Hydrologic Network Design Formulation

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Abstract
Existing methods of hydrologic network design are reviewed and a formulation based on Shannon’s information theory is presented. This type of formulation involves the computation of joint entropy terms which can be computed by discretizing hydrologic time series data collected at station locations. The computation of discrete entropy terms is straightforward but in handling large numbers of stations enormous computation time and storage is required. In order to minimize these problems, bivariate and multivariate continuous distributions are used to derive entropy terms. The information transmission at bivariate level is derived for normal, lognormal, gamma, exponential, and extreme value distributions. At the multivariate level, multivariate form of normal and lognormal probability density functions are used.In order to illustrate the applicability of the derived information relationship for various bivariate and multivariate probability distributions, daily precipitation data for a period of two years collected at some selected locations in the lower Mainland Region of British Columbia was used in this study. Information transmission between station pairs was calculated for different cases of probability distributions and based on information maximization principles and the optimum locations of the stations to be retained were identified.

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