Vízügyi Közlemények, 1984 (66. évfolyam)
4. füzet - Mekis Éva-Szöllősi-Nagy András: Numerikus sztochasztikus csapadék-előrejelző modell - folyamatos lefolyás-előrejelzés időelőnyének növeléséhez
540 Mekis É . és Szöllösi-Nagy A. A numerical stochastic precipitation forecasting model to increase the lead time in forecasting of runoff by E. MEKIS (Miss) Meteorologist-Mathematician and Dr. A. SZÖLLŐSI-NAGY, Civil Engineer Under today's operative conditions input of real-time forecasting models for runoff are causative variables (mainly precipitation) and their output is the expected, future information of the consequences (e. g. runoff). It is obvious that by knowing more about future inputs, the time advantage and accuracy of forecasts of runoff may be increased. In a network of rivers this problem can be solved by a modular decomposition of the system, while in the case of preciptation/runoff calculations the only possibility is to predict the future pattern of precipitation. Starting with the general form of the equation for the prediction of precipitation volumes Mrs. Bodolai (1975) proved that the synoptic processes of precipitation are determined by four main factors in the catchment of rivers Danube and Tisza: potential precipitable water content of the air, vertical velocity, dynamic saturation deficit and available precipitation. It is known that the volume of precipitation is linearly related to precipitable water content and vertical velocity, and inversely to dynamic saturation deficit. If linearity can be assumed, an auto and cross-regressive model may be set up characterized by Eq. (1). Unknown parameters of the model are contained in vector (2) and the historic values of meteorological variables in vector (4). By use of these vectors the model can be described according to Eq. (5). Nothing is known a priori about the dynamics of the parameters. Therefore, it was assumed that they are changing according to a random walk model (6). Dimensions of the model are determined from auto- and cross-correlation functions of the variables. Unknown parameters are estimated by use of the algorithm of linear Kalman-filter (7)-(ll). The one step forecast of precipitation was calculated by Eq. (12). For a problem area the catchment of the Körös River has been selected. Figs. 2 to 5 contain the time series of dependent and independent variables of the model. Due to the fact that a larger part of precipitation is a consequence of the motion of frontal systems, rainfall data for the Körös catchment were taken from the records of meteorological stations of Szeged, Uzgorod and Belgrade. Figs. 6 and 7 are for the presentation of the results of the correlation analyses. The model characterized by Eq. (13) has been set up for the Körös Valley combined with a parameter (14) and with an observation vector (15). Initial values of the model were determined by trial and error (Table I). Forecasts given by the stochastic model and by the Central Forecasting Institute of the Meteorological Service (Budapest) are presented in Fig. 10. Values obtained by the model are somewhat lower but their standard deviation is less. Forecasted precipitation time series are input values in a linear discrete cascade model (DLCM) constructed earlier for the prediction of runoff (Szöllősi-Nagy 1982). Fig. 11 shows the time series of measured and forecasted discharges at Gyula, the latter calculated by use of the forecasted precipitation and by the use of DLCM, then from forecasted precipitation plus a combined DLCM-ARIMA model. The deterministic cascade model has not reduced the error hidden in input time series (in forecasted precipitation). It was transferred to forecasted runoff. A stochastic submodel, however, could reduce this shortage substantially. The stochastic submodel hascompensated the inaccuracy in the forecasted precipitation values. * * *
