Deterministic Methods in Systems Hydrology - Chapter 4

Phân tích hộp đen của Dòng chảy bão trực tiếp4,1 CÁC VẤN ĐỀ CỦA HỆ THỐNG NHẬN DẠNG phương pháp tiếp cận hộp đen để phân tích hệ thống đã được xử lý trong phác thảo trong Chương 1. Nó dựa trên các khái niệm về hệ thống hoạt động được hiển thị trong hình 1.1. Các vấn đề cơ bản của hộp đen xác định là việc xác định và mô tả toán học của hệ thống hoạt động trên cơ sở các hồ sơ đầu vào và đầu ra có liên quan. Trong chương đó, nó đã được...
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Deterministic Methods in Systems Hydrology - Chapter 4 CHAPTER 4 Black-Box Analysis of Direct Storm Runoff 4.1 THE PROBLEM OF SYSTEM IDENTIFICATION The black-box approach to the analysis of systems has already been dealt with in outline in Chapter 1. It is based on the concept of system operation shown in Figure 1.1. The basic problem of black-box identification is the determination and mathematical description of the system operation on the basis of records of related inputs and outputs. In that chapter, it was pointed out that for the case of a lumped linear time- invariant system with continuous inputs and outputs, this mathematical description is given by the impulse response of the system. This contains all the information required for the prediction of the operation of such a system on other inputs. In the case of a linear lumped time-invariant system in which the input and output data are given in discrete form, the operation of the system can be mathematically described in terms of the pulse response. Of necessity, the pulse response contains less information than the impulse response. But it is adequate for predicting for any given input the corresponding output at discrete values of the sampling interval. Accordingly, as pointed out in Section 1.4, the problem of the identification of a lumpedPulse response time-invariant system by black-box analysis amounts to a solution of the set of linear algebraic equations y=Xh (4.1) where h is the vector of unknown ordinates of the pulse response, y is the vector of the known ordinates of the output and X is the matrix formed as follows from the vector of the known input ordinates. The basis for equation (4.2) is given in Chapter 1, where they appear as equations (1.20) and (1.21) respectively. The unit hydrograph approach that is described in Chapter 2 of this book has been seen to be based on the assumption that the catchment converts effective rainfall to direct storm runoff in a lumped linear time-invariant fashion. The finite-period unit hydrograph is then seen to correspond to the pulse response of systems analysis and the instantaneous unit hydrograph to the impulse response. As mentioned in Chapter 2, in the early years unit hydrographs were derived either by trial and error (graphical or numerical) or by the solution of the linear equation by forward substitution. In obtaining these derived unit hydrographs by hand, any obvious errors were adjusted subjectively according to preconceived - 58 - ideas concerning a realistic shape for the unit hydrograph. Later on, attempts were made to derive objective methods of unit hydrograph derivation, which could be applied to complex storm records and automated for the digital computer. Some of these approaches were briefly mentioned in Chapter 3 on Systems Mathematics. Since the derivation of the unit hydrograph is essentially an inversion process, the effects ofInversion process error in the data may appear in a magnified form in the derived unit hydrograph. It is always possible to derive an apparent unit hydrograph from a record of effective precipitation and direct storm runoff. Unless the method of derivation is grossly unsuitable or inaccurate, the recorded output can be approximated closely by the reconstructed output obtained by convoluting the recorded input and this estimated unit hydrograph. Unfortunately, however, the degree of correspondence between the predicted and the recorded output may, as a result of errors in the data, be a poor indicator of the correspondence of the estimated unit hydrograph to the true pulse response. Consequently, the ability of the estimated unit hydrograph to predict the direct storm response for a given pattern of effective precipitation, different to that from which it is derived, cannot be judged on the basis of the ability of the deriv ...