Prediction of Rain-fall flow Time Series using Auto-Regressive Models

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1 Available online a Advances in Applied Science Research, 2011, 2 (2): ISSN: CODEN (USA): AASRFC Predicion of Rain-fall flow Time Series using Auo-Regressive Models SK Khadar Babu 1, K. Karhikeyan 2, M. V. Ramanaiah 3 and D. Ramanah 4 VIT-Universiy, Vellore, TN School of Advance Science (SAS), S.V. Universiy, Tirupahi. AP. Deparmen of Saisics, S.V. Universiy, Tirupahi. AP. ABSTRACT Rain-fall flow daa of a meeorological saion like Vellore in Tamil Nadu have been used for mean monhly flow of rain-fall daa using auo regressive approach. These approaches can be used for regeneraing he fuure sequence preserving he inheried properies of he observed daa. The main saisical properies used for hese purpose are mean, sandard deviaion and he serial correlaion coefficiens. The comparison of he observed rain-fall flow and he synheically generaed daa shows ha he saisical characerisics are saisfacorily preserved. Keywords: rain-fall flow, ARMA, forecasing, Vellore disric. INTRODUCTION The increasing demand of energy, he growing environmenal concern and rapidly depleing reserves of fossil fuel have made planner and policy makers hink and search for ways o supplemen he energy base wih renewable energy sources. In Vellore, a lo of hourly rain-fall flow daa is been colleced by Auomaic Weaher Saion (AWS) a VIT-Universiy campus (ISRO119) Vellore, TN. Designing a proper rain-fall flow sysem requires he predicion of average rain-fall flow saisical parameers [1]. Besides, hese parameers imporan for designing wind sensiive srucures and for sudying air polluion. In he auo-regressive processes where, persisence is presen, ha is he even ou come of he fuure is dependen on he presen period magniude. The Auo Regressive Moving Average (ARMA) processes represen a sysem of elemens moving from one sae o anoher over ime. In a MARKOV processes, he order of he chain gives he number of imes seps in he fas influencing he probabiliy disribuion of he presen sae, which can be greaer han one [2]. The MARKOV chain modeling approach has frequenly been used for he synheic generaion 128

2 SK Khadar Babu e al Adv. Appl. Sci. Res., 2011, 2 (2): of he rain-fall daa. Thomas and Fiering [3] used a firs order MARKVO chain model o generaed sream flow daa. Srikanhan and Mohan [4] used and recommended a firs order MARKOV chain model o generae annual rain-fall daa. Shamshad e al [5] compared performance of sochasic approaches for forecasing river waer qualiy. However a few sudies have been done on he synheic generaion of rail-fall flow daa using ARMA approach. ARMA approach is generally used for modeling and simulaion of rain-fall flow daa. In his sudy, he synheic ime series are generaed using monhly average rain-fall flow daa of abou hree years from 2008 o 2010 (Nov). The AWS is in VIT-Universiy campus locaed a laiude: and longiude: measured a differen ground levels (fig 1). In order o forecas he fuure mean rain-fall flow based on he previous observed informaion ARMA was used (able 1). Fig 1. Sudy area 129

3 SK Khadar Babu e al Adv. Appl. Sci. Res., 2011, 2 (2): Table 1: Daa from AWS-VIT-Vellore Saion Week Monh Rain-Fall Aug Sep Sep Aug Sep Oc Nov

4 SK Khadar Babu e al Adv. Appl. Sci. Res., 2011, 2 (2): Model Developmen 2.1. Auo-Regressive Model: In a series where persisency is presence, ha is he even ou come of (+1) h period is dependen on he presen h period magniude and hose preceding values, hen for such a series, he observed sequences X 1,X 2,.,X is used o fi he AR model. X µ = β µ β µ β µ ) ) K k ) i.(1) 2 Where, µ is he mean of he series, is he random viiae wih zero mean and varianceσ. Which is known as k h order AR model. 3. Daa Analysis Table 1: Esimaion of saisical parameers Sl.No Discharge M 3 (X /sec ) 2 (X ) * (X - (X ) * (X ) ) Toal The firs order AR model is represened as X = β 1 µ 1 µ ) +..(2) i 131

5 SK Khadar Babu e al Adv. Appl. Sci. Res., 2011, 2 (2): and is found o be very useful in waer resource engineering Moving Average model: The equaion for moving model for generaing he values X a any insan in he series is as X µ = + α α... α k k...(3) Where k demoes he order of he moving averages, α 1, α 2,. α k are he coefficiens 2.3. ARIMA model: An Auo-Regressive-Inegraed-Moving-Average (ARIMA) model of level (1,0,1), which is popular used in hydrological sysem and his beer reprenesed as ARIMA (1,0,1). The model is expressed as µ ) + β1 1 µ ) = + α1 1 (4) from able 1, mean= m 3 /sec. r 1 =04547 r = = ( ) σ = ( ) = σ = m 3 /sec. From equaion (2), X = X hen, esimaed X 28 = From equaion (3) Mean = 798.2m 3 2 /sec, r 1 =0.3628, r 2 =0.2532, β 1 =0.3120, β 2 =0.1400, σ = , σ = m 3 /sec. X = (X ) +0.14(X ) X 28 = m 3 /sec. CONCLUSION From he resuls, X 28 value for AR-1 is more applicable, esimaed and compare o X 28 value of AR-2, and also calculae he mean monhly rain-fall flow. In his sudy he fuure mean values prediced based on he previous observed mean values. ARMA is useful o sudy abou he synheic generaion for he wind flow ime series daa analysis. I is observed ha ARIMA approach is more appropriae predicion for he fuure meeorological parameers compare wih 132

6 SK Khadar Babu e al Adv. Appl. Sci. Res., 2011, 2 (2): he probabiliy MARKOV chain models. These models can be useful in missing observaion daa ses. REFERENCES [1] Casino F., Fesa R., Rao CF, Journal of wind engineering in Aerodyn, 1998; 74 (76); [2] Heiko B, Ecol Model, 2000; 126; [3] Thomas H.A., Fiering,M.P., Mahemaical synhesis of seam flow sequences for he analysis of river basins for simulaions, Harvard Universiy press; 1962 : [4] Srikanhan, R., Mc Monan T.A., Sochasic generaion of rain-fall and evaporaion daa. AWRC echnical paper No: 84, 1984, 301 [5] Shamshad A, M.A.Bawada, W.M.A.Wan Hussan, T.A. Mazid, S.A.M.Sanusi., Energy; 2005; 30: