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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 atmore »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.« less

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 dynamicmore »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.« less

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 themore »physical significance of outputs.« less

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 resultingmore »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.

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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.

Can the Second Law of Thermodynamics explain why ecosystems naturally organize into a complex structure composed of multiple vegetation species and functional groups? Ecosystem structure, which refers to the number and type of plant functional groups, is the result of self-organization, or the spontaneous emergence of order from random fluctuations. By considering ecosystems as open thermodynamic systems, we model and study these fluctuations of throughput signatures on short timescales to determine the drivers and characteristics of ecosystem structure. This diagnostic approach allows us to use fluxes of energy and entropy to calculate an ecosystem’s estimated work and understand the thermodynamic behavior of the system. We use a multi-layer canopy-root-soil model to calculate the energy and entropy fluxes of different scenarios for field sites across various climates. At each site, scenarios comprised of native individual plant functional groups and a coexisting multi-group composition scenario including all functional groups observed at the site are compared. Ecosystem-scale calculations demonstrate that entropy fluxes and work efficiency—the work performed for the amount of radiation entering the ecosystem—are greatest in the multi-group scenario when its leaf area is significantly larger than each of its individual functional groups. Thus, we conclude that ecosystems self-organize towards themore »vegetation structure with the greatest outgoing entropy flux and work efficiency, resulting in the coexistence of multiple functional groups and performing the maximum amount of work within the constraints of locally available energy, water, and nutrients.

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