Complexity of the space-time structure of rainfall.

Understanding precipitation processes has important practical implications comprising the dimensioning of rainwater evacuation structures, disaster prevention planning, territorial occupation planning, water resources management and the performance of natural, agricultural and urban ecosystems. However, its inherent irregularity has not been deciphered. There are various mathematical developments attempting to describe the space - time dynamics of this complex hydrological process, but they are not adequate enough. Among the former works reported in the scientific literature, the study of the space - time structure of rainfall was rendered by mean of statistical analyzes in order to characterize the variability and randomness of their observations. But even in this field there are limitations for a complete description of the stochastic structure of rainfall fields, traditional models have not been appropriated, they produce smooth functions to characterize a very irregular field and the improvement of these models requires the proliferation of parameters and hypothesis, which is not satisfactory. In addition to the challenges of finding adequate descriptions, it has become crucial to incorporate the dynamics of the physical process, which should come from an integration of thermodynamics, atmospheric dynamics and turbulence, enabling some progress in prediction. This review paper describes the main features of the space - time structure of the precipitation fields, points out the difficulties for its understanding and explores the challenges coming from its complexity. [ABSTRACT FROM AUTHOR]