HYDROLOGIC UNCERTAINTY MEASURE AND NETWORK DESIGN

ABSTRACT: This paper presents a simple methodology, using the entropy concept, to estimate regional hydro logic uncertainty and information at both gaged and ungaged grids in a basin. The methodology described in this paper is applicable for (a) the selection of the optimum station from a dense network, using maximization of information transmission criteria, and (b) expansion of a network using data from an existing sparse network by means of the information interpolation concept and identification of the zones from minimum hydrologic information. The computation of single and joint entropy terms used in the above two cases depends upon single and multivariable probability density functions. In this paper, these terms are derived for the gamma distribution. The derived formulation for optimum hydrologic network design was tested using the data from a network of 29 rain gages on Sleeper River Experimental Watershed. For the purpose of network reduction, the watershed was divided into three subregions, and the optimum stations and their locations in each subregion were identified. To apply the network expansion methodology, only the network consisting of 13 stations was used, and feasible triangular elements were formed by joining the stations. Hydrologic information was calculated at various points on the line segments, and critical information zones were identified by plotting information contours. The entropy concept used in this paper, although derived for single and bivaviate gamma distribution, is general in type and can easily be modified for other distributions by a simple variable transformation criterion.