the initial abstraction is not included.In this study,the LCM model and SCS-CN method were compared in rainfall-runoff analysis,and the original twoparameter LCM model was rede fined as a three-parameter model,including the initial abstraction coef ficient λ,the initial abstractionIa,and the rainfall loss coef ficientR. Parameter values of the improved LCM model for 15 flood events in the Hongde Basin were determined at the watershed scale using the trial method.

Table 1 Values of parameters R and r for LCM model(Liu and Wang,1980).

2.Methods

2.1.Improved LCM model and trial method

Both the SCS-CN method and the LCM model describe watershed runoff at the macroscopic scale and take into account the relationship between the cumulative actual retention and cumulative rainfall.The LCM model considers it a power function relationship,while,the SCS-CN method considers their reciprocals to be linearly related.In the two-parameter LCM model,the relationship between the average rainfall loss ratio and the average rainfall intensity is formulated as

where μ is the average rainfall loss ratio during the runoff period(mm/h),and α is the average rainfall intensity during the runoff period(mm/h).Li et al.(2015)compared the LCM model with the SCS-CN method and used a Taylor series expansion to develop another format of the SCS-CN method as follows:

wherePis the cumulative rainfall(mm),andFis the cumulative infiltration during the runoff period(mm).Eq.(2)can be solved when

After rearranging Eq.(3)under the condition ofP＞F,one can obtain

Eq.(4)shows that the condition for the establishment of a standard SCS-CN method with λ=0.2 isF/P≤0.4775, which forms a restrictive condition of the SCS-CN method. Compared with the SCS-CN method,the LCM model does not have this limitation,which means that the LCM model has a wider scope of application.

By setting μ and α as μ=F/Tand α=（P-Ia）/T,the LCM model can be rewritten as

whereTis the rainfall duration with runoff generation.From this analysis,we can determine that the SCS-CN method does not consider the rainfall duration with runoff generation,but the LCM model does consider this factor.By using the oneorder term of a Taylor series expansion of Eq.(5)with the variablex=1/（P-Ia）at the point 1/a0,Eq.(6)can be derived:

Combining Eqs.(2)and(6),we can obtain

Then,a0is approximated as follows:

Based on the empirical relationship ofIaandSin the SCSCN method,i.e.,Ia=λS,a0can be considered the initial abstraction,i.e.,

In order to maintain high accuracy for the LCM model,Rin the LCM model is regarded as a comprehensive parameter, depending on the parameterr,the initial abstractionIa,and the rainfall duration with runoff generationT.The parameterrin the LCM model is considered the deformation of λ in the SCSCN method.Therefore,randRin the LCM model can be calculated,respectively,as

Thus,the LCM model can be redefined as follows:

Therefore,the improved LCM model contains three parameters at the watershed scale:the initial abstraction coeff icient λ,the initial abstractionIa,and the rainfall loss coefficientR.

The LCM model originates from the artificial rainfall tests at the slope scale.However,because of uneven spatial distribution of rainfall,some sub-watersheds have rainfall but without runoff generation,i.e.,for a sub-watershedmwith the total rainfallPm≤Ia,its total runoffQm=0.At the watershed scale,those regions with rainfall but without runoff generation can often lead to the error in runoff estimation.Therefore,we deduct this part of rainfall and rewrite the water balance equation as

where the subscriptsk,m,andnrepresent any one of the sub-watersheds,a sub-watershed without runoff generation, and a sub-watershed with runoff generation,respectively;Ais the area of a sub-watershed;Qis the runoff generation of a sub-watershed;andVoutis the runoff volume of the whole basin.

To test the effective values of the LCM model parametersIaandR,the trial method was used according toIa=λS,withS=25400/CN-254,whereCNis the curve number in the SCS-CN method.The range of λ was set to be［0.01，0.5］,with a step size set at 0.01;the range ofCNwas set to be［5，59］, with a step size set at 0.1;and the range ofRwas set to be［0.15，2］.

The total rainfall loss obtained from the observed results of the total rainfall,ineffective rainfall without yielding runoff, and total runoff is as follows:

The simulated value of the total rainfall loss of subwatersheds from the LCM model is as follows:

In this study,the parameter values of λ,Ia,andRwere considered a reasonable parameter combination whenand the regularity of this combination for each flood event was further studied.

2.2.Triangular irregular network interpolation method for sub-watershed rainfall

The triangular irregular network(TIN)interpolation method was used to calculate the rainfall of sub-watersheds.It was assumed that the rainfall at the central point of a subwatershed,N(x,y),represented the average rainfall in this sub-watershed.For a triangular element△ABCwith vertexes atA（xa，ya）,B（xb，yb）,andC（xc，yc）,the rainfall at the centerN(x,y)was calculated with the following formula:

wherexba=xb-xa;xca=xc-xa;yba=yb-ya;yca=yc-ya;Pba=Pb-Pa;andPca=Pc-Pa,wherePa,Pb, andPcare rainfall at vertexesA,B,and C,respectively.

3.Materials

3.1.Study area

The Hongde Basin is located upstream of the Jinghe Basin with an area of about 4649 km2,ranging from 106°37′34′′E to 107°37′19′′E and 36°39′58′′N to 37°24′35′′N(Fig.1).Located in the Loess Plateau of China,this region is an arid/semi-arid area,with an average annual rainfall of nearly 348 mm and an average annual runoff depth of 16.1 mm.However,the region is prone to short-duration and high-intensity heavy rains and disastrous floods.Loess predominates the soil type in thisregion,accounting for 95%.The region also suffers soil erosion at one of the highest rates in the world.Cropland and grassland are the main types of land use,accounting for 40.8% and 56.23%,respectively.

Based on a 90 m SRTM DEM(supported by the International Scienti fic and Technical Data Mirror Site,the Computer Network Information Center,the Chinese Academy of Sciences)and the traditional DEM hydrological analysis,the Hongde Basin was divid2ed into 2079 sub-watersheds with an average area of 2.2 km in order to obtain the spatial distribution of rainfall accurately.

3.2.Data collection

Fifteen large independent flood events in the Hongde Basin from 2001 to 2012 were analyzed,with hydrological data listed in Table 2.Fig.2 shows the flood hydrograph of each flood event.The time interval of the discharge record at the Hongde Hydrological Station was half an hour.The spatial distributions of the total rainfall of 15 flood events were obtained with Eq.(16)using the original data of 17 rainfall stations,and the time interval of the rainfall record was 1 h.

Fig.3 shows the spatial rainfall distribution of 15 flood events in the Hongde Basin from 2001 to 2012.It can be seen that three flood events(No.2,No.8,and No.12)cover the whole basin,and the other flood events are more concentrated in some parts of the basin.

Fig.1.Hongde Basin.

4.Results and discussion

Using the trial method,the effective values of the improved LCM model parameters for the 15 flood events in the Hongde Basin from 2001 to 2012 were ascertained.Fig.4 shows a coupling relationship between parametersrandR.As thervalue grows,theRvalue becomes smaller.In hydrological models,effective parameters for simulating flood hydrographs must be suitable for calculation of the total runoff.However, effective parameters for simulating the total runoff are not necessarily effective for simulating flood hydrographs.In consideration of this factor,the trial method used in the present study to determine the model parameters based on calculation of the total runoff gives the maximum range of the model parameters for simulation of flood hydrographs.Fig.4 reveals that the parametersrandRhave a high degree of overlap for different flood events and parameterRranges widely from 0.5 to 2.0.From the trial results we can conclude that assumingr=0.833 with λ=0.2 according to Eq.(10)is reasonable for simplifying calculation.

Fig.5 shows that different flood events have different values of parameterIa,and they rarely overlap for different flood events.The No.2 flood event has a maximum value ofIa, because the No.2 flood event started in June,the driest time of the year in the Hongde Basin.Due to the high variability of each flood,Iais the most critical parameter in the LCM model. The Hongde Basin is a small basin with uniform soil and land use.Therefore,the high variability ofIacan only be explained by means of different antecedent moisture conditions(AMC) for each flood event.In the existing SCS-CN method,AMC iscategorized into three levels according to different values ofCN:AMC I refers to dry soil conditions,AMC II refers to the normal conditions with average soil moisture,and AMC III refers to wet soil conditions of a watershed(Mishra and Singh, 2003).The method for determination ofIain the SCS-CN method can be used in the LCM model.The USDA-SCS (1971,1985)provided further background and details about the use of the curve number to determineIabased on land cover,hydrologic soil groups(HSG),and AMC.

Table 2 Hydrological data of flood events in Hongde Basin.

Fig.2.Hydrographs of 15 flood events in Hongde Basin from 2001 to 2012.

Fig.3.Spatial rainfall distributions of 15 flood events in Hongde Basin from 2001 to 2012.

Fig.6 shows that,with a larger initial abstraction,the proportion of the rainfall without yielding runoff to the total rainfall is larger as well.Because of the uneven spatial distribution of rainfall(Fig.3),many sub-watersheds do not produce runoff when their total rainfall is less than the initial abstraction.If this portion of rainfall is used to determine the model parameters,it exaggerates the effective rainfall.For the runoff calculation using the SCS-CN method,withthe exaggerated effectiverainfall may lead to a low value of λ.A very small λ may lead to an r value approaching 1 according to Eq.(10),which will lead to the failure of the SCS-CN method and LCM model. Therefore,rainfall without yielding runoff should be deducted from the total rainfall when the SCS-CN method and LCM model are used in arid and semi-arid regions.

Fig.4.Relationships between r and R for 15 flood events.

Fig.5.Relationships between r and Iafor 15 flood events.

Fig.6.Relationships between initial abstraction and proportion of rainfall without yielding runoff to total rainfall for 15 flood events.

Table 3 Results of LCM model parameters for 15 flood events in Hongde Basin.

Table 3 shows the result of the LCM model parameters for 15 flood events in the Hongde Basin.By setting r=0.833,the parameters R and Iaare obtained from Figs.4 and 5,respectively.Using the obtained parameter values,the relative error between the simulated and observed values of the total runoff is less than 0.5%.Table 3 shows that the rainfall without yielding runoff accounts for 1.5%-37.9%of the total rainfall. Even in the sub-watersheds with runoff generation,the proportion of initial abstraction to total rainfall is very large,with the lowest being 18.6%and the highest being 61.2%.The average runoff coefficient of 15 flood events,i.e.,the averageof the proportion of runoff generation to total rainfall,is very small,only 13.3%.

5.Conclusions

There is a restrictive condition for the establishment of a standard SCS-CN method,i.e.,F/P≤0.4775 for λ=0.2,but the LCM model does not have this limitation,meaning that the LCM model has a wider scope of application.The SCS-CN method does not consider the rainfall duration with runoff generation,but the LCM model considers this factor,which makes the LCM model more accurate for estimation of rainfall-runoff.

When the LCM model is redefined as a three-parameter model,including the initial abstraction coefficient λ,the initial abstractionIa,and the rainfall loss coefficientR,its adaptation is extended to the entire rainfall period.The rainfall loss coefficientRin the improved LCM model is a comprehensive parameter that considers the initial rainfall loss indexr,the initial abstractionIa,and the rainfall duration with runoff generationT.The initial rainfall loss indexrcan be calculated with the initial abstraction coefficient in the SCS-CN method asr=1/（1+λ）.

Effective parameter values of λ,Ia,andRof the LCM model for 15 flood events in the Hongde Basin were deduced. Largerrvalues are associated with smallerRvalues,andRranges widely from 0.5 to 2.0.r=0.833 with λ=0.2 is reasonable for simplifying calculation.When the LCM model is used in arid and semi-arid regions with runoff generated in only some parts of the regions,rainfall without yielding runoff in some sub-watersheds should be deducted from the total rainfall for more accurate estimation of rainfall-runoff.

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Received 12 July 2016;accepted 10 October 2016

Available online 9 March 2017

This work was supported by the National Natural Science Foundation of China(Grants No.41271048 and 41330529).

*Corresponding author.

E-mail address:junli@imde.ac.cn(Jun Li).

Peer review under responsibility of Hohai University.

http://dx.doi.org/10.1016/j.wse.2017.03.006

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?2017 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http:// creativecommons.org/licenses/by-nc-nd/4.0/).