Modelling Opeki River flow for sustainable rural developmen

Boluwade Alaba (7230143)

English

Loughborough University Institutional Repository

ALABA17329th WEDC International Conference Abuja, Nigeria, 2003Modelling Opeki river flow for sustainable rural developmentBoluwade Alaba, NigeriaTOWARDS THE MILLENNIUM DEVELOPMENT GOALSTHE MODELLING OF Opeki River  flow using  an iterative,powerful but rather complicated modelling  procedurecalled Box-Jenkins methodology is presented. This tech-nique involves identification, estimation and diagnosticcheck stages. The Autocorrelation (ACF) and PartialAutocorrelation (PACF) are demonstrated to be usefulidentification tools. Average monthly discharges from 1981to 1997 were used for the model development, three modelswere entertained. When Portmanteau lack of fit test wasperformed on these models, they show adequacy. AkaikeInformation Criterion (AIC) was used to select the’ best’model. The potentials of Opeki River could now be realizedin form of irrigation practice, hydroelectricity generationand water supply.Keywords: Box-Jenkins methodology, Opeki River flow,average monthly discharge, Portmanteau test, AIC, sus-tainable developmentIntroductionIt is very imperative to know the importance of modellingriver flow and its contributions to sustainable develop-ment. Modelling river flow has strong attachments toeconomic, social and environment(pillars of sustainabledevelopment (DFID, 2002)) concerns of the rural dwellers.Generally, river flow modelling involves the developmentof a model. When such model has been developed, it istested to see if it is adequate for the intended purpose, if not,it may be improved  by the abstraction of additionalfeatures of the series until the model is considered valid.Validity of a model means gaining confidence that theinformation it provides about the series is accurate for itsintended purposes.Aim of studyDevelopment of a model for Opeki River flow ( Eruwa,Oyo state, Nigeria) which can be a designing and planningtool for planners and decision-makers.Materials and methodsOpeki River is a major river in Eruwa area of Oyo State,Nigeria. It is a seasonal river with high rainfall amountduring the rainy season and a lesser amount in the dryseason. It is a tributary to the Ogun River, Ogun State,Nigeria where there had been various irrigation schemesand dam development (Ogun River Basin, 1980). Theaverage monthly discharges of Opeki River was obtainedfrom Ogun Oshun River Basin Authority, Abeokuta, Ni-geria, the custodian of such information. The data was thensubjected  to analysis using the Box – Jenkins modelingprocedure (Box – Jenkins, 1970; Drako, 2002; Fuller ,1996; Maddala, 2001). A Statistical Package for SocialScience (SPSS) was used to facilitate the analysis. Themodelling procedure is as follows; tentative models  iden-tification (ACF and PACF acted as the useful aid), coeffi-cients estimation ( modified sum of squares technique),diagnostic checking ( Portmanteau lack of fit test) AkaikeInformation Criterion (AIC) (ensuring model parsimony),and use model for data generation, forecasting and control.Results and discussionsThree models were entertained by visual inspection of theACF and PACF. They are;Autoregressive Integrated Moving Average (ARIMA)(5,0,0) , ARIMA(1,1,1) and ARIMA(2,1,2).Following the Box- Jenkins mathematical  procedure;ARIMA(5,0,0) becomes;Ø5(B)(1-B)lnZt = at                                                                 (1)whereØ5 = 5th order autoregressive coefficientsB = backshift operatorlnZt = transformed seriesat = white noise (error)likewise:ARIMA(1,1,1);Ø1(B)(1-B)lnZt =è1(B1) at                                                                (2)ARIMA(2,1,2);Ø2(B)(1-B)lnZt =è2(B2)at                                                                                                 (3)è1 and è2 are the 1st  and 2nd  moving average coefficientsrespectively.The models coefficients were successfully estimated andthe residuals did show evidence of randomness about zero.All the models passed the diagnostic stage. The calculatedChi-square values were less then the tabulated values. Themodels could be said to be adequate. Akaike InformationCriterion (AIC) helped to select the’ best’ model. ARIMA( 2,1,2) (equation 3) was discovered to be the‘best’ model that represents the observed  records (Figure1). This model has the lowest AIC value of 454.22 compareALABA174to 467.10 and 477.26 of ARIMA(5,0,0) and ARIMA(1,1,1)respectively.ConclusionsThe modelling of Opeki River flow as it relates to sustain-able development has been described. The simulated valuesusing the ‘ best’ model looks reasonable when tested (Figure1). The AIC technique that selects the’ best’ model has beenemployed to ensure model validity. Modelling properlyand selecting the right model especially in hydrologicdesigns often prevent the grave social and economicalconsequences that occur once the project is constructed.The cost of developing an ARIMA model are insignificantwhen compared to the penalty that arise if river flow seriesis poorly modelled.Having  followed this Box –Jenkins methodology, deci-sion-makers and planners will be able to use this developedmodel for planning and designing of flood controls, irriga-tion, inland waterway projects, water supply etc ‘withoutfear’ on Opeki River which would invariably  reducepoverty and maintain livelihood into the future for Eruwadwellers.ReferencesBox, G. E. P and G. M  Jenkins 1970. Time Series Analysis:Forecasting and Control. Holden-Day Inc. San Fran-cisco,  CaliforniaDFID, 2002. A Key to Sustainable Development. A Speechby Clare Short, Secretary of State for International Devel-opment at the Royal Geographical Society, London.Drako, K. 2002. Introduction to Time Series Analysis:Course outline. University of Essex, United Kingdom.Fuller, W. A . 1996. Introduction  to Time Series. 2ndEdition, John Wiley.  New York.Maddala, E. 2001. Introduction to Econometrics. JohnWiley. New YorkOgun River Basin, 1980. A Draft Report. Ogun OshunRiver Basin Authority, Abeokuta, Nigeria.BOLUWADE ALABA, Department of Agricultural Engi-neering, University of Ibadan, Ibadan, Nigeria.abolu2002@yahoo.com020406080100120140160YearsAverage monthly discharge (m3 /sec)ObservedFitted1981            1982      1983    1984     1985     1986      1987       1988  1989      1990      1991      1992          1993      1994    1995     1996    1997Figure 1. Forecasting analysis for ARIMA(2,1,2) model

Modelling Opeki River flow for sustainable rural development

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Modelling Opeki River flow for sustainable rural development

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