Spatially heterogeneous drought analysis theory and future trends

Abstract

• Spatial drought occurrences and areal coverage probabilities. • Heterogeneous probability values for each sub-area. • Extreme value probability coverage probability formulations. • Suggestions for future research on spatial drought analysis. Most often drought analysis methodologies are based on point-wise time series record assessments with very specific local conclusions, but their areal, regional and in general spatial properties are examined to a lesser extent. This paper will provide general description of droughts in addition to the regional methodological approaches with rather simple but innovative manner. The study area is thought as composed of a set of sub-areas each with different dry (wet) period probabilities. In general, heterogeneous region has different probability of dry(wet) spell occurrence at each sub-area. In fact, whenever the probability at each sub-area is not equal to any other sub-area, it corresponds to heterogeneous region. The areal cover probability (ACP) of the region is derived by considering the point-wise probabilities on the assumptions that the occurrences of dry (wet) spells are mutually exclusive, independent with heterogeneous probability patterns. Additionally extreme value probabilities of areal drought coverage are derived for heterogeneous sub-area probabilities. All of the heterogeneous drought probability expressions reduce down to homogeneous case provided that sub-areal probabilities are equal to each other. The methodology presented in this paper paves ways for more realistic drought phenomenon spatial probability of occurrences when the sub-areal dry spell probabilities are dependent on each other but heterogeneous.