Base flow separation using exponential smoothing and its impact on continuous loss estimates

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1 Base flow separaton usng exponental smoothng and ts mpact on contnuous loss estmates Author Tularam, Gurudeo, Ilahee, Mahbub Publshed 7 Conference Ttle MODSIM 7 Internatonal Congress on Modellng and Smulaton Copyrght Statement 7 Modelllng & Smulaton Socety of Australa & New Zealand. Ths s the authormanuscrpt verson of ths paper. Reproduced n accordance wth the copyrght polcy of the publsher. Please refer to the conference lnk for access to the defntve, publshed verson. Downloaded from Lnk to publshed verson Grffth Research Onlne

2 Base flow Separaton usng Exponental Smoothng and ts mpact on Contnuous Loss estmates Gurudeo Anand Tularam and Mahbub Ilahee Lecturer - Mathematcs and Statstcs, Faculty of Scence, Technology and Envronment (ENV), Grffth Unversty, Brsbane, Australa. Fellow - Faculty of Scence, Technology and Envronment (ENV), Grffth Unversty, Brsbane Australa Keywords: Baseflow separaton, ranfall, streamflow, contnung loss, desgn floods, loss estmates. ABSTRACT Ranfall runoff models are used to estmate desgn floods. These models requre several nputs such as, ranfall duraton, ntensty, loss etc. For baseflow separaton n desgn flood estmaton the estmaton of contnung loss (CL) s vtal. The surface runoff has to be separated from the stream flow hydrograph. To obtan the volume of surface runoff, the use of an approprate baseflow separaton method s essental and n ths paper an exponental method s used to assess the mpact of baseflow on contnung loss estmates. The senstvty analyss shows that the requred baseflow separaton coeffcent (α) could be estmated usng to 5 ranfall streamflow events from the study catchment. The selected α can then be appled to other ranfall streamflow events of the same catchment to observe the senstvty on contnung loss estmate. It has been observed that a small degree of error n the selecton of α value does not sgnfcantly affect the estmates of the CL values. Rather than usng complex rules, the method and procedure used n ths research for baseflow separaton can be used to estmate α for all other Queensland catchments. Correspondng author: Dr G A Tularam, Grffth Unversty, Grffth School of Envronment, Nathan Campus, Kessels Rd, Brsbane 4; Emal: a.tularam@grffth.edu.au: Tel: Fax:

3 . INTRODUCTION Flood estmaton s often requred n hydrologc desgn (Hscock, 5: Snorasson, ). Ranfall-based flood estmaton technques requre a number of nputs/parameters to convert desgn ranfalls to desgn floods. Of the nputs, loss has been noted as an mportant parameter. It s the amount of precptaton that does not appear as drect surface runoff (IEA, 998). In most flood estmaton, the smplfed lumped conceptual loss models are generally used because of ther smplcty and ablty to approxmate catchment runoff behavour (Hll et al, 996). In Australa, the most commonly adopted conceptual loss model s the ntal loss -contnung loss (IL-CL) model (Hll et al, 996). For a specfc part of the catchment, the ntal loss occurs pror to the commencement of surface runoff, and thus can be consdered to be composed of the ntercepton loss, depresson storage and nfltraton that occur before the sol surface saturates (IEA, 998). CL s the average rate of loss throughout the remander of the storm. To compute the CL value of any study catchment (ncludng nput/losses such as proportonal loss and volumetrc runoff coeffcent) from any observed ranfall event, the total volume of the surface runoff from a selected ranfall event needs to be estmated. The observed streamflow data conssts of surface runoff, whch results from the same ranfall event and the groundwater flow (baseflow). Hence, t s requred to separate the total streamflow nto surface runoff and baseflow. Lttle senstvty analyss work has been done n ths area n recent tmes even when rather complex and data ntensve methods have been proposed. Ths paper explores an exponental smoothng technque consderng t a more practcal method than complex methods avalable n desgn loss studes. An acceptable technque s used to determne an approprate baseflow separaton coeffcent (α). Senstvty analyss of contnung loss to alpha n base flow separaton s also nvestgated.. BASEFLOW SEPARATION METHODS A number of studes have nvestgated surface flow and baseflow (Eckhardt, 5; Hughes and Hannart, ; Dcknson et al, 967; Hall 97; Shrmohammad et al. 984). In loss studes ranfall runoff/fltraton s classfed as quck flow (surface runoff) and baseflow (groundwater flow). It s assumed that a threshold amount of ranfall s needed to ntate surface runoff and assumptons are made about the duraton of surface runoff for any ranfall event. Boughton (987)and Lyne and Hollck (979) used stream flow parttonng nto quck and slow runoff components on the bass of tme. Authors have varous methods over tme such as electrcal conductance, temperature dfference, and sotopes of oxygen (Hno and Hasebe 985; Kobayash, 985, 986; Plgrm et al. 979). In most cases, the data used are not readly or easly avalable. Jackman and Hornberger (99) have shown that after applyng a non-lnear loss functon to the ranfall data, the response of a wde range of catchments s well represented by a lnear model wth two components, nterpreted as defnng a quck flow and slow flow response to the fltered ranfall. Ths suggests that more complex analyss does not appear to lead to better representaton n routne baseflow separaton. O Loughln et al. (98), Hll (99) and Nathan and McMahon 7 (99) and Smakhtn () separated the flow components on the bass of travel tmes. The old flow s dentfed as beng water that was already n the catchment before the start of ranfall, whle the new flow has smlar qualty characterstcs as the ncomng ranfall Chapman and Maxwell (996) showed that the old flow has many of the characterstcs of quck flow, and although the old flow can be modelled by algorthms used for baseflow separaton, selecton of parameter values requres expermental data from tracer experments.. Bethlahmy (974) used a smoothng type method to separate the streamflow nto quck flow and baseflow; the rate of baseflow at any tme (B ) s made equal to the sum of the baseflow rate at the prevous tme (B - ) and an ncremental value (U) as shown n Equaton : B = B - + U () The ncremental values for baseflow and nterflow separatons were calculated usng complex functons of the rate of ncrease of total flow. The reasons behnd the calculatons were not clearly descrbed. Instead of the many complex functons, a smpler exponental smoothng model can be used n extensvely. The exponentally weghted movng average (EWMA) model (Equaton ) appears practcal and easer to apply when compared to most models. A varant of the model s examned here. For example for any tme perod t, the smoothed value B t of a tme seres data found by usng Equaton : 77

4 B = α y < α, + ( α) B t ; () where y s the observed value and B the smoothed value. In Equaton, the parameter α s called the smoothng constant. Ths smoothng scheme begns by settng B to y, where B stands for smoothed observaton or EWMA, and y stands for the orgnal observaton. The subscrpts refer to the tme perods, to n. For example for the thrd perod, B4 = α y + ( α) B and so on; there s no B thus the frst observed value s usually equated to B. The new seres starts wth the smoothed value of the second observaton. As the method to be chosen for ths study ought to be not only acceptable n the lterature but must also allow model parameters to be estmated easly from the observed ranfall and/or streamflow data. Boughton (988) compared two methods of separaton of baseflow of whch one of them s smlar to that descrbed n Equaton. Both models allow user dentfcaton of a pont on a hydrograph at whch the separaton of flow components s apparent. The methods of parttonng of streamflow can be performed n both ways usng daly streamflow data as well as hourly streamflow data for flood hydrograph studes. These methods use manual dentfcaton of one or more ponts that mark the end of surface runoff but dffer n assumptons. Model assumes constant rates of baseflow ncrease wth tme; that s, the ncrease n baseflow and the rate of recharge of baseflow depend on tme. The overall ncrease n the rate of baseflow n the streamflow s closely related to the duraton of the surface runoff. Model shows that the rate of ncrease of baseflow depends on the fracton of the surface runoff; that s, the ncrease n baseflow and the recharge of baseflow depend on runoff volume. The man dfference between the two models s that Model estmates more surface runoff and less baseflow than Model for the large events; whle Model estmates less surface runoff and more baseflow than Model for small runoff events. Further, Model estmates some surface runoff at every rse n the hydrograph whle Model treats many small rses as ncreases n baseflow as shown n Fgure. Daly dscharge - M Model 5 5 Model Days Fg. : Base flow separaton by Models and Streamflow Fg. : Baseflow n large and small runoff events (Y axs s the Daly Dscharge (ml)) Dckson et al. (967) argued that n the small rses of hydrograph the baseflow dscharge shows very quck rse and fall n Model was consdered unreasonable. Model appeared a better choce for the general purpose of ranfall-runoff modelng. Model s based on the sngle exponental smoothng method n tme seres. It s used to partton the stream flow tme seres by makng the rate of ncrease of the baseflow proportonal to the rate of surface runoff 9,. The rate of ncrease of baseflow n ths model depends on the fracton (α) of the surface runoff (A ). The rate of baseflow at any tme step s B, and the separated surface runoff at the same tme step s consdered to be A. Model can be stated as: B = B + α A () where A = TS B ; TS s the stream flow at the same tme step of A. Another way of wrtng Equaton s B = B + α ( TS αts + ( α) B Model Model Days B ) = (4) 77

5 In ths research 5 years of ranfall and streamflow data were used and a separate computer program was wrtten (Fortran) whch fts well wth the Boughton separaton process (Model ). A smpler and practcal Boughton s method was examned n ths study. Whle the form s smlar to the sngle exponental smoothng the base flow observed data s not avalable; exceptng the ntal value and fnal pont (pont of nflecton approxmated from graphs of daly dscharge). The equaton s smlar to Robert (959), who used the observaton at tme t for ths value rather than at tme t- n Equaton. Usually, the state of control of the process at any tme (t,) depends solely on the most recent measurement from the process but n the EWMA technque used, the decson depends on the EWMA statstc; an exponentally weghted average of all pror values. By the choce of weghtng factor (α ), the EWMA control procedure can be made senstve to a small or gradual drft n the process. separately to observe the effects of α on baseflow separaton. Fgure ndcates that a value of α =.4 provdes a more acceptable baseflow separaton ft for Event ; the straght lne part of both curves are matched together from the pont of recesson starts (In the case of α =.5 and α =.8 the streamflow and baseflow separaton lnes merged before pont of recesson curve starts and for α =. both the streamflow and baseflow separaton lnes merged after the pont of recesson curve starts) METHOD The study s based on hourly streamflow and ranfall data. Two rural catchments Bremer Rver catchment (4A, catchment area sq km ) and Tenhll Creek catchment (4A, catchment area 447 sq km ) were selected from Queensland. From each catchment four dfferent ranfall streamflow events were selected to estmate an approprate α value for each catchment. A FORTRAN program was developed to nvestgate the mpact on CL due to the separaton of baseflow usng exponental smoothng method from the stream flow analyss (Equaton ). The outputs of the FORTRAN program were used to compute the total streamflow, baseflow and CL values out of the total ranfall volume. 4. RESULTS When the streamflow dagram s plotted on a sem-log graph paper, the recesson curve (the rght secton of the graph) of the streamflow dagram becomes a lne (rather than a curve) wth constant slope (Fgure ). To provde the acceptable baseflow separaton from the streamflow the value α should be selected n such manner that the baseflow separaton lne (upper curve) can jon the start of the recesson part of the streamflow hydrograph; that s, at the start pont of the straght lne secton of the streamflow dagram. Out of many ranfall streamflow events, one ranfall streamflow event was selected and four dfferent values of α were used n that event Fg. : Streamflow components (sem-log graph) for Event : when α =.,.4,.5,.8 (Bremer Rver) The alpha value selected above for Event (α =.4) s used to conduct base flow separaton for other events n the same catchment. Fgure 4 shows that the value of α =.4 provdes acceptable base flow separaton for the other 77

6 events of the same catchment. Ths analyses showed that for the Bremer Rver catchment a value of α =.4 can be used for baseflow separaton for all other streamflow events Fg. 4: Acceptable value of α =.4 used n events, and 4 n the Bremer Rver catchment. The senstvty of computed loss values wth α was then studed. Table shows that for Event n the Bremer Rver catchment when α =.4, CL =.6, f α s ncreased by 5%, the value of CL s vared by.%, f α s decreased by 5%, the value of CL s vared by.8%. Lttle varaton n CL value was observed (even wth % varaton n α). Fgure 5 shows that a small error n selecton of α does not seem to affect the value of CL sgnfcantly. Table : Senstvty of CL wth dfferent α value Event No α CL Event Event Event Contnung loss Alpha Fg. 5: CL vs α for Bremer Rver catchment In the case of Tenhll Creek catchment, a sngle α dd not provde acceptable baseflow separaton. α s of.,.,.8 and. provded acceptable baseflow separaton as shown n Fgure

7 Fg.6: Tenhll Creek catchment: Event (α =.); Event (α =.); Event (α =.8); Event 4 (α =.) The medan (.55) was then explored for separaton. Fgure 6 shows the medan value provdes a reasonable baseflow separaton for the Tenhll Creek catchment usng the nflecton matchng technque descrbed earler Fg. 7: In all,,, and 4 events of Tenhll Creek, the α =.5 s used. Table : Senstvty of CL wth dfferent α value As before, α was vared to examne the senstvty of computed CL values. Table shows that for Event (Tenhll Creek), when α s.55 CL s.7, and f α s ncreased by %, the value of CL s vared by.78%; f α s decreased by %, the value of CL s vared by.46%. Thus a 6% varaton n the value of α resulted n only 4.8% varaton n CL. For the Events and, the varaton n α value by about 6% causes about % and % varaton n CL value. Fgure 8 confrm shows that a small error n selectng α does not affect the value of CL sgnfcantly. Contnung lossa Event No α CL Event Event Event Event Alpha Fg. 8: CL vs α for Tenhll Creek catchment 774

8 Fgure 8 shows that small varaton n alpha values dd not seem to make a sgnfcant dfference n the estmated CL values for the Tenhll Creek catchment. 5. SUMMARY AND CONCLUSION The exponental smoothng based method of baseflow separaton was used to examne the mpact of contnung loss for medum szed Queensland rural catchments. It was noted that an acceptable baseflow separaton coeffcent (α) can be selected for a catchment usng a (Fortran) tral 6. ACKNOWLEDGEMENTS The authors wsh to thank Brsbane Water (Brsbane Cty Councl - S. Hoverman) and the drector of the Centre for Envronment Systems Research (Prof R Braddock) and Grffth Unversty. 7. REFERENCES Bethalmy, 974, Smoothng methods n statstcs. Sprnger-Verlag, New York. Or Nst/Ematech., 7. e-handbook of Statstcal Methods, Engneerng statstcs hand book. U.S.A. Boughton, W. C., 987. Hydrograph analyss as a bass of water balance modellng. The Insttuton of Engneers, Australa, Cvl Engneerng Transacton, CE9(): 8 -. Boughton, W.C., 988. Parttonng streamflow by computer. The Insttuton of Engneers, Australa, Cvl Engneerng Transacton, pp: Chapman, T.G. and Maxwell, A.I., 996. Baseflow separaton comparson of numercal methods wth tracer experments, Hydrology and Water Resources Symposum, Insttuton of Engneers, Australa, Hobart, pp: Dcknson, W. T., Holland, M. E. and Smth, G.L., 967. An expermental ranfall runoff faclty. Hydrology paper no. 5, Colorado State Unversty, pp:78. Eckhardt K, 5. How to construct recursve dgtal flters for baseflow separaton. Hydrologcal Processes 9, Hall, A.J., 97. Baseflow recessons and the baseflow hydrograph separaton problem. Hydrology papers 97, The Insttuton of Engneers, Australa, pp: based method together wth CL senstvty analyss. Such a process only requres a small number of stream flow events ( to 4 streamflow events) thus ncurrng mnmal data, computaton and practcal costs. It was found that contnung loss was not senstve to small changes n α. A large (5%) change n α made less than % varaton n contnung loss suggestng that such a method can be reled upon to make approxmatons methods can be relably used. Ths procedure may be used to estmate nput values n desgn flood estmatons. Hll, P.I., Maheepala, U., Men, R. G., Wenmann, P. E., Emprcal analyss of data to derve losses for desgn flood e+-stmaton n South-Eastern Australa. CRC for Catchment Hydrology, Report 96/5, 996. Hll, P.I., 99. Extreme flood estmaton for the Onkaparnga Rver catchment. M. Eng., Scence Thess, Department of Cvl and Envronmental Engneerng. Unversty of Adelade, 99. Hscock, K., 5. Hydrology prncples and practce, Blackwell Publshng, Oxford, UK. Hno, M. and Hasebe, M., 985. Separaton of a storm hydrograph nto runoff components by both flter separaton AR method and envronmental sotope tracers. Journal of Hydrology, 85: Hughes. D. and Hannart. P., A desktop model used to provde an ntal estmate of the ecologcal nstream flow requrements of rvers n South Afrca. J. Hydrol. (In press). Insttuton of Engneers, Australa., 998. Australan Ranfall and Runoff. Insttuton of Engneers, Australa, 987 and 998. Jackman, A. J. and Hornberger, G.M., 99. How much complexty s warranted n a ranfall-runoff model? Water Resources Research, 9: Kobayash, D., 985. Separaton of the snowmelt hydrograph by stream temperatures. Journal of Hydrology, 76: Kobayash, D., 986. Separaton of a snowmelt hydrograph by stream conductance. Journal of Hydrology, 84: Lyne, V. D. and Hollck, M., 979. Stochastc tme-varable ranfall-runoff modellng, Insttuton of Engneers, Australa, Hydrology and Water Resources Symposum, Perth, pp:

9 Lyne, V. D. and Hollck, M., 979. Stochastc tme-varable ranfall-runoff modellng, Insttuton of Engneers, Australa, Canberra, pp: Nathan, R. J. and McMahon, T.A., 99. Evaluaton of automated technques for baseflow Natonal Symposum of Forest Hydrology, Melbourne, Insttuton of Engneers, Australa. Nat. Conf. Pub. No. 8/6, pp: 8. and recesson analyss, Water Resources Research, 6(7): O Loughln, E.M., Cheney, N.P., Burns, J., 98. The bushranger experment: Hydrologcal response of a eucalypt catchment to fre. The Frs Plgrm, D., Huff, D. and Steels, T., 979. Use of specfc conductance and contact tme relatons for separatng flow components n storm runoff. Water Resources Research, 5(): 9 9. Roberts, 959. In Nst/Ematech., 7. e- Handbook of Statstcal Methods, Engneerng statstcs hand book. U.S.A. Shrmohammad, A., Knsel, W. G. and Sherdan, J.M., 984. An approxmate method of parttonng daly streamflow data. Journal of Hydrology, 74: Smakhtn VY,. Low flow hydrology: a revew. Journal of Hydrology 4: Snorasson, A., Fnnsdottr, H.P., Moss, M.,. The extremes of the extremes: extraordnary floods, IAHS publcaton no 7, UK,. 776