Definition of homogeneous regions through entropy theory

An important topic for regional flow frequency analysis is the definition of regions, within which the hydrological information can be transferred. In particular, a homogeneous region is a set of catchments, that can be considered homogeneous in terms of hydrologic response and statistical distribution of the hydrological extremes. In the scientific literature different techniques are presented and utilized to group catchments, such as the so called region of influence, the canonical correlation analysis, the correspondence analysis and the L-moments. The first two methods are used to determine the region of influence (ROI) of a particular drainage basin. For these procedures each target site is assumed to have its own homogeneous region. The last two methods are used to identify a fixed region. In this work the issue of identifying an homogeneous region is handled by a standard method (ROI defined by Euclidean distance) and by a new entropy based approach. Since basins are defined homogeneous if sharing redundant information, they are characterized by an high value of total correlation (i.e. a measure of redundancy). On the other hand the grouped basins must provide a relevant amount of information, that is measured through their joint entropy (i.e. measure of joint information). In this framework the cluster problem is faced through the definition of a new index (named SNI) that represents the rate between the redundant information and the joint information provided by couple of stations. The higher the value of SNI, the higher the relationship between the two considered stations. From the analysis of the SNI values it is possible to associate to each station the most related ones. Statistical tests are then carried out to establish whether the grouped data arises from a common regional distribution.