Spatiotemporal analysis and modeling of nonstationarity in hydrological time series

Detection of nonstationarity in hydrological time series is most commonly done through one or two unit root tests, which usually do not account for all the possible reasons that could induce nonstationarity in a time series. To overcome this, we carried out five different unit root tests, i.e., Augmented Dickey-Fuller (ADF) test, Kwiatkowski Phillips Schmidt Shin (KPSS) test, Phillips Perron (PP) test, Variance Ratio (V ratio) test, and Leybourne McCabe (LMC) test, along with the line spectrum analysis in the frequency domain. These tests were conducted on daily rainfall data at forty contiguous grid points around the Malaprabha basin in India using data from the Indian Meteorological Department. The main goal was to find different nonstationary time series and investigate the spatiotemporal patterns of the nonstationarity and use that information to further develop nonstationary time series models through three different modeling approaches, i.e., Seasonal Autoregressive Integrated Moving Average (SARIMA), Exponential Smoothing (ES), and Long Short-Term Memory (LSTM). The performance of these models was evaluated on the basis of Nash Sutcliffe Efficiency (NSE) and R² value.