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Abstract Governing equations are foundations for modelling, predicting, and understanding the Earth system. The Earth system is undergoing rapid change, and the conventional approaches for establishing governing equations, such as empirical generalisations, are becoming increasingly challenging to deal with the complexity and diversity of the geoscience processes we study today. In this Perspective, we explore data-driven equation discovery, a novel scientific artificial intelligence pathway, for advancing geosciences. Data-driven equation discovery identifies hidden patterns from data and transforms them into interpretable equation representations, automating and accelerating equation discovery processes. It provides a practical approach for geoscientists to model and understand complex geoscience processes based on big Earth data. The final vision is to uncover new clear, describable, and quantifiable equations in various geoscience disciplines. We summarize opportunities and highlight that challenges in this field should be addressed by interdisciplinary collaborations.

Abstract Interpretable Machine Learning (IML) has rapidly advanced in recent years, offering new opportunities to improve our understanding of the complex Earth system. IML goes beyond conventional machine learning by not only making predictions but also seeking to elucidate the reasoning behind those predictions. The combination of predictive power and enhanced transparency makes IML a promising approach for uncovering relationships in data that may be overlooked by traditional analysis. Despite its potential, the broader implications for the field have yet to be fully appreciated. Meanwhile, the rapid proliferation of IML, still in its early stages, has been accompanied by instances of careless application. In response to these challenges, this paper focuses on how IML can effectively and appropriately aid geoscientists in advancing process understanding—areas that are often underexplored in more technical discussions of IML. Specifically, we identify pragmatic application scenarios for IML in typical geoscientific studies, such as quantifying relationships in specific contexts, generating hypotheses about potential mechanisms, and evaluating process‐based models. Moreover, we present a general and practical workflow for using IML to address specific research questions. In particular, we identify several critical and common pitfalls in the use of IML that can lead to misleading conclusions, and propose corresponding good practices. Our goal is to facilitate a broader, yet more careful and thoughtful integration of IML into Earth science research, positioning it as a valuable data science tool capable of enhancing our current understanding of the Earth system.

Abstract Natural and anthropogenic disturbances are important drivers of tree mortality, shaping the structure, composition, and biomass distribution of forest ecosystems. Differences in disturbance regimes, characterized by the frequency, extent, and intensity of disturbance events, result in structurally different landscapes. In this study, we design a model‐based experiment to investigate the links between disturbance regimes and spatial biomass patterns. First, the effects of disturbance events on biomass patterns are simulated using a simple dynamic carbon cycle model based on different disturbance regime attributes, which are characterized via three parameters: μ (probability scale), α (clustering degree), and β (intensity slope). 856,800 dynamically stable biomass patterns were then simulated using combined disturbance regime, primary productivity, and background mortality. As independent variables, we use biomass synthesis statistics from simulated biomass patterns to retrieve three disturbance regime parameters. Results show confident inversion of all three “true” disturbance parameters, with Nash‐Sutcliffe efficiency of 94.8% for μ, 94.9% for α, and 97.1% for β. Biomass histogram statistics primarily dominate the prediction of μ and β, while texture features have a more substantial influence on α. Overall, these results demonstrate the association between biomass patterns and disturbance regimes. Given the increasing availability of Earth observation of biomass, our findings open a new avenue to understand better and parameterize disturbance regimes and their links with vegetation dynamics under climate change. Ultimately, at a large scale, this approach would improve our current understanding of controls and feedback at the biosphere‐atmosphere interface in the present Earth system models.

Abstract Soil is central to the complex interplay among biodiversity, climate, and society. This paper examines the interconnectedness of soil biodiversity, climate change, and societal impacts, emphasizing the urgent need for integrated solutions. Human‐induced biodiversity loss and climate change intensify environmental degradation, threatening human well‐being. Soils, rich in biodiversity and vital for ecosystem function regulation, are highly vulnerable to these pressures, affecting nutrient cycling, soil fertility, and resilience. Soil also crucially regulates climate, influencing energy, water cycles, and carbon storage. Yet, climate change poses significant challenges to soil health and carbon dynamics, amplifying global warming. Integrated approaches are essential, including sustainable land management, policy interventions, technological innovations, and societal engagement. Practices like agroforestry and organic farming improve soil health and mitigate climate impacts. Effective policies and governance are crucial for promoting sustainable practices and soil conservation. Recent technologies aid in monitoring soil biodiversity and implementing sustainable land management. Societal engagement, through education and collective action, is vital for environmental stewardship. By prioritizing interdisciplinary research and addressing key frontiers, scientists can advance understanding of the soil biodiversity–climate change–society nexus, informing strategies for environmental sustainability and social equity.

Abstract Existing methods for fine-scale air quality assessment have significant gaps in their reliability. Purely data-driven methods lack any physically-based mechanisms to simulate the interactive process of air pollution, potentially leading to physically inconsistent or implausible results. Here, we report a hybrid multilevel graph neural network that encodes fluid physics to capture spatial and temporal dynamic characteristics of air pollutants. On a multi-air pollutant test in China, our method consistently improved extrapolation accuracy by an average of 11–22% compared to several baseline machine learning methods, and generated physically consistent spatiotemporal trends of air pollutants at fine spatial and temporal scales.

Abstract The response of vegetation physiology to drought at large spatial scales is poorly understood due to a lack of direct observations. Here, we study vegetation drought responses related to photosynthesis, evaporation, and vegetation water content using remotely sensed data, and we isolate physiological responses using a machine learning technique. We find that vegetation functional decreases are largely driven by the downregulation of vegetation physiology such as stomatal conductance and light use efficiency, with the strongest downregulation in water-limited regions. Vegetation physiological decreases in wet regions also result in a discrepancy between functional and structural changes under severe drought. We find similar patterns of physiological drought response using simulations from a soil–plant–atmosphere continuum model coupled with a radiative transfer model. Observation-derived vegetation physiological responses to drought across space are mainly controlled by aridity and additionally modulated by abnormal hydro-meteorological conditions and vegetation types. Hence, isolating and quantifying vegetation physiological responses to drought enables a better understanding of ecosystem biogeochemical and biophysical feedback in modulating climate change.

Abstract Fundamental axes of variation in plant traits result from trade-offs between costs and benefits of resource-use strategies at the leaf scale. However, it is unclear whether similar trade-offs propagate to the ecosystem level. Here, we test whether trait correlation patterns predicted by three well-known leaf- and plant-level coordination theories – the leaf economics spectrum, the global spectrum of plant form and function, and the least-cost hypothesis – are also observed between community mean traits and ecosystem processes. We combined ecosystem functional properties from FLUXNET sites, vegetation properties, and community mean plant traits into three corresponding principal component analyses. We find that the leaf economics spectrum (90 sites), the global spectrum of plant form and function (89 sites), and the least-cost hypothesis (82 sites) all propagate at the ecosystem level. However, we also find evidence of additional scale-emergent properties. Evaluating the coordination of ecosystem functional properties may aid the development of more realistic global dynamic vegetation models with critical empirical data, reducing the uncertainty of climate change projections.

Current strategies to hold surface warming below a certain level, e. g., 1.5 or 2°C, advocate limiting total anthropogenic cumulative carbon emissions to ∼0.9 or ∼1.25 Eg C (1018 grams carbon), respectively. These allowable emission budgets are based on a near-linear relationship between cumulative emissions and warming identified in various modeling efforts. The IPCC assesses this near-linear relationship with high confidence in its Summary for Policymakers (§D1.1 and Figure SPM.10). Here we test this proportionality in specially designed simulations with a latest-generation Earth system model (ESM) that includes an interactive carbon cycle with updated terrestrial ecosystem processes, and a suite of CMIP simulations (ZecMIP, ScenarioMIP). We find that atmospheric CO2 concentrations can differ by ∼100 ppmv and surface warming by ∼0.31°C (0.46°C over land) for the same cumulated emissions (≈1.2 Eg C, approximate carbon budget for 2°C target). CO2 concentration and warming per 1 Eg of emitted carbon (Transient Climate Response to Cumulative Carbon Emissions; TCRE) depend not just on total emissions, but also on the timing of emissions, which heretofore have been mainly overlooked. A decomposition of TCRE reveals that oceanic heat uptake is compensating for some, but not all, of the pathway dependence induced by the carbon cycle response. The time dependency clearly arises due to lagged carbon sequestration processes in the oceans and specifically on land, viz., ecological succession, land-cover, and demographic changes, etc., which are still poorly represented in most ESMs. This implies a temporally evolving state of the carbon system, but one which surprisingly apportions carbon into land and ocean sinks in a manner that is independent of the emission pathway. Therefore, even though TCRE differs for different pathways with the same total emissions, it is roughly constant when related to the state of the carbon system, i. e., the amount of carbon stored in surface sinks. While this study does not fundamentally invalidate the established TCRE concept, it does uncover additional uncertainties tied to the carbon system state. Thus, efforts to better understand this state dependency with observations and refined models are needed to accurately project the impact of future emissions.

Abstract Latent and sensible heat flux observations are essential for understanding land–atmosphere interactions. Measurements from the eddy covariance technique are widely used but suffer from systematic energy imbalance problems, partly due to missing large eddies from sub‐mesoscale transport. Because available energy drives the development of large eddies, we propose an available energy based correction method for turbulent flux measurements. We apply our method to 172 flux tower sites and show that we can reduce the energy imbalance from −14.99 to −0.65 W m−2 on average, together with improved consistency between turbulent fluxes and available energy and associated increases in r2 at individual sites and across networks. Our results suggest that our method is conceptually and empirically preferable over the method implemented in the ONEFlux processing. This can contribute to the efforts in understanding and addressing the energy imbalance issue, which is crucial for the evaluation and calibration of land surface models.

Abstract Drought's intensity and duration have increased in many regions over the last decades. However, the propagation of drought‐induced water deficits through the terrestrial water cycle is not fully understood at a global scale. Here we study responses of monthly evaporation (ET) and runoff to soil moisture droughts occurring between 2001 and 2015 using independent gridded datasets based on machine learning‐assisted upscaling of satellite and in‐situ observations. We find that runoff and ET show generally contrasting drought responses across climate regimes. In wet regions, runoff is strongly reduced while ET is decoupled from soil moisture decreases and enhanced by sunny and warm weather typically accompanying soil moisture droughts. In drier regions, ET is reduced during droughts due to vegetation water stress, while runoff is largely unchanged as precipitation deficits are typically low in these regions and ET decreases are buffering runoff reductions. While these water flux drought responses are controlled by the large‐scale climate regimes, they are additionally modulated by local vegetation characteristics. Land surface models capture the observed water cycle responses to drought in the case of runoff, but not for ET where the ET deficit (surplus) is overestimated (underestimated), related to a misrepresentation of the general soil moisture‐evaporation interplay. In summary, our study illustrates how the joint analysis of machine learning‐enhanced Earth observations can advance the understanding of global eco‐hydrological processes, as well as the validation of land surface models.

Hybrid modeling integrates machine learning with scientific knowledge to enhance interpretability, generalization, and adherence to natural laws. Nevertheless, equifinality and regularization biases pose challenges in hybrid modeling to achieve these purposes. This paper introduces a novel approach to estimating hybrid models via a causal inference framework, specifically employing double machine learning (DML) to estimate causal effects. We showcase its use for the Earth sciences on two problems related to carbon dioxide fluxes. In the Q _10 model, we demonstrate that DML-based hybrid modeling is superior in estimating causal parameters over end-to-end deep neural network approaches, proving efficiency, robustness to bias from regularization methods, and circumventing equifinality. Our approach, applied to carbon flux partitioning, exhibits flexibility in accommodating heterogeneous causal effects. The study emphasizes the necessity of explicitly defining causal graphs and relationships, advocating for this as a general best practice. We encourage the continued exploration of causality in hybrid models for more interpretable and trustworthy results in knowledge-guided machine learning.

Vegetation plays an essential role in regulating carbon and water cycles, e.g. by taking up atmospheric CO _2 through photosynthesis and by transferring soil water to the atmosphere through transpiration. Vegetation function is shaped by its structure and physiology: vegetation structure is determined by the amount of materials for plants and how it is organised in space and time, while vegetation physiology controls the instantaneous response of vegetation function to environmental conditions. Recognizing and disentangling these aspects of vegetation is key to understanding and predicting the response of the terrestrial biosphere to global change. This is now possible, as comprehensive measurements from Earth observations, both from satellites and the ground, provide invaluable data and information. This review introduces and describes vegetation structure and physiology, and summarises, compares, and contextualises recent literature to illustrate the state of the art in monitoring vegetation dynamics, quantifying large-scale vegetation physiology, and investigating vegetation regulation on the changes of global carbon and water fluxes. This includes results from remote sensing, in-situ measurements, and model simulations, used either to study the response of vegetation structure and physiology to global change, or to study the feedback of vegetation to global carbon and water cycles. We find that observation-based work is underrepresented compared with model-based studies. We therefore advocate further work to make better use of remote sensing and in-situ measurements, as they promote the understanding of vegetation dynamics from a fundamental data-driven perspective. We highlight the usefulness of novel and increasing satellite remote sensing data to comprehensively investigate the structural and physiological dynamics of vegetation on the global scale, and to infer their influence on the land carbon sink and terrestrial evaporation. We argue that field campaigns can and should complement large-scale analyses together with fine spatio-temporal resolution satellite remote sensing to infer relevant ecosystem-scale processes.

Water availability is a major control of vegetation dynamics and terrestrial carbon cycling. Here, the authors show that vegetation sensitivity to soil moisture has been increasing in the last 36 years, especially in (semi)arid areas, and that state-of-the-art land surface models fail to capture this trend.

Local studies and modeling experiments suggest that shallow groundwater and lateral redistribution of soil moisture, together with soil properties, can be highly important secondary water sources for vegetation in water-limited ecosystems. However, there is a lack of observation-based studies of these terrain-associated secondary water effects on vegetation over large spatial domains. Here, we quantify the role of terrain properties on the spatial variations of dry season vegetation decay rate across Africa obtained from geostationary satellite acquisitions to assess the large-scale relevance of secondary water effects. We use machine learning based attribution to identify where and under which conditions terrain properties related to topography, water table depth, and soil hydraulic properties influence the rate of vegetation decay. Over the study domain, the machine learning model attributes about one-third of the spatial variations of vegetation decay rates to terrain properties, which is roughly equally split between direct terrain effects and interaction effects with climate and vegetation variables. The importance of secondary water effects increases with increasing topographic variability, shallower groundwater levels, and the propensity to capillary rise given by soil properties. In regions with favorable terrain properties, more than 60% of the variations in the decay rate of vegetation are attributed to terrain properties, highlighting the importance of secondary water effects on vegetation in Africa. Our findings provide an empirical assessment of the importance of local-scale secondary water effects on vegetation over Africa and help to improve hydrological and vegetation models for the challenge of bridging processes across spatial scales.

Describing ecosystem carbon fluxes is essential for deepening the understanding of the Earth system. However, partitioning net ecosystem exchange (NEE), i.e. the sum of ecosystem respiration (Reco) and gross primary production (GPP), into these summands is ill-posed since there can be infinitely many mathematically-valid solutions. We propose a novel data-driven approach to NEE partitioning using a deep state space model which combines the interpretability and uncertainty analysis of state space models with the ability of recurrent neural networks to learn the complex functions governing the data. We validate our proposed approach on the FLUXNET dataset. We suggest using both the past and the future of Reco’s predictors for training along with the nighttime NEE (NEEnight) to learn a dynamical model of Reco. We evaluate our nighttime Reco forecasts by comparing them to the ground truth NEEnight and obtain the best accuracy with respect to other partitioning methods. The learned nighttime Reco model is then used to forecast the daytime Reco conditioning on the future observations of different predictors, i.e., global radiation, air temperature, precipitation, vapor pressure deficit, and daytime NEE (NEEday). Subtracted from the NEEday, these estimates yield the GPP, finalizing the partitioning. Our purely data-driven daytime Reco forecasts are in line with the recent empirical partitioning studies reporting lower daytime Reco than the Reichstein method, which can be attributed to the Kok effect, i.e., the plant respiration being higher at night. We conclude that our approach is a good alternative for data-driven NEE partitioning and complements other partitioning methods.

Abstract Hydrological interactions between vegetation, soil, and topography are complex, and heterogeneous in semi‐arid landscapes. This along with data scarcity poses challenges for large‐scale modeling of vegetation‐water interactions. Here, we exploit metrics derived from daily Meteosat data over Africa at ca. 5 km spatial resolution for ecohydrological analysis. Their spatial patterns are based on Fractional Vegetation Cover (FVC) time series and emphasize limiting conditions of the seasonal wet to dry transition: the minimum and maximum FVC of temporal record, the FVC decay rate and the FVC integral over the decay period. We investigate the relevance of these metrics for large scale ecohydrological studies by assessing their co‐variation with soil moisture, and with topographic, soil, and vegetation factors. Consistent with our initial hypothesis, FVC minimum and maximum increase with soil moisture, while the FVC integral and decay rate peak at intermediate soil moisture. We find evidence for the relevance of topographic moisture variations in arid regions, which, counter‐intuitively, is detectable in the maximum but not in the minimum FVC. We find no clear evidence for wide‐spread occurrence of the “inverse texture effect” on FVC. The FVC integral over the decay period correlates with independent data sets of plant water storage capacity or rooting depth while correlations increase with aridity. In arid regions, the FVC decay rate decreases with canopy height and tree cover fraction as expected for ecosystems with a more conservative water‐use strategy. Thus, our observation‐based products have large potential for better understanding complex vegetation‐water interactions from regional to continental scales.

Data is central in almost all scientific disciplines nowadays. Furthermore, intelligent systems have developed rapidly in recent years, so that in many disciplines the expectation is emerging that with the help of intelligent systems, significant challenges can be overcome and science can be done in completely new ways. In order for this to succeed, however, first, fundamental research in computer science is still required, and, second, generic tools must be developed on which specialized solutions can be built. In this paper, we introduce a recently started collaborative project funded by the Carl Zeiss Foundation, a virtual manufactory for digitization in the sciences, the “Werkstatt”, which is being established at the Michael Stifel Center Jena (MSCJ) for data-driven and simulation science to address fundamental questions in computer science and applications. The Werkstatt focuses on three key areas, which include generic tools for machine learning, knowledge generation using machine learning processes, and semantic methods for the data life cycle, as well as the application of these topics in different disciplines. Core and pilot projects address the key aspects of the topics and form the basis for sustainable work in the Werkstatt.

Tree-ring chronologies encode interannual variability in forest growth rates over long time periods from decades to centuries or even millennia. However, each chronology is a highly localized measurement describing conditions at specific sites where wood samples have been collected. The question whether these local growth variabilites are representative for large geographical regions remains an open issue. To overcome the limitations of interpreting a sparse network of sites, we propose an upscaling approach for annual tree-ring indices that approximate forest growth variability and compute gridded data products that generalize the available information for multiple tree genera. Using regression approaches from machine learning, we predict tree-ring indices in space and time based on climate variables, but considering also species range maps as constraints for the upscaling. We compare various prediction strategies in cross-validation experiments to identify the best performing setup. Our estimated maps of tree-ring indices are the first data products that provide a dense view on forest growth variability at the continental level with 0.5° and 0.0083° spatial resolution covering the years 1902–2013. Furthermore, we find that different genera show very variable spatial patterns of anomalies. We have selected Europe as study region and focused on the six most prominent tree genera, but our approach is very generic and can easily be applied elsewhere. Overall, the study shows perspectives but also limitations for reconstructing spatiotemporal dynamics of complex biological processes. The data products are available at https://www.doi.org/10.17871/BACI.248.

Heatwaves are weather hazards that can influence societal and natural systems. Recently, heatwaves have increased in frequency, duration, and intensity, and this trend is projected to continue as a consequence of climate change. The study of heatwaves is hampered by the lack of a common definition, which limits comparability between studies. This applies in particular to the considered time scale for utilised metrics. Here, we study which durations of heatwaves are most impact-relevant for various types of impacts. For this purpose, we analyse societal metrics related to health (heat-related hospitalisations, mortality) and public attention (Google trends, news articles) in Germany. Country-averaged temperatures are calculated for the period of 2010–2019 and the warmest periods of all time scales between 1 and 90 days are selected. Then, we assess and compare the societal response during those periods to identify the heatwave durations with the most pronounced impacts. Note that these durations are based on average temperatures across the given time frame while individual days may be less warm. The results differ slightly between the considered societal metrics but indicate overall that heatwaves induce the strongest societal response at durations between 2 weeks and 2 months for Germany. Finally, we show that heatwave duration affects the societal response independent of, and additionally to, heatwave temperatures. This finding highlights the relevance of making informed choices on the considered time scale in heatwave analyses. The approach we introduce here can be extended to other societal indices, countries, and hazard types to reveal more meaningful definitions of climate extremes to guide future research on these events.

The process of evapotranspiration transfers liquid water from vegetation and soil surfaces to the atmosphere, the so-called latent heat flux ( ${Q_{{\text{LE}}}}$ ), and modulates the Earth’s energy, water, and carbon cycle. Vegetation controls ${Q_{{\text{LE}}}}$ by regulating leaf stomata opening (surface resistance ${r_{\text{s}}}$ in the Big Leaf approach) and by altering surface roughness (aerodynamic resistance ${r_{\text{a}}}$ ). Estimating ${r_{\text{s}}}$ and ${r_{\text{a}}}$ across different vegetation types is a key challenge in predicting ${Q_{{\text{LE}}}}$ . We propose a hybrid approach that combines mechanistic modeling and machine learning for modeling ${Q_{{\text{LE}}}}$ . The hybrid model combines a feed-forward neural network which estimates the resistances from observations as intermediate variables and a mechanistic model in an end-to-end setting. In the hybrid modeling setup, we make use of the Penman–Monteith equation in conjunction with multi-year flux measurements across different forest and grassland sites from the FLUXNET database. This hybrid model setup is successful in predicting ${Q_{{\text{LE}}}}$ , however, this approach leads to equifinal solutions in terms of estimated physical parameters. We follow two different strategies to constrain the hybrid model and therefore control for the equifinality that arises when the two resistances are estimated simultaneously. One strategy is to impose an a priori constraint on ${r_{\text{a}}}$ based on mechanistic assumptions (theory-driven strategy), while the other strategy makes use of more observational data and adds a constraint in predicting ${r_{\text{a}}}$ through multi-task learning of both latent and sensible heat flux ( ${Q_{\text{H}}}$ ; data-driven strategy) together. Our results show that all hybrid models predict the target variables with a high degree of success, with ${R^2}$ = 0.82–0.89 for grasslands and ${R^2}$ = 0.70–0.80 for forest sites at the mean diurnal scale. The predicted ${r_{\text{s}}}$ and ${r_{\text{a}}}$ show strong physical consistency across the two regularized hybrid models, but are physically implausible in the under-constrained hybrid model. The hybrid models are robust in reproducing consistent results for energy fluxes and resistances across different scales (diurnal, seasonal, and interannual), reflecting their ability to learn the physical dependence of the target variables on the meteorological inputs. As a next step, we propose to test these heavily observation-informed parameterizations derived through hybrid modeling as a substitute for ad hoc formulations in Earth system models.

Tropical ecosystems experience particularly fast transformations largely as a consequence of land use and climate change. Consequences for ecosystem functioning and services are hard to predict and require analyzing multiple data sets simultaneously. Today, we are equipped with a wide range of spatio-temporal observation-based data streams that monitor the rapid transformations of tropical ecosystems in terms of state variables (e.g., biomass, leaf area, soil moisture) but also in terms of ecosystem processes (e.g., gross primary production, evapotranspiration, runoff). However, the underexplored joint potential of such data streams, combined with deficient access to data and processing, constrain our understanding of ecosystem functioning, despite the importance of tropical ecosystems in the regional-to-global carbon and water cycling. Our objectives are: 1. To facilitate access to regional “Analysis Ready Data Cubes” and enable efficient processing 2. To contribute to the understanding of ecosystem functioning and atmosphere-biosphere interactions. 3. To get a dynamic perspective of environmental conditions for biodiversity. To achieve our objectives, we developed a regional variant of an “Earth System Data Lab” (RegESDL) tailored to address the challenges of northern South America. The study region extensively covers natural ecosystems such as rainforest and savannas, and includes strong topographic gradients (0–6,500 masl). Currently, environmental threats such as deforestation and ecosystem degradation continue to increase. In this contribution, we show the value of the approach for characterizing ecosystem functioning through the efficient implementation of time series and dimensionality reduction analysis at pixel level. Specifically, we present an analysis of seasonality as it is manifested in multiple indicators of ecosystem primary production. We demonstrate that the RegESDL has the ability to underscore contrasting patterns of ecosystem seasonality and therefore has the potential to contribute to the characterization of ecosystem function. These results illustrate the potential of the RegESDL to explore complex land-surface processes and the need for further exploration. The paper concludes with some suggestions for developing future big-data infrastructures and its applications in the tropics.

Questions of causality are ubiquitous in Earth system sciences and beyond, yet correlation techniques still prevail. This Perspective provides an overview of causal inference methods, identifies promising applications and methodological challenges, and initiates a causality benchmark platform.

Abstract Enhancing the capacity of social‐ecological systems (SES) to adapt to climate change is of crucial importance. While gradual climate change impacts have been the main focus of much recent research, much less is known about how SES are impacted by climate extremes and how they adapt. Here, based on an advanced conceptualization of social‐ecological resilience, performed by an interdisciplinary group of scientists, we outline three major challenges for operationalizing the resilience concept with particular focus on climate extremes. First, we discuss the necessary steps required to identify and measure relevant variables for capturing the full response spectrum of the coupled social and ecological components of SES. Second, we examine how climate extreme impacts on coupling flows in SES can be quantified by learning from past societal transitions or adaptations to climate extremes and resulting changes in ecosystem service supply. Last, we explore how to identify management options for maintaining and enhancing social‐ecological resilience under a changing regime of climate extremes. We conclude that multiple pathways within adaptation and mitigation strategies which enhance the adaptive capacity of SES to absorb climate extremes will open the way toward a sustainable future.

Extreme hydrological and meteorological conditions can severely affect ecosystems, parts of the economy, and consequently society. These impacts are expected to be aggravated by climate change. Here we analyze and compare the impacts of multiple types of extreme events across several domains in Europe, to reveal corresponding impact signatures. We characterize the distinct impacts of droughts, floods, heat waves, frosts and storms on a variety of biophysical and social variables at national level and half-monthly time scale. We find strong biophysical impacts of droughts, floods, heat waves and frosts, while public attention and property damage are more affected by storms and floods. We show unexpected impact patterns such as reduced human mortality during floods and storms. Comparing public attention anomalies with impacts across all other considered domains we find that attention on droughts is comparatively low despite the significant overall impacts. Resolving these impact patterns highlights large-scale vulnerability and supports regional extreme event management to consequently reduce disaster risks.

Process understanding and modeling is at the core of scientific reasoning. Principled parametric and mechanistic modeling dominated science and engineering until the recent emergence of machine learning (ML). Despite great success in many areas, ML algorithms in the Earth and climate sciences, and more broadly in physical sciences, are not explicitly designed to be physically-consistent and may, therefore, violate the most basic laws of physics. In this work, motivated by the field of algorithmic fairness, we reconcile data-driven ML with physics modeling by illustrating a nonparametric and nonlinear physics-aware regression method. By incorporating a dependence-based regularizer, the method leads to models that are consistent with domain knowledge, as reflected by either simulations from physical models or ancillary data. The idea can conversely encourage independence of model predictions with other variables that are known to be uncertain either in their representation or magnitude. The method is computationally efficient and comes with a closed-form analytic solution. Through a consistency-vs-accuracy path diagram, one can assess the consistency between data-driven models and physical models. We demonstrate in three examples on simulations and measurement data in Earth and climate studies that the proposed ML framework allows us to trade-off physical consistency and accuracy.

Abstract Background Information on the spatial distribution of aboveground biomass (AGB) over large areas is needed for understanding and managing processes involved in the carbon cycle and supporting international policies for climate change mitigation and adaption. Furthermore, these products provide important baseline data for the development of sustainable management strategies to local stakeholders. The use of remote sensing data can provide spatially explicit information of AGB from local to global scales. In this study, we mapped national Mexican forest AGB using satellite remote sensing data and a machine learning approach. We modelled AGB using two scenarios: (1) extensive national forest inventory (NFI), and (2) airborne Light Detection and Ranging (LiDAR) as reference data. Finally, we propagated uncertainties from field measurements to LiDAR-derived AGB and to the national wall-to-wall forest AGB map. Results The estimated AGB maps (NFI- and LiDAR-calibrated) showed similar goodness-of-fit statistics (R2, Root Mean Square Error (RMSE)) at three different scales compared to the independent validation data set. We observed different spatial patterns of AGB in tropical dense forests, where no or limited number of NFI data were available, with higher AGB values in the LiDAR-calibrated map. We estimated much higher uncertainties in the AGB maps based on two-stage up-scaling method (i.e., from field measurements to LiDAR and from LiDAR-based estimates to satellite imagery) compared to the traditional field to satellite up-scaling. By removing LiDAR-based AGB pixels with high uncertainties, it was possible to estimate national forest AGB with similar uncertainties as calibrated with NFI data only. Conclusions Since LiDAR data can be acquired much faster and for much larger areas compared to field inventory data, LiDAR is attractive for repetitive large scale AGB mapping. In this study, we showed that two-stage up-scaling methods for AGB estimation over large areas need to be analyzed and validated with great care. The uncertainties in the LiDAR-estimated AGB propagate further in the wall-to-wall map and can be up to 150%. Thus, when a two-stage up-scaling method is applied, it is crucial to characterize the uncertainties at all stages in order to generate robust results. Considering the findings mentioned above LiDAR can be used as an extension to NFI for example for areas that are difficult or not possible to access.

A Correction to this paper has been published: https://doi.org/10.1038/s41597-021-00851-9.

Across a landscape, aquatic-terrestrial interfaces within and between ecosystems are hotspots of organic matter (OM) mineralization. These interfaces are characterized by sharp spatio-temporal changes in environmental conditions, which affect OM properties and thus control OM mineralization and other transformation processes. Consequently, the extent of OM movement at and across aquatic-terrestrial interfaces is crucial in determining OM turnover and carbon (C) cycling at the landscape scale. Here, we propose expanding current concepts in aquatic and terrestrial ecosystem sciences to comprehensively evaluate OM turnover at the landscape scale. We focus on three main concepts toward explaining OM turnover at the landscape scale: the landscape spatio-temporal context, OM turnover described by priming and ecological stoichiometry, and anthropogenic effects as a disruptor of natural OM transfer magnitudes and pathways. A conceptual framework is introduced that allows for discussing the disparities in spatial and temporal scales of OM transfer, changes in environmental conditions, ecosystem connectivity, and microbial–substrate interactions. The potential relevance of priming effects in both terrestrial and aquatic systems is addressed. For terrestrial systems, we hypothesize that the interplay between the influx of OM, its corresponding elemental composition, and the elemental demand of the microbial communities may alleviate spatial and metabolic thresholds. In comparison, substrate level OM dynamics may be substantially different in aquatic systems due to matrix effects that accentuate the role of abiotic conditions, substrate quality, and microbial community dynamics. We highlight the disproportionate impact anthropogenic activities can have on OM cycling across the landscape. This includes reversing natural OM flows through the landscape, disrupting ecosystem connectivity, and nutrient additions that cascade across the landscape. This knowledge is crucial for a better understanding of OM cycling in a landscape context, in particular since terrestrial and aquatic compartments may respond differently to the ongoing changes in climate, land use, and other anthropogenic interferences.

Forests play a crucial role in the global carbon (C) cycle by storing and sequestering a substantial amount of C in the terrestrial biosphere. Due to temporal dynamics in climate and vegetation activity, there are significant regional variations in carbon dioxide (CO2) fluxes between the biosphere and atmosphere in forests that are affecting the global C cycle. Current forest CO2 flux dynamics are controlled by instantaneous climate, soil, and vegetation conditions, which carry legacy effects from disturbances and extreme climate events. Our level of understanding from the legacies of these processes on net CO2 fluxes is still limited due to their complexities and their long-term effects. Here, we combined remote sensing, climate, and eddy-covariance flux data to study net ecosystem CO2 exchange (NEE) at 185 forest sites globally. Instead of commonly used non-dynamic statistical methods, we employed a type of recurrent neural network (RNN), called Long Short-Term Memory network (LSTM) that captures information from the vegetation and climate's temporal dynamics. The resulting data-driven model integrates interannual and seasonal variations of climate and vegetation by using Landsat and climate data at each site. The presented LSTM algorithm was able to effectively describe the overall seasonal variability (Nash-Sutcliffe efficiency, NSE = 0.66) and across-site (NSE = 0.42) variations in NEE, while it had less success in predicting specific seasonal and interannual anomalies (NSE = 0.07). This analysis demonstrated that an LSTM approach with embedded climate and vegetation memory effects outperformed a non-dynamic statistical model (i.e. Random Forest) for estimating NEE. Additionally, it is shown that the vegetation mean seasonal cycle embeds most of the information content to realistically explain the spatial and seasonal variations in NEE. These findings show the relevance of capturing memory effects from both climate and vegetation in quantifying spatio-temporal variations in forest NEE.

Sun-Induced fluorescence at 760 nm (F760) is increasingly being used to predict gross primary production (GPP) through light use efficiency (LUE) modeling, even though the mechanistic processes that link the two are not well understood. We analyzed the effect of nitrogen (N) and phosphorous (P) availability on the processes that link GPP and F760 in a Mediterranean grassland manipulated with nutrient addition. To do so, we used a combination of process-based modeling with Soil-Canopy Observation of Photosynthesis and Energy (SCOPE), and statistical analyses such as path modeling. With this study, we uncover the mechanisms that link the fertilization-driven changes in canopy nitrogen concentration (N%) to the observed changes in F760 and GPP. N addition changed plant community structure and increased canopy chlorophyll content, which jointly led to changes in photosynthetic active radiation (APAR), ultimately affecting both GPP and F760. Changes in the abundance of graminoids, (%graminoids) driven by N addition led to changes in structural properties of the canopy such as leaf angle distribution, that ultimately influenced observed F760 by controlling the escape probability of F760 (Fesc). In particular, we found a change in GPP−F760 relationship between the first and the second year of the experiment that was largely driven by the effect of plant type composition on Fesc, whose best predictor is %graminoids. The P addition led to a statistically significant increase on light use efficiency of fluorescence emission (LUEf), in particular in plots also with N addition, consistent with leaf level studies. The N addition induced changes in the biophysical properties of the canopy that led to a trade-off between surface temperature (Ts), which decreased, and F760 at leaf scale (F760leaf,fw), which increased. We found that Ts is an important predictor of the light use efficiency of photosynthesis, indicating the importance of Ts in LUE modeling approaches to predict GPP.

The authors modify the schematic plots in their article [...]

Changing trends in ecosystem productivity can be quantified using satellite observations of Normalized Difference Vegetation Index (NDVI). However, the estimation of trends from NDVI time series differs substantially depending on analyzed satellite dataset, the corresponding spatiotemporal resolution, and the applied statistical method. Here we compare the performance of a wide range of trend estimation methods and demonstrate that performance decreases with increasing inter-annual variability in the NDVI time series. Trend slope estimates based on annual aggregated time series or based on a seasonal-trend model show better performances than methods that remove the seasonal cycle of the time series. A breakpoint detection analysis reveals that an overestimation of breakpoints in NDVI trends can result in wrong or even opposite trend estimates. Based on our results, we give practical recommendations for the application of trend methods on long-term NDVI time series. Particularly, we apply and compare different methods on NDVI time series in Alaska, where both greening and browning trends have been previously observed. Here, the multi-method uncertainty of NDVI trends is quantified through the application of the different trend estimation methods. Our results indicate that greening NDVI trends in Alaska are more spatially and temporally prevalent than browning trends. We also show that detected breakpoints in NDVI trends tend to coincide with large fires. Overall, our analyses demonstrate that seasonal trend methods need to be improved against inter-annual variability to quantify changing trends in ecosystem productivity with higher accuracy.

Information on the spatial distribution of forest structure parameters (e.g., aboveground biomass, vegetation height) are crucial for assessing terrestrial carbon stocks and emissions. In this study, we sought to assess the potential and merit of multi-temporal dual-polarised L-band observations for vegetation height estimation in tropical deciduous and evergreen forests of Mexico. We estimated vegetation height using dual-polarised L-band observations and a machine learning approach. We used airborne LiDAR-based vegetation height for model training and for result validation. We split LiDAR-based vegetation height into training and test data using two different approaches, i.e., considering and ignoring spatial autocorrelation between training and test data. Our results indicate that ignoring spatial autocorrelation leads to an overoptimistic model’s predictive performance. Accordingly, a spatial splitting of the reference data should be preferred in order to provide realistic retrieval accuracies. Moreover, the model’s predictive performance increases with an increasing number of spatial predictors and training samples, but saturates at a specific level (i.e., at 12 dual-polarised L-band backscatter measurements and at around 20% of all training samples). In consideration of spatial autocorrelation between training and test data, we determined an optimal number of L-band observations and training samples as a trade-off between retrieval accuracy and data collection effort. In summary, our study demonstrates the merit of multi-temporal ScanSAR L-band observations for estimation of vegetation height at a larger scale and provides a workflow for robust predictions of this parameter.

Tree–grass ecosystems are widely distributed. However, their phenology has not yet been fully characterized. The technique of repeated digital photographs for plant phenology monitoring (hereafter referred as PhenoCam) provide opportunities for long-term monitoring of plant phenology, and extracting phenological transition dates (PTDs, e.g., start of the growing season). Here, we aim to evaluate the utility of near-infrared-enabled PhenoCam for monitoring the phenology of structure (i.e., greenness) and physiology (i.e., gross primary productivity—GPP) at four tree–grass Mediterranean sites. We computed four vegetation indexes (VIs) from PhenoCams: (1) green chromatic coordinates (GCC), (2) normalized difference vegetation index (CamNDVI), (3) near-infrared reflectance of vegetation index (CamNIRv), and (4) ratio vegetation index (CamRVI). GPP is derived from eddy covariance flux tower measurement. Then, we extracted PTDs and their uncertainty from different VIs and GPP. The consistency between structural (VIs) and physiological (GPP) phenology was then evaluated. CamNIRv is best at representing the PTDs of GPP during the Green-up period, while CamNDVI is best during the Dry-down period. Moreover, CamNIRv outperforms the other VIs in tracking growing season length of GPP. In summary, the results show it is promising to track structural and physiology phenology of seasonally dry Mediterranean ecosystem using near-infrared-enabled PhenoCam. We suggest using multiple VIs to better represent the variation of GPP.

Forests dominate carbon (C) exchanges between the terrestrial biosphere and the atmosphere on land. In the long term, the net carbon flux between forests and the atmosphere has been significantly impacted by changes in forest cover area and structure due to ecological disturbances and management activities. Current empirical approaches for estimating net ecosystem productivity (NEP) rarely consider forest age as a predictor, which represents variation in physiological processes that can respond differently to environmental drivers, and regrowth following disturbance. Here, we conduct an observational synthesis to empirically determine to what extent climate, soil properties, nitrogen deposition, forest age and management influence the spatial and interannual variability of forest NEP across 126 forest eddy-covariance flux sites worldwide. The empirical models explained up to 62% and 71% of spatio-temporal and across-site variability of annual NEP, respectively. An investigation of model structures revealed that forest age was a dominant factor of NEP spatio-temporal variability in both space and time at the global scale as compared to abiotic factors, such as nutrient availability, soil characteristics and climate. These findings emphasize the importance of forest age in quantifying spatio-temporal variation in NEP using empirical approaches.

Climate extremes have the potential to cause extreme responses of terrestrial ecosystem functioning. However, it is neither straightforward to quantify and predict extreme ecosystem responses, nor to attribute these responses to specific climate drivers. Here, we construct a factorial experiment based on a large ensemble of process-oriented ecosystem model simulations driven by a regional climate model (12 500 model years in 1985–2010) in six European regions. Our aims are to (1) attribute changes in the intensity and frequency of simulated ecosystem productivity extremes (EPEs) to recent changes in climate extremes, CO _2 concentration, and land use, and to (2) assess the effect of timing and seasonal interaction on the intensity of EPEs. Evaluating the ensemble simulations reveals that (1) recent trends in EPEs are seasonally contrasting: spring EPEs show consistent trends towards increased carbon uptake, while trends in summer EPEs are predominantly negative in net ecosystem productivity (i.e. higher net carbon release under drought and heat in summer) and close-to-neutral in gross productivity. While changes in climate and its extremes (mainly warming) and changes in CO _2 increase spring productivity, changes in climate extremes decrease summer productivity neutralizing positive effects of CO _2 . Furthermore, we find that (2) drought or heat wave induced carbon losses in summer (i.e. negative EPEs) can be partly compensated by a higher uptake in the preceding spring in temperate regions. Conversely, however, carry-over effects from spring to summer that arise from depleted soil moisture exacerbate the carbon losses caused by climate extremes in summer, and are thus undoing spring compensatory effects. While the spring-compensation effect is increasing over time, the carry-over effect shows no trend between 1985–2010. The ensemble ecosystem model simulations provide a process-based interpretation and generalization for spring-summer interacting carbon cycle effects caused by climate extremes (i.e. compensatory and carry-over effects). In summary, the ensemble ecosystem modelling approach presented in this paper offers a novel route to scrutinize ecosystem responses to changing climate extremes in a probabilistic framework, and to pinpoint the underlying eco-physiological mechanisms.

Understanding the impacts of climate extremes on the carbon cycle is important for quantifying the carbon-cycle climate feedback and highly relevant to climate change assessments. Climate extremes and fires can have severe regional effects, but a spatially explicit global impact assessment is still lacking. Here, we directly quantify spatiotemporal contiguous extreme anomalies in four global data sets of gross primary production (GPP) over the last 30 years. We find that positive and negative GPP extremes occurring on 7% of the spatiotemporal domain explain 78% of the global interannual variation in GPP and a significant fraction of variation in the net carbon flux. The largest thousand negative GPP extremes during 1982–2011 (4.3% of the data) account for a decrease in photosynthetic carbon uptake of about 3.5 Pg C yr ^−1 , with most events being attributable to water scarcity. The results imply that it is essential to understand the nature and causes of extremes to understand current and future GPP variability.

We present a simple method of probabilistic risk analysis for ecosystems. The only requirements are time series—modelled or measured—of environment and ecosystem variables. Risk is defined as the product of hazard probability and ecosystem vulnerability. Vulnerability is the expected difference in ecosystem performance between years with and without hazardous conditions. We show an application to drought risk for net primary productivity of coniferous forests across Europe, for both recent and future climatic conditions.

In the northern high latitudes, alternative hypotheses with regards to how warming-related shifts in seasonality influence ecosystem productivity exist. Increased plant growth associated with a longer growing season may enhance ecosystem productivity, but shifts to earlier springs may also negatively influence soil moisture status and productivity during the peak of the growing season. Here, we analyzed nearly three decades (1982–2008) of observational records and derived products, including satellite microwave and optical imagery as well as upscaled ecosystem flux observations, to better understand how shifts in seasonality impact hydrology and productivity in the North American boreal forests. We identified a dominant adverse influence of earlier springs on peak summer forest greenness, actual evapotranspiration and productivity at interannual time scales across the drier western and central sections of the North American boreal forests. In the vast regions where this spring onset mechanism operates, ecosystem productivity gains from earlier springs during the early portion of the growing season are effectively cancelled through corresponding losses in the later portion. Our results also indicate that recent decadal shifts towards earlier springs and associated drying in the midst of the growing season over western North American boreal forests may have contributed to the reported declines in summer productivity and increases in tree mortality and fire activity. With projections of accelerated northern high-latitude warming and associated shifts to earlier springs, persistent soil moisture deficits in peak summer may be an effective mechanism for regional-scale boreal forest dieback through their strong influence on productivity, tree mortality and disturbance dynamics.

As the lifetime of regional flux networks approach twenty years, there is a growing number of papers that have published long term records (5 years or more) of net carbon fluxes between ecosystems and the atmosphere. Unanswered questions from this body of work are: 1) how variable are carbon fluxes on a year to year basis?; 2) what are the biophysical factors that may cause interannual variability and/or temporal trends in carbon fluxes?; and 3) how does the biophysical control on this carbon flux variability differ by climate and ecological spaces? To address these questions, we surveyed published data from 59 sites that reported on five or more years of continuous measurements, yielding 544 site-years of data.We found that the standard deviation of the interannual variability in net ecosystem carbon exchange (162gCm−2y−1) is large relative to its population mean (−200gCm−2 y−1). Broad-leaved evergreen forests and crops experienced the greatest absolute variability in interannual net carbon exchange (greater than ±300gCm−2y−1) and boreal evergreen forests and maritime wetlands were among the least variable (less than ±40 gCm−2y−1).A disproportionate fraction of the yearly variability in net ecosystem exchange was associated with biophysical factors that modulated ecosystem photosynthesis rather than ecosystem respiration. Yet, there was appreciable and statistically significant covariance between ecosystem photosynthesis and respiration. Consequently, biophysical conditions that conspired to increase ecosystem photosynthesis to from one year to the next were associated with an increase in ecosystem respiration, and vice versa; on average, the year to year change in respiration was 40% as large as the year to year change in photosynthesis. The analysis also identified sets of ecosystems that are on the verge of switching from being carbon sinks to carbon sources. These include sites in the Arctic tundra, the evergreen forests in the Pacific northwest and some grasslands, where year to year changes in respiration are outpacing those in photosynthesis.While a select set of climatic and ecological factors (e.g. light, rainfall, temperature, phenology) played direct and indirect roles on this variability, their impact differed conditionally, as well as by climate and ecological spaces. For example, rainfall had both positive and negative effects. Deficient rainfall caused a physiological decline in photosynthesis in temperate and semi-arid regions. Too much rain, in the humid tropics, limited photosynthesis by limiting light. In peatlands and tundra, excess precipitation limited ecosystem respiration when it raised the water table to the surface. For deciduous forests, warmer temperatures lengthened the growing season, increasing photosynthesis, but this effect also increased soil respiration.Finally, statistical analysis was performed to evaluate the detection limit of trends; we computed the confidence intervals of trends in multi-year carbon fluxes that need to be resolved to conclude whether the differences are to be attributed to randomness or biophysical forcings. Future studies and reports on interannual variations need to consider the role of the duration of the time series on random errors when quantifying potential trends and extreme events.