Entropy theory for analysing water resources in northeastern region of Brazil

Using the Shannon entropy, the space-time variability of rainfall and streamflow was assessed for daily rainfall and streamflow data for a 10-year period from 189 stations in the northeastern region of Brazil. Mean values of marginal entropy were computed for all observation stations 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. The marginal entropy values of rainfall and streamflow were higher for locations and periods with the highest amounts of rainfall. The entropy values were higher where rainfall was higher. This was because the probability distributions of rainfall and the resulting streamflow were more uniform and less skewed. 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.