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Shannon’s information theory in hydrologic network design and estimation Husain, Tahir

Abstract

The hydrologic basin and its data collection network is treated as a communication system. The spatial and temporal characteristics of the hydrologic events throughout the basin are represented as a message source and this message is transmitted by the network stations to a data base. A measure of the basin information transmitted by the hydrologic network is derived using Shannon's multivariate information. An optimum network station selection criterion, based on Shannon's methodology, is established and is shown to be independent of the estimation of the events at ungauged locations. Multivariate information transmission for the hydrologic network is initially computed using the discrete entropy concept. The computation of the multivariate entropy is then extended to the case of variables represented by continuous distributions. Bivariate and multivariate forms of the normal and lognormal distributions and the bivariate form of gamma, extreme value and exponential probability density functions are considered. Computational requirements are substantial when dealing with large numbers of grid points in the basin representation, and in the combinatorial search for optimum networks. Computational aids are developed which reduce the computational load to a practical level. The performance of optimal information transmission networks is compared with networks designed by existing methods. The ability of Shannon's theory to cope with the multivariate nature of the output from a network is shown to provide network designs with generally superior estimation performance. Although the optimal information transmission criterion avoids the necessity of specifying the estimators for events at ungauged locations, the criterion can also be applied to the determination of optimal estimators. The applicability of the information transmission criterion in determining optimal estimation parameters is demonstrated for simple and multiple linear regression and Kalman filter estimation. Information transmission criterion is applied to design the least cost network where a choice of instrument precision exists.

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