Models to predict lake annual mean total phosphorus

Abstract

A lake is a product of processes in its watershed, and these relationships should be empirically quantifiable. Yet few studies have made that attempt. This study quantifies and ranks variables of significance to predict annual mean values of total phosphorus (TP) in small glacial lakes. Several new empirical models based on water chemistry variables, on ‘map parameters’ of the lake and its catchment, and combinations of such variables are presented. Each variable provides only a limited (statistical) explanation of the variation in annual mean values of TP among lakes. The models are markedly improved by accounting for the distribution of the characteristics (e.g., the mires) in the watershed. The most important map parameters were the proportion of the watershed lying close to the lake covered by rocks and open land (as determined with the drainage area zonation method), relief of the drainage area, lake area and mean depth. These empirical models can be used to predict annual mean TP but only for lakes of the same type. The model based on ‘map parameters’ (r ²=0.56) appears stable. The effects of other factors/variables not accounted for in the model (like redox-induced internal loading and anthropogenic sources) on the variation in annual mean TP may then be estimated quantitatively by residual analysis. A new mixed model (which combines a dynamic mass-balance approach with empirical knowledge) was also developed. The basic objective was to put the empirical results into a dynamic framework, thereby increasing predictive accuracy. Sensitivity tests of the mixed model indicate that it works as intended. However, comparisons against independent data for annual mean TP show that the predictive power of the mixed model is low, likely because crucial model variables, like sedimentation rate, runoff rate, diffusion rate and precipitation factor, cannot be accurately predicted. These model variables vary among lakes, but this mixed model, like most dynamic models, assumed that they are constants.