Scale effects on information theory-based measures applied to streamflow patterns in two rural watersheds

Abstract

Summary Understanding streamflow patterns in space and time is important for improving flood and drought forecasting, water resources management, and predictions of ecological changes. Objectives of this work include (a) to characterize the spatial and temporal patterns of streamflow using information theory-based measures at two thoroughly-monitored agricultural watersheds located in different hydroclimatic zones with similar land use, and (b) to elucidate and quantify temporal and spatial scale effects on those measures. We selected two USDA experimental watersheds to serve as case study examples, including the Little River experimental watershed (LREW) in Tifton, Georgia and the Sleepers River experimental watershed (SREW) in North Danville, Vermont. Both watersheds possess several nested sub-watersheds and more than 30 years of continuous data records of precipitation and streamflow. Information content measures (metric entropy and mean information gain) and complexity measures (effective measure complexity and fluctuation complexity) were computed based on the binary encoding of 5-year streamflow and precipitation time series data. We quantified patterns of streamflow using probabilities of joint or sequential appearances of the binary symbol sequences. Results of our analysis illustrate that information content measures of streamflow time series are much smaller than those for precipitation data, and the streamflow data also exhibit higher complexity, suggesting that the watersheds effectively act as filters of the precipitation information that leads to the observed additional complexity in streamflow measures. Correlation coefficients between the information-theory-based measures and time intervals are close to 0.9, demonstrating the significance of temporal scale effects on streamflow patterns. Moderate spatial scale effects on streamflow patterns are observed with absolute values of correlation coefficients between the measures and sub-watershed area varying from 0.2 to 0.6 in the two watersheds. We conclude that temporal effects must be evaluated and accounted for when the information theory-based methods are used for performance evaluation and comparison of hydrological models.