Error propagations in step-by-step predictions: examples for environmental management using regression models for lake ecosystems

摘要

In step-by-step predictions a desired y-variable is predicted in several steps in such a way that the model variables used to predict y are themselves predicted variables. The aim of this paper is not to discuss mathematica1/analytical aspects of error propagation, since this has been treated before, but to utilise a comprehensive set of data from lakes to illustrate and discuss some inherent problems with step-by-step predictions in ecosystem modelling. Data from real ecosystems are always more or less flawed/uncertain due to technical and economical restraints related to sampling, sample preparation and analytical methods, and it is often impossible to find "independent" operationally defined variables (like water chemical and/or biological variables) for natural ecosystems, where "everything depends on everything else". A central question in this work is. How is error propagation manifested for step-by-step predictions for regression models based on such data? Monte Carlo simulations have been used to study error propagations since this method is very useful for such quantifications. In the first case study, the objective is to predict lake morphometric variables from catchment area maps. The second example concerns regression models for mercury in lakes. Predictive accuracy is generally lost at all steps in step-by-step predictive models. This means that the confidence limits may be very wide if many steps are used in the prediction. It therefore follows that regression models of this kind should use the fewest possible steps and that critical tests of the predictions s hould be undertaken.