Stochastic Modeling for Irrigation Planning of Natuwadi Medium irrigation Project of Konkan region, Maharashtra
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Date
2010
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MPUAT, Udaipur
Abstract
The present study entitled “Stochastic modeling for irrigation planning of Natuwadi medium irrigation project of Konkan region, Maharashtra” was undertaken considering the stochastic nature of inflow to Choriti river in Ratnagiri district of Maharashtra.
One of the objectives of the present study was to develop and validate appropriate stochastic model for Choriti river inflows. Monthly inflow data of Choriti river for a period of 20 years (1988-2007) were collected. Various stochastic models were evaluated for forecasting river inflow. Statistical analysis of the data showed that, the Choriti river is a monsoonal river having most of its inflow in wet season and less than 5% inflow in the dry season. The turning point test, Kendall’s correlation test and regression test performed on seasonal data confirmed that the inflow series is random and trend is found in the series, which was removed by suitable seasonal differencing operation.
The autocorrelation function, partial autocorrelation function, were analyzed to identify the class and order of stochastic model to represent the Choriti river inflows. In all 208 linear nonstationary stochastic models of Seasonal Autoregressive Integrated Moving Average (SARIMA) i.e. SARIMA (p,d,q) x (P,D,Q)12 of models, having non seasonal parameters, (AR and MA), p=0,1,2, and 3 q=0,1, and 2 respectively, seasonal parameters (AR and MA), P=0,1,2, Q=0,1,2 respectively, and non seasonal differencing operation d=0, 1 and seasonal differencing D=0,and 1 were indentified for investigation. The parameters of the identified models were estimated by maximum likelyhood estimation by using “GenStat” software, out of 208 models, 74 models passed the t- test and out of 74 models, 40 SARIMA models passed the ACF & PACF residual test. Finally, 10 SARIMA models namely SARIMA (1,0,0)x(0,1,2)12, SARIMA (1,0,0)x(2,1,0)12, SARIMA (1,0,0)x(2,1,2)12, SARIMA (0,0,1)x(0,1,1)12, SARIMA (0,0,1)x(0,1,2)12, SARIMA(0,0,1) x(2,1,0)12, SARIMA (0,1,1)x(2,1,2)12, SARIMA (2,0,0)x(0,1,2)12, SARIMA (2,0,0)x(2,1,0)12, SARIMA (0,1,2)x(2,1,1)12, based on lowest AIC values are selected for forecasting.
One-time step ahead monthly forecasts were made by all the 10 models and the series is generated for next 49 years. The root mean squared error (RMSE), mean relative error (MRE) and integral square error (ISE) criterion were used for selecting the most appropriate model. It is revealed that, SARIMA (0,0,1) x (0,1,1)12 model was proved to be best among 10 selected models, having lowest RMSE, MRE and ISE values i.e.1.67, 0.88 and 0.57 respectively. Also, the basic characteristics such as mean, standard deviation, variance, coefficient of variation, skewness coefficient, kurtosis and lag-one serial correlation coefficients of the generated series were compared with those of the actual inflow series. It was found that the statistical characteristics of the actual series except mean were distorted in the generated series. The chi-square test applied to judge the adequacy of the forecast, revealed that, all the 10 models forecasted the inflow without significant error in the wet season. It revealed that, SARIMA (0,0,1) x (0,1,1)12 model was proved to be the best model. Therefore, considering the overall process of model building and comparing the results obtained from forecasting by all the 10 models, it can be stated that the Choriti river monthly inflows can at best be forecasted by SARIMA (0,0,1) x (0,1,1)12 model which may be used for water resources planning. With the most appropriate model SARIMA (0,0,1) x (0,1,1)12 forecasting with more lead time was done for the year 2007 to 2008. The inflows forecasted for the year 2007 was utilized further in formulating stochastic linear programming model.
The stochastic linear programming (SLP) model was formulated for arriving at an optimal cropping pattern in Rabi season and reservoir release for the command area. The crop water requirements for the major Rabi crops viz. rice, banana, sugarcane, groundnut, watermelon, chilli, brinjal, cucumber, tomato and fodder maize were computed by Penman- Monteith method using computer programme CROPWAT and these were used in the formulation of SLP model. The model has been developed considering the stochastic nature of inflows in to the storage dam. The linear programming optimization model was solved for two objective functions namely benefit maximization and production maximization under the constraints of capacity, water requirement of the crops, continuity, land availability, etc. The computer software called TORA the optimization software was used to solve the SLP model. The solution of SLP model revealed that, banana is the most profitable crop in the command area. The acreage under banana crop with objective of benefit maximization was 1018.6 ha, which is almost 50% of the net cultural command area.
In view of above, it can be concluded that stochastic linear programming technique is a very useful tool for determining the optimal cropping pattern and derivation of reservoir operation rule curves considering stochastic monthly inflows into the reservoir. Therefore, the present study can be considered as guideline for knowing optimum crop plans and deciding the operational schedule.
Description
Stochastic Modeling for Irrigation Planning of Natuwadi Medium irrigation Project of Konkan region, Maharashtra
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Citation
Ayare and Sharma, 2010