Daily Streamflow Time Series Modeling by Using a Periodic Autoregressive Model (ARMA) Based on Fuzzy Clustering

Abstract

The behavior of hydrological processes is periodic and stochastic due to the influence of climatic factors. Therefore, it is crucial to develop the models based on their periodicity and stochastic nature for prediction. Furthermore, forecasting the streamflow, as one of the main components of the hydrological cycle, is a primary subject. In this study, a statistical method, Fuzzy C-means clustering, was used to find the periodicity in the daily discharge time series, whereas autoregressive moving average, ARMA, was used in modeling every cluster. Dividing the daily stream flow time series into smaller groups based on their similar statistical behavior by using a statistical method for analyzing and a combination of Fuzzy C-means clustering and ARMA modeling is the innovation of this study. We draw on the daily discharge data of four different river stations in Hesse state in Germany. The collected data cover 18 years, from 2000 to 2017. Root mean square error (RMSE) was used to evaluate the accuracy. The results revealed that the performance of ARMA in four stations for predicting every cluster was reliable. In addition, it must be highlighted that by clustering the daily stream flow time series into smaller groups, forecasting different days of the year will be possible.