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Application of linear stochastic models for drought forecasting in the Büyük Menderes river basin, western Turkey

Abstract

In the present study, a seasonal and non-seasonal prediction of the Standardized Precipitation Index (SPI) time series is addressed by means of linear stochastic models. The methodology presented here is to develop adequate linear stochastic models known as autoregressive integrated moving average (ARIMA) and multiplicative seasonal autoregressive integrated moving average (SARIMA) to predict drought in the Büyük Menderes river basin using SPI as drought index. Temporal characteristics of droughts based on SPI as an indicator of drought severity indicate that the basin is affected by severe and more or less prolonged periods of drought from 1975 to 2006. Therefore, drought prediction plays an important role for water resources management. ARIMA modeling approach involves the following three steps: model identification, parameter estimation, diagnostic checking. In model identification step, considering the autocorrelation function (ACF) and partial autocorrelation function (PACF) results of the SPI series, different ARIMA models are identified. The model gives the minimum Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC) is selected as the best fit model. Parameter estimation step indicates that the estimated model parameters are significantly different from zero. Diagnostic check step is applied to the residuals of the selected ARIMA models and the results indicated that the residuals are independent, normally distributed and homoscedastic. For the model validation purposes, the predicted results using the best ARIMA models are compared to the observed data. The predicted data show reasonably good agreement with the actual data. The ARIMA models developed to predict drought found to give acceptable results up to 2 months ahead. The stochastic models developed for the Büyük Menderes river basin can be employed to predict droughts up to 2 months of lead time with reasonably accuracy.

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Correspondence to Ömer Faruk Durdu.

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Durdu, Ö.F. Application of linear stochastic models for drought forecasting in the Büyük Menderes river basin, western Turkey. Stoch Environ Res Risk Assess 24, 1145–1162 (2010). https://doi.org/10.1007/s00477-010-0366-3

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  • DOI: https://doi.org/10.1007/s00477-010-0366-3

Keywords

  • Stochastic modeling
  • ARIMA
  • SPI
  • Drought forecasting