Lijing Wang

Accurate characterization of the subsurface thermal environment (STE) is crucial for sustainable geothermal energy and urban heat management, yet it remains challenged by pronounced subsurface heterogeneity at the city scale. Conventional approaches, which primarily rely on deterministic numerical modeling based on sparse observations, fail to capture the heterogeneity and spatial distribution of the subsurface thermal environment (STE). Here, we introduce an integrated modeling framework that synergistically combines geostatistics, physics-based modeling, and Bayesian inference to reconstruct the STE under steady-state thermal conditions and quantify its uncertainty. Applied to Changzhou in the densely populated Yangtze River Delta, our framework probabilistically reveals the distribution of key factors (lithology, upper temperature, basal heat flow, thermal conductivity, Darcy flux, and subsurface temperature). A key finding from the sensitivity analysis identifies the upper temperature boundary as the dominant source of modeling uncertainty. We estimate the shallow geothermal potential of Changzhou to be approximately 2.7 × 10⁴ GWh, sufficient to meet its winter heating demand and highlighting its potential as a sustainable energy source for the Yangtze River Delta. Our scalable and uncertainty-aware framework offers a pathway for the global assessment and management of subsurface thermal resources.

Bathymetry beneath ice shelves in West Antarctica plays an important role in the delivery and circulation of warm waters to the ice-shelf bottom and grounding line. Large-scale bathymetric estimates can only be inferred through inversion of airborne gravity measurements. However, previous bathymetry inversions have not robustly quantified uncertainty in the bathymetry due to assumptions inherent in the inversion, and typically only produce a single model, making it difficult to propagate uncertainty into ocean and ice-sheet models. Previous inversions have sometimes considered uncertainties in bathymetry models due to background densities but have not quantified the uncertainty due to the non-uniqueness inherent in gravity and geological variability below ice shelves. To address these issues, we develop a method to generate ensembles of bathymetry models beneath the Crosson, Dotson, and Thwaites Eastern ice shelves with independent realizations of background density and geological variability, represented through the Bouguer gravity disturbance. We sample the uncertainty in the unknown geology below the ice shelves by interpolating the Bouguer disturbance using Sequential Gaussian Simulation. Each inversion is efficiently computed using a random walk Metropolis Markov Chain Monte Carlo approach which randomly updates blocks of bathymetry and accepts or rejects updates. Our ensembles of bathymetry models differ from previous estimates of bathymetry by hundreds of meters in some areas and show that the uncertainty in the Bouguer disturbance is the largest source of uncertainty. The different bathymetry models in the ensembles can be used in oceanographic models to place better bounds on sub-ice-shelf melting and future grounding line retreat.

Bathymetry beneath ice shelves in West Antarctica plays an important role in the delivery and circulation of warm waters to the ice-shelf bottom and grounding line. Large-scale bathymetric estimates can only be inferred through inversion of airborne gravity measurements. However, previous bathymetry inversions have not robustly quantified uncertainty in the bathymetry due to assumptions inherent in the inversion, and typically only produce a single model, making it difficult to propagate uncertainty into ocean and ice-sheet models. Previous inversions have sometimes considered uncertainties in bathymetry models due to background densities but have not quantified the uncertainty due to the non-uniqueness inherent in gravity and geological variability below ice shelves. To address these issues, we develop a method to generate ensembles of bathymetry models beneath the Crosson, Dotson, and Thwaites Eastern ice shelves with independent realizations of background density and geological variability, represented through the Bouguer gravity disturbance. We sample the uncertainty in the unknown geology below the ice shelves by interpolating the Bouguer disturbance using Sequential Gaussian Simulation. Each inversion is efficiently solved using a random walk Metropolis Markov Chain Monte Carlo approach which randomly updates blocks of bathymetry and accepts or rejects updates. Our ensembles of bathymetry models differ from previous estimates of bathymetry by hundreds of meters in some areas and show that the uncertainty in the Bouguer disturbance is the largest source of uncertainty. The different bathymetry models in the ensembles can be used in oceanographic models to place better bounds on sub-ice-shelf melting and future grounding line retreat.

Bathymetry beneath ice shelves in West Antarctica plays an important role in the delivery and circulation of warm waters to the ice-shelf bottom and grounding line. Large-scale bathymetric estimates can only be inferred through inversion of airborne gravity measurements. However, previous bathymetry inversions have not robustly quantified uncertainty in the bathymetry due to assumptions inherent in the inversion, and typically only produce a single model, making it difficult to propagate uncertainty into ocean and ice-sheet models. Previous inversions have sometimes considered uncertainties in bathymetry models due to background densities but have not quantified the uncertainty due to the non-uniqueness inherent in gravity and geological variability below ice shelves. To address these issues, we develop a method to generate ensembles of bathymetry models beneath the Crosson, Dotson, and Thwaites Eastern ice shelves with independent realizations of background density and geological variability, represented through the Bouguer gravity disturbance. We sample the uncertainty in the unknown geology below the ice shelves by interpolating the Bouguer disturbance using Sequential Gaussian Simulation. Each inversion is efficiently solved using a random walk Metropolis Markov Chain Monte Carlo approach which randomly updates blocks of bathymetry and accepts or rejects updates. Our ensembles of bathymetry models differ from previous estimates of bathymetry by hundreds of meters in some areas and show that the uncertainty in the Bouguer disturbance is the largest source of uncertainty. The different bathymetry models in the ensembles can be used in oceanographic models to place better bounds on sub-ice-shelf melting and future grounding line retreat.

In the Anthropocene—a period marked by rapid environmental change—understanding the critical zone (CZ), the Earth's outer layer where rock, soil, water, air, and living organisms interact, is crucial. This review emphasizes data‐model integration, the process of combining observational data (collected from field and laboratory settings) with computational models (representations of processes) to enhance understanding of coupled systems, validate model predictions, and improve simulation accuracy in response to natural and anthropogenic drivers. We propose a three‐tiered framework for data‐model integration in CZ science. Tier 1 incorporates observational data into model inputs to test hypotheses and explore processes where understanding is limited, providing insights into CZ functions over long timescales or in data‐scarce areas. Tier 2 compares model outputs with observations and focuses on validation and calibration. Tier 3 involves iterative data‐model integration, in which models are continuously refined through feedback from new data and evolving scientific questions. While rare in CZ science, this approach holds promise for guiding new data collection, improving predictive accuracy and enabling hindcasts and earthcasts. We illustrate each tier with curated examples and discuss how the tiers reflect varying levels of knowledge about CZ function and may guide knowledge transfer to understudied areas. Finally, we identify key challenges and future directions, including scale integration, non‐stationarity, model limitations, and the need for transparent sharing of data‐model integration processes. This article is categorized under: Science of Water > Hydrological Processes Science of Water > Water Quality Science of Water > Methods

Mountainous headwater streams are sustained by both snowmelt‐driven streamflow and groundwater discharge in the Upper Colorado River Basin. However, predicting headwater stream discharge magnitude and peak flow timing is challenging in mountainous terrains, where snowmelt rates vary with vegetation type and elevation, and heterogeneous subsurface physical properties influence groundwater storage and its release. We used a model‐data integration approach to investigate the roles of snowmelt and subsurface structure in stream discharge and groundwater level. We ran an ensemble of 100 integrated surface‐subsurface hydrologic models for a mountainous headwater catchment near Crested Butte, Colorado, USA. We also evaluated and calibrated these models against observed data sets, including snow depth measurements using distributed temperature probes, stream discharge, and groundwater levels. Calibration with multiple data sources using neural density estimators has further constrained uncertainty in subsurface properties and snowmelt rates. Results indicated that observed slower snowmelt rates in evergreen forests delayed the peak flow and baseflow onset. In upstream areas with lower subsurface permeability, water was stored within the subsurface but was not released as interflow or shallow groundwater flow, and thereby not contributing to downstream streamflow during recession limb periods. Double peaks in groundwater occurred in areas with spatial subsurface heterogeneity, in our case due to the contrast between granodiorite and Mancos shale. These process‐based insights into groundwater and snowmelt dynamics in mountainous headwaters will help improve predictions of headwater hydrology.

Mountainous headwater streams are sustained by both snowmelt-driven streamflow and groundwater discharge in the Upper Colorado River Basin. However, predicting headwater stream discharge magnitude and peak flow timing is challenging in mountainous terrains, where snowmelt rates vary with vegetation type and elevation, and heterogeneous subsurface physical properties influence groundwater storage and its release. We used a model-data integration approach to investigate the roles of snowmelt and subsurface structure in stream discharge and groundwater level. We ran an ensemble of 100 integrated surface-subsurface hydrologic models for a mountainous headwater catchment near Crested Butte, Colorado, USA. We also evaluated and calibrated these models against observed datasets, including snow depth measurements using distributed temperature probes, stream discharge, and groundwater level. Calibration with multiple data sources using neural density estimators has further constrained uncertainty in subsurface properties and snowmelt rates. Results indicated that observed slower snowmelt rates in evergreen forests delayed the peak flow and baseflow onset. In upstream areas with lower subsurface permeability, water was stored within the subsurface but was not released as interflow or shallow groundwater flow, and thereby not contributing to downstream streamflow during recession limb periods. Double peaks in groundwater occurred in areas with spatial subsurface heterogeneity, in our case due to the contrast between granodiorite and Mancos shale. These process-based insights into groundwater and snowmelt dynamics in mountainous headwaters will help improve predictions of headwater hydrology.

Beavers (Castor canadensis) alter river corridor hydrology by creating ponds and inundating floodplains, and thereby improving surface water storage. However, the impact of inundation on groundwater, particularly in mountainous alluvial floodplains with permeable gravel/cobble layers overlain by a soil layer, remains uncertain. Numerical modeling across various floodplain structures considers topographic and sediment complexity and multidirectional flow, linking inundation to groundwater response. This study develops a model‐data integration workflow to address uncertainty in groundwater response to beaver‐induced inundations in a mountainous alluvial floodplain in the Upper Colorado River Basin. Uncertain factors include seasonal hydrologic dynamics, hydraulic conductivities, floodplain structures, and meteorological forcings. We employed an ensemble of groundwater models, based on geophysical and hydrologic data, with machine learning‐based calibration using a neural density estimator. This allowed us to quantify the vertical flux from the soil layer to the permeable gravel bed, the down‐valley underflow within the gravel bed, and their ratios. Results show a significant increase in the vertical flux relative to down‐valley underflow, from 2 during dry pond periods to 20 during wet periods, serving as an analogy for conditions without and with beaver ponds. The study highlights the influence of floodplain structure on groundwater storage, water balance, and water quality impacted by beaver ponds. A thick gravel bed layer, with a large down‐valley underflow, minimizes the effect of beaver‐induced inundation on water quality. We emphasize the need for field‐scale measurements of floodplain structure and improved characterization of evapotranspiration changes to reduce uncertainty in groundwater response.

Bathymetry beneath ice shelves in West Antarctica plays an important role in the delivery and circulation of warm waters to the ice-shelf bottom and grounding line. Large-scale bathymetric estimates can only be inferred through inversion of airborne gravity measurements. However, previous bathymetry inversions have not robustly quantified uncertainty in the bathymetry due to assumptions inherent in the inversion, and typically only produce a single model, making it difficult to propagate uncertainty into ocean and ice-sheet models. Previous inversions have sometimes considered uncertainties in bathymetry models due to background densities but have not quantified the uncertainty due to the non-uniqueness inherent in gravity and geological variability below ice shelves. To address these issues, we develop a method to generate ensembles of bathymetry models beneath the Crosson, Dotson, and Thwaites Eastern ice shelves with independent realizations of background density and geological variability, represented through the Bouguer gravity disturbance. We sample the uncertainty in the unknown geology below the ice shelves by interpolating the Bouguer disturbance using Sequential Gaussian Simulation. Each inversion is efficiently solved using a random walk Metropolis Markov Chain Monte Carlo approach which randomly updates blocks of bathymetry and accepts or rejects updates. Our ensembles of bathymetry models differ from previous estimates of bathymetry by hundreds of meters in some areas and show that the uncertainty in the Bouguer disturbance is the largest source of uncertainty. The different bathymetry models in the ensembles can be used in oceanographic models to place better bounds on sub-ice-shelf melting and future grounding line retreat.