Process connectivity in river deltas : quantifying information flow from system drivers to sinks with information theory
River deltas are complex systems that emerge through dynamic interactions between external drivers including river discharge, tides, wind, and waves, and deltaic sinks of water, sediment, and nutrients. The range of spatial and temporal scales over which external drivers and sinks interact with each other to build deltas and influence ecogeomorphic evolution of the deltaic plain is still largely unknown. In this dissertation, the spatial and temporal scales of driver-sink interactions are quantified in Wax Lake Delta (WLD), LA, USA, using a mix of field and numerical modeling data. Drivers and sinks are conceptualized as nodes in a network that exchange information with each other, referred to as process connectivity. The statistics of information theory (IT), mathematics related to the communication of information, are explored to quantify process connectivity where information exchange represents a reduction in uncertainty when one variable informs on another variable through information sharing or transferring. In the first study, process connections are quantified between drivers and water level at the delta scale over timescales of hours to months. The results reveal that wind acts as a driver of hydrologic process connectivity by causing water level setups that increase hydrologic connectivity. Timescales of information flow range between 10-30 hours for discharge, 25-30 hours for tides, and 5-40 hours for wind, dependent on location in the delta and local variability. In the second study, process connections are quantified at six locations within a deltaic island. Multi-variate process connectivity is measured among water level, turbidity, temperature, nitrate, and external drivers where relationships between two sources on one sink are partitioned into unique, synergistic (two variables work together), and redundant (two variables provide the same information) components. Water levels show distinct spatial relationships with each other spanning 250m to 1km across the island related to vegetation patches. Turbidities show little connection to each other over space suggesting sediment is redistributed over short length scales. Nitrate variability is heavily influenced by the synergistic forcing between temperature, turbidity, and water level at various locations, balancing hydrologic and biogeochemical controls on nutrient processing. The third study assesses the ability of hydrodynamic models to reproduce process connections, by comparing modeled and field-based process connections in a channel and island. Models are able to reproduce couplings, yet they overestimate channel couplings and underestimate couplings on islands suggesting that dynamics of channel-island connectivity are not fully captured by the model. The final study quantifies the information that is shared between river discharge and land elevation of the deltaic islands in WLD, measured in two lidar surveys in 2009 and 2013. The age and location of the islands in the deltaic network strongly affect results; down-delta islands share little information (< 0.03 bits of information) with each other between 2009 and 2013, suggesting external drivers more strongly reworked sediment distributions on more hydrologically connected islands. All island locations share more information with more recent time series of river discharge compared to longer term measurements, suggesting an optimal timescale of discharge reworking on sediment. The results of these four studies provide a comprehensive analysis of the complexity of processes in a river delta and a deeper understanding of the mechanisms by which drivers and sinks interact with each other that can inform modelers and coastal scientists.