Ecological Modelling, 12 (1981) 83--103 83 Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands A CONTROL MODEL FOR PHOSPHORUS LOADING REDUCTION UNDER UNCERTAINTY ISTVAN BOGARDI Mining Development Institute, 1037 Budapest III Mikoviny u. 2--4 (Hungary) LUCIEN DUCKSTEIN Department of Systems & Industrial Engineering and Department of Hydrology & Water Resources, University of Arizona, Tucson, AZ 85721 (U.S.A.) FERENC SZIDAROVSZKY Department of Computer Sciences, University of Agriculture, H-1113 Budapest XI Villanyi ut 29--35 (Hungary) (Accepted for publication 6 August 1980) ABSTRACT Bogardi, I., Duckstein, L. and Szidarovszky, F., 1981. A control model for phosphorus loading reduction under uncertainty. Ecol. Modelling, 12: 83--103~ The control of nutrient loading into lakes causing eutrophication is examined using the loading of phosphorus into Lake Balaton in Hungary as a case study. A system model composed of the state vector, consisting of dissolved P and sediment-fixed P, and the probability density function (pdf) of these quantities is used. The action space has six pure strategies, namely: the control of (1) point source pollution; (2) fertilizer; (3) ero- sion; (4) land use; (5) runoff; and (6), sediment yield. These six pure actions lead to the definition of eight mixed alternatives. The objective of the control to be maximized is the probability uj, that alternative j results in the largest decrease of P-loading. The model is applied to actual data from a sub- watershed of Lake Balaton. The estimation of model parameters using available data or published tables and graphs is shown, and uncertainty problems are discussed. In the Balaton example, the tertiary treatment alternative appears to maximize ui. INTRODUCTION The aim of this paper is to develop a system model which is capable of selecting the best alternative scheme for controlling phosphorus loading into a lake under uncertain conditions. Eutrophication of natural or man-made water bodies is generally caused by excessive nutrient input, mostly phosphorus or nitrogen (Wetzel, 1975). In most cases, a considerable proportion of the total loading stems from non-point sources such as agricultural activity (Golubev et al., 1978). The 0304--3800/81/0000--0000/$02.50 © 1981 Elsevier Scientific Publishing Company