Analysis of stationarity and low frequency variability of the streamflow time series from the national interconnected system (NIS)

Abstract

A common approach in the hydrological time series modeling is the assumption that the series is stationary, although this belief has been questioned due to the impacts of climatic changes and land use change motived by anthropogenic actions. Thus, the present work intends to make a diagnosis of streamflow time series of the National Interconnected System (NIS) in Brazil analysing the stationary, trend and mode of variation. Then, the analysis is performed for the low frequency only (16-32 years), decomposed by the wavelet transform, and use the Standard Runoff Index (SRI), changepoint and a Hidden Markov Model (HMM) to identify the different states of the Sobradinho’s reservoir inflow, in order to understand the impacts of this frequency in the time series and develop a forecast model. It was used the Autoregressive model and a HMM to predict the next state in the low frequency time series. First, the stationarity was analyzed by statistical and unit root tests. In order to evaluate the presence of trend was used the Mann-Kendall and Sen’s slope tests. Then, the time series were decomposed by Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Wavelet Transform. Results between the statistical and unit root tests showed similar results for the stationarity analysis except for the south region and both types of test classified more than a half of the series as nonstationary. It was evaluated that the unit root tests are more indicated when modeling series with the presence of a trend. The analysis with the changepoint showed a better result in the identification of extreme events of the low frequency in relation to SRI due to its power to identify significant changes in the series statistics. It was evaluated the cumulative distribution function using the original time series and was observed that the they have different distributions for years classified as dry/wet years, thus, the proposal to identify the states and forecast the next state was justified. A forecasting model was developed adjusting an autoregressive model to the low frequency time series, however it presented good results for 1- year ahead forecast only. Regarding the HMM model, the results shown a reduction of the wet period between the years 2010-2016 and an increasing probability of a normal period was verified. For a short-term, it is possible to identify the next most probable state for the Sobradinho’s reservoir and the next state was a good indication compared to the historical time series using the HMM. In conclusion, most of the station gage analyzed are not stationary, although they are still model as such and the HMM forecast for Sobradinho’s reservoir inflow proved to be an important tool to assist in predicting the next state of the low frequency variability, thus, providing an mechanism to managing and operating reservoirs, especially for the one in this study due to its economic importance for the hydroelectric sector.