By Dr.-Ing. Alexander Lattermann (auth.)
Modelling of hydrological rainfall-runoff approaches is facilitated through the appliance of the systemtheoretical method of linear, nonlinear and stochastic versions. To this objective, the variables excited about equipment for determinating areal precipitation and baseflow separation are mentioned. The convolution theorem within the idea of linear structures and the mathematical rework approach (Laplace-, Z-transformation) are used to spot features of the watershed, and simulate hydrological procedures. To aid the calculation of version output features, laptop courses are integrated within the textual content. This quantity is appropriate as a textual content for hydrology classes at universities or engineering academies.
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Extra info for System-Theoretical Modelling in Surface Water Hydrology
To obtain an explicit expression for the response function, the integral must be solved with known input and output functions. If the system behaviour can be described by differential equations, the integral equation can be transformed into a differential equation, and the result of both equations is the same. As is known, each differential equation can be transformed into an integral equation, but conversely each integral equation cannot be transformed into a differential equation. Consequently, integral equations can be considered a more comprehensive tool for description of linear systems, and those that can be described by differential equations form a special group among them.
The decomposition of analytical functions is preferably done with functions mathematically simple in handling. 1(t), or exponential functions exp(s). The decomposition in delta functions or step functions can be developed relatively easily and in this procedure the independent time variable (t) is maintained. The field of application for this type of function is called time domain. The decomposition in exponential functions can be carried out by the Laplace transformation method, and in this procedure the independent time variable (t) appears in the form of a complex number representing any frequency.
They do not change with time. This means that the results of system analysis are time independent, and can therefore be used directly for model application at any time. In the case of hydrological systems and their stationarity, normally no time independence of the behaviour is given owing to the influence of seasons, climates, periods, etc. In this text dealing with an approximation of system behaviour for hydrological systems, time independence is assumed. Input function PI q Input function t Output function t r q t q(t) - H[p(t)] PI Output function r t q(t-r) = H[p(t-r)] Fig.