The Propagation of Errors and Uncertainty in Forecasting Water Quality - Part I: Method

Beck, M.B., Halfon, E., & Straten, G. van (1979). The Propagation of Errors and Uncertainty in Forecasting Water Quality - Part I: Method. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-79-100

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Abstract

A method is proposed for recursive computation of the propagation of forecasting error covariances where the forecast is derived from a nonlinear state space model of water quality dynamics. This particular method, based on the idea of an extended Kalman filtering algorithm, is more commonly applied to the problem of real-time state and parameter estimation and to the problem of model calibration. This paper exploits that connection in order to stress the close relationship between model calibration and the use of models for forecasting the future behavior of a system. It is argued that the analyst is frequently unaware of the levels of uncertainty in a calibrated water quality model; nor is it obvious how this uncertainty is distributed among the individual relationships that make up the model. Such uncertainty in the model, i.e., the model parameter estimation errors, has a significant effect on the confidence that can be assigned to model-based forecasts. A partitioned form of the algorithm is presented. This not only permits a considerable saving in computational effort but it also provides useful insight into the way in which the various sources of uncertainty propagate forward in time with the forecast.

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