Application of artificial neural networks in flow discharge prediction for the Fitzroy River, Australia

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1 Applcaton of artfcal neural networks n flow dscharge predcton for the Ftzroy Rver, Australa Author Joorabch, Amrhassan, Zhang, Hong, Blumensten, Mchael Publshed 2007 Journal Ttle Journal of Coastal Research Copyrght Statement 2007 CERF. The attached fle s reproduced here n accordance wth the copyrght polcy of the publsher. Please refer to the journal's webste for access to the defntve, publshed verson. Downloaded from Lnk to publshed verson Grffth Research Onlne

2 Journal of Coastal Research SI ICS2007 (Proceedngs) Australa ISS Applcaton of artfcal neural networks n flow dscharge predcton for the Ftzroy Rver, Australa A. Joorabch, H. Zhang and M. Blumensten Grffth School of Engneerng School of Informaton And Communcaton Technology Grffth Unversty, Gold Coast Campus Grffth Unversty, Gold Coast Campus Queensland 4217, Australa Queensland 4217, Australa A.Joorabch@grffth.edu.au M.Blumensten@grffth.edu.au Hong.Zhang@grffth.edu.au ABSTRACT JOORABCHI, A. ZHAG, H. and BLUMESTEI, M, Applcaton of artfcal neural networks n flow dscharge predcton for the Ftzroy Rver, Australa. Journal of Coastal Research, SI 50 (Proceedngs of the 9th Internatonal Coastal Symposum), Gold Coast, Australa, ISS Predcton of flow dscharge, and n partcular floods, n rvers s one of the basc and key nformaton n regards to operaton and management of the rver systems. The Ftzroy Rver, one of the largest Australan rver systems, has a hstorcal recordng of heavy floods and there s a concern for the people of that area to have a clear predcton of the stream dscharge to avod damages. In ths paper a feed-forward artfcal neural network (A) model has been used to forecast the daly flow dscharge of the Ftzroy Rver up to four days ahead. The feed-forward neural network uses error Back-propagaton learnng algorthm. A cross valdaton method s appled to prevent the over-fttng problem. The network uses multple nputs ncludng the daly values of dscharge. The network output conssts of four neurons n respect to the number of forecasted days. A sutable number of nputs for tme-seres data were selected by tral and error. Two dfferent mult-layer networks were compared to fnd the optmsed network. The results show an accurate forecastng of flow dscharge durng flood events. However, the neural network overestmates durng low dscharge wth a mean value of 80 (m 3 /s). ADDITIOAL IDEX WORDS: Flood, Back-propagaton, Tme-seres predcton ITRODUCTIO The applcaton of artfcal neural networks (As) has been wdely appled to the varous areas. umerous A models have been used as alternatves to the tradtonal numercal models. For example, n water resource engneerng a neural network model was developed for rver flood forecastng by CAMPOLO, et al (1997). FRECH et al. (1992) appled As to forecast the ranfall ntensty. Most recently, SAHOO et al. (2006) establshed a neural network to predct the flash flood and attendant water qualtes of a mountanous stream. Ftzroy catchment s the second largest catchment n Australa after the Murray-Darlng Basn. It covers twce the sze of Tasmana. The Ftzroy Rver (Fgure 1) s one of the man rvers n ths catchment that pass the cty of Rockhampton. It has a number of dams and wers to provde the fresh water to the cty and ts surroundng area. The mportance of ths area for scentfc study s due to ts sgnfcant loads of sedment and nutrents that are transported through ths rver and frequent flood events. In the last few years Coastal Cooperatve Research Centres (Coastal CRC) studed ths area on a number of projects. A one-dmensonal hydrodynamc, sedment transport and bochemstry model s avalable for the Ftzroy estuary (MARGVELASHVILI et al., 2003 and 2005) based on conceptual model (WEBSTER et al., 2003). KELLY and WAG (1996) study the sedment transport n the Ftzroy Rver durng flood events. utrent dynamcs and sedment budgets for the estuary durng a flood event are examned by FORD et al., (2006). Predcton of rver flow and n partcular flood forecastng s an mportant element of flood control systems. The early predcton helps us to mnmse the flood damage. The results of floods n low lyng areas are loss of communcaton and transport system problems. Due to low annual precptaton, runoff and elevated evaporaton rates, Australa has a hghly varable flow wth large peaks and annual floods (WARER, 1986). The Ftzroy Rver has had a number of hstorcal floods caused by heavy rans wth extended perods of low flow. It usually happens between January and Aprl (Table 1). A flood warnng system has been nstalled by the Bureau of Meteorology (BOM, 2005) whch measures the water elevaton and has a warnng tme of up to 60 hours for floods comng from the hnterland to the Rockhampton cty. The Department of atural Resources and Water operates a number of statons along the Ftzroy Rver to control a few parameters ncludng stream water level and dscharge (RW, 2006). In ths study a neural network model was developed and traned based on the 64 years of daly dscharge measured snce 1964 up to the end of 2005 n The Gap staton (23 5' 18" S and 150 6' 28" E). Fgure 2 shows the maxmum measured value of dscharge happened each year (from 1964 to 2006) at The Gap staton. The presented neural network model, due to ndependency of the physcal parameters such as boundary condtons, ntal condton and bathymetry as well as relable results and real-tme predcton of flow dscharge, could outper-

3 288 Joorabch et al. Table 1: Hstorcal flood on Rockhampton Cty (from Bureau of Meteorology) Date Flood gauge heght (m) Jan Feb Jan/Feb May Mar Jan Fgure 1. The Ftzroy Rver, Central Queensland, Australa form the conventonal statstcal and numercal models. In general, although tranng and optmsng a neural network for a long perod of data s tme consumng, smulaton of a new data s very fast and can be used for real tme forecastng. Rver Dscharge (m 3 /s) Date (Year) Fgure 2. Maxmum flow dscharge happened each year at Ftzroy Rver (The Gap staton) from 1964 to (Data source: RW, 2006) Fgure 3. Structure of the proposed artfcal neural networks wth 1 hdden layer wth 10 neurons (top) and 2 hdden layers wth 10 neurons n each layer (bottom). IW and LW ndcate nterconnecton weghts and b denotes bases for each layer. METHODS As use a parallel computng system wth nterconnectons smlar to bologcal neural networks. Snce the prncples of A models has been documented n the lterature, for example refer to (HAYKI, 1994) and (WASSERMA, 1989), the general concept of Back-propagaton neural network s summarsed here. In partcular, applcaton of neural networks n hydrology s descrbed by ASCE, (2000). Back-propagaton developed by RUMELHART et al. (1986) s one the most used methods of A tranng n Engneerng problems. In ths study, two dfferent A models wth Back-propagaton algorthm are appled by tral and error to fnd an optmum network structure, number of nputs, outputs and hdden layers (Fgure 3). The nput layer ncludes 15 nputs, the hdden layers have 10 neurons and the output layer conssts of 4 neurons as well as nterconnecton weghts and bases are also depcted. The nput layer receves the nputs from the tranng data and the hdden layer and output layer receves t from the nterconnectons. eurons use Log-sgmod and hyperbolc tangent sgmod transfer functons to produce ther output. In the Back-propagaton algorthm, nterconnecton weghts are adjusted accordng to the error convergence technque to obtan the requred output for the gven nputs. The nterconnecton weghts are adjusted based on the followng equaton E Δwj ( n) = ε + α Δwj ( n 1) (1) w j where ε and α are the learnng rate and the momentum, respectvely. Δ w j (n) and Δw j ( n 1) n equaton (1) are the ncrement of weghts between nodes and j for the n-th and (n- 1)-th teraton. Tranng of a neural network s controlled by supervsed or unsupervsed learnng algorthms. The dfference between these two s that n supervsed learnng both nput and output data are requred for calculaton of the error of the network based on the dfference between the calculated output and gven output. However, unsupervsed tranng uses the nput data only. In ths model, a supervsed learnng algorthm s used. Selecton of the number of hdden layers and number of neurons n each layer s one of the most mportant factors n the applcaton of the neural network. In general, there s not a certan rule to estmate

4 Applcaton of As n flow dscharge predcton 289 Fgure 4a. Frst day predctons (R=0.99, RMSE=139 m 3 /s and SI=0.77) Fgure 4b. Second day predctons (R=0.97, RMSE=256 m 3 /s and 1.25) Fgure 4c. Thrd day predctons (R=0.93, RMSE=315 m 3 /s and SI=1.76) Fgure 4d. Fourth day predctons (R=0.85, RMSE=442 m 3 /s and SI=2.52) Fgure 5a. Tme seres of measured and predcted flow dscharge n the frst day of predcton for low dscharge values. Fgure 5b. Tme seres of measured and predcted flow dscharge n the frst day of predcton for hgh dscharge values.

5 290 Joorabch et al. Table 2: Verfcaton statstcs of Ftzroy Rver flow dscharge for dfferent predcted day. Here, R s correlaton coeffcent, RMSE s root mean square error and SI s scatter ndex. etwork Days R RMSE (m 3 /s) SI A wth 1 hdden layer A wth 2 hdden layer the number of neurons for hdden layers and the optmum topology s obtaned by tral and error. Some methods such as cascade-correlaton (FAHLMA and LEBIERE, 1990) are developed to fnd the optmum hdden unts. In some cases wth an extensve number of nputs and data sets, the hgher number of neurons n the hdden layers and number of hdden layers prevents the neural network from generatng poor results and ncreases the accuracy of forecastng. However, a greater number of hdden layers and neurons causes more computaton tme and for some partcular cases t may result n over-fttng. In general, over-fttng s one of the problems that happens durng tranng of a neural network. Snce the network has memorsed the tranng pattern t can not generalse to new data. In ths case the error for a tranng set s very small but the network results nto large error for new data sets. Cross valdaton method was used to mprove the generalsaton. The exstng data set conssted of tranng pars wth 15 daly rver flow dscharge values n cubc metres per second and 4 outputs representng the rver dscharge n the next four days. The data was dvded nto three subsets nclude tranng, valdaton and testng sets. The valdaton error s montored durng the tranng process. The errors on the valdaton and tranng set usually decrease durng the ntal phase of tranng and as soon as the network begns to overft the data, the valdaton error ncreases for a number of teratons (here t s fve teratons), the tranng s stopped. RESULTS AD DISCUSSIOS The A model was valdated n terms of a correlaton coeffcent (R), root mean square error (RMSE) and scatter ndex (SI). RMSE = R = = 1 = 1 2 ( y x ) ( x x)( y 2 ( x x) = 1 = y) 2 ( y y) (2) (3) RMSE SI = (4) x where x s the observed values at the -th tme step, y s the smulated values, s the number of tme ncrements, x and y are the mean value of observatons and smulatons, respectvely. Smulaton results for testng set (Table 2) show that the neural network wth two hdden layers could outperform the network wth one hdden layer. The dfference between two proposed network structures was ncreasng wth more number of flow dscharge predctons. The proposed neural network wth two hdden layers resulted n 20% more accuracy for predcton of the flow dscharge n the fourth day. Therefore, the mult-layer neural network wth two hdden layers was selected to smulate and forecast the flow dscharge tme-seres. After 28 teratons, tranng s stopped by cross valdaton method to avod the over-fttng. When short predcton ntervals of one to three days are consdered, the flow dscharge smulated by ths network has a hgh accuracy. Fgures 4a to 4d llustrate the comparson between the measured and the predcted flow dscharge wth 2992 number of testng pars (equal to 20% of total data) for the frst to fourth days of predcton. The RMSE are equal to 139, 256 and 315 (m 3 /s) for the frst to the thrd day flow dscharge predcton respectvely. The correlaton coeffcents that ndcate the strength of the relatonshp between observed and predcted data are hgher than 0.9 (maxmum scale s 1) for the frst three days. The best result was predcted for the frst day predcton wth a correlaton coeffcent equals The scatter ndexes for the frst three day predctons are 0.77, 1.25 and 1.76 respectvely. The predcton of flow dscharge s less relable for the fourth day. However, t has reasonable values equal to 442 m 3 /s, 0.85 and 2.52 for RMSE, R and SI respectvely. The neural network overestmated the dscharge for dry seasons (Fg. 5a) wth a mean value equals 80 (m 3 /s). It s due to extreme varaton between flood events and dred season wth maxmum value of (m 3 /s). However, the man applcaton of ths model s predcton of flood and that the neural network could predct t wth a hgh accuracy (Fg 5b). Fgure 5b ndcates the peak flows (floods) are well smulated. There s a potental further study to nvestgate the applcaton of dfferent learnng algorthm as well as the senstvty of mappng scale to avod the over-predcton n dry seasons. COCLUSIO An artfcal neural network model wth a feed-forward Back-propagaton learnng algorthm s adopted to predct the daly flow dscharge n the Ftzroy Rver up to four days ahead by a learnng and recallng process. Two dfferent network structures were compared. The network wth two hdden layers had better outcomes. A cross valdaton method was used to prevent the network from over-fttng. Results show the neural network provdes a hgh accuracy predcton of flow dscharge for the next three days and has a relable predcton for the fourth day. One of the advantages of the presented model compared to the ordnary numercal models s that t s not dependent on the ntal and boundary condtons. However, the relablty of results s dependent on how much data s avalable for tranng the network. The proposed neural network model can predct flood events very accurately. However, t over predcts low flow dscharge

6 Applcaton of As n flow dscharge predcton 291 wth average value of 80 (m 3 /s). Further nvestgaton s suggested to use other network structures, transfer functons and mappng scale to expand ths model from flood predcton to drought predcton. ACKOWLEDGEMETS The authors are grateful to Prof. Bofu Yu for hs helpful suggestons. The authors are also thankful for support from Grffth Unversty Research Grant (GURG, 2006). The Department of atural Resources and Water s gratefully acknowledged for provdng data. LITERATURE CITED ASCE (Task Commttee on Applcaton of Artfcal eural etworks n Hydrology)., 2000b. Artfcal neural networks n hydrology. II: Hydrologc applcatons. Journal of Hydrologc Engneerng 5(2), BOM (Bureau Of Meteorology)., Flood warnng system for the Ftzroy Rver. [onlne] Avalable from: < /ftzroy.shtml> (Accessed 15/08/2006). CAMPOLO, M., ADREUSSI, P. and SOLDATI, A., Rver flood forecastng wth a neural network model. Water Resources Research, 35(4), FAHLMA, S.E. and LEBIERE, C., The cascade-correlaton learnng archtecture. In: TOURETZKY, D.S. (Ed.), Advances n eural Informaton Processng Systems 2. Morgan Kaufmann San Mateo, CA. FORD, P.W utrent dynamcs and sedment budgets n the Ftzroy estuary durng a flood event. Coastal CRC Techncal Report o. 72. CRC for Coastal Zone, Estuary and Waterway Management; Indoorooplly, 20p. FRECH, M.., KRAJEWSKI, W.F., and CUYKEDALL, R.R., Ranfall forecastng n space and tme usng a neural network. Journal of Hydrology, 137, HAYKI, S., eural networks: a comprehensve foundaton. Mac-Mllan, ew York, 842p. KELLY, J.. and WOG W. T., Sedment transport n the Ftzroy Rver durng flood events. Proceedngs Stream Management 96: 1st Australan Stream Management Conference, February 1996, Merryjg, Vctora. (Eds: I RUTHERFORD, and M. WALKER) pp CRC for Catchment Hydrology, Clayton, Vctora. MARGVELASHVILI,., ROBSO B., SAKOV P., WEBSTER I.T., PARSLOW J., HERZFELD M. and ADREWARTHA J., umercal modellng of hydrodynamcs, sedment transport and bogeochemstry n the Ftzroy estuary. Coastal CRC Techncal Report o. 10. CRC for Coastal Zone, Estuary and Waterway Management; Indoorooplly, 70p. MARGVELASHVILI,., HERZFELD M., and WEBSTER I.T., Modellng of fne sedment transport n Ftzroy Estuary and Keppel Bay. CRC CZEWM Techncal Report 9. Cooperatve Research Centre for Coastal Zone, Estuary, and Waterway Management. Indoorooplly, Australa, 40p. RW (Department of atural Resources and Water)., Watershed database. [onlne] Avalable from: < (Accessed 12/06/2006). RUMELHART, D.E., HITO, G.E., and WILLIAMS, R.J., Learnng representatons by Back-propagatng errors. ature 323, SAHOO, G.B., RAY, C., and DE CARLO, E.H., Use of neural network to predct flash flood and attendant water qualtes of a mountanous stream on Oahu, Hawa. Journal of Hydrology, 327(3-4), WARER, RF., Hydrology. In: JEA, D.., (ed.), Australa A Geography Volume One: The atural Envronment, Sydney Unversty Press. pp WASSERMA, P. D., eural computng: theory and practce. Van ostrand Renhold, ew York, 230p. WEBSTER, I.T., FORD P.W., ROBSO B., MARGVELASHVILI., and PARSLOW J., Conceptual model of the hydrodynamcs, fne sedment dynamcs, bogeochemstry and prmary producton n the Ftzroy estuary. Coastal CRC Techncal Report o. 8. CRC for Coastal Zone, Estuary and Waterway Management; Indoorooplly, 43 p.