Spatiotemporal analysis of the annual rainfall in the Kingdom of Saudi Arabia: predictions to 2030 with different confidence levels

Predictions of future water resources are essential for the strategic plans of any country especially in arid regions such as Saudi Arabia (SA). This paper presents a modeling study of the temporal annual rainfall variability over SA, evaluating the best model for future rainfall predictions and mapping spatiotemporal rainfall over SA. Common time series models of orders p and q such as autoregressive, AR(p), moving average, MA(q), and the combined autoregressive-moving average, ARMA(p,q), models are utilized. The models are applied to 28 metrological stations distributed over SA. Spatiotemporal statistical analysis of rainfall data is performed over a period between 1970 and 2012. The minimum and maximum fitted parameters of the models are φ1 =  − 0.55, 0.46 for ARMA (1,0), θ1 =  − 0.66, 0.17 for ARMA (0,1) and φ1 =  − 0.84, 0.94, θ1 =  − 0.87, 0.78 for ARMA (1,1), respectively. It has been shown that ARMA (1,0) is the best to model the temporal variability based on the Akaike information criterion (AIC), the correlation coefficient (R), and the root mean square error (RMSE). The Monte Carlo method is used to make future predictions (100 realizations) with the confidence levels (CIs) based on ARMA (1,0). Spatial distribution of the ensemble predictions and their CIs are presented graphically at the upper limit of 95%, 97.5%, and 99% and the lower limit of 5%, 2.5%, and 1% confidence, respectively, for the year 2030 to help decision-makers for future water resources planning of the country. Abha city has the highest annual rainfall prediction in 2030 (221 mm) with upper confidences (436, 533, and 643 mm) for 95%, 97.5%, and 99%, respectively. The prediction results indicate that the high mountainous areas (Asir and Taif) are expected to have more rainfall in the future than the rest of the regions in SA. The use of non-traditional water resources is the solution to future challenges.