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At the biosphere–atmosphere interface, nonlinear interdependencies among components of an ecohydrological complex system can be inferred using multivariate high frequency time series observations. Information flow among these interacting variables allows us to represent the causal dependencies in the form of a directed acyclic graph (DAG). We use high frequency multivariate data at 10 Hz from an eddy covariance instrument located at 25 m above agricultural land in the Midwestern US to quantify the evolutionary dynamics of this complex system using a sequence of DAGs by examining the structural dependency of information flow and the associated functional response. We investigate whether functional differences correspond to structural differences or if there are no functional variations despite the structural differences. We base our analysis on the hypothesis that causal dependencies are instigated through information flow, and the resulting interactions sustain the dynamics and its functionality. To test our hypothesis, we build upon causal structure analysis in the companion paper to characterize the information flow in similarly clustered DAGs from 3-min non-overlapping contiguous windows in the observational data. We characterize functionality as the nature of interactions as discerned through redundant, unique, and synergistic components of information flow. Through this analysis, we find that in turbulence at the biosphere–atmosphere interface, the variables that control the dynamic character of the atmosphere as well as the thermodynamics are driven by non-local conditions, while the scalar transport associated with CO2 and H2O is mainly driven by short-term local conditions. 

Future sea-level rise projections are characterized by both quantifiable uncertainty and unquantifiable structural uncertainty. Thorough scientific assessment of sea-level rise projections requires analysis of both dimensions of uncertainty. Probabilistic sea-level rise projections evaluate the quantifiable dimension of uncertainty; comparison of alternative probabilistic methods provides an indication of structural uncertainty. Here we describe the Framework for Assessing Changes To Sea-level (FACTS), a modular platform for characterizing different probability distributions for the drivers of sea-level change and their consequences for global mean, regional, and extreme sea-level change. We demonstrate its application by generating seven alternative probability distributions under multiple emissions scenarios for both future global mean sea-level change and future relative and extreme sea-level change at New York City. These distributions, closely aligned with those presented in the Intergovernmental Panel on Climate Change Sixth Assessment Report, emphasize the role of the Antarctic and Greenland ice sheets as drivers of structural uncertainty in sea-level change projections.

 

Eddy covariance measurements quantify the magnitude and temporal variability of land-atmosphere exchanges of water, heat, and carbon dioxide (CO 2 ) 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 CO 2 fluxes ( F c ) 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. 

At the edge of alpine and Arctic ecosystems all over the world, a transition zone exists beyond which it is either infeasible or unfavorable for trees to exist, colloquially identified as the treeline. We explore the possibility of a thermodynamic basis behind this demarcation in vegetation by considering ecosystems as open systems driven by thermodynamic advantage—defined by vegetation’s ability to dissipate heat from the earth’s surface to the air above the canopy. To deduce whether forests would be more thermodynamically advantageous than existing ecosystems beyond treelines, we construct and examine counterfactual scenarios in which trees exist beyond a treeline instead of the existing alpine meadow or Arctic tundra. Meteorological data from the Italian Alps, United States Rocky Mountains, and Western Canadian Taiga-Tundra are used as forcing for model computation of ecosystem work and temperature gradients at sites on both sides of each treeline with and without trees. Model results indicate that the alpine sites do not support trees beyond the treeline, as their presence would result in excessive CO$$_2$$${}_2$loss and extended periods of snowpack due to temperature inversions (i.e., positive temperature gradient from the earth surface to the atmosphere). Further, both Arctic and alpine sites exhibit negative work resulting in positive feedback between vegetation heat dissipation and temperature gradient, thereby extending the duration of temperature inversions. These conditions demonstrate thermodynamic infeasibility associated with the counterfactual scenario of trees existing beyond a treeline. Thus, we conclude that, in addition to resource constraints, a treeline is an outcome of an ecosystem’s ability to self-organize towards the most advantageous vegetation structure facilitated by thermodynamic feasibility.

 

Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. In this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs. 

Soil respiration that releases CO 2 into the atmosphere roughly balances the net primary productivity and varies widely in space and time. However, predicting its spatial variability, particularly in intensively managed landscapes, is challenging due to a lack of understanding of the roles of soil organic carbon (SOC) redistribution resulting from accelerated soil erosion. Here we simulate the heterotrophic carbon loss (HCL)—defined as microbial decomposition of SOC—with soil transport, SOC surface redistribution, and biogeochemical transformation in an agricultural field. The results show that accelerated soil erosion extends the spatial variation of the HCL, and the mechanical-mixing due to tillage further accentuates the contrast. The peak values of HCL occur in areas where soil transport rates are relatively small. Moreover, HCL has a strong correlation with the SOC redistribution rate rather than the soil transport rate. This work characterizes the roles of soil and SOC transport in restructuring the spatial variability of HCL at high spatio-temporal resolution.