Deterministic Methods in Systems Hydrology - Chapter 6

Lắp ghép những mô hình dữ liệuBài học chính được học từ các cuộc thảo luận của chương 5 là có thể xuất hiện sự khác biệt nhỏ trong hình dạng giữa một mô hình khái niệm cũng được lựa chọn hai tham số và một với một số lượng lớn các thông số này sẽ khuyến khích chúng tôi cố gắng để phù hợp với hydrographs đơn vị mô hình khái niệm dựa trên hai hoặc ba thông số, chứ không phải là mô hình khái niệm phức tạp với một số lượng lớn các thông số. Một lợi...
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Deterministic Methods in Systems Hydrology - Chapter 6 CHAPTER 6 Fitting the Model to the Data The main lesson to be learned from the discussion of Chapter 5 is that there may appear little difference in shape between a well chosen two-parameter conceptual model and one with a larger number of parameters, This would encourage us to attempt to fit unit hydrographs with conceptual models based on two or three parameters, rather than on more complex conceptual models with a large number of parameters. An additional advantage of using a small number of parameters is that this enables us to concentrate the information content of the data into this small number of parameters, which increases the chances of a reliable correlation with catchment characteristics. In choosing a conceptual model the principle of parsimony should be followed and thePrinciple of parsimony number of parameters should only be increased when there is clear advantage in doing so. These conclusions, based on an analytical approach, are confirmed by numerical experiments on both synthetic and natural data, which are described below. 6.1 USE OF MOMENT MATCHING Once a conceptual model has been chosen for testing, the parameters for the conceptual model must be optimised i.e. must be chosen so as to simulate as closely as possible the actual unit hydrograph in some defined sense. In the present chapter attention will be concentrated on the optimisation of model parameters by momentOptimisation of matching i.e. by setting the required number of moments of the conceptual model equal tomodel parameters the corresponding moments of the derived unit hydrograph and solving the resulting equations for the unknown parameter values. This approach has the advantage that the moments of the unit hydro-graph can be derived from the moments of the input and of the output through the relationship between the cumulants for a linear time-invariant system as given by equation (3.75). It has the second advantage that the moment relationship can be used to simplify the derivation for the moments or cumulants of conceptual models built up from simple elements in the manner described in the last two sections of Chapter 5. The use of moment matching may be illustrated for the case of a cascade of linear reservoirs, which is one of the most popular conceptual models used to simulate the direct storm response. Since this is a two-parameter model we use the equations for the first and second moments and set these equal to the derived moments. The first moment is given by nK  U1 ( h)  U 1 ( y )  U1 ( x) (6.1) and the second moment by 2 (6.2) nK  U 2 (h)  U 2 ( y )  U 2 ( x ) Once the first moment about the origin and second moment about the centre for the unit hydrograph have been determined from the corresponding moments of the effective precipitation and direct storm runoff, it is a simple matter to solve equations (6.1) and - 92 - (6.2) in order to determine the values of n and K which are optimum in the moment matching sense. Where a conceptual model is based on the routing of a particular shape of time-Time-area- area-concentration curve through a linear reservoir, the cumulants of the resultingconcentration conceptual model can be obtained by adding the cumulants of the geometrical figurecurve representing the timearea-concentration curve and the cumulants of the linear reservoir. Thus, for the case of a routed isosceles triangle where the base of the triangle is given ...