Investigation with Kendall plots of infiltration index–maximum rainfall intensity relationship for regionalization

For Horton overland flows, the determination of effective rainfall intensities is still complex, despite the important number of works, since the thirties. The infiltration phi-index (ϕ-index) method provides an approximation of the infiltration process estimation and is often used in practice. Several studies show that effective rainfall depends on total rainfall intensities, soil characteristics, antecedent conditions and moisture index. In this work, the first stage is identifying and modeling the relationship between this index and the maximum intensity of rainfall (Imax). The investigation concerns 22 catchments (areas between 1 km2 to 10 km2) situated in Tunisia (from 35°N to 37°N, from 8°E to 11°E), in a semi-arid climate zone (average annual rainfall between 280 mm and 500 mm). For this purpose, we propose to adopt Kendall plots which are a recent graphical method based on rank statistics, and which allow the detection of nonlinear dependence between two variables. In addition, the use of rank correlation Kendall’s tau (τ) allows measuring the degree of dependence. This exploration has shown a positive correlation between ϕ-index and Imax. Indeed, the estimated τ vary from 0.47 to 0.91. This reveals the important dependence between the studied variables. Therefore to model this correlation, Gumbel copula has been adopted, with parameter ranging between 1.9 and 11.1. The key question is: which catchments characteristic factors explain the inter-site variability of the copula parameter? Thus the further stage of this study concerns the regionalization of copula parameter using the physiographic and geographical characteristics of basin. The idea is to achieve a bivariate analysis of the copula parameter set in comparison to each set of characteristics. τ values characterize the degree of implication of factors in the relationship of ϕ-index–Imax. The results show that the percentage of forest cover, the percentage of anti-erosive practices and the geographical location, i.e. the north latitude, are the explanatory variables of the relationship. Consequently, the copula parameter regionalization leads to distinguish four different regions: the catchments situated in the North with a weak percentage of forest cover and with a percentage of less than 20% of anti-erosive practices, the South catchments with a percentage of less than 20% of anti-erosive area practices and with a percentage of less than 15% of forest cover, the catchments with a percentage of more than 20% of anti-erosive practices, and finally the catchments with forest cover. It is worth noting that the catchments in a same region are not necessarily geographically contiguous. The regionalization has concerned the delineation of hydro-physiographical regions.