Source Relationships and Model Structures Determine Information Flow Paths in Ecohydrologic Models

In a complex ecohydrologic system, vegetation and soil variables combine to dictate heat fluxes, and these fluxes may vary depending on the extent to which drivers are linearly or nonlinearly interrelated. From a modeling and causality perspective, uncertainty, sensitivity, and performance measures all relate to how information from different sources "flows" through a model to produce a target, or output. We address how model structure, broadly defined as a mapping from inputs to an output, combines with source dependencies to produce a range of information flow pathways from sources to a target. We apply information decomposition, which partitions reductions in uncertainty into synergistic, redundant, and unique information types, to a range of model cases. Toy models show that model structure and source dependencies both restrict the types of interactions that can arise between sources and targets. Regressions based on weather data illustrate how different model structures vary in their sensitivity to source dependencies, thus affecting predictive and functional performance. Finally, we compare the Surface Flux Equilibrium theory, a land-surface model, and neural networks in estimating the Bowen ratio and find that models trade off information types particularly when sources have the highest and lowest dependencies. Overall, this study extends an information theory-based model evaluation framework to incorporate the influence of source dependency on information pathways. This could be applied to explore behavioral ranges for both machine learning and process-based models, and guide model development by highlighting model deficiencies based on information flow pathways that would not be apparent based on existing measures

Temporal information partitioning networks to infer ecohydrologic behaviors

An ecohydrologic system is a complex network, in which the shifting behavior of individual components and the connectivity between them determines the dynamics. This connectivity between components can act to constrain, accentuate, or otherwise modify the variability of individuals. In an ecohydrologic system, connectivity exists in the form of many time dependent relationships between states and fluxes related to water, energy, nutrients, soils, and vegetation. Although relationships are constrained by conservation laws, they exhibit a wide range of variability at many timescales due to non-linear interactions, threshold behavior, forcing, and feedback. Moreover, these aspects of connectivity and variability exist at a single location or over a spatial gradient. The understanding of this connectivity within the system as a whole necessitates an appropriate framework, in which evolving interactions are identified from time-series observations. The goals of this thesis are to (i) develop a Temporal Information Partitioning Network (TIPNet) framework for understanding the joint variability of network components as characterized by time-series data, and (ii) apply this framework to understand ecohydrologic systems across climate gradients based on flux tower and weather station observations. In the TIPNet framework, nodes in the network are time-series variables, and links are information theoretic measures that quantify multivariate lagged time-dependencies from lagged "source" nodes to "target" nodes. The strength of this framework is its ability to characterize information flow between variables over short time windows, and further distinguish aspects of unique, redundant, and synergistic dependencies. Redundant information is overlapping information provided by multiple sources to a target, unique information is only provided by a single target, and synergistic information is provided only when two or more sources are known together. Based on data from three Critical Zone Observatories, we find that network structure shifts according to conditions at sub-daily time scales and constraints imposed by seasonal energy and water availability. TIPNets constructed from 1-minute weather station data reveal shifts in time-scales and levels of uniqueness, synergy, and redundancy between wet and dry conditions. A more complex network of synergistic interactions characterizes several-hour windows when surfaces are wet, and peaks in information flow during the growing season correspond to shifts in precipitation patterns. Networks based on half hourly flux tower data reveal seasonal shifts in the nature of forcing to carbon and heat fluxes from radiation, atmospheric, and soil subsystems. Along two study transects, we attribute variability in heat and carbon fluxes within constraints imposed by energy and moisture availability to joint interactions that are more synergistic in the spring and redundant in the fall. Finally, we explore the nature of information flow along an elevation gradient from flux towers located along a transect to gauge local versus non-local connectivity. While the strength of shared information between variables at a site reflects local connectivity, shared information between variables at different sites reflects non-local connectivity. Along two elevation transects, we find that information flow between distant sites indicates directional connectivity that is related to dominant weather patterns. At the Southern Sierra CZO in California, non-local information flow is dominantly west to east, corresponding to weather forcing from the Pacific Ocean eastward, while non-local flow has less directionality at Reynolds Creek CZO, where sites are much closer together and there is no dominant weather forcing direction along the transect. The developed framework and applications presented in this thesis reveal the common presence of multivariate process interactions at timescales from minutes to hours, many of which would not be detected using traditional approaches. For an ecohydrologic system, the complex network of relationships dictates ecosystem resilience to perturbations such as climate change, drought, or human influences. More broadly, the methods and framework developed here contribute toward a holistic understanding of complex systems, and are applicable to a range of studies of evolving networks

Landscape vulnerability to flood impacts in a human-dominated floodplain

The variable flood regime of a natural floodplain supports a variety of vegetation and habitat niches and regenerates the landscape through erosion and deposition. However, flooding of human-dominated landscapes are termed ``natural disasters'' due to potential devastating impacts such as the loss of lives and property, agricultural damage, or undesirable erosion and deposition. Natural hazards and climate change fields employ the vulnerability concept to assess various aspects of human susceptibility to disturbances or altered conditions. Vulnerability is generally defined as the likelihood of harm. It is a function of exposure, sensitivity, and adaptive capacity of a system. This study implements a mathematical framework, 2D flow modeling, and spatial mapping to present an analysis of vulnerability to erosion and deposition due to the activation of Bird's Point-New Madrid Floodway in May 2011. The historic pre-conceived levee breach and subsequent inundation of the agricultural floodplain represents a large-scale experiment to assess vulnerability of intensively managed landscapes to extreme events. Pre-flood and post-flood high-resolution Lidar topography datasets are analyzed and compared to vegetated land cover, soil properties, topographical legacies, and measured and modeled flow characteristics to quantify their potential contributions to vulnerability in the Floodway. It was found that the most significant erosional feature occurred at O'Bryan Ridge, an agricultural region at a low ridge formed by a historic meander of the Mississippi River. Areas of significant erosion corresponded to highly erodible soils, high simulated flows, and an absence of woody vegetation. Deposition throughout the Floodway was generally mitigated due to low river-to-floodplain connectivity and moderate sediment input from the river. Other relict meanders within the Floodway were found to be less vulnerable than O'Bryan Ridge due to lower flood exposure caused by gradients, vegetation, floodplain width, and backwater flooding. This analysis demonstrates the importance of vegetation for the protection of otherwise vulnerable regions. The methodology of this analysis can be used to locate regions of high vulnerability in future floodplain management to mitigate potentially catastrophic landscape change

Information Theoretic Measures to Infer Feedback Dynamics in Coupled Logistic Networks

A process network is a collection of interacting time series nodes, in which interactions can range from weak dependencies to complete synchronization. Between these extremes, nodes may respond to each other or external forcing at certain time scales and strengths. Identification of such dependencies from time series can reveal the complex behavior of the system as a whole. Since observed time series datasets are often limited in length, robust measures are needed to quantify strengths and time scales of interactions and their unique contributions to the whole system behavior. We generate coupled chaotic logistic networks with a range of connectivity structures, time scales, noise, and forcing mechanisms, and compute variance and lagged mutual information measures to evaluate how detected time dependencies reveal system behavior. When a target node is detected to receive information from multiple sources, we compute conditional mutual information and total shared information between each source node pair to identify unique or redundant sources. While variance measures capture synchronization trends, combinations of information measures provide further distinctions regarding drivers, redundancies, and time dependencies within the network. We find that imposed network connectivity often leads to induced feedback that is identified as redundant links, and cannot be distinguished from imposed causal linkages. We find that random or external driving nodes are more likely to provide unique information than mutually dependent nodes in a highly connected network. In process networks constructed from observed data, the methods presented can be used to infer connectivity, dominant interactions, and systemic behavioral shift

Evaluating Ecohydrological Model Sensitivity to Input Variability with an Information-Theory-Based Approach

Ecohydrological models vary in their sensitivity to forcing data and use available information to different extents. We focus on the impact of forcing precision on ecohydrological model behavior particularly by quantizing, or binning, time-series forcing variables. We use rate-distortion theory to quantize time-series forcing variables to different precisions. We evaluate the effect of different combinations of quantized shortwave radiation, air temperature, vapor pressure deficit, and wind speed on simulated heat and carbon fluxes for a multi-layer canopy model, which is forced and validated with eddy covariance flux tower observation data. We find that the model is more sensitive to radiation than meteorological forcing input, but model responses also vary with seasonal conditions and different combinations of quantized inputs. While any level of quantization impacts carbon flux similarly, specific levels of quantization influence heat fluxes to different degrees. This study introduces a method to optimally simplify forcing time series, often without significantly decreasing model performance, and could be applied within a sensitivity analysis framework to better understand how models use available information

Data_Sheet_1_Inside the flux footprint: The role of organized land cover heterogeneity on the dynamics of observed land-atmosphere exchange fluxes.PDF

Eddy covariance measurements quantify the magnitude and temporal variability of land-atmosphere exchanges of water, heat, and carbon dioxide (CO2) among others. However, they also carry information regarding the influence of spatial heterogeneity within the flux footprint, the temporally dynamic source/sink area that contributes to the measured fluxes. A 25 m tall eddy covariance flux tower in Central Illinois, USA, a region where drastic seasonal land cover changes from intensive agriculture of maize and soybean occur, provides a unique setting to explore how the organized heterogeneity of row crop agriculture contributes to observations of land-atmosphere exchange. We characterize the effects of this heterogeneity on latent heat (LE), sensible heat (H), and CO2 fluxes (Fc) using a combined flux footprint and eco-hydrological modeling approach. We estimate the relative contribution of each crop type resulting from the structured spatial organization of the land cover to the observed fluxes from April 2016 to April 2019. We present the concept of a fetch rose, which represents the frequency of the location and length of the prevalent upwind distance contributing to the observations. The combined action of hydroclimatological drivers and land cover heterogeneity within the dynamic flux footprint explain interannual flux variations. We find that smaller flux footprints associated with unstable conditions are more likely to be dominated by a single crop type, but both crops typically influence any given flux measurement. Meanwhile, our ecohydrological modeling suggests that land cover heterogeneity leads to a greater than 10% difference in flux magnitudes for most time windows relative to an assumption of equally distributed crop types. This study shows how the observed flux magnitudes and variability depend on the organized land cover heterogeneity and is extensible to other intensively managed or otherwise heterogeneous landscapes.</p

Original LiDAR differential digital elevation model

Original LiDAR differential DEM (2011 - 2005 elevations) derived from USACE LiDAR data, 1.524 meter resolution, shows flight line stripin

BPNM_Publication

This collection includes data developed and used for the analysis of the Birds Point-New Madrid (BPNM) Floodway activation in 2011. The data collection includes 10 items, all of which present the processed and derived data. The processed differential LiDAR is the 2005 (pre-flood) LiDAR subtracted from the 2011 (post-flood) LiDAR and corrected for flight line errors. The original LiDAR data were obtained from US Army Corps of Engineers. There are 5 simulated maximum velocity data items from HydroSed2D at two locations (O’Bryan Ridge and Ten Mile Pond) and 2 simulation cases (vegetation and no vegetation). The maximum velocity data for the entire Floodway is for the vegetated case. The NASA AVIRIS dataset is classified into classes representing woody vegetation and bare soil. The soil dataset (K/T) is an erodibility index derived from USDA SSURGO data. Additional data for this study was provided by the USGS, and is available along with the report at the following site: http://pubs.usgs.gov/pp/1798e/. This data includes ADCP (Acoustic Doppler Current Profiler) flow measurements from the inflows an outflows of the Floodway, and HOBO depth sensor measurements from various points within the Floodway. This data were used to validate the HydroSed2D simulations