Spatio-temporal Prediction of Drought by Using SPEI in North-East of Iran

Background and objectives: Drought is one of the most complex and dangerous natural disasters that changes both in space and time. Global warming has intensified such extreme events in recent years. Thus, the use of drought indices that consider both the effects of precipitation and temperature, as well as the use of joint spatio-temporal methods, which are the extensions of spatial statistics, can probably lead to better drought monitoring and thereby increasing the accuracy of predictions. The data correlation structure is determined by the spatio-temporal covariance functions in these methods. The aim of this study is to use and compare a number of spatio-temporal variograms for predicting and spatio-temporal mapping of drought by using the 12- month SPEI index.
Materials and methods: In this research, the monthly rainfall and temperature data of 48 stations in the northeast of Iran during the statistical period of 1981-2012 were used to calculate the SPEI index in a 12-month time scale. The exploratory analysis of the data was studied in terms of stationarity and isotropy assumptions. The data were divided into two groups of training and experimental data of 2012. The separable, metric, sum-metric and product-sum spatio-temporal covariance functions were fitted to determine the best combination of spherical, linear and exponential variograms for each of the spatial and temporal variograms on training data. The best model was selected using the MSE and MSPE statistical criteria, and the required parameters were estimated. Finally, using spatio-temporal kriging, the experimental data were predicted, mapped, and compared with the map of the observed values. Cross-validation of spatio-temporal and purely spatial models was done via COR, ME, MAE and RMSE statistical criteria by using 25 and 47 neighborhoods.
Results: The test of the stationarity of spatio-temporal data showed the spatial stationary. Drawing of the average time series data showed a decreasing trend, which was modeled by a simple regression with the use of SPEI index values as dependent variable and time as an explanatory variable, and the data were detrended. The spatial variogram in four directions of 0°, 45°, 90° and 135° did not show a significant difference between the four variograms and the assumption of isotropy was therefore accepted. The separable, metric, sum-metric and product-sum models were used to determine the correlation structure of data. The comparison of models by means of MSE criteria showed that product-sum and sum-metric models have less error as compared with the other two models. Comparison of these two models in the prediction of unobserved values selected the product-sum model as the better model with the linear variogram for both the space and time via the MSPE criteria. After estimating the model parameters and using spatio-temporal kriging, the SPEI values were predicted for the experimental data and their spatio-temporal maps were plotted. The similarity of the map of the predicted values and that of observed values indicated the good performance of the model in predicting the unobserved values. Cross-validation of spatio-temporal and purely spatial models also showed that the performances of various models were very close to each other.
Conclusion: The results of this study showed that the product-sum spatio-temporal covariance model has a good ability to predict the unobserved values as compared to other models, and with the aid of these models, the values of the desired variable can be predicted in any spatial location and at any time scale. Also, cross-validation of the models showed that the different spatio-temporal and purely spatial models do not differ significantly from one another, and the precision of the models have not increased as compared to the purely spatial state.