Multivariate streamflow forecasting using independent component analysis

Abstract

Seasonal forecasting of streamflow provides many benefits to society, by improving our ability to plan and adapt to changing water supplies. A common approach to developing these forecasts is to use statistical methods that link a set of predictors representing climate state as it relates to historical streamflow, and then using this model to project streamflow one or more seasons in advance based on current or a projected climate state. We present an approach for forecasting multivariate time series using independent component analysis (ICA) to transform the multivariate data to a set of univariate time series that are mutually independent, thereby allowing for the much broader class of univariate models to provide seasonal forecasts for each transformed series. Uncertainty is incorporated by bootstrapping the error component of each univariate model so that the probability distribution of the errors is maintained. Although all analyses are performed on univariate time series, the spatial dependence of the streamflow is captured by applying the inverse ICA transform to the predicted univariate series. We demonstrate the technique on a multivariate streamflow data set in Colombia, South America, by comparing the results to a range of other commonly used forecasting methods. The results show that the ICA-based technique is significantly better at representing spatial dependence, while not resulting in any loss of ability in capturing temporal dependence. As such, the ICA-based technique would be expected to yield considerable advantages when used in a probabilistic setting to manage large reservoir systems with multiple inflows or data collection points.Seth Westra, Ashish Sharma, Casey Brown and Upmanu Lal