Comparing evaporative sources using relative entropy – a tool to diagnose the origins of droughts

An established method of linking precipitation events to the evaporative sources of water vapor supplying those events (the Quasi-Isentropic Back Trajectory (QIBT) method) produces maps of the mass-weighted probability of likelihood that the water falling as rain over that location originated as surface evaporation from any place in the world. These probability distributions vary somewhat with season, and more generally for the precipitation at any location they vary in size, shape and structure over time depending on the prevailing winds, atmospheric conditions and evaporation rates over surrounding areas. Relative entropy (also known by other names, e.g., Kullback–Leibler divergence) is an objective quantification of the similarity between two probability distributions. It is frequently applied to one-dimensional probability distributions, but the mathematics are valid at higher dimensionalities as well. We apply this method to the two-dimensional patterns of evaporative sources calculated from MERRA data and observed rainfall to determine whether their normalized distributions during situations of drought or flood are significantly different from their climatological patterns. If the distributions are similar to climatology (relative entropy is low), we may conclude that the general circulation and remote conditions are not the driving factor behind precipitation extremes. There is a general tendency for droughts to have higher relative entropy than flood cases using monthly data, meaning droughts are more likely to result from circulation anomalies than wet conditions on these time scales. Humid climates, such as over the tropics in the vicinity of the ITCZ, monsoon regions in the wet season, and rainy mid-latitude zones, are least likely to experience precipitation extremes linked to shifts in evaporative moisture sources, suggesting local feedbacks may play an important role.