Development of a mathematical model for hydroclimatological drought forecasting

Knowledge of hydrological conditions and forecasting its occurrence for planning and for efficient use of water resources are essential. In this regard, the phenomenon of drought poses some destructive environmental effects on various aspects of hydrological processes. Anticipating the start of a drought phenomenon is very complex. Nevertheless, it is crucial to determine the most probable hydrological condition, after a certain condition of meteorological drought has occurred. Determining how long it will take for the hydrological conditions to be affected by the meteorological drought is also an important issue. The main purpose of this research lies in attaining a method for predicting the occurrence of different hydrological conditions (states) according to various meteorological conditions for a time step ahead, in a basin. For this purpose, a stochastic model that comprises the hydro-climatological variables, based on Markov chain theory is developed. To accomplish this, meteorological and hydrological drought indices were employed. In this case, the time series of precipitation and streamflow were used to determine the different meteorological and hydrological states. Performance of some of the well known meteorological drought indices were evaluated for the selected study area, which was the Semi-Mediterranean region in the North of Iran. Different meteorological and hydrological states were determined using the appropriate drought indices. Besides, the lag time between different meteorological and hydrological states was recognized using the monthly precipitation and streamflow time senes. Probabilities of occurrence of different meteorological states were predicted via a one-dimensional transition probability matrix (ODTPM). Then, with the concept borrowed from the Markov chain theory and with regards to the basin lag time, the ODTPM was further developed into a twodimensional transition probability matrix (TDTPM). This procedure led to a matrix as the main output of this study, which is called the Hydroclimatological Matrix (HCM). Thus, employing the ODTPM and TDTPM, probabilities of occurrence of different hydrological states were forecasted via a Prediction Matrix. Forecast verification was carried out via discrete predictors as a categorical method. Furthermore, the cross-validation approach and root mean square error (RMSE) methods were used for checking the consistence of probability shifts and robustness of the desired matrices. In particular, three study areas, which were Frizi, Joestan and Chalus Basins with various hydroclimatical variables were selected on which the proposed method could be implemented. From this study, it is found that the non-parametric Deciles meteorological drought index method is the appropriate index. The flow duration curve (FDC) method was selected for categorizing the hydrological drought occurrence as an analogue method with the Deciles index. Following this, threshold levels in the range from Q50 to Q95 were adopted to distinguish corresponding levels of hydrological drought severity.The Hydroclimatological matrices (HCM) have shown that a matrix with singletimescale is appropriate with a small basin like the Frizi, and in contrast, for large basins like the Chalus and Joestan, a multi-timescale matrix is more appropriate. Hence, the probabilities of occurrence of events in the Frizi Basin have indicated that hydrologic response of the river basin to climatic variation occurs in a short period of time. Comparison of the probability values related to the Frizi River has illustrated that the probability of occurrence of hydrological drought will increase by about 64.5% when the meteorological state changes from the 'Wet' to the 'Severe Dry' states for the following month in this basin. Notably, the 'Severe Drought' as another meteorological state has a significant impact on the occurrence of hydrological drought during the next three months in this case study. In the Joestan Basin, when the meteorological state changes from the Wet state to the Mild Drought, the river basin will have been trapped in drought with 76% probability. This process will continue with 58% probability, until the following four months for the river basin. In the case of the Chalus Basin, if the basin is attacked by the onset of a Severe meteorological drought in a given month, the hydrological drought streamflow will be experienced with 53.4% probability of occurrence with three months delay. The probability of detection (Hit rate) shows that the verification of forecast performance of the hydroclimatological matrix (HCM) can be adopted as satisfactory forecast. Likewise, results of the Cross-Validation approach and RMSE method exhibit the fact that the probability shifts are consistent in the matrices obtained, so that the HCM as a reference matrix has excelled in the robustness testing. Accordingly, in terms of the river basin management, the implementation of the proposed method for triggering warning towards an impending drought is its significant benefit.

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