Shannon information entropy for assessing space-time variability of rainfall and streamflow in semiarid region

The principle of maximum entropy can provide consistent basis to analyze water resources and geophysical processes in general. In this paper, we propose to assess the space-time variability of rainfall and streamflow in northeastern region of Brazil using the Shannon entropy. Mean values of marginal and relative entropies were computed for a 10-year period from 189 stations in the study area and entropy maps were then constructed for delineating annual and seasonal characteristics of rainfall and streamflow. The Mann-Kendall test was used to evaluate the long-term trend in marginal entropy as well as relative entropy for two sample stations. High degree of similarity was found between rainfall and streamflow, particularly during dry season. Both rainfall and streamflow variability can satisfactorily be obtained in terms of marginal entropy as a comprehensive measure of the regional uncertainty of these hydrological events. The Shannon entropy produced spatial patterns which led to a better understanding of rainfall and streamflow characteristics throughout the northeastern region of Brazil. The total relative entropy indicated that rainfall and streamflow carried the same information content at annual and rainy season time scales.