ARTIFICIAL NEURAL NETWORK MODELS FOR ESTIMATION OF SEDIMENT LOAD IN AN ALLUVIAL RIVER IN INDIA

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1 JOURNAL OF ENVIRONMENTAL HYDROLOGY The Electroic Joural of the Iteratioal Associatio for Evirometal Hydrology O the World Wide Web at VOLUME ARTIFICIAL NEURAL NETWORK MODELS FOR ESTIMATION OF SEDIMENT LOAD IN AN ALLUVIAL RIVER IN INDIA Archaa Sarkar Rakesh Kumar Sajay K. Jai R.D. Sigh Natioal Istitute of Hydrology Roorkee, Idia. The magitude of sedimet trasport by rivers is a major cocer for water resources plaig ad maagemet. The methods available for sedimet estimatio are largely empirical, with sedimet ratig curves beig the most widely used i Idia. I this study, sedimet ratig curve ad artificial eural etwork (ANN) techiques have bee applied to model the sedimetdischarge relatioship of a alluvial river. Daily data of sedimet load ad discharge of the Kosi River i Idia have bee used. A compariso has bee made betwee the results obtaied usig ANNs ad sedimet ratig curves. The sedimet load estimatios i the river obtaied by ANNs have bee foud to be sigificatly superior to the correspodig classical sedimet ratig curve oes. Also, a ANN approach ca give iformatio about the structure of evets (e.g., hysteresis i the sedimet-discharge relatioship) which is ot possible to achieve with sedimet ratig curves. Joural of Evirometal Hydrology

2 INTRODUCTION The sedimet outflow from the watershed is iduced by processes of detachmet, trasportatio ad depositio of soil materials by raifall ad ruoff. The assessmet of the volume of sedimets beig trasported by a river is required i a wide spectrum of problems such as the desig of reservoirs ad dams; trasport of sedimet ad pollutats i rivers, lakes ad estuaries; desig of stable chaels, dams ad debris basis; udertakig cleaup followig floods; determiatio of the effects of watershed maagemet; ad evirometal impact assessmet. Fie sedimet has log bee idetified as a importat factor for the trasport of utriets ad cotamiats such as heavy metals ad micro-orgaics. Suspeded sedimet is importat i its ow right, sice its presece or absece exerts a importat cotrol o geomorphological ad biological processes i rivers ad estuaries (Morris ad Fa, 997). Sedimet ratig curves are widely used to estimate the sedimet load beig trasported by a river. Sedimet load is defied as the sedimet flow i a river measurable at a poit of referece durig a specified period of time. A sedimet ratig curve is a relatio betwee the sedimet ad river discharges. Such a relatioship is usually established by a regressio aalysis, ad the curves are geerally expressed i the form of a power equatio. Ratig curves are developed o the premise that a stable relatioship betwee cocetratio ad discharge ca be developed which, although exhibitig scatter, will allow the mea sedimet yield to be determied o the basis of the discharge history. A problem iheret i the ratig curve techique is the high degree of scatter, which may be reduced but ot elimiated. Cocetratio does ot ecessarily icrease as a fuctio of discharge. Mathematically, a ratig curve may be costructed by log-trasformig all data ad usig a liear least squares regressio to determie the lie of best fit. The log-log relatioship betwee load ad discharge is of the form (Morris ad Fa, 997) S = aq b () ad the log-trasformed form will plot as a straight lie o log-log paper log S =log a + b log (Q) (2) where, S = sedimet load, Q = discharge, log a ad b are regressio costats. A regressio equatio will miimize the sum of squared deviatios from the log-trasformed data, which is ot the same as miimizig the sum of squared deviatios from the origial dataset ad which itroduces a bias that uderestimates the load at ay discharge. Ferguso (986) reports that this bias may result i uderestimatio by as much as 50 percet. Ferguso ad others have suggested bias correctio factors, but their appropriateess is ucertai (Wallig ad Webb, 988). The ratig curve techique is ot adequate i view of the complexity of the problem. O the other had, the applicatio of physics-based distributed process computer simulatio offers aother possible method of sedimet predictio. But the applicatio of these complex software programs is ofte problematic, due to the use of idealized sedimetatio compoets, or the eed for massive amouts of detailed spatial ad temporal data which are ot available. Simpler approaches are therefore required i the form of coceptual solutios or black-box modellig techiques. Neurocomputig provides oe possible aswer to the problematic task of sedimet trasfer predictio. Recetly, artificial eural etworks (ANN) have emerged as powerful tools to model oliear processes. The artificial eural etworks operate i a maer Joural of Evirometal Hydrology 2

3 aalogous to that of biological euro systems ad offer several advatages over covetioal computig methods. A ANN is a computig system made up of a highly itercoected set of simple iformatio processig elemets, aalogous to a euro, called uits. The euro collects iputs from both a sigle ad multiple sources ad produces output i accordace with a predetermied oliear fuctio. A ANN model is created by itercoectio of may of the euros i a kow cofiguratio. The primary elemets characterizig the eural etwork are the distributed represetatio of iformatio, local operatios ad oliear processig. Figure shows the geeral structure of a three layer back propagatio ANN. The theory of ANN has bee described i may textbooks such as Hayki (994). The mai priciple of eural computig is the decompositio of the iput-output relatioship ito series of liearly separable steps usig hidde layers (Hayki, 994). Geerally there are four distict steps i developig a ANN-based solutio. The first step is the data trasformatio or scalig. The secod step is the etwork architecture defiitio, where the umber of hidde layers, the umber of euros i each layer, ad the coectivity betwee the euros are set. I the third step, a learig algorithm is used to trai the etwork to respod correctly to a give set of iputs. Lastly, comes the validatio step i which the performace of the traied ANN model is tested through some selected statistical criteria. There are umerous studies related to the applicatio of ANNs to various problems frequetly ecoutered i water resources (ASCE Task Committee, 2000). But the applicatio of the ANN approach for modellig sedimet-discharge process is very recet, ad has already produced very ecouragig results. I a research project by Rosebaum (2000), ANN techique has bee used to predict sedimet distributio i Swedish harbors. Jai (200) used the ANN approach to establish a itegrated stage-discharge-sedimet cocetratio relatio for two sites o the Mississippi River. Based o the compariso of results for two gaugig sites, he has show that the ANN results Figure. Structure of a multi-layer Feed Forward Artificial Neural Network Model. Joural of Evirometal Hydrology 3

4 are much closer to the observed values tha the covetioal techique. I a study by Nagy et al. (2002), a ANN is used to estimate the atural sedimet discharge i rivers i terms of sedimet cocetratio. They have addressed the importace of choosig a appropriate eural etwork structure ad providig field data to that etwork for the traiig purpose ad foud that the ANN approach gives better results compared to several commoly used formulas of sedimet discharge. Yitia ad Gu (2003) applied the ANN techique to modellig daily discharge ad aual sedimet discharges i the Jigjiag reach of the Yagtze River ad Dogtig Lake, Chia. The authors demostrated that the ANN techique is a powerful tool for real-time predictio of flow ad sedimet trasport i a complex etwork of rivers. Agarwal et al. (2004) developed daily, weekly, te-daily ad mothly sedimet yield ANN models for the Vamsadhara River basi i Idia. Raghuwashi et al. (2006) also developed ANN models to predict ruoff ad sedimet yield o a daily ad weekly basis for a small agricultural watershed i the upper Siwae River i Idia. The authors foud the performace of ANN models superior to regressio models. Cigizoglu ad Alp (2007) used the geeralized regressio eural etwork techique for river suspeded sedimet estimatio i the Juiata Catchmet i the USA. The authors foud ANN estimatios sigificatly superior to covetioal method results. I the preset study, the ANN techique alog with the covetioal sedimet ratig curve techique has bee applied to model the sedimet-discharge relatioship of the Kosi River i Idia usig daily data of sedimet load ad discharge at the Birpur gaugig site. PERFORMANCE EVALUATION CRITERIA The statistical ad hydrological evaluatio criteria used i the preset study are root mea square error (RMSE), correlatio coefficiet (r), coefficiet of efficiecy (CE) or coefficiet of determiatio (r 2 ) ad volumetric error (EV). Root Mea Square Error (RMSE) It yields the residual error i terms of the mea square error expressed as (Yu, 994) RMSE = residual variace = (Y 2 j Ŷ j) / /2 (3) where, Y ad Ŷ are the observed ad estimated values respectively ad is the umber of observatios. Correlatio Coefficiet (r) It is expressed as (Haa, 977) r = ) {( Yj - Y )( Yj - Ŷ) } 2 2 ( Yj - Y) ( Ŷj - Ŷ) / 2 x 00 (4) where, $ Y ad $ Y are the meas of observed ad estimated values. Joural of Evirometal Hydrology 4

5 Coefficiet of Efficiecy (CE) Based o the stadardizatio of residual variace with iitial variace, the coefficiet of efficiecy ca be used to effectively compare the relative performace of the two approaches (Nash ad Sutcliffe, 970). It is expressed as CE = { - residual variace } x 00 = { - iitial variace (Y Ŷ ) j (Y Y) j j 2 2 } x 00 (5) The coefficiet of efficiecy is also commoly kow as the coefficiet of determiatio (r 2 ) which may be writte i a umber of ways ad represets the fractio of variace that is explaied by regressio. The closer this ratio is to uity, the better is the regressio relatio (Haa, 977). Volumetric Error (EV) This is also called relative absolute error i volume (Yu, 994) ad is estimated as EV = { ( Ŷj Y j) / (Yj) } x 00 (6) THE STUDY AREA AND DATA AVAILABILITY I the preset study, time series data of sedimet load for oe gaugig statio o the Kosi River i the state of Bihar i Idia has bee used. Kosi is a large alluvial river with low gradiets ad wide flood plais. Meaderig or lateral shiftig of alluvial rivers produces cutoff meaders, oxbow lakes ad distictive ladforms. Tectoic ad evirometal chages ca cause aggradatios ad degradatio i alluvial rivers ad lead to high soil erosio ad meaderig. The Kosi River carries a mea aual discharge of.6x0 3 m 3 /sec, with mosoo discharge 0 times the lea period discharge. The river carries a very high cocetratio of suspeded sedimet load durig the mosoo moths. The ormal flood discharge of the Kosi usually varies from.5 to 2.0 millio cusecs. About 75 to 84 percet of the total ruoff occurs i the mosoo moths of Jue to October. O a average total sedimets are 0.20 percet of the total ruoff. About 95 percet of the silt load comes dow the river durig the mosoo floods ad oly 5 percet of the sedimets come dow i the remaiig o-mosoo moths. The total ruoff durig the o-mosoo moths, however is o a average about 9 percet of the total aual ruoff. For the preset study, discharge ad sedimet load data for a period of five years ( ) have bee used. However, durig this period some of the data are missig ad therefore data of 502 days have bee used. These data are available at the Birpur gaugig site. There is a barrage at Ido-Nepal border ear Birpur. The uit of discharge data is cusec while sedimet load data is i cubic feet (cft) per day. Ratig Curve Aalysis METHODOLOGY I this study, a regressio aalysis has bee carried out to develop the sedimet ratig equatio for the Kosi river at the Birpur gaugig site. For this purpose, the available data have bee Joural of Evirometal Hydrology 5

6 cosidered i two parts. The first part is used to calibrate the mathematical equatio for sedimet ratig ad the secod, to validate it. Out of 502 days of data, 002 days data were used for the calibratio of the ratig curve ad the remaiig 500 days data for validatio. The sedimet ratig equatio betwee sedimet load ad discharge for Kosi River at Birpur site is developed i the form of Equatio () S = Q (7) where S = Sedimet load i the River Kosi at the Birpur site i 0 3 cft. Q= Discharge i the River Kosi at the Birpur site i 0 3 cusec. Artificial Neural Network Aalysis For the developmet of ANN models the total data have bee divided ito traiig ad testig periods of 002 days ad 500 days respectively. The models provide the sedimet load at time step t, with S t as output. It has bee show by may ivestigators that the curret sedimet load ca be better mapped by cosiderig, i additio to the curret value of discharge, the sedimet ad discharge at previous times. Therefore, i additio to Q t, i.e., discharge at time step t, other variables such as Q t-, Q t-2, etc. ad S t-, S t-2, etc were cosidered as the iput. Various combiatios of iput variables cosidered for traiig of ANN i the preset study are give i Table together with the output variables. From the may differet types of ANNs that have bee developed with differet objectives, the multilayer perceptro was chose for applicatio i this research, as it is particularly suited to regressio problems ad is the most commo type of etwork applied to modellig of various hydrological problems (Hsu et al., 995). These ANNs model complex multivariate oliear fuctios, such as the sigmoid fuctio. The composite fuctio is fitted to the data by modifyig the shape-defiig parameters of the compoet oliear fuctios i a iterative traiig process, which miimizes the error betwee the estimated outputs ad the target outputs. I the course of this ivestigatio, eural etwork aalysis was coducted usig the Neural Power-2.5 ANN package (NeuralPower, 2003). A back-propagatio ANN with the geeralized delta rule as the traiig algorithm has bee employed i this study. The structure for all simulatio models are three layer BPANN which utilizes a oliear sigmoid activatio fuctio uiformly betwee the layers. Nodes i the iput layer are equal to umber of iput variables, odes i hidde layer are varied from the default value by the NP package (2 to 7) for various ANN models to approximately double of iput odes (Zhu et al., 994) ad the odes i the output layer is oe as the models provide sigle output. The modellig of ANN started with the ormalizatio (re-scalig) of all iputs ad output with the maximum value of respective variable reducig the data i the rage 0 to to avoid ay Table. Descriptio of various ANN models for traiig. ANN Model Iput Variables Output Variables ANN - Q t S t ANN - 2 Q t, Q t-, S t- S t ANN - 3 Q t, Q t-, Q t-2, S t-, S t-2 S t ANN - 4 Q t, Q t-, Q t-2, Q t-3, S t-, S t-2, S t-3 S t ANN - 5 Q t, Q t-, Q t-2, Q t-3, Q t-4, S t-, S t-2, S t-3, S t-4 S t Joural of Evirometal Hydrology 6

7 saturatio effect that may be caused by the use of sigmoid fuctio (accomplished through the Neural Power package). All itercoectig liks betwee odes of successive layers were assiged radom values called weights. A costat value of 0.5 ad 0.8 respectively has bee cosidered for the learig rate µ ad the mometum term α which were selected after hit ad miss trials. The quick propagatio (QP) learig algorithm has bee adopted for the traiig of all the ANN models. QP is a heuristic modificatio of the stadard back propagatio ad is very fast (NeuralPower, 2003). The etwork weights were updated after presetig each patter from the learig data set, rather tha oce per iteratio. The criterio selected to avoid over traiig was geeralizatio of ANN through crossvalidatio (Hayki, 994). For this purpose, the traiig data set for all the models was further divided i two subsets. First subset (800 datasets) for estimatio of weights of the ANN model ad secod subset (202 dataset) for evaluatio of the performace of ANN model with data of first subset. Traiig was stopped whe the error for the secod subset started icreasig. I this way, the traiig set has bee used to assess the performace of various cadidate model structures, ad thereby choose the best oe. The particular ANN model with the best performig parameter values was the traied o the full traiig data set (502 daily data), ad the geeralized performace of the resultig etwork has bee measured o the test data set (500 daily data) to which it has ever before bee exposed. The performace of the model was tested through the statistical criterio discussed earlier. DISCUSSION OF RESULTS The values of the performace criteria from various ANN models as well a ratig curve for both traiig (calibratio) ad testig (validatio) data sets are preseted i Table 2. The traiig ad testig results are discussed separately. Calibratio (Traiig) Results It ca be see from Table 2 that all the ANN models have outperformed the covetioal sedimet ratig curve techique i terms of various performace criteria. I terms of root mea Table 2. Comparative performace of various ANN models ad covetioal sedimet ratig curve. Model Calibratio (Traiig) Validatio (Testig) RMSE r CE/r 2 EV RMSE r CE/r 2 EV ANN Model (Iput, Hidde, Output) ANN (,2,) ANN (3,3,) ANN (5,4,) ANN (7,6,) ANN 5 (9,7,) Covetioal Procedure Sedimet Ratig Curve Joural of Evirometal Hydrology 7

8 square error (RMSE), ratig curve model performed the worst (8038.7), whereas, ANN-4 model performed the best (2802.). The correlatio coefficiet (r) ad coefficiet of determiatio (R 2 ) for various ANN models have bee higher tha the covetioal sedimet ratig curve techique. However, both the values have bee highest for ANN-4 model (r = 98.%, r 2 = 96.2%), whereas the values for ratig curve are oly 92.6% ad 85.7% respectively. I terms of volumetric error (EV), the performace of ANN-4 model has bee the best with the least error (9.24), whereas the ratig curve model performed the worst with highest value of error 40.68) which is almost double the ANN error. Validatio (Testig) Results All the ANN models have outperformed the covetioal sedimet ratig curve techique i terms of various performace criteria durig testig/validatio also. I terms of RMSE, agai the ratig curve model performed the worst (5252.2), whereas, ANN-4 model performed the best (2965.6). I terms of r ad r 2, ANN-4 model performed the best (97.6% ad 95.2% respectively). The ratig curve model performed the worst for r ad R 2 also (95.7% ad 9.6% respectively). The volumetric error (EV) has bee lowest for ANN-2 model (2.8), whereas, it has bee highest for the ratig curve model (39.4). The best performig ANN model i other criteria, i.e., ANN-4 model has also got a low value of EV (23.3). Therefore, it ca be observed from the results of calibratio as well as validatio that the performace of ANN-4 model has bee the best except i terms of volumetric error durig validatio. However, i terms of EV also, its performace has bee very close to the best oe. It ca be oted that by the iclusio of iput variables of previous time steps, the model performace improves up to the previous three days iputs. Beyod that, i.e., whe the iputs of previous fourth day are icluded i the model, the performace starts deterioratig. It implies that beyod the previous three days values, o ew iformatio is actually supplied to the ANN model for traiig. Ad with higher umber of iput variables, the etwork becomes more complicated ad may overfit the data. The plots betwee observed sedimet load ad estimated sedimet load (usig the covetioal ad ANN approach) for the calibratio as well as validatio period have bee illustrated i Figure 2 (a), (b), (c) ad (d) respectively. It is observed that the ANN (ANN-4) estimates show a better match with the observed values. It is also see from the graph that there is a large variatio i the covetioal approach estimates (for both calibratio ad validatio period). However, the ANN estimates (for both calibratio & validatio period) show a fairly good agreemet with the observed values eve at the high extremes. The temporal variatio of observed sedimet load ad the estimate usig the covetioal techique ad ANN (ANN 4 model) for the calibratio period is plotted i Figure 3. It is see from the compariso of the graphs that the ANN estimates of sedimet load very closely follow the observed curve, whereas the covetioal approach has sigificat mismatch, particularly ear the peaks. Usig the weights obtaied i the traiig phase for each combiatio, the performace or i other words, the geeralizatio capability of the ANN was tested usig the validatio period data. Figure 4 cotais the graphical presetatio of the results of the validatio phase. Compariso of the sedimet load estimates with the observed oes usig the covetioal approach ad ANN approach are show i the figure. Agai here the ANN estimates are closer to the correspodig observed oes. The covetioal approach estimates agai show sigificat deviatios from the correspodig observed oes. Joural of Evirometal Hydrology 8

9 Figure 2. Plot betwee observed ad estimated sedimet load Oserved Ratig curve ANN - 4 Sedimet load (cft) Time (days) Figure 3. Compariso of observed ad estimated sedimet load durig calibratio. To be able to test whether the ANN approach ca give iformatio about the structure of evets, the hysteresis i the sedimet load obtaied by ANNs ad the sedimet ratig relatio are compared with the correspodig observed oes i Figure 5 for all the 502 data sets. It ca be see that the hysteresis estimated by ANNs is almost the same as the observed oe. Joural of Evirometal Hydrology 9

10 Based o these results, it is clear that the sedimet load estimatios obtaied by the ANN techique are sigificatly superior to the correspodig classical sedimet ratig curve oes. It may also be added that as a result of traiig, a set of weights that represets the kowledge of ANN is obtaied ad oe does ot get a explicit equatio to work with. The weight distributios for the traied ANN-4 model are show i Figure 6. CONCLUSIONS The ANN techique has bee utilized for modellig the sedimet-discharge process i a alluvial river. The data of the Birpur gaugig site of the River Kosi i Idia have bee used for the aalysis. The results of the ANN have bee compared with those of the covetioal sedimet ratig curve approach. The ANN results have bee foud to be much closer to the observed values tha the covetioal techique. The study shows that the ANN techique ca be successfully applied for the developmet of reliable relatioships betwee sedimet ad discharge i a river Observed Ratig curve ANN Sedimet load (cft) Time(days) Figure 4. Compariso of observed ad estimated sedimet load durig validatio Observed sedimet Estimated sedimet(ratig curve) Estimated sedimet (ANN) Sedimet Load (cft) Discharge (cusec) Figure 5. Compariso of the observed hysteresis with the estimated hysteresis. Joural of Evirometal Hydrology 0

11 Weight Values Weight Numbers Figure 6. Weights distributio for the ANN-4 model. whe other approaches caot succeed due to the high o-liearity i the relatioship, especially i alluvial rivers. A sigificat advatage of usig the ANN approach is that it ca successfully model the hysteresis effect i the sedimet-discharge relatioship. Moreover, the ANN techique has preferece over the covetioal methods as ANNs ca accept ay umber of effective variables as iput parameters without omissio or simplificatio as is commoly doe i the covetioal methods. The preseted ANN models have bee developed by usig oly field river data, ad they have o boudary coditios i applicatio. The oly restrictio is that the models caot estimate accurately the sedimet load for data out of the rage of the traiig patter data. Such a problem ca easily be overcome by feedig the traiig patters with a wide rage of data. Site egieers ca calculate sedimet load usig the ANN without prior kowledge of the sedimet trasport theories, provided they kow the bouds of the data used to geerate the ANN. ACKNOWLEDGMENTS The authors are thakful to the two reviewers, Dr. Naya Sharma, Professor, Dept of Water Resources Developmet ad Maagemet, Idia Istitute of Techology, Roorkee, Idia ad Dr. S. P. Agarwal, Scietist E, Water Resources Divisio, Idia Istitute of Remote Sesig, Dehradu, Idia. Their valuable suggestios helped to improve the quality of paper. REFERENCES Agarwal, A., R.D. Sigh, S.K. Mishra, ad P.K. Bhuya ANN-based sedimet yield models for Vamsadhara River basi (Idia). Water SA, Vol. 3(), pp ASCE Task Committee o Applicatio of Artificial Neural Networks i Hydrology Artificial eural etworks i hydrology II: Hydrologic applicatios. Joural of Hydrologic Egieerig, ASCE, Vol. 5(2), pp Cigizoglu, H.K., ad M. Alp Geeralized regressio eural etwork i modellig river sedimet yield. Advaces i Egieerig Software, Vol. 37, Issue 2, pp Ferguso, R.I River loads uderestimated by ratig curves. Water Resources Research, Vol. 22(), pp Joural of Evirometal Hydrology

12 Haa, C.T Statistical methods i hydrology. The Iowa State Uiversity Press, USA. Hayki, S Neural etworks - A comprehesive foudatio. Macmilla, New York. Hsu, K., H.V. Gupta, ad S. Sorooshia Artificial eural etwork modellig of the raifall-ruoff process. Water Resources Research, Vol. 3(0), pp Jai, S.K Developmet of itegrated sedimet ratig curves usig ANNs. Joural of Hydraulic Egieerig, ASCE, Vol. 27(), pp Karuaithi, N., W.J. Greey, D. Whitley, ad K. Bovee Neural Networks for River Flow Predictio. Joural of Computig i Civil Egieerig, ASCE, Vol. 8(2), pp Morris, G.L., ad J. Fa Reservoir sedimetatio hadbook. McGraw-Hill, New York. Nagy, H.M., B. Wataabe, ad M. Hirao Predictio of sedimet load cocetratio i rivers usig artificial eural etwork model. Joural of Hydraulic Egieerig, ASCE, Vol. 28(6), pp Nash, J.E, ad J.V. Sutcliffe River flow forecastig through coceptual models. Joural of Hydrology, Vol.0, pp NeuralPower Neural etworks professioal versio 2.5. CPC-X Software, Copyright: , Demo versio from the iteret, Raghuwashi, N.S., R. Sigh, ad L.S. Reddy Ruoff ad sedimet yield modellig usig artificial eural etworks: Upper Siwae River, Idia. Joural of Hydrologic Egieerig, ASCE, Vol. (), pp Rosebaum, M Harbours - siltig ad evirometal sedimetology (H-SENSE). Fial Report, Dept. of Civil & Structural Egieerig, The Nottigham Tret Uiversity, Nottigham, UK. HSese/ Rumelhart, De.E., G.E. Hito, ad R.J. Williams Learig represetatio by back propagatig errors. Nature, Vol. 323(9), pp Wallig, D.E., ad B.W. Webb The reliability of ratig curve estimates of suspeded sedimet yield: some further commets. Sedimet Budgets, IAHS Publ. 74, Walligford, U.K., pp Yitia, L., ad R.R. Gu Modellig flow ad sedimet trasport i a river system usig a artificial eural etwork. Evirometal Maagemet, Vol. 3(), pp Yu, P.S., C.L. Liu, ad T.Y. Lee Applicatio of a trasfer fuctio model to a storage ruoff process. Stochastic ad Statistical Methods i Hydrology ad Evirometal Egieerig, Vol. 3, K.W. Hipel et al., eds., Kluwer, Dordrecht, The Netherlads, pp Zhu, M., M. Fujita, ad N. Hashimoto Applicatio of eural etworks to ruoff predictio. Stochastic ad Statistical Method i Hydrology ad Evirometal Egieerig, Vol. 3, K.W. Hipel et al., eds., Kluwer, Dordrecht, The Netherlads, pp ADDRESS FOR CORRESPONDENCE Archaa Sarkar Natioal Istitute of Hydrology Roorkee Idia archaa_ih@yahoo.co.i Joural of Evirometal Hydrology 2