Dynamic Quantile Regression for Trend Analysis of Streamflow Time Series

Water availability is an essential factor in maintaining the integrity of ecological processes and is a source of socio-economic development. However, socio-economic development increases the pressure on water resources. Thus, understanding the flow regime in a watershed is essential to correct water resource management. In this study, we propose using dynamic quantile regression (DQR) to analyse trends in streamflow time series. DQR is a subset of the general class of semi-parametric quantile regression models, which is tailored for time series modelling. It allows for autoregressive dynamics and modelling of trending behaviour and seasonal fluctuations. With a single model, it is possible to estimate the impacts of predictor variables on any given quantile of the response distribution instead of simply evaluating such effects on the mean response, as is typically done in other statistical approaches. In other words, it is possible to gain knowledge on how predictors impact the magnitude of streamflow in wet (upper quantiles) and dry seasons (lower quantiles) separately. We used DQR to model a streamflow time series of 27 gauges, distributed in the Araguaia watershed in central Brazil. The results show that, except for a single gauge (Alto Araguaia), there are downward streamflow trends, thus non-stationary behaviour. The model yielded excellent data fits (pseudo-R-2 above 0.80), and it was possible to obtain a confidence interval for each slope. In our analysis, the usefulness of DQR modelling for assessing trends in streamflow time series is shown and, consequently, for achieving efficient water resource management.