Uncertainty in the Parameters and Predictions of Phytoplankton Models

Di Toro, D.M. & Straten, G. van (1979). Uncertainty in the Parameters and Predictions of Phytoplankton Models. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-79-027

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Abstract

A methodology is developed to evaluate in quantitative terms the effect of uncertainty in the data and the model on the reliability of parameter estimates in phytoplankton models, and to assess the effect of the resulting parameter uncertainty on model predictions. The method of maximum likelihood is adopted as the basis of the analysis, resulting in a weighted least squares estimation problem. The analysis provides an estimate for both the weights and the model errors, where the weights appear to be determined by the data errors and the model errors simultaneously.

A preliminary application of the method is presented for a 16 state variable, 20 parameter phytoplankton model for Lake Ontario. Extensive data for 14 of the 36 state variables is used to calculate the parameter uncertainty covariance matrix and model error variances. The degree of uncertainty of parameters and their mutual cross-correlations are assessed in terms of the subjective options held by workers in the field. Also a preliminary estimate of the effects of the quantity of data available is presented. Finally, the consequences of parameter uncertainty on the prediction error are indicated. It follows that the presence of cross-correlation in the parameter set resulting from the calibration considerably mitigates the error of prediction.

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