A Stochastic Model of Phosphorus Loading from Non-Point Sources

Bogardi, I. & Duckstein, L. (1978). A Stochastic Model of Phosphorus Loading from Non-Point Sources. IIASA Research Memorandum. IIASA, Laxenburg, Austria: RM-78-033

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Abstract

A stochastic model is presented and applied for Lake Balaton, Hungary to estimate the phosphorus (P) loading from non-point sources. Rainfall events cause surface runoff events and erosion events; all three events are random. P is carried by runoff into the lake in two forms: (1) dissolved P and (2) sediment, absorbed or fixed P. P loading is thus considered as a random variable, whose probability density function (pdf) per event is to be estimated. Pdf of seasonal (e.g. annual) loading is determined as the sum of a random number of random events.

The annual mass balance of P stored in lake sediment leads to a first order difference equation, the solution of which can be used to predict the expected P available for release at future times The model is applied for the Tetves subwatershed (70 sq. km.) of Lake Balaton. Preliminary results show that during relatively short runoff events about as much P reaches the lake as during the rest of the year and that more sediment P is produced than dissolved P. Since a considerable variance apppears in the annual amounts of P loading, the use of stochastic models to estimate the loading conditions seems to be most appropriate. The stochastic loading model should be incorporated into a broader control model. Elements of such a control model are given in the form of possible P loading reduction measures; also, economic trade-off between these measures is discussed.

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