QUANTITATIVE ANALYSIS OF RELATIONSHIPS IN RIVER DELTAS: INSIGHTS FROM USING INFORMATION THEORY (Invited Presentation)

River deltas are complex environments where fluxes of water, sediment, and nutrients interact with drivers such as river discharge, tides, and wind to influence delta functioning and evolution. The relationships among these system variables represent important processes that display temporal and spatial heterogeneities, feedbacks, and nonlinearities. A question to ask is how to robustly uncover the dependencies between these variables at multiple scales without bias? One such approach is with information theory (IT): mathematics that measure the communication of information among variables such as the reduction in uncertainty that results when information flows from one variable to another. The advantage of using IT over other correlation statistics is that it uses the probability density function of variables, thus making no assumption on the dynamics. Further, parameters such as mutual information (MI) and transfer entropy (TE), which measure the information shared and transferred among variables, capture the strength, timescale, and direction of relationships, and allow for a classification of variable interaction.

In this talk, I discuss how IT was applied to quantify relationships among variables measured in the Wax Lake Delta in coastal Louisiana, USA. With an overall aim to measure information flow from system drivers (discharge, tides, and wind) to sinks (water, sediment, and nutrients), IT was used to explore delta dynamics at the island, reach, and delta scale based on datasets that include field collected time series, numerically modeled data, and lidar data. By using signal processing techniques to isolate periods of interest and calculating MI and TE over time for those periods, the timescales and strengths of interaction were elucidated for multiple spatial locations in the delta. Through this approach we quantified the role of wind in promoting surface water connectivity and differentiated the effect of drivers and sink variables on nitrate variability. At the delta scale, MI was used to link elevation change with fluctuations in discharge, tides, and wind. The comparison of TE results for field and modeled data provided an approach for hydrodynamic model validation. Ultimately, IT offers a way to comprehensively assess dynamics that can be applied to many types of landscapes.