Model appropriateness for simulation climate change and river flooding

An important question in water resources and related subjects is how an appropriate model should look given a specific research area and objective. This question is dealt with by developing a model appropriateness procedure based on model uncertainties. The procedure has been applied to a river basin model meant to assess the impact of climate change on flooding in a large river basin to illustrate the approach. This application indicated that the procedure gives a nice indication in which direction most profit can be gained when an appropriate model should be obtained. Moreover, the results showed that a decrease of input uncertainties and uncertainties associated with the transformation of rainfall to effective rainfall were of particular importance. However, these latter results should be interpreted with caution given the uncertainties in the procedure. discharges, here extrapolated to the design discharge. This is the discharge with a probability of occurrence once in a very long period (for river management in The Netherlands 1250 years). The direction of model appropriateness improvement is determined by a cost function dependent on model output uncertainty. This model output uncertainty is assessed by means of sensitivity and uncertainty analysis with respect to the main inputs, parameters and process descriptions. Finally, the point of minimum costs should be approached to a certain extent sufficient for the user or it turns out that this point will not be reached at all. This final stage is not the main objective and is beyond the scope of this paper. In this paper, first an outline of the model appropriateness procedure is given, then descriptions of the stochastic rainfall model and the river basin model are presented and finally results are discussed and conclusions are drawn. 2 MODEL APPROPRIATENESS PROCEDURE The procedure for the analysis and improvement of model appropriateness will be presented here. The way of analyzing model appropriateness is shown and the method of model appropriateness improvement is presented. 2.1 Analysis of model appropriateness In the procedure, a cost function dependent on model output uncertainty C(y 2 ) is assumed. This cost function consists of two components, the costs necessary to obtain a specific uncertainty level for the input, parameters or model (e.g. model development, data exploration) Cx and the expected costs as a result of the output uncertainty (in water management e.g. damage, dikes) Cy. A model is assumed to be appropriate for a specific research objective when the output uncertainty results in more or less minimal total costs. This is illustrated in Figure 1 (situation A). For simplicity it is assumed that Cx is a block function instead of a declining one (situation B in Fig. 1). This reduces the appropriateness criterion to C(y 2 ) = C((y 2 )B) or, when only uncertainties are considered, y 2 = (y 2 )B = G (constant value). Then model appropriateness can be evaluated by comparing model output uncertainty y 2 with a specific G. It is assumed that the model to be used is approximately smooth and linear and the inputs are independent. Then, model output uncertainty is expressed as (e.g. Morgan & Henrion 1990): Figure 1. Costs as a function of output uncertainty y 2 for