Input for a stochastic control model of P loading

Abstract

In most lakes, phosphorus (P) appears to be the nutrient controlling eutrophication. Furthermore, half of the P loading stems from non-point sources, especially agricultural fertilizers. For the purpose of controlling eutrophication, the uncertainty in P loading is described in two separate categories: P dissolved in runoff, and P fixed or sorbed by sediments. The stochastic model defines hydrologic events as follows: a source of P is available, transport is triggered by rainfall events, which cause both runoff volume V and sediment yield Z. Amount X 1, duration X 2, and interarrival time T are used characterize rainfall events. The amount of dissolved P transported is estimated by multiplying the concentration C 1 of dissolved P runoff volume V; the amount of sorbed P is estimated by multiplying concentration C 2 of P fixed to sediments by sediment yield Z per event. The latter quantity is calculated by means of the Universal Soil Loss equation, while U.S. Soil Conservation Service empirical formulas are used to obtain estimates of peak flow and runoff volumes. Next, total seasonal loading is calculated as the sum of a random number of random P-loading events. Then, loadings from subcatchments around the lake can be added under certain assumptions about the dynamics of the lake, which are discussed. Long-term accumulation of P in the lake is described in terms of solutions of a first order difference equation in three extreme cases: no loading, constant loading and linearly increasing loading. Alternative control methods of P loading from non-point agricultural sources are presented and discussed. The case study of Lake Balaton in Hungary is used throughout the paper to illustrate the stochastic methodology; a numerical example using data from the Tetves subwatershed of Lake Balaton provides preliminary practical results.