Keywords: uncertainty, information, entropy, regional floods, information transferability, flood gauging network.

There are basically two phases in activities for coping with floods: (a) procurement of sufficient and reliable information on flood characteristics, and (b) planning, implementation and operation of flood control measures. The second phase is dependent on the former as the reliability and the effectiveness of flood control measures cannot exceed the level of available information on floods. Thus, reduction of uncertainty, or increase in information about flood characteristics within a basin is the most crucial step towards coping with floods.

Regional flood analysis techniques have been widely used to improve the available information about floods either at a point or at all points of interest in a region. This is realized by combining all or most of the regional information available, with the idea that the region should contain more information on floods than a single point within it. The extensions of such regional analyses cover multiple regression techniques to transfer information from points with sufficient information to those where information is needed.

The question is then whether the available regional information "does" reduce the uncertainty about flood characteristics within the region. Or, if it does, to what extent is the uncertainty reduced? Thus, the prerequisite for any regional flood study appears to be the assessment of regional uncertainty and available information. To this end, the entropy principle is employed here as a convenient statistical tool in evaluating regional flood information and uncertainty. The concept of entropy as defined in information theory is a quantitative measure of information, which describes the utility or usefulness of data [1].

Although the entropy principle has been used in the form of POME (Principle of Maximum Entropy) to infer on distributions of flood events[2,3,4], it may also be employed as Shannon's informational entropy to assess the regional information about floods within a basin. Accordingly, the total uncertainty about flood events observed by a number of streamgaging stations in a basin, can be described as the joint entropy of multi-variables, with each variable representing observations at particular space points. Next, the contribution of each station to the reduction of this total regional uncertainty may be assessed by considering the joint entropy of different combinations of stations[5,6]. Then, the combination which produces maximum reduction in the total uncertainty of the basin about flood events will be accepted as the required system of stations to characterize the floods at a regional scale. If certain stations do not contribute significantly to uncertainty reduction, their observations may be considered redundant with respect to basin-wide information gathering. On the contrary, the existing stations may prove to be insufficient in producing the required information about flood events. Then, new space points may be considered as potential sites of observation to reduce the total regional uncertainty. The work presented demonstrates the use of the entropy concept in assessing the regional uncertainty and indirectly the regional information available about floods within a basin. The purpose here is to show the applicability of the method in evaluating an existing system of streamgaging stations, particularly in cases where a decision must be as to the transferability of regional information. The procedure further indicates needs for expansion of a flood monitoring network in the space domain. Along similar lines, needs for removal of particular existing observation sites may also be delineated. In the study, the applicability of the proposed approach is demonstrated in the case of the Bakircay River basin in Turkey, where coping with floods is a significant problem. The strengths and specific shortcomings of the method are further discussed, with recommendations for future research on the application of the entropy principle in evaluating regional transfer of information about floods.

1

Harmancioglu, N.B., Alpaslan, N., "Water quality monitoring network design: a problem of multi-objective decision-making", Water Resources Bulletin, 28(1), 1-14, 1992.

2

Jowitt, P.W., "The extreme value type-1 distribution and the principle of maximum entropy", Journal of Hydrology, 42, 23-38, 1979. doi:10.1016/0022-1694(79)90004-0

3

Jain, D., Singh, V.P., "Estimating parameters of EVI distribution of flood frequency analysis", Water Resources Bulletin, 23(1), 59-71, 1987.

4

Singh, V.P., Rajagopal, A.K., Singh, K., "Derivation of some frequency distributions using the principle of maximum entropy (POME)", Advanced Water Resources, 9(2), 91-106, 1986. doi:10.1016/0309-1708(86)90015-1

5

Harmancioglu, N.B., Singh, V.P., Alpaslan, N., "Versatile uses of the entropy concept in water resources", Maratea (Potenza), Italy, International Conference on Entropy and Energy Dissipation in Water Resources, June 26-28, 1991.

6

Harmancioglu N. B., "Assessment of Information and Uncertainty Related to Floods" in Coping with Floods, G. Rossi, N. Harmancioglu, V. Yevjevich, (Editors), NATO ASI Series E, Kluwer Academic Publishers, 257, 171-183, 1994.

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