The frequency response method used in modelling environmental systems: a working example

This paper proposes the frequency response method as a suitable approach to the construction and analysis of dynamic models for environmental systems. The method is one of the major tools of the theory of linear dynamic systems. It is based on an approximation of the frequency characteristic function of a linear dynamic system, calculated from input-output measurements, by a frequency model of the system transfer function in the form of the ratio of two frequency-dependent polynomials in the frequency domain. A frequency domain model is a counterpart of a time domain model in the form of a differential equation. After a brief theoretical section, the frequency response method is demonstrated on the modelling of environmental systems defined on the basis of data recorded in London during periods of culminating fog in December 1952 such as the number of deaths, the mean atmospheric sulphur dioxide content and the mean atmospheric smoke. The results obtained are compared with those calculated by the method of linear regression. It is shown that the regression method failed to determine an adequate interplay of these environmental variables. On the other hand, the frequency response method yielded sufficient models for delineating dynamic changes in the number of deaths that occurred as the consequence of dynamic changes in the environmental conditions.