A Sensitivity and Error Analysis Framework for Lake Eutrophication Modeling1

Abstract

ABSTRACT: A framework for sensitivity and error analysis in mathematical modeling is described and demonstrated. The Lake Eutrophication Analysis Procedure (LEAP) consists of a series of linked models which predict lake water quality conditions as a function of watershed land use, hydrolgic variables, and morphometric variables. Specification of input variables as distributions (means and standard errors) and use of first‐order error analysis techniques permits estimation of output variable means, standard errors, and confidence ranges. Predicted distributions compare favorably with those estimated using Monte‐Carlo simulation. The framework is demonstrated by applying it to data from Lake Morey, Vermont. While possible biases exist in the models calibrated for this application, prediction variances, attributed chiefly to model error, are comparable to the observed year‐to‐year variance in water quality, as measured by spring phosphorus concentration, hypolimnetic oxygen depletion rate, summer chlorophyll‐a, and summer transparency in this lake. Use of the framework provides insight into important controlling factors and relationships and identifies the major sources of uncertainty in a given model application.