The role of characteristic coefficients of variation in uncertainty and sensitivity analyses, with examples related to the structuring of lake eutrophication models

The new results of this work concern (1) the presentation of characteristic coefficients of variation (CV=SD/MV; SD=standard deviation; MV=mean value) for a comprehensive set of lake variables, (2) the use of these CV-values in sensitivity and uncertainty tests, and (3) the implication this has for the structuring of lake management models. Two modelling approaches for lake eutrophication have been used to illustrate the basic points of this work. (1) The classical modelling approach where a dynamic (compartment) mass-balance model (using differential equations) is used to calculate concentrations for total phosphorus (TP), which is related to an operational target effect variable (here maximum phytoplankton volume) by means of a regression based on empirical data. (2) This work also uses a more comprehensive dynamic model for lake eutrophication (the LEEDS-model; lake eutrophication, effect, dose, sensitivity). It is demonstrated how characteristic CV-values for important lake variables can be used not just in the traditional sense to test models, but also to build and structure models. This means that the method discussed here based on characteristic CV-values could be seen as a complement to traditional mechanistic, process-oriented methods to build dynamic models. To meet demands in lake management on generality, practical usefulness and predictive power, models should not just be as small as possible and driven by readily accessible variables, but also be well balanced, which means that the predictions of the target variables do not depend too much on inherent uncertainties (CV) associated with just one or a few critical model variables, like the tributary TP-concentration in classical lake eutrophication models of the Vollenweider-type. Such poorly balanced models have generic problems, which means that they will have good predictive power only in a restricted domain. The method discussed in this work using characteristic CV-values for model variables in uncertainty and sensitivity analyses as a basis for model structuring is valid not just for phosphorus in dynamic eutrophication models for lakes, but for chemical substances in dynamic models in general. It has been shown that the choice of the frequency distribution (normal or log-normal) in these tests is markedly subordinate to the choice of the CV-value. A key factor to achieve well balanced models yielding high predictive power today does not lie so much in the sensitivity and/or uncertainty analyses as such, but to gain access to even more reliable empirically-based characteristic CV-values for important lake variables.