real-time error correction method combined with combination flood forecasting technique for...

Journal of Hydrology 521 (2015) 157–169

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Journal of Hydrology

journal homepage: www.elsevier .com/ locate / jhydrol

Real-time error correction method combined with combination floodforecasting technique for improving the accuracy of flood forecasting

http://dx.doi.org/10.1016/j.jhydrol.2014.11.0530022-1694/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: College of Hydropower & Information Engineering,Huazhong University of Science & Technology, Wuhan 430074, China.

E-mail address: [email protected] (L. Chen).

Lu Chen a,b,c,⇑, Yongchuan Zhang a, Jianzhong Zhou a, Vijay P. Singh b,c, Shenglian Guo d, Junhong Zhang e

a College of Hydropower & Information Engineering, Huazhong University of Science & Technology, Wuhan 430074, Chinab Dept. of Biological and Agricultural Engineering, Texas A&M University, 2117 TAMU, College Station, TX 77843-2117, USAc Zachry Dept. of Civil Engineering, Texas A&M University, 2117 TAMU, College Station, TX 77843-2117, USAd State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, Chinae Dept. of Environmental Engineering, South-Central University for Nationalities, Wuhan 430074, China

a r t i c l e i n f o

Article history:Received 23 April 2014Received in revised form 10 November 2014Accepted 19 November 2014Available online 26 November 2014This manuscript was handled by AndrasBardossy, Editor-in-Chief, with theassistance of Niko Verhoest, Associate Editor

Keywords:Flood error correctionMulti-model composition techniqueCombined methodThree Gorges ReservoirJinsha River

s u m m a r y

Flood forecasting has been recognized as one of the most important and reliable ways for flood manage-ment. It is therefore necessary to improve the reliability and accuracy of the flood forecasting model.Flood error correction (FEC) and multi-model composition (MC) methods are two effective ways toenhance the model performance. The current focus seems to be on either of these two methods. In thisstudy, we combine these two methods and propose three combined methods, namely flood error correc-tion together with multi-model composition method (FEC–MC), multi-model composition methodtogether with flood error correction (MC–FEC), and global real-time combination method (GRCM). TheThree Gorge Reservoir (TGR) and Jinsha River are selected as case studies. First, the flood error correctionmethod and multi-model composition techniques are used separately. Then, the three combined meth-ods are employed. The performances of the five models are compared using the root-mean-square error(RMSE), Nash–Sutcliffe efficiency R2, and qualified rate a. Results show that the combined methods per-form better than the single FEC and MC methods. The proposed GRCM method is found to be the mosteffective method for improving the accuracy of discharge predicted by the flood forecasting model.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Flood forecasting has been recognized as one of the most impor-tant and reliable ways for flood management. However, in anyflood forecast system, there are three types of uncertainty causedby a number of factors: input uncertainty, model structure uncer-tainty and parameter uncertainty (Liu and Gupta, 2007). In order toreduce uncertainty and improve accuracy, real-time correction andmulti-model composition forecasting methods have beenemployed as two effective measures (Ajami et al., 2006; Bognerand Pappenberger, 2011; Liao and Lei, 2012).

There are some methods to accomplish error correction, such asthe Kalman filter, methods based on neural networks and fuzzylogic, and autoregressive (AR) method. The Kalman filter updatingmethod can reflect various hydrological and hydraulic flow-fieldsby updating model input or parameters, but it tends to require along computational time (Wu et al., 2012). A comparison of neural

networks and autoregressive models for error correction con-cluded that similar results could be obtained with both methods.Xiong and O’Connor (2002) state that efficiency of the simple stan-dard autoregressive model is not improved by any of the morecomplicated methods that they have tested. Wu et al. (2012) indi-cated that the AR model has proved to be more effective and sim-pler than any other methods mentioned above. Therefore, the ARmodel was considered in this study.

In addition, until now, lots of hydrologic models are in existence,with more likely to emerge in the future. The multi-model combina-tion approach advocates the synchronous use of the simulated dis-charges of a number of models to produce an overall integratedresult which can be used as an alternative to that produced by a sin-gle model (Fernando et al., 2011). Shamseldin et al. (1997) first intro-duced the multi-model combination concept into the hydrologicfield. Since then there have been several more studies which havedealt with multi-model combination of hydrological models(Shamseldin and O’Connor, 1999; See and Openshaw, 2000;Xiong et al., 2001; Abrahart and See, 2002; Coulibaly et al., 2005;Ajami et al., 2006; Hsu et al., 2009; Shamseldin et al., 2007;Fernando et al., 2011). Georgakakos et al. (2004) indicated that the

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158 L. Chen et al. / Journal of Hydrology 521 (2015) 157–169

multi-model ensemble averages are more skillful and reliable thanthe single-model ensemble averages. Therefore, the multi-modelcombination method was used in this study.

The above-mentioned investigations mainly focused on eitherreal time flood error correction or combination flood forecastingtechniques. The real-time error correction was applied only to asingle hydrological model. And the combination concept wasapplied only to the flood forecasting results of hydrological models.Little research work has been reported on combining the twomethods. Shamseldin and O’Connor (1999) proposed a real-timemodel output combination method (RTMOCM) based on the struc-ture of the Linear Transfer Function Model (LTFM) and utilizing theconcept of the Weighted Average Method (WAM) for model outputcombination. Wu et al. (2012) employed the forecast combinationmethod for the correction of forecasted water stage by first com-bining the forecast error estimated by several time series models.However, these studies only discuss one combined method anddid not analyze the combined methods comprehensively. In thisstudy, three methods were introduced to combine the real-timeerror correction method and multi-model composition techniquesto improve the accuracy of the flood forecasting system.

The objective of this paper is, therefore, to employ the real-timeflood error correction (FEC) and combine it with the multi-modelcombination (MC) technique for improving the accuracy of predic-tion results. The traditional AR model was used for FEC, and theWeighted Average Method was applied for MC. Three combinationmethods, including FEC–MC, MC–FEC and global real-time combi-nation method (GRCM) were proposed. The Three Gorges Reservoir(TGR) and Jinsha River were selected as case studies. The predictedstreamflow was improved by the single FEC, MC and three com-bined models. Finally, the predicted results of those five methodswere compared and the method that performed best was selected.

2. Flood error correction and multi-model composition method

2.1. Flood error correction

The discrepancy between the model-predicted discharge andthe actually observed past discharge is defined as error whichcan be used as information for correction. If this error signal hascorrelation, it can probably be used for improved prediction(Broerse, 2007). With a time-series model of the error signal, animproved discharge forecast can be made by adding the error termto the previous model results. In this study, the error term wasestimated using an AR model which can be expressed as:

et ¼Xp

k¼1

hiet�k þ n ð1Þ

where e is the flood forecasting error time series; p represents theorder of the autoregressive model; h1,. . ., hp are the parameters ofthe autoregressive model; and n is a pure white noise sequence hav-ing variance r2.

Order selection criteria were used to determine the appropriateorder. The Akaike information criterion (AIC) was used in thisstudy, which can be expressed as:

AIC ¼ n lnðMSEÞ þ 2k ð2Þ

where n is the number of observations; k is the number of theparameters; and MSE is mean squared error.

2.2. Multi-model combination method (MC)

A combined estimate of discharge, Q ct, of N rainfall-runoff mod-

els for the tth period of time is formally defined, in the presentpaper, as a function F(d) of the estimated discharges of the N

models for that time period, that can be expressed as(Shamseldin et al., 1997):

Qct¼ FðbQ 1;t ; bQ 2;t; � � � ; bQ j;t ; � � � bQ N;tÞ ð3Þ

where Qct is the combined discharge at time t; bQ j;t is the estimateddischarge of the jth model at time t; and N is the number of models.

One of multi-model combination methods is called theWeighted Average Method (WAM). The Weighted Average Method(WAM) for combining the estimated model outputs, in the case ofN rainfall-runoff models, can be expressed as (Shamseldin et al.,1997):

Qct¼XN

j¼1

ajbQ j;t þ nt ð4Þ

where aj is the weight assigned to the jth model; and nt is the com-bination error term.

In order to obtain the weights aj, an objective function can bedescribed as:

Min EðQct�Qobs;tÞ2 ¼Min Eða1

bQ 1;tþa2bQ 2;tþ�� þaN

bQ N;t�Q obs;tÞ2

¼Min E½a1ðe1;tþQ obs;tÞþa2ðe2;tþQ obs;tÞþ �� þaNðeN;tþQobs;tÞ�Qobs;t �2

¼Min Eða1e1;tþa2e2;tþ�� þaNeN;tÞ2

Subject to ðS:T:Þ : a1þa2þ��þaN ¼1

8>>>>><>>>>>:ð5Þ

where Qobs,t is the observed discharge at time t; and E represents theexpected value.

One simple way to achieve the maximization is the use of themethod of Lagrange multipliers. The Lagrange function can bedefined as:

Lða; b; c;d; kÞ ¼ E½ða1e1;t þ a2e2;t þ � � � þ aNeN;tÞ2�þ kða1 þ a2 þ � � � þ aN � 1Þ ð6Þ

Differentiate L in Eq. (6) with respect to aj and equating it tozero.

@Laj¼ 0 ð7Þ

Based on Eq. (7), we can obtain the following equation

@L@a1¼ 2a1Eðe1;te1;tÞ þ 2a2Eðe1;te2;tÞ þ � � � þ 2aNEðe1;teN;tÞ þ k ¼ 0

@L@a2¼ 2a1Eðe2;te1;tÞ þ 2a2Eðe2;te2;tÞ þ � � � þ 2aNEðe2;teN;tÞ þ k ¼ 0

..

.

@L@aN¼ 2a1EðeN;te1;tÞ þ 2a2EðeN;te2;tÞ þ � � � þ 2aNEðeN;teN;tÞ þ k ¼ 0

@L@k ¼ a1 þ a2 þ � � � þ aN � 1 ¼ 0

8>>>>>>>><>>>>>>>>:ð8Þ

The weights a1, a2, . . ., aN can be obtained by solving Eq. (8).

3. Real time flood error correction combined with the multi-model composition

In this study, both methods, namely real time flood error cor-rection (FEC) and multi-model combination (MC) method, wereused together in order to improve the accuracy of flood forecasting.In this section, we attempt to answer the questions: which methodshould be used first? How much is the accuracy improved, if theflood error correction and multi-model combination methods areused together?

In the following, three methods are discussed. For the firstmethod, the real-time FEC method was employed first for eachhydrologic model, and then based on the corrected forecasted flow,the multi-model combination method was used. For the second

L. Chen et al. / Journal of Hydrology 521 (2015) 157–169 159

method, the multi-model combination method was used first, andthen the real-time flood error correlation method was applied tothe combined flow. For the third method, the two methods weretaken into account together, parameters of those two methodswere calibrated together, and the optimization algorithm was usedto determine those parameters. We designate the first method asthe FEC–MC method, the second method as the MC–FEC methodand the third method as the global real-time combination method(GRCM). Details of these methods are described in the following.

3.1. FEC–MC method

In this method, the flood error correction method was used first.The AR method was used for predicting the error term over thedesired lead-time. The parameters of the AR model were estimatedby minimizing the sum of the squares of the differences betweenobserved and forecasted discharges. The updated error informationwas added to the predicted discharge, and the estimated floodforecasted discharge then was corrected.

In the second step, the updated discharge estimates of singlehydrological models were used for the multi-model combinationflood forecasting. The weights were determined using the methoddescribed above. Finally, the multi-model combination flood fore-casting model with error-correcting data was used to improvethe accuracy and reliability of the flood forecasting system.

Similar research was done by Shamseldin and O’Connor (1999).The first method was the further extension of the use of the multi-model combination concept to the case of hydrological real-timeforecasting, where an updating procedure was used to providefeedback information in the form of the most recently observedoutflow data in order to enhance the corresponding simulationmodel forecasts (Shamseldin and O’Connor, 1999).

3.2. MC–FEC method

In this method, the MC method was used first, and then the pre-dicted discharge of the combined model was derived. The errorcharacteristics of the combined discharge forecasts were investi-gated. The real-time error correction method was applied to thecombined discharge. The AR model described in Section 2.1 wasused to estimate the error value at time t of the combined dis-charge obtained by the MC method. The method for FEC is as thesame as for the FEC–MC method. The only difference is the input.For the first method, the input error is the one estimated by thesingle rainfall-runoff model. For the second method, the input erroris the one estimated from the combined multi-models.

3.3. Global real-time combination method (GRCM)

In this method, the flood error correction technique was usedfirst. The AR method was used for flood error correction. AssumeN hydrological models were used to simulate the rainfall-runoffrelation. The combination flood forecasting discharge can beobtained by:

Q ct¼XN

j¼1

ajbQ j;t ¼ a1

bQ 1;t þ a2bQ 2;t þ � � � þ aN

bQ N;t

¼ a1ðQobs;t þ e1;tÞ þ a2ðQ obs;t þ e2;tÞ þ � � � þ aNðQ obs;t þ eN;tÞ ð9Þ

where Qct is the combined discharge at time t; bQ j;t is the predicteddischarge of the jth model at time t; ej,t is the flood forecasting errorterm of the jth model at time t; Qobs,t is the observed discharge attime t; and aj (j = 1, 2,. . ., N) is the weight.

According to the theory of ordinary least squares, good floodforecasting model should minimize the sum of squares of the

differences between observed discharges and estimated dis-charges, and can be expressed as:

Min EðQ ct� Qobs;tÞ2 ð10Þ

S:T: a1 þ a2 þ � � � þ aN ¼ 1

Substituting Eq. (9) into Eq. (10), the result can be expressed as:

Min EðQ ct� Q obs;tÞ2 ¼Min E½ða1ðQ obs;t þ e1;tÞ þ a2ðQ obs;t þ e2;tÞ

þ � � � þ aNðQobs;t þ eN;tÞ � Qobs;tÞ2�¼ Min E½ða1e1;t þ a2e2;t þ � � � þ aNeN;tÞ2� ð11Þ

From Eq. (1), the flood error at time t can be obtained based onthe AR model. Substituting Eq. (1) into Eq. (11), the result can beexpressed as:

Min EðQ ct � Qobs;tÞ2 ¼Min E½ða1e1;t þ a2e2;t þ � � � þ aNeN;tÞ2�

¼Min E a1

Xp1

k¼1

h1;ke1;t�k þ a2

Xp2

k¼1

h2;ke2;t�k

"

þ � � � aj

Xpj

k¼1

hj;kej;t�k � � � þ aN

Xp2

k¼1

hN;keN;t�k

#ð12Þ

S:T: a1 þ a2 þ � � � þ aN ¼ 1

where pj and h1,j,. . .,hp,j represent the order and parameters of theautoregressive method in terms of the jth rainfall-runoff model,respectively; and ej;t�k is the forecasting error at time t�k corre-sponding to the jth rainfall-runoff model. Parameters a1, a2, . . ., aN

and hj,k can be obtained based on the optimization algorithm. In thisstudy, the progressive optimization algorithm was used to calibratethe model parameters.

Using Eq. (12), the parameters can be calculated. Knowing theseparameter a1; a2; . . . ; aN and hj,k, the corrected flow Q GRCMt by GRCMmodel at time t can be calculated by

QGRCMt¼XN

j¼1

ajbQ j;t �

Xpj

k¼1

hj;kej;t�k

!ð13Þ

where pj and h1,j,. . ., hp,j represent the order and parameters of theautoregressive method in terms of the jth rainfall-runoff model,respectively; and ej;t�k is the forecasting error at time t�k corre-sponding to the jth rainfall-runoff model.

4. Performance measures

The performance of the hydrological forecasting models wasassessed in accordance with the criteria specified by the Ministryof Water Resources of China (MWR, 2006). Three criteria wereused. They are the Nash–Sutcliffe efficiency R2, qualified rate (a),and the root-mean-square error (RMSE).

4.1. Nash–Sutcliffe efficiency R2

For the long time series data, the Nash–Sutcliffe efficiency R2,was used and defined as:

R2 ¼ 1�Pm

t¼1ðQ t � bQ tÞ2Pm

t¼1ðQ t � QÞ2

24 35 ð14Þ

where m represents total number of observations; Qt and bQ t repre-sent the observed and predicted discharges at time t, respectively;and Q means the mean value of Qt.

Fig. 1. Sketch of the TGR intervening basin.

Table 1Description of the gauging stations on the mainstream of Jinsha River.

Mainstream Gauging station Catchment area (km2) Length of the data

Calibration Validation

Jinsha River Sanduizi 176,765 2004–2009 2010–2013Longjie 187,047 2004–2009 2010–2013Wudongde 195,046 2004–2009 2010–2013Huatan 213,909 2004–2009 2010–2013Xiluodu 224,824 2004–2009 2010–2012Xiangjiaba 226,739 2006–2009 2010–2012

Table 2Description of the gauging stations on the tributaries of Jinsha River.

Tributaries Gauging station Catchment area (km2) Number of flood events

Calibration Validation

Heishui Ningnan 2925 54 29Xixi Zhaojue 648 42 16Meigu Meigu 1638 31 17Tuanjie Damaocun 443 31 12Dawenxi Xinhua 402 28 10Xining Oujiacun 971 26 13Zhongdu Longshancun 369.2 19 13


Fig. 2. Sketch of the Jinsha River basin.


4.2. Qualified rate

For flood events, the Chinese flood forecasting guidelines sug-gest using the qualified rate (a) to estimate the flood forecastingperformances. The qualified rate of both the magnitude and theoccurrence time of flood peak were calculated.

A forecast peak discharge is termed ‘qualified’, when the differ-ence between the predicted and the recorded (observed) value iswithin ±20% of the recorded (observed) value (Li et al., 2010).The qualified rate of flood magnitude aM can be calculated by

aM ¼1m

Xm

i¼1

ljbQ p � Qpj

Qp6 0:2

!ð15aÞ

where l(�) is the indicator function; bQ p is the predicted magnitudeof flood peak; Qp is the recorded or observed magnitude of floodpeak; and m is the number of flood events.

A forecasting occurrence time of flood peak is termed ‘qualified’,when the difference between the predicted and recorded(observed) occurrence times of flood peak is within the allowableerror, which is equal to 30% of the observed occurrence time offlood peak. The qualified rate of flood occurrence time aT can becalculated by

aT ¼1m

Xm

i¼1

ljbT � Tj

T6 0:3

!ð15bÞ

where T and bT are the observed and predicted occurrence times offlood peak, respectively, which are equal to the time that flood peakoccurs minus the time that the flood forecasting is made at.

The mean value of the two qualified rate �a was calculated as:

�a ¼ ðaM þ aTÞ=2 ð15cÞ

4.3. Root-mean-square error

The root-mean-square error (RMSE) between the observed andpredicted flood value was also used as a performance criterion inthis study. The root-mean-square error can be defined as:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPmt¼1ðQ t � bQ tÞ

2

m

sð16Þ

5. Case study

This study used real-time observed and predicted dischargesfrom TGR and Jinsha River to evaluate the applicability and

efficiency of the real-time flood error correction combined withthe multi-model composition method. Four rainfall-runoff models,Xinanjiang model, Tank model, Artificial Neural Network (ANN)model, and antecedent precipitation index (API) based model, wereused to obtain the predicted discharge in this study. The proposedreal-time error correction combined with multi-model composi-tion method was continuously operated in predicting the dischargeof TGR and Jinsha River to improve the accuracy of predicted flow.

5.1. Data

5.1.1. Data of Three Gorges Reservoir (TGR)The Upper Reach of the Yangtze River was selected for applica-

tion of the proposed method. For the Yangtze River, floods arecaused by unusually high precipitation between June and August.Summer is the main flood season due to the heavy monsoon rain-fall (Chen et al., 2013). Floods in the middle and lower reaches ofthe Yangtze River mainly stem from the upper region of theYichang Station, which is also the control station for the ThreeGorges Reservoir. The inflow of TGR consists of three components,the main upstream inflow, the tributary inflow from the Wu River,and the rainfall-runoff from the TGR intervening basin as shown inFig. 1 (Li et al., 2010). The intervening basin has a catchment area of55,907 km2, about 5.6% of the upstream Yangtze River basin (Liet al., 2010). Over the whole intervening basin, there are 40 rainga-uging stations and two hydrological stations (Cuntan and Wulong),which control the upstream inflow and tributary inflow, respec-tively. The data of the Yichang gauging station were also used.The data is available every 4 h. In other words, the forecast leadtime is 6-h. We used 3 years (2004–2006) of data for calibratingthe parameters of the model, and one year (2007) for modelvalidation.

5.1.2. Data of the Jinsha RiverThe Jinsha River, which is recognized as part of the Yangtze

River and shown in Fig. 1, was selected as a case study. The dataof six gauging stations in the mainstream and seven in the tributar-ies were used. The data is available every 1 h. In other words, theforecast lead time is 1 h. For the mainstream, continuous simula-tion with the long time series data was used. Table 1 describesthe characteristics of the gauging stations in the mainstream. Forthe tributaries, since it is difficult to collect the continuous data,the event data was applied to calibrate and verify model parame-ters. The same method was employed by Giang and Phuong(2010) and has been frequently used in China (MWR, 2006). Gen-erally, there are two criteria for selecting the flood events. First,the flood event with high flood peak and large flood volume is usu-ally considered; and second we usually select the flood events, inwhich the flood volume has high positive correlation with rainfall.Table 2 describes the characteristics of gauging stations in the trib-utaries of the Jinsha River. The sketch of the mainstream and trib-utaries of the Jinsha River basin can be seen in Fig. 2.

5.2. Rainfall-runoff simulation

5.2.1. Simulation results of the TGRThe three chosen rainfall-runoff models (Xinanjiang, Tank and

ANN) were applied to the data of the Three Gorges Reservoir.The Xinanjiang model was developed by a Chinese named Zhao

et al. (1980) for forecasting flows in the Xinanjiang reservoir,China. The model has been widely applied for flood forecasting inlarge basins all over the world, especially in China. Until now, thismodel is the most popular rainfall-runoff hydrological model inChina for streamflow forecasting in humid and semi-humid areas.Since the TGR is located in the south of China, which consists ofhumid and semi-humid regions, the Xinanjiang model was used.

Fig. 3. Flow predicted by single hydrologic models.


Its main feature is the concept of runoff formation on the repletionof storage, which denotes that runoff is not produced until the soilmoisture content of the aeration zone reaches field capacity (Zhao,1992). The Xinanjiang model includes two components, namely,

runoff generating and runoff routing. It has 17 parameters thatinclude seven runoff generating component parameters and 10runoff routing parameters. These parameters are abstract concep-tual representations of non-measurable watershed characteristics

Fig. 3 (continued)

Table 3Comparisons of original flood forecasting results and corrected flood forecastingresults calculated by FEC method using three performance indexes for the calibrationperiod of TGR.

Model Types Qualified rate �a (%) R2 RMSE (m3/s)

Xinanjiang Original results 94 0.94 2303Corrected results 100 1.00 585

Tank Original results 96 0.96 1979Corrected results 100 1.00 533

ANN Original results 73 0.97 1770Corrected results 99 1.00 657

Table 4Comparisons of original flood forecasting results and corrected flood forecastingresults calculated by FEC method using three performance indexes for the validationperiod of TGR.

Model Types Qualified rate �a (%) R2 RMSE (m3/s)

Xinanjiang Original results 91 0.95 1817Corrected results 100 1.00 378

Tank Original results 92 0.96 1739Corrected results 99 1.00 364

ANN Original results 68 0.96 1763Corrected results 99 1.00 511


that have to be calibrated by an optimization method. Detailedinformation about the meaning and range of parameters can befound in Xu et al. (2013).

Tank model is a synthetic flow model, which was developed andintroduced in 1956 by Sugawara, and has been widely used inmany Asian countries, such as Japan and China, to forecast floodsand manage water resources (Ngoc et al., 2013). The mainadvantage of the Tank model is that its structures are very simple,

usually composed of several vertical tanks. The Tank model used inthis study has a simple structure with 4 tanks, a surface tank (A),an intermediate tank (B), a sub-base tank (C), and a base tank(D), laid vertically in a series. Each tank has a vertical outlet atthe bottom (except tank D) and one horizontal outlet at the side(except tank A, which typically has 2 horizontal outlets).

Artificial Neural Networks (ANNs), a black box model, haveproved to be an efficient alternative to traditional methods forhydrological modeling (Chen et al., 2013). In this study, multi-layerfeed forward models were used. A representative ANN model forrainfall-runoff model can be defined as:

bQ t ¼ f ðQ t�l1 ; Rt�l2 ; Xt�l3 Þ ð17Þ

where bQ t stands for the predicted flow at time instance t; Qt�l1 isthe antecedent flow (up to t�l1 time steps); Rt�l2 is the antecedentrainfall, and Xt�l3 represents the observed runoff at a neighboringsub-basin in this study.

The predicted results of these models in both calibration andvalidation periods are shown in Fig. 3. The flood forecasting errorsare also shown in Fig. 3. It can be seen from the figures that thosethree models basically performed well. However, there were someflood errors. The flood error was large, when peak flow occurred.The flood error of Xianjiang model had a more significant variationthan any other model. The flood error of the Tank model tended tobe negative. The error of ANN model was around zero.

In addition to the visual comparison of the forecasted andobserved flows, a comparison was also carried out by means of cal-culating the performance indices. The root-mean-square error(RMSE) between the observed and predicted flood values, qualifiedrate (�a) and Nash–Sutcliffe efficiency (R2) were used to estimatethe performance of these rainfall-runoff models. The predictedresults of the three models can be seen in Tables 3 and 4 for

Table 5Flood forecasting performance estimates based on the qualified rate for the gauging station on the tributaries of Jinsha River.

Gauging station Periods Models Qualified rate (%)

Flood peak Flood peak occurrence time Mean value

Ningnan Calibration API 63.0 70.4 66.7Tank 50.00 84.62 67.31Xinanjiang 65.38 76.92 71.15

Validation API 61.54 84.62 73.08Tank 53.80 69.20 61.50Xinanjiang 61.50 84.60 73.05

Zhaojue Calibration API 61.9 71.4 66.65Tank 57.1 78.6 67.9Xinanjiang 52.4 76.2 64.3

Validation API 62.5 93.8 78.15Tank 50 93.8 71.9Xinanjiang 62.5 93.8 78.15

Meigu Calibration API 62.5 87.5 75Tank 66.7 87.5 71.1Xinanjiang 48.4 87.1 67.7


Oujiacun Calibration API 63.0 70.4 66.7Tank 50 84.6 67.3Xinanjiang 65.4 76.9 71.15


Longshacun Calibration API 63.2 68.42 65.8Tank 42.11 73.68 65.6Xinanjiang 52.63 63.15 57.89


Damaocun Calibration API 61.29 83.87 72.58Tank 60.60 66.67 61.54Xinanjiang 59.4 87.5 73.45

Validation API 58.33 75 66.67Tank 63.64 61.54 76.92Xinanjiang 69.2 84.6 76.9

Xinhua Calibration API 64 89 76.5Tank 57 64 60.5Xinanjiang 46 54 50

Validation API 50 90 70Tank 70 90 80Xinanjiang 60 90 75


calibration and validation period, respectively. It can be seen thatfor qualified rate, the Tank model performs the best, and forNash–Sutcliffe efficiency R2 and RMSE, the ANN model generallyperforms better.

This analysis shows that there is a great need to carry out thereal-time error correction in order to reduce the error term inthe future, especially for peak flows. Considering different advanta-ges of those three models, it is desirable to employ multi-modelcomposition method in the flood forecasting system.

5.2.2. Simulation results of the Jinsha RiverFor the Jinsha River, besides the Xinanjiang and Tank models, the

antecedent precipitation index (API) model was also used. Koehlerand Linsley (1951) defined the antecedent precipitation index. Ante-cedent precipitation is precipitation falling before, but influencingthe runoff yields of, a given rainfall event (Ali et al., 2010). Anteced-ent precipitation index (API) is a measure of the soil moisturesbefore a flood event. API is often used for the estimation of runoffyields from rainfall events by describing the relationship betweenrainfall and runoff for a given API value. By employing the API forevent-based rainfall, a number of investigators (Sittner et al.,1969; Rose, 1998; Descroix et al., 2002) simulated runoff yieldsand streamflow. The advantages of API model is that it is often used

for the estimation of runoff yields from rainfall events on thosewatersheds whose auxiliary data are limited, or not available (Aliet al., 2010). Considering that the data from the tributaries of JinshaRiver is very limited and this model has been currently used in theJinsha River, the API model was employed in this study.

In order to obtain the flow in the mainstream, the flow of trib-utaries was first predicted. For the tributaries, since it is difficult tocollect the continuous data, the event data were applied to cali-brate and verify the model parameters. The qualified rate was usedto estimate the performance of the three models, and the resultsare shown in Table 5. Then, the discharge in the mainstream waspredicted. The Nash–Sutcliffe efficiency R2 was used to estimatethe performance of the three models, and the results are shownin Table 6. It is seen from Table 5 that the qualified rate is not highin the tributaries. On the contrary, in Table 6, the predicted resultsof the mainstream are good. This is because the flow in the main-stream mainly stems from the main upstream inflow.

5.3. Improvement of flood forecasting accuracy

5.3.1. Results of FEC methodThe AR model was used for error correction in TGR. The param-

eters of AR model can be calibrated according to the least squares

Table 6Flood forecasting performance estimates based on Nash–Sutcliffe efficiency R2 for thegauging station on the mainstream of Jinsha River.

Gauging station Periods Models R2

Sanduizi Calibration API 0.9952Tank 0.984Xinanjiang 0.9804

Validation API 0.9979Tank 0.9896Xinanjiang 0.990

Longjie Calibration API 0.9987Tank 0.993Xinanjiang 0.9857


Wudongde Calibration API 0.9977Tank 0.967Xinanjiang 0.991


Huatan Calibration API 0.9974Tank 0.875Xinanjiang 0.946


Xiluodu Calibration API 0.9887Tank 0.823Xinanjiang 0.8202


Xiangjiaba Calibration API 0.9954Tank 0.978Xinanjiang 0.9756


Fig. 4. The AIC values for different orders of AR models.


method. The model order can be selected with an Akaike informa-tion criterion (AIC). Three models, namely Xinanjiang, Tank, andArtificial Neural Network models, were used for flood forecastingin TGR. The best order for each model type was separately selectedby the program. The order ranges from 0 to 30 were used to estab-lish the AR model. The calculated results are shown in Fig. 4. Theorder with the minimum AIC value was selected for each AR model.The AR models for each hydrological model are given as follows.

For Xianjiang model, the AR (2) model was selected which canbe expressed as:

et ¼ 1:4575et�1 � 0:5271et�2 ð18Þ

For the Tank model, the AR (2) model was selected which can beexpressed as:

et ¼ 1:3615et�1 � 0:4281et�2 ð19Þ

For the ANN model, the AR (7) model was selected which can beexpressed as:

et ¼ 1:1392et�1 � 0:4481et�2 þ 0:3084et�3 � 0:1567et�4

þ 0:0681et�5 � 0:0588et�6 þ 0:0831et�7 ð20Þ

The established AR models were used for flood error correctionand the corrected results are also given in Tables 3 and 4 for cali-bration and validation period, respectively, which indicate thatthe corrected result is better than the original one for each perfor-mance index.

The data from the tributary in the Jinsha River was also used tofurther test the FEC method. Three models, namely Xinanjiang,

Tank and API models, were used for rainfall-runoff simulation.The corrected results of these three models at the gauging stationsNingnan, Zhaojue and Meigu are given in Table 7. It can be seenfrom Table 7 that the performance of FEC method is better thaneach single hydrological model.

5.3.2. Results of MC methodThe multi-model composition forecasting model was devel-

oped, based on the concept described in Section 2.2. The calculatedweights for the Xinanjiang, Tank and ANN models were �0.356,0.836 and 0.52, respectively. It shows the weight is negative. Asimple example is given to illustrate it. Assuming that there aretwo hydrological models, in one of which all flood forecastingerrors are equal to 1, and in the other all flood forecasting errorsare equal to �1. The multi-model composition method was usedto minimize the flood forecasting error. For this special case, whenboth of the weights equal 0.5, the error reaches the minimum andequals 0. On the contrary, assuming that there are two hydrologicalmodels and the flood forecasting errors of the two hydrologicalmodels are the same or nearly the same and equal 1. The multi-model composition method was used to minimize the flood fore-casting error. If we want the error term to be 0, the weights mustbe equal to 0.5 and �0.5, respectively. Therefore, we concluded

Table 8Dependence analysis of the flood forecasting error derived by Xinanjiang, ANN andTank models for TGR.

Models Xinanjiang Tank ANN

Xinanjiang 1.00 0.96 �0.04Tank 0.96 1.00 �0.07ANN �0.04 �0.07 1.00

Table 9Results of evaluation of multi-model combined flood forecasting system for TGR.

Models Periods Qualifiedrate �a (%)

R2 RMSE(m3/s)

Combined results Calibration 96 0.98 1282Validation 91 0.97 1365

The best results for singerainfall-runoff model

Calibration 96 0.97 1770Validation 92 0.96 1739

Table 10Results of real-time error correction combined with multi-model combination modelsfor TGR.

Models Periods Qualified rate �a (%) R2 RMSE (m3/s)

FEC–MC Calibration 99.7 0.997 519Validation 99.7 0.998 357

MC–FEC Calibration 99.9 0.997 519Validation 99.7 0.998 407

GRCM Calibration 99.9 0.999 152Validation 99.9 0.999 134

Table 7Results of FEC and MC methods for the Ningnan, Zhaojue and Meigu guaging stations on the tributaries of Jinsha River.

Gauging station Periods Model Qualified rate a (%)


Ningnan Calibration API-FEC 85.15 69.45 77.3Tank-FEC 90.75 76.85 83.8Xinanjiang-FEC 89.8 72.2 81MC 66.7 87 76.9

Validation API-FEC 92.6 72.25 82.4Tank-FEC 94.45 75.95 85.2Xinanjiang-FEC 92.6 77.8 85.2MC 74.1 88.9 81.5

Zhaojue Calibration API-FEC 61.9 90.5 76.2Tank-FEC 90.5 88.1 89.3Xinanjiang-FEC 81 92.9 87.0MC 64.3 81 72.7

Validation API-FEC 75 100 87.5Tank-FEC 81.2 68.8 75Xinanjiang-FEC 81.2 87.5 84.4MC 68.8 100 84.4

Meigu Calibration API-FEC 95.2 79 87.1Tank-FEC 96.8 88.7 92.8Xinanjiang-FEC 90.3 90.35 90.3MC 58.1 90.3 74.2

Validation API-FEC 88.2 53.0 70.6Tank-FEC 100 73.5 86.8Xinanjiang-FEC 70.6 82.4 76.5MC 70.6 88.2 79.4


that if the correlation between the errors derived by differenthydrological models is positive, the weights may be negative. Posi-tive correlation means that if the flood forecasting error in one ofthe hydrological model is large, there is a strong possibility thatthe error in the other hydrological model is also large, and viceversa. When this situation occurs, the weights will tend to be neg-ative. In the following, we calculated the pair-wise dependence of

the flood error calculated by different hydrological models in theThree Gorges Reservoir, and the results are shown in Table 8. Itcan be seen that high positive correlation occurs between the floodforecasting errors of the Xinanjiang and Tank models. The correla-tion coefficient is 0.96. That is why the weight representing theXinanjiang model is negative.

Using Eq. (4), the combined flood forecasting results of the TGRwere obtained. The performances were evaluated using RMSE,qualified rate �a and the Nash–Sutcliffe efficiency R2. The resultsof evaluation are given in Table 9. The best results of a single rain-fall-runoff model are also given in Table 9. Results of comparisonindicate that the combined results are generally better than thepredicted results obtained by a single hydrological model.

In order to further test the MC method, the data from the tribu-tary of the Jinsha River was used. Three models, namely, Xinanjiang,Tank, and API models, were employed for rainfall-runoff simulation.Results of the MC method at the gauging stations Ningnan, Zhaojueand Meigu are given in Table 7. It can be seen from Table 7 that theperformance of the MC method is generally better than any singlehydrological model.

Shamseldin et al. (1997) illustrate that the main disadvantage ofthe MC method is that it may suffer from the problem of multicollin-earity which could reduce the considerable advantages of combin-ing different model outputs. The multicollinearity is a statisticalphenomenon where two or more predictor variables in a multipleregression model are highly correlated. According to Table 8, weknow that high positive correlation occurs between the Xinanjiangand Tanks models. Considering that the Xinanjiang and Tank modelsperform well in predicting the inflow of TGR and are currently used,these two models were employed in this paper. Results indicate thecomposition method of these three models is better than the singlehydrological model. In practical use, it is better to avoid the occur-rence of multicollinearity when selecting hydrological models.

5.3.3. Results of real time error correction combined multi-modelcomposition flood forecasting system

Both of the methods, namely real time flood error correctionand multi-model combination method, were used together inorder to improve the accuracy of flood forecasting. Three combined

0

10000

20000

30000

40000

50000

60000

2007-1-1 2007-2-1 2007-3-1 2007-4-1 2007-5-1 2007-6-1 2007-7-1 2007-8-1 2007-9-1 2007-10-1 2007-11-1 2007-12-1

Flo

w (

m 3

/s)

Date (Year-Month-Day)

Observed

Xinanjiang

GRCM

Fig. 5. Comparison of observed, calculated and corrected flows in 2007 (the Xinanjiang model was used to predicted the flow, and the GRCM method was used to improve theforecasting results).

Table 11Comparison of the results calculated by FEC–MC, MC–FEC and GRCM methods for the tributaries of Jinsha River.

Gauging stations Periods Models Qualified rate a (%)


Ningnan Calibration FEC–MC 88.9 75.95 82.425MC–FEC 88.9 75.95 82.425GRCM 100 100 100

Validation FEC–MC 98.15 83.35 90.75MC–FEC 98.15 85.2 91.675GRCM 100 100 100

Zhaojue Calibration FEC–MC 83.3 95.2 89.25MC–FEC 90.5 90.5 90.5GRCM 100 100 100

Validation FEC–MC 87.5 100 93.75MC–FEC 81.2 93.8 87.5GRCM 100 100 100

Meigu Calibration FEC–MC 96.8 87.1 91.95MC–FEC 96.8 87.1 91.95GRCM 100 100 100

Validation FEC–MC 88.2 82.35 85.275MC–FEC 100 79.4 89.7GRCM 100 100 100

Oujiacun Calibration FEC–MC 76.7 70 73.35MC–FEC 76.7 70 73.35GRCM 100 100 100


Longshacun Calibration FEC–MC 73.7 81.55 77.625MC–FEC 65.75 76.3 71.025GRCM 100 100 100


Damaocun Calibration FEC–MC 80.65 67.7 74.175MC–FEC 79 67.7 73.35GRCM 100 100 100


Xinhua Calibration FEC–MC 75 92.9 83.95MC–FEC 71.45 92.9 82.175GRCM 100 100 100

Validation FEC–MC 65 90 77.5MC–FEC 55 95 75GRCM 100 100 100


methods were considered. Both the TGR and Jinsha River wereselected as case studies.

First, the FEC–MC method was used both for TGR and JinshaRiver, in which the error correction method was employed first,

and then the multi-model composition method was applied forthe updating of predicted discharge. Second, the FEC–MC methodwas employed, in which the multi-model combination methodwas first used, and then the real-time error correction method

Table 12Comparision of the results calculated by FEC–MC, MC–FEC and GRCM methods for themainstream of Jinsha River.

Gauging stations Periods Models R2

Sanduizi FEC–MC 0.998Calibration MC–FEC 0.9968

GRCM 0.9999FEC–MC 0.9988

Validation MC–FEC 0.9979GRCM 0.9999

Longjie FEC–MC 0.999Calibration MC–FEC 0.9989

GRCM 0.9999FEC–MC 0.9992


Wudongde FEC–MC 0.9991Calibration MC–FEC 0.9991

GRCM 0.9999FEC–MC 0.9989


Huatan FEC–MC 0.9989Calibration MC–FEC 0.9988

GRCM 0.9999FEC–MC 0.9994


Xiluodu FEC–MC 0.9942Calibration MC–FEC 0.9942

GRCM 0.9999FEC–MC 0.9999


Xiangjiaba FEC–MC 0.9991Calibration MC–FEC 0.9998

GRCM 0.9999FEC–MC 0.9999



was applied to the combined predicted discharge data. Third, theglobal real-time combination model (GRCM) was used where theAR (2) model was used for real-time error correction. The objectivefunction was given by Eq. (12). Parameters of the global modelwere estimated using the Particle Swarm Optimization (SWO). Per-formances of those three real-time combination methods wereevaluated based on the indices listed in Section 4.

The results of the TGR are given in Table 10. It is seen that thethree combined methods perform better than the single FEC andMC methods. Among the three combined methods, the globalreal-time combination method performs extremely well and betterthan the other two methods. The performances of the other twocombined methods are nearly the same. The observed, predictedand corrected inflow of TGR in 2007 is shown in Fig. 5. Take theannual maximum flood for example. The observed annual maxi-mum (AM) flood peak occurring in 7-30-2007 is 52,500 m3/s. Theflood peaks calculated by the Xinanjiang model and corrected byGRCM are 47,889 and 52,452 m3/s, respectively. For the correctedone, its only 48 m3/s deviation from the observed flow.

The three proposed methods, namely FEC–MC, MC–FEC andGRCM were used to correct the flood forecasting results for boththe tributaries and mainstream of the Jinsha River. The perfor-mances of those three real-time combination methods were evalu-ated, based on the qualified rate and the Nash–Sutcliffe efficiencyR2 for tributaries and mainstream, respectively. The evaluationresults are given in Tables 11 and 12, respectively. It is seen thatfor the gauging stations both on the tributaries and mainstream,the three combined methods perform better than the single API,

Tank or Xinanjiang model, among which the global real-time com-bination method (GRCM) performs extremely well and better thanthe other two methods. In addition, for the tributaries, 100% doesnot mean the corrected values are equal to the observed ones. Itmeans that the difference between the predicted and recorded val-ues is within the allowable error, whose definition can be found inSection 4. The proposed method performs extremely well forimproving the flood forecasting accuracy. The proposed methodhas been installed in the flood forecasting system of the JinshaRiver and will predict the discharge of the whole Jinsha River inJune next year.

6. Conclusions

This paper discusses FEC and MC methods, and proposes themethods combining FEC with MC for improving the accuracy offlood forecasting. The Three Gorges Reservoir and Jinsha Riverare selected as case studies. The main conclusions are summarizedas follows.

(1) The FEC model was used to improve the accuracy of floodforecasting. The AR method was used for error correction.The order of AR method can be selected using Akaike infor-mation criterion. Results show that the order used in ARmodel is usually less than 10. The corrected results of bothTGR and Jinsha River indicate that the performance of FECmethod is better than each single hydrological model.

(2) MC method was used to improve the accuracy of flood fore-casting. The Weighted Average Method was used for com-bining the estimated model. Results show that the MCmethod is generally better than any single hydrologicalmodel. The main disadvantages of MC method is that itmay suffer from the problem of multicollinearity, which isa statistical phenomenon where two or more variables in amultiple regression model are highly correlated. In practicaluse, it is better to avoid the occurrence of multicollinearitywhen selecting hydrological models.

(3) Using either the error correction or the multi-model compo-sition method can improve the accuracy of the flood fore-casting model. Therefore, it is necessary to use these twomethods to improve the reliability and accuracy of the pre-dicted discharge. Generally, the flood error correctionmethod performs better than the multi-model compositionmethod. Thus, if one chooses one of these two methods toenhance the flood forecasting accuracy then it is better toselect the real-time error correction method.

(4) The paper proposes three methods combining flood errorcorrection with multi-model composition, namely FEC–MCmethod, MC–FEC method and global real-time combinationmethod (GRCM) to improve the accuracy of flood forecast-ing. Results show that the performances of FEC–MC andMC–FEC methods are nearly the same. The calculation pro-cess of MC–FEC method is easier than that of FEC–MC. Theglobal method gives the best performance among the threemethods. Therefore, we can finally choose the global methodfor establishing the flood forecasting system.

Acknowledgments

The project was financially supported by the National NaturalScience Foundation of China (NSFC Grants 51309104 and51239004), and Wuha Planning Project of Science and Technology(2014060101010064).


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http://dx.doi.org/10.1029/2010WR009137



http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000932


















http://link.springer.com/chapter/10.1007/978-3-642-34289-9_44

http://link.springer.com/chapter/10.1007/978-3-642-34289-9_44

http://dx.doi.org/10.1029/2006WR005756

http://dx.doi.org/10.1029/2006WR005756





























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