Allison Eva Goodwell

Machine-learning models can predict eddy covariance fluxes accurately, but similar predictive skill of two models does not necessarily mean that models represent observed flux--driver relationships in the same way. This distinction is difficult to evaluate when predictive modeling and process-oriented diagnostics are applied separately. We introduce MeaningFlux , an open-source workflow that links machine-learning prediction with information-theoretic analysis to evaluate both flux reconstruction and the structure of environmental information associated with observed and modeled fluxes. A standardized ML--IT bridge aligns environmental drivers, observations, out-of-sample predictions, residuals, timestamps, and evaluation labels so that predictive performance can be compared directly with observed driver--flux dependence. We demonstrate MeaningFlux using daily carbon dioxide flux (FC) from four forest, cropland, and wetland sites, a common set of environmental drivers, and five contrasting model classes. Information-theoretic diagnostics revealed site-specific differences in nonlinear dependence, lagged directional information transfer, and redundant, unique, and synergistic information among drivers. Across models, models with similar out-of-sample predictive skill differed in how well they preserved the observed information relationships between environmental drivers and fluxes. These results show that predictive accuracy alone provides an incomplete description of model behavior. MeaningFlux provides a reproducible framework for evaluating what predictive models reconstruct and what relationships they preserve. The workflow can be applied to post-processed carbon dioxide, methane, nitrous oxide, water, and energy eddy covariance flux data and produces standardized outputs for transparent site-level analysis and cross-site synthesis.

Evapotranspiration (ET) plays a key role in agricultural water resources management. However, it is challenging to predict as it is driven by water and energy availability as well as soil, vegetation, and meteorological factors, and models vary widely in complexity and assumptions. Causal discovery methods can identify drivers and interactions based on time‐series data from both observations and models, and can be used as metrics of model “functional performance” that evaluate how models capture source‐target relationships. With many approaches to causal discovery, it is important to compare how functional performance metrics align with predictive accuracy and behave across temporal scales. We compare four methods (Granger causality, Transfer Entropy, PCMCI, and Convergent Cross Mapping) to analyze the functional performance of ET models in a corn‐soybean agricultural landscape based on 7 years of eddy covariance measurements, which we use as an empirical reference benchmark. We identify causal sources, among observed weather and soil variables, for Priestly‐Taylor (PT), Surface Flux Equilibrium (SFE), Soil Water Balance (SWB), and satellite‐based ET products from OpenET, and evaluate how closely model‐derived and observation‐based causal structures align. Methods consistently identify model forcings as sources, but otherwise vary widely in terms of sources and strengths across sub‐hourly to weekly timescales. OpenET products have high functional performance, indicating that they capture key processes although they are not forced by tower observations. Finally, some functional metrics align better with predictive performance than others, which highlights the importance of selecting robust metrics that both capture interactions and align with predictive accuracy.

High‐frequency measurements of stream solute dynamics reveal fluctuations across a multitude of time‐scales. At the storm‐event time‐scales they expose solute specific rapid mobilization or dilution effects, in addition to hysteresis. For various applications, predictions of these dynamics at measurement sites are desired to inform impending events such as harmful algal blooms. To aid in such efforts, we present a machine learning adaptive model. It builds on the well‐established Long Short‐Term Memory (LSTM) model, but introduces important modifications to capture dynamical attributes such as hysteresis, mobilization, and dilution. These modifications incorporate flow and flux gates that embed flow‐ and flux‐gradients directly into the traditional model architecture alongside the input, output, and forget gates. These gates are activated when flow or flux gradients or both exceed certain thresholds. The success of these activations in improving model performance indicates that they capture processes that better inform predictability of dynamical attributes embedded in the observed solute variability. The study is performed using data from a RiverLab, a stream chemistry laboratory located on the bank of a stream, at two sites. The first site is the Upper Sangamon Basin in Illinois, U.S.A., and the second in Orgeval, France. Both are tile drained loess covered agricultural watersheds, but of different drainage areas and in different climates. We assess the model performance using various metrics aligned with our goal to capture key dynamical features. The results justify the need for going beyond the standard formulations of LSTM to better accommodate the nuanced dynamics of natural systems.

In highly productive agricultural landscapes, human impacts combine with naturally variable climate conditions and geologic legacies to fundamentally alter critical zone (CZ) processes. For example, artificial drainage and fertilizer applications impact riverine transport of water and nutrients, and abrupt transitions in vegetation states impact land‐atmosphere fluxes of water and energy. Subsystem components may switch from being nearly independent to tightly synchronized, and drivers may elicit non‐linear or threshold responses. These shifts have implications for predictive understanding, but are challenging to identify and quantify. We present a flexible, data‐driven framework that identifies temporal regimes in CZ behavior, associated with particular environmental drivers and modes of variability. We integrate unsupervised clustering, dimensionality reduction, and information‐theoretic metrics to isolate temporal regimes and assess changes in drivers and predictability across several case studies. Specifically, we analyze high‐frequency time‐series data sets of root‐soil gases, land‐atmosphere fluxes, and river chemistry in intensively managed and more natural CZ study sites. Clusters and variability in these multivariate systems relate to rapid seasonal transitions in agricultural relative to prairie sites, and impacts of fertilizer timing on solute responses to events. Environmental drivers have variable explanatory power over system states that align with growing season, flows, or management. This study objectively detects dynamic transitions in CZ systems, and is more broadly applicable to any Earth system time‐series data or model evaluation to detect behavioral regimes and shifts in predictability of complex systems.

High-frequency measurements of stream solute dynamics reveal fluctuations across a multitude of time-scales. At the storm-event time-scales they expose solute specific rapid mobilization or dilution effects, in addition to hysteresis. For various applications, predictions of these dynamics at measurement site are desired to inform impending events such as harmful algal blooms. To aid in such efforts, we present a machine learning adaptive model. It builds on the well-established Long Short-Term Memory (LSTM) model, but introduces important modifications to capture dynamical attributes such as hysteresis, mobilization, and dilution. These modifications incorporate flow and flux gates that embed flow- and flux-gradients directly into the traditional model architecture alongside the input, output, and forget gates. These gates are activated when flow or flux gradients or both exceed certain thresholds. The success of these activations in improving model performance indicates that they capture processes that better inform predictability of dynamical attributes embedded in the observed solute variability. The study is performed using RiverLab data, a stream chemistry laboratory in the field located on the bank of a stream, at two sites. The first site is the Upper Sangamon Basin in Illinois, U.S.A., and the second in Orgeval, France. Both are tile drained loess covered agricultural watersheds, but of different drainage areas and in different climates. We assess the model performance using various metrics aligned with our goal to capture key dynamical features. The results justify the need for going beyond the standard formulations of LSTM to better accommodate the nuanced dynamics of natural systems.

CINet Goose Creek Tower: raw and corrected eddy covariance, met, soil data

Surface runoff and infiltrated water en route to the stream interact with dynamic landscape properties, ranging from vegetation and microbial activities to soil and geological attributes. Stream solute concentrations are highly variable and interconnected due to these interactions, flow paths, and residence times, and often exhibit hysteresis with flow. Significant unknowns remain about how point measurements of stream solute chemistry reflect interdependent hydrobiogeochemical and physical processes, and how signatures are encapsulated as nonlinear dynamical relationships between variables. We take a Machine Learning (ML) approach to understand and capture these dynamical relationships and improve predictions of solutes at short and long time scales. We introduce a physical process‐based “flow‐gate” into an Long Short‐Term Memory (LSTM) model, which enables the model to learn hysteresis behaviors if they exist. Further, we use information‐theoretic metrics to detect how solutes are interdependent and iteratively select source solutes that best predict a given target solute concentration. The “flow‐gate LSTM” model improves model predictions (1%–32% decreases in RMSE) relative to the standard LSTM model for all nine solutes included in the study. The predictive improvements from the flow‐gate LSTM model highlight the importance of lagged concentration and discharge relationships for certain solutes. It also indicates a potential limitation in the traditional LSTM model approach since flow rates are always provided as input sources, but this information is not fully utilized. This work provides a starting point for a predictive understanding of geochemical interdependencies using machine‐learning approaches and highlights potential improvements in model architecture.