Climate variability in space-time variogram models of annual rainfall in arid regions

Global climate change affects weather patterns around the world. Rainfall variability, especially in arid regions, can increase or decrease drastically in the space and time domains. To determine the spatial and temporal continuity of rainfall phenomena, geostatistical models and variograms are key tools for estimating and modeling the space and time dependence in a data set. The basic steps in any regional modeling method involve obtaining the experimental variogram and fitting a model to the experimental variogram. Theoretical matching is performed for the experimental variogram considering the sill, nugget, and other features, which reflect the regional characteristics of the phenomena concerned. In this study, a product-sum space-time-standardized variogram procedure is proposed and used to identify the spatial and temporal structures of annual rainfall in the western part of Saudi Arabia. The standardized variogram is, in fact, the reduced scale of the original form without the loss of the characteristics of the underlying phenomena. The results of the space-time-standardized experimental and variogram models indicate that the average annual spatial variograms have a continuous structure based on an exponential model with a small nugget. The average annual temporal variograms have a continuous structure based on an exponential model with a large nugget. These results confirm the high variation in the rainfall pattern in the time domain and low variation in the spatial domain.