Models that can predict the impact of human activities on the environment are a prerequisite for efficient environmental management. Most of the models currently in use are based on either very simple empirical relationships or very complex mathematical descriptions of the major physical, chemical, and biological processes that influence the system under consideration. The studies underlying this thesis show when and how it is possible to derive simple statistical models, so-called metamodels, that are consistent with the behaviour of complex, process-oriented models of substance transport in soil. In particular; it proved possible to derive such models for long-term leaching of nitrogen. Meta-models are especially valuable in decision support tools for environmental management, because they are easy to comprehend, and they highlight the minimum amount of information that is needed to estimate the effects that a given human activity will have on the environment. The merits of metamodels are greatly enhanced if they include linear structures, which can allow spatially distributed inputs to be replaced with spatially aggregated inputs without jeopardising the accuracy of spatially aggregated model outputs.

The derivation of meta-models involves thorough statistical analysis to identify the dominant structures of the underlying process-oriented models. Here, extensive Monte-Carlo simulations involving a basically non-linear soil nitrogen model revealed two situations in which linear structures emerged. First, the meteorologically induced variation in annual or multi-annual model outputs was almost completely explained by linear functions of daily meteorological data. Second, a study of long-term nitrogen flows showed that the amount of nitrogen leached from the root zone was an almost linear function of the amount of nitrogen removed through harvesting. Moreover, a method based on partial least squares regression was described for quantification of the impact of daily and monthly meteorological inputs on annual outputs. Also, a stochastic weather generator that can produce an arbitrarily long time series of meteorological data was constructed, and such generated data was used in the Monte-Carlo simulations.