Volume 8 • Issue 2 • 1000299 J Civil Environ Eng, an open access journal ISSN: 2165-784X Nayab and Faisal, J Civil Environ Eng 2018, 8:2 DOI: 10.4172/2165-784X.1000299 Research Article Open Access Jo u r n a l o f C i v i l & E n v iro n m e n t a l E n g i n e e ri n g ISSN: 2165-784X Journal of Civil & Environmental Engineering Water Management in Tarbela Dam By using Bayesian Stochastic Dynamic Programming in Extreme Inflow Season Ayesha Nayab* and Muhammad Faisal Department of Statistics, Quaid I Azam University, Islamabad, Pakistan Abstract Existing method of forecasting inlows at Tarbela have some limitations, also system needs an adequate operating policy model to deal with highly volatile inlow of summer months of June, July, August and September. In this paper, historical data of inlows from 1986 to 2014 have been used to forecast upcoming inlows at dam. Bayesian predictive distribution is used to predict future inlows. These forecasted inlows were further incorporated into operating policy model to determine the optimal release during the prescribed months. Weather volatility is a major factor causing unstable inlows. High temperature during summer period cause high inlows at dam. Considering weather volatility, this policy model is proposed for the lood season (15th June to 30th September), in which inlows and outlows are higher than rest of the year. This model maximizes the expected proit from hydro power production, minimizes the expected loss from lood damage and updates the proper estimate of current stage of reservoir storage. *Corresponding author: Ayesha Nayab, Department of Statistics, Quaid I Azam University, Islamabad, 45320, Pakistan, Tel: +92519064000; E-mail: ayesha.nayab@mail.au.edu.pk Received November 07, 2017; Accepted February 02, 2018; Published February 07, 2018 Citation: Nayab A, Faisal M (2018) Water Management in Tarbela Dam By using Bayesian Stochastic Dynamic Programming in Extreme Inlow Season. J Civil Environ Eng 8: 299. doi: 10.4172/2165-784X.1000299 Copyright: © 2018 Nayab A, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Keywords: Temperature volatility and inlow forecast; Release policy; Bayesian stochastic dynamic programming Introduction Water inlow is the uncertain element which directly afects the release policy of the dam. Inlow into the reservoir is usually high in summer due to snowmelt from high temperature. Also rain in the upstream catchment area is the most critical lood-producing factor of the basin. Monsoon caused heavy rain during summer and water elevation at dam surface oten rose to the peak. To manage available water to generate maximum hydropower and prevent from lood and damage in downstream area is a big challenge in summer because of high volatility of temperature. Tarbela is a multipurpose reservoir, irstly it provides water for irrigation and almost 50% of the country irrigation system is run by Tarbela dam. Secondly, it stores water during lood season to escape from high damage at downstream areas. hirdly, it ofers generation of hydropower to satisfy 30% of the energy needs. To achieve these objectives at their best, system needs a reliable forecast for the inlows and operating policy model. Table 1 presents the water discharge limits at diferent levels of loods. At minimum lood limit release estimate is 7000 m 3 /second and at maximum this release estimate goes to 23000 m 3 /second. In lood season, when the water rises beyond the capacity of the dam, we need to appropriately utilize the substantial amount of available water in such a way that we can generate maximum hydropower with minimum damage at downstream area. herefore, we need to account uncertainty of the inlow in optimal operating policy. he concept of addressing forecast uncertainty along with inlow uncertainty was presented by many authors in the past. Bayesian Stochastic Dynamic Programming model incorporates Bayesian approach within classical Stochastic Dynamic Programming (SDP) formulation [1]. herefore we used Inlow data as prior knowledge and forecasted data as sample information. Posterior distribution was a conditional distribution of forecast over actual inlow to the reservoir. Use of Bayesian Decision heory (BDT) and Bayesian inference for predicting upcoming lows of water along with classical forecasting methods take into account relatively complex problems of natural resource management [2]. Bayesian Stochastic Dynamic Programming (BSDP) is also used as stochastic optimization tool for the development of operating policy model, which incorporates a Bayesian approach within the classical Stochastic Dynamic Programming (SDP) formulation (Table 2) [3]. he use of linear autoregressive (AR) model and linear autoregressive- moving-average (ARMA) model in reservoir optimization is available in literature. he multi lag autocorrelation model by a single hydrologic variable, the value of which changes from day to day and is equal to the conditional mean of the daily inlow [4]. Algorithm which can take into account the inlow stochasticity for calculating optimal operating strategies in a multi-reservoir hydroelectric system does not require discretization of the state space [5]. Case studies with the Brazilian systems give the comparison of Flood Stage Discharge (m 3 /second) Low 7000 Medium 10500 Average 14000 High 18500 Very High 23000 (Source: WAPDA Pakistan, Flood Management Manual 2011) Table 1: Flood limits at Tarbela. Notation Description I t . Inlow at time t nh t . Net head available at time t Ƞ Plant eficiency C t Cost at time t due to excess outlow in downstream area S t Storage at time t R t Rain at time t E t Evaporation at time t O t Outlow at time t λ Estimated threshold level for damage Table 2: Notations used in BSDP model with description.