Stochastic Modeling of Annual Maximum and Minimum Streamflow of Kelkit Stream

Abstract

The aim of this study is to determine whether the daily extreme streamflows could be generated by stochastic models. For the study, a linear stochastic model known as either Box-Jenkins or ARIMA was used. A Mann-Kendal nonparametric test was applied to the daily extreme data sequences to examine the existence of trends. This test showed that there was no trend in the daily data sequences. The ARIMA model is referred as ARMA since there was no trend in the data sequences and thus, the non-seasonal differencing operator is equal to zero. By using the graphs of ACF and PACF, alternative ARMA models were determined. The plots of the ACF show that there was no linear dependence between the daily maximum streamflows, whereas a linear dependence was observed between the daily minimum streamflows. Therefore, modeling of daily maximum data sequences was discarded. There are four ARMA models that fulfilled all the diagnostic checks among selected models from the graphs of ACF and PACF for the daily minimum data sequences. But ARMA (1, 0) with a constant was chosen as the best model by considering Schwarz Bayesian Criterion (SBC). In addition, error estimates were also shown that ARMA (1, 0) with a constant was the best model.