Fourier-ARIMA modelling of the multiannual flow variation

I. Haidu Department of Geography University of Cluj-Mapoca, Str. Tâsnad, Nr. 20, Bl. E3, Sc. IV, Ap. 39,3400', Cluj-Napoca, Romania P. Serbrn & M. Simota Institute of Meteorology and Hydrology, Sos. Bucuresti-Ploiesti, Nr. 97 Bucharest, Romania ABSTRACT In order to analyse multiannual flow variations, Fourier, ARIMA and combined Fourier-ARIMA models were usedo The combined Fourier-ARIMA model takes into account the following components: the general trends, the periodical component, the moving average and the random component. Eleven chronological series of annual mean discharges, extending over periods of 55-145 years, were analysed by means of the models. Relative error analysis of the mean annual computed hydrograph and the mean annual measured hydrograph emphasized the superiority of the combined Fourier-ARIMA model over the Fourier and ARIMA models. This combined model provides for a substantially more accurate eleboration of a flow prognosis for groups of years with different qualitative hydrologie characteris­tics. Modelisation Fourier-ARIMA de la variation multiannuelle de l'ecoulement RESUME Modeles du type Fourier, ARIMA et une combinaison des modeles Fourier et ARIMA ont ete utilises pour analyser la variation multiannuelle de l'ecoulement. Le modele combine Fourier+ARIMA tient compte des composantes suivanles: la tendance generale, la composante periodique en forme des series Fourier. La composante autoregressive et moyen glise, et le component aleatoire. En utilisant ces modeles on a analyse onze series chronologiques des debits moyens annuels ayant une duree de 55-145 ans, representant des unites climatiques homogenes du basin du Danube. L'analyse des erreurs relatives entre les debits moyens annuels calcules et mesures a mis en evidence la superiorite du modele combine Fourier-ARIMA par comparison aux modeles Fourier ou ARIMA. Le modele Fourie-ARIMA permet d elaborer avec une precision suffisante de la prognose de l'ecoulement pour des groupes d annees ayant des caracteristiques qualitativement differentes. 281