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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Developing A Large Time Step, Robust, and Low Communication Multi-Moment PDE Integration Scheme for Exascale Applications

The Boundary Averaged Multi-moment Constrained finite-Volume (BA-MCV) method is de- rived, explained, and evaluated for 1-D transport to assess accuracy, maximum stable time step (MSTS), oscillations for discontinuous data, and parallel communication burden. The BA-MCV scheme is altered from the original MCV scheme to compute the updates of point wise cell boundary derivatives entirely locally. Then it is altered such that boundary moments are replaced with the interface upwind value. The scheme is stable at a maximum stable CFL (MSCFL) value of one no matter how high-order the scheme is, giving significantly larger time steps than Galerkin methods, for which the MSCFL decreases nearly quadratically with in- creasing order. The BA-MCV method is compared against a SE method at varying order, both using the ADER-DT time discretization. BA-MCV error for a sine wave was comparable to the same order of accuracy for a SE method. The resulting large time step, multi-moment, low communication scheme is of great interest for exascale architectures.

Norman, Matthew R.↗
DOE OSTI2020

Performance and Accuracy Implications of Parallel Split Physics-Dynamics Coupling in the Energy Exascale Earth System Atmosphere Model

Simultaneous calculation of atmospheric processes is faster than calculating processes one at a time. This type of parallelism is beneficial or perhaps even necessary to provide good performance on modern supercomputers, which achieve faster performance through increased processor count rather than improved clock speed. The scalability of the Energy Exascale Earth System Model (E3SM) Atmosphere Model (EAM) is limited by the fluid dynamics which scales up to the number of mesh cells in the global mesh. In contrast, the suite of physics parameterizations in EAM is scalable up to the total number of physics columns, which is an order of magnitude greater than the number of mesh cells. A proposed solution to unlocking the greater potential performance from the physics suite is to solve the physics and dynamics in parallel. This work represents a first attempt at parallel splitting of the grid-scale fluid dynamics model and the subgrid-scale physics parameterizations in a global atmosphere model. We will demonstrate that switching to parallel physics-dynamics coupling extends the scalability of the EAM to up to 3 times the previous peak scalability limit and is up to 20% faster than the sequentially split coupling at the highest core counts and the same time step. Decadal simulations of both coupling approaches show very little impact to the model climate. This improved performance does not come without drawbacks, however. Parallel splitting requires a shorter time step and other modifications which largely offset performance gains. A mass fixer is required for conservation. Techniques for mitigating these issues are also discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

The Energy Exascale Earth System Model Simulations With High Vertical Resolution in the Lower Troposphere

Abstract General circulation models (GCMs) are typically run with coarse vertical resolution. For example, the Energy Exascale Earth System Model (E3SM) has a vertical resolution of about 200 m in the boundary layer, which is far too coarse to resolve sharp gradients often found in the thermodynamic fields capping subtropical marine stratocumulus. In this article, we present a series of multiyear atmosphere only simulations of E3SM version 1 where we progressively increase the vertical resolution in the lower troposphere to scales approaching those often used in large eddy simulation (LES). We report marginal impacts in regards to the simulation of boundary layer clouds when vertical resolution is moderately increased, yet find significant positive impacts when the vertical resolution approaches that typically used in LES (∼10 m). In these experiments, there is a marked change in the simulated turbulence and thermodynamics which leads to more abundant marine stratocumulus. However, these simulations are burdened with excessive computational cost. They are also subject to degradations in overall climate metrics due to time step sensitivities and because some processes and parameterizations are sensitive to changes in the vertical resolution.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

The Implementation of Framework for Improvement by Vertical Enhancement Into Energy Exascale Earth System Model

Abstract The low cloud bias in global climate models (GCMs) remains an unsolved problem. Coarse vertical resolution in GCMs has been suggested to be a significant cause of low cloud bias because planetary boundary layer parameterizations cannot resolve sharp temperature and moisture gradients often found at the top of subtropical stratocumulus layers. This work aims to ameliorate the low cloud problem by implementing a new computational method, the Framework for Improvement by Vertical Enhancement (FIVE), into the Energy Exascale Earth System Model (E3SM). Three physics schemes representing microphysics, radiation, and turbulence as well as vertical advection are interfaced to vertically enhanced physics (VEP), which allows for these processes to be computed on a higher vertical resolution grid compared to the rest of the E3SM model. We demonstrate the better representation of subtropical boundary layer clouds with FIVE while limiting additional computational cost from the increased number of levels. When the vertical resolution approaches the large eddy simulation‐like vertical resolution in VEP, the climatological low cloud amount shows a significant increase of more than 30% in the southeastern Pacific Ocean. Using FIVE to improve the representation of low‐level clouds does not come with any negative side effects associated with the simulation of mid‐ and high‐level cloud and precipitation, that can occur when running the full model at higher vertical resolution.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Diurnal rainfall response to the physiological and radiative effects of CO 2 in tropical forests in the Energy exascale earth system model v1

Understanding how the connection between rainfall and tropical forests will respond to increasing CO$_2$ concentrations is a key element in understanding how the tropical water cycle will respond to increasing CO$_2$. The plant physiological and radiative impacts of CO$_2$ on rainfall patterns over tropical forest regions are examined in the Energy Exascale Earth System Model version 1.1 (E3SMv1.1-BGC) biogeochemistry experiments. Composite analysis reveals a dampening of the diurnal cycle of rainfall over the Amazon, Congo, and Maritime Continent in response to rising CO$_2$ levels, regardless of the sign of total rainfall change. A full factorial model experiment confirms that the CO$_2$ radiative and CO$_2$ plant physiological effects can individually or jointly reduce the magnitude of the rainfall diurnal cycle, though the physical pathway giving rise to the reduction differs between the two effects. For the physiological response, stomatal closure reduces evapotranspiration, which dries the boundary layer and raises the lifting condensation level. These effects combine to reduce deep convective rainfall during its peak occurrence in the late daytime to early nighttime period. For the radiative response, a relative reduction in daytime CAPE (consistent with a reduction in the diurnal temperature range) leads to less frequent triggering of deep convection and a reduction of rainfall diurnal amplitude. These diurnal rainfall changes are structurally similar across seasons, and show little sensitivity to representation of nutrient coupling for the land biogeochemistry. In agreement with previous findings, the physiological response has only minor impact on extreme rainfall relative to the radiative response.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

More Realistic Intermediate Depth Dry Firn Densification in the Energy Exascale Earth System Model (E3SM)

Abstract Earth system models account for seasonal snow cover, but many do not accommodate the deeper snowpack on ice sheets (aka firn) that slowly transforms to ice under accumulating snowfall. To accommodate and resolve firn depths of up to 60 m in the Energy Exascale Earth System Model's land surface model (ELM), we add 11 layers to its snowpack and evaluate three dry snow compaction equations in multi‐century simulations. After comparing results from ELM simulations (forced with atmospheric reanalysis) with empirical data, we find that implementing into ELM a two‐stage firn densification model produces more accurate dry firn densities at intermediate depths of 20–60 m. Compared to modeling firn using the equations in the (12 layer) Community Land Model (version 5), switching to the two‐stage firn densification model (with 16 layers) significantly decreases root‐mean‐square errors in upper 60 m dry firn densities by an average of 41 kg m −3 (31%). Simulations with three different firn density parameterizations show that the two‐stage firn densification model should be used for applications that prioritize accurate upper 60 m firn air content (FAC) in regions where the mean annual surface temperature is greater than roughly −31°C. Because snow metamorphism, firn density, and FAC are major components in modeling ice sheet surface albedo, melt water retention, and climatic mass balance, these developments advance broader efforts to simulate the response of land ice to atmospheric forcing in Earth system models.

58 GEOSCIENCES↗
DOE OSTI2022

Development of Land‐River Two‐Way Hydrologic Coupling for Floodplain Inundation in the Energy Exascale Earth System Model

Abstract Floodplain inundation links river and land systems through significant water, sediment, and nutrient exchanges. However, these two‐way interactions between land and river are currently missing in most Earth System Models. In this study, we introduced the two‐way hydrological coupling between the land component, E3SM Land Model, and the river component, Model for Scale Adaptive River Transport, in Energy Exascale Earth System Model (E3SM) to study the impacts of floodplain inundation on land and river processes. We calibrated the river channel geometry and developed a new data‐driven inundation scheme to improve the simulation of inundation dynamics in E3SM. The new inundation scheme captures 96% of the spatial variation of inundation area in a satellite inundation product at global scale, in contrast with 7% when the default inundation scheme of E3SM was used. Global simulations including the new inundation scheme performed at resolution with and without land‐river two‐way coupling was used to quantify the impact of coupling. Comparisons show that two‐way coupling modifies the water and energy cycle in 20% of the global land cells. Specifically, riverine inundation is reduced by two‐way coupling, but inland inundation is intensified. Wetter periods are more impacted by the two‐way coupling at the global scale, while regions with different climates exhibit different sensitivities. The two‐way exchange of water between the land and river components of E3SM provides the foundation for enabling two‐way coupling of land‐river sediment and biogeochemical fluxes. These capabilities will be used to improve understanding of the interactions between water and biogeochemical cycles and their response to human perturbations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

An Assessment of Nonhydrostatic and Hydrostatic Dynamical Cores at Seasonal Time Scales in the Energy Exascale Earth System Model (E3SM)

Abstract In global atmospheric modeling, the differences between nonhydrostatic (NH) and hydrostatic (H) dynamical cores are negligible in dry simulations when grid spacing is larger than 10 km. However, recent studies suggest that those differences can be significant at far coarser resolution when moisture is included. To better understand how NH and H differences manifest in global fields, we perform and analyze an ensemble of 28 and 13 km seasonal simulations with the NH and H dynamical cores in the Energy Exascale Earth System Model global atmosphere model, where the differences between H and NH configurations are minimized. A set of idealized rising bubble experiments is also conducted to further investigate the differences. Although NH and H differences are not significant in global statistics and zonal averages, significant differences in precipitation amount and patterns are observed in parts of the tropics. The most prominent differences emerge near India and the Western Pacific in the boreal summer, and the central‐southern Indian Ocean and Pacific in the boreal winter. Tropical differences influence surrounding regions through modification of the regional circulation and can propagate to the extratropics, leading to significant temperature and geopotential differences over the middle to high latitudes. While the dry bubble experiments show negligible deviation between H and NH dynamics until grid spacing is below 6.25 km, precipitation amount and vertical velocity are different in the moist case even at 25 km resolution.

58 GEOSCIENCES↗
DOE OSTI2022

The Madden–Julian Oscillation in the Energy Exascale Earth System Model Version 1

Abstract The present study examines the characteristics of the Madden–Julian Oscillation (MJO) events represented in the Energy Exascale Earth System Model version 1 (E3SMv1), DOE’s new Earth system model. The coupled E3SMv1 realistically simulates the eastward propagation of precipitation and moist static energy (MSE) anomalies associated with the MJO. As in observations, horizontal moisture advection and longwave radiative feedback are found to be the dominant processes in E3SMv1 that lead to the eastward movement and maintenance of the MJO MSE anomalies, respectively. Modulation of the diurnal cycle of precipitation in the Maritime Continent region by the MJO is also well represented in the model despite systematic biases in the magnitude and phase of the precipitation diurnal cycle. On the MJO impact over the midlatitude, E3SMv1 reasonably captures the pattern of the MJO teleconnections across the North Pacific and North America, with improvement in the performance in a high‐resolution version, despite the magnitude being a bit weaker than the observed. Regarding the interannual variability of the MJO, the El Niño‐Southern Oscillation (ENSO) modulation of the zonal extent of MJO’s eastward propagation, as well as associated changes in the mean state moisture gradient in the tropical west Pacific, are well reproduced in the model. However, MJO in E3SMv1 exhibits no sensitivity to the Quasi‐Biennial Oscillation (QBO), with the MJO propagation characteristics being almost identical between easterly QBO and westerly QBO years. Processes that have been suggested as critical to MJO simulation are also examined by utilizing recently developed process‐oriented diagnostics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Future Changes in Active and Inactive Atlantic Hurricane Seasons in the Energy Exascale Earth System Model

Abstract North Atlantic tropical cyclones (TCs) have considerable interannual variability, with La Niña and the positive phase of the Atlantic Meridional Mode (AMM) tending to drive active hurricane seasons, and El Niño and the negative AMM often driving inactive seasons. Here, we analyze how active and inactive Atlantic hurricane seasons may change in the future using the high resolution Energy Exascale Earth System Model (E3SM). We performed atmosphere‐only simulations forced by sea‐surface temperature patterns characteristic of La Niña and the positive AMM jointly, and El Niño and the negative AMM jointly, in historical and future climates. Projected Atlantic TCs become more frequent in the future by approximately 34% during El Niño and negative AMM and by 66% during La Niña and positive AMM, with a significant increase in the portion of intense TCs. Warmer SSTs increase TC potential intensity, with reduced wind shear and increased mid‐tropospheric humidity further supporting TC activity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Evaluating the Water Cycle Over CONUS at the Watershed Scale for the Energy Exascale Earth System Model Version 1 (E3SMv1) Across Resolutions

Abstract The water cycle is an important component of the earth system and it plays a key role in many facets of society, including energy production, agriculture, and human health and safety. In this study, the Energy Exascale Earth System Model version 1 (E3SMv1) is run with low‐resolution (roughly 110 km) and high‐resolution (roughly 25 km) configurations—as established by the High Resolution Model Intercomparison Project protocol—to evaluate the atmospheric and terrestrial water budgets over the conterminous United States (CONUS) at the large watershed scale. The warm season water cycle slows down in the HR experiment relative to the LR, with decreasing fluxes of precipitation, evapotranspiration, atmospheric moisture convergence, and runoff. The reductions in these terms exacerbate biases for some watersheds, while reducing them in others. For example, precipitation biases are exacerbated at HR over the Eastern and Central CONUS watersheds, while precipitation biases are reduced at HR over the Western CONUS watersheds. The most pronounced changes with resolution to the water cycle come from reductions in precipitation and evapotranspiration. The reduction in evapotranspiration reduces the biases across nearly all of the CONUS. Additional exploratory metrics show improvements to water cycle extremes (both in precipitation and streamflow), fractional contributions of different storm types to total precipitation, and mountain snowpack.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Ensemble Spread Behavior in Coupled Climate Models: Insights From the Energy Exascale Earth System Model Version 1 Large Ensemble

AbstractAssessing uncertainty in future climate projections requires understanding both internal climate variability and external forcing. For this reason, single‐model initial condition large ensembles (SMILEs) run with Earth System Models (ESMs) have recently become popular. Here we present a new 20‐member SMILE with the Energy Exascale Earth System Model version 1 (E3SMv1‐LE), which uses a “macro” initialization strategy choosing coupled atmosphere/ocean states based on inter‐basin contrasts in ocean heat content (OHC). The E3SMv1‐LE simulates tropical climate variability well, albeit with a muted warming trend over the twentieth century due to overly strong aerosol forcing. The E3SMv1‐LE's initial climate spread is comparable to other (larger) SMILEs, suggesting that maximizing inter‐basin ocean heat contrasts may be an efficient method of generating ensemble spread. We also compare different ensemble spread across multiple SMILEs, using surface air temperature and OHC. The Community Earth system Model version 1, the only ensemble which utilizes a “micro” initialization approach perturbing only atmospheric initial conditions, yields lower spread in the first ∼30 years. The E3SMv1‐LE exhibits a relatively large spread, with some evidence for anthropogenic forcing influencing spread in the late twentieth century. However, systematic effects of differing “macro” initialization strategies are difficult to detect, possibly resulting from differing model physics or responses to external forcing. Notably, the method of standardizing results affects ensemble spread: control simulations for most models have either large background trends or multi‐centennial variability in OHC. This spurious disequlibrium behavior is a substantial roadblock to understanding both internal climate variability and its response to forcing.

Stevenson, Samantha↗
DOE OSTI2023

Incorporating an Interactive Fire Plume-Rise Model in the DOE's Energy Exascale Earth System Model Version 1 (E3SMv1) and Examining Aerosol Radiative Effect

The vertical distribution of biomass burning aerosol (BBA) is important in regulating their impacts on weather and climate. The plume-rise process affects the injection height of BBA and interacts with the air parcel lifting and cloud processes. However, these processes are not represented in most global climate models. In this study, we replaced the fixed vertical profiles of monthly BBA emissions in the Department of Energy's Energy Exascale Earth System Model version 1 (E3SMv1) with an interactive fire plume-rise model. The vertical distribution of BBA emissions was calculated as a function of ambient thermodynamic conditions from the host E3SMv1, with distributions of fire sizes and sensible heat fluxes derived from the observations. The maximum fire radiative power (FRP) technique was used to determine the fire size. Scaling-FRP technique is used to calculate the wildfire heat release. Daily BBA emission, superimposed with a fire diurnal cycle retrieved from the satellite observation, was included in model simulations. The model shows improved agreement with satellite retrievals and in situ measurement during the National Oceanic and Atmospheric Administration Wildfire Experiment for Cloud chemistry, Aerosol absorption, and Nitrogen campaign. The model-observation comparison demonstrates the importance of the plume-rise model and fire diurnal cycle assumption in determining the BBA fields. We also find that E3SMv1 with new features produces a larger carbonaceous aerosol burden, leading to 0.13 W m –2 warming at the top of atmosphere compared to the default E3SMv1. This highlights the importance of accurately representing the BBA injection height and indicates a no-linear nature in the BBA-induced radiative effect.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Mechanisms in Regulating the Quasi‐Biennial Oscillation in Exascale Earth System Model Version 2

Abstract The update to the deep convection parameterization in the energy exascale Earth system model version 2 (E3SMv2) makes the simulated quasi‐biennial oscillation (QBO) have a shorter period than without the update when other tunable parameters the same since the update makes convection more intense but less frequent while leaving the time‐mean convective heating tendency almost unchanged. Amplitudes of momentum fluxes of parameterized gravity waves (GWs) are intensified since they are determined by the square of convective heating tendency. In addition, stronger planetary waves are simulated in E3SMv2 with the convection scheme update, partially due to the tropospheric precipitation change. Furthermore, there is evidence that planetary waves are intensified in the stratosphere due to the dissipation of enhanced parameterized GWs. These factors are found to be responsible for modulating the QBO simulated in E3SMv2.

Li, Yuanpu [Climate and Global Dynamics Division U↗
DOE OSTI2026

Subseasonal Tropical Convection Characteristics in the Energy Exascale Earth System Model Version 2

Accurate simulation of subseasonal tropical moist convection remains a key challenge for Earth system models. The difficulties stem from the reliance of cumulus cloud processes on model parameterizations and the need to represent the multiscale nature of interactions among clouds, radiation, moisture, circulation, and surface energy fluxes. Equatorial convection drives circulation anomalies that can affect weather patterns and extremes globally, motivating efforts to better understand and simulate these tropical disturbances. Here, a detailed review of subseasonal tropical convective behavior as simulated in the Energy Exascale Earth System Model version 2 (E3SMv2) is presented, with comparison to its predecessor version 1 (E3SMv1) and reference data sets. Model structural changes to the deep convective trigger function and surface fluxes, along with parametric tuning of the cloud and microphysics schemes, together result in an improved depiction of organized tropical convection across scales. In particular, E3SMv2 exhibits a more realistic Madden‐Julian oscillation (MJO) and low‐frequency Kelvin waves—owing to a sharper time mean equatorial meridional moisture gradient and improved convection‐circulation coupling —as well as a better depiction of MJO Northern Hemisphere teleconnections. Despite these improvements, subseasonal precipitation variance continues to be strongly underestimated in E3SMv2. Use of a cloud plume model also reveals that the coupling between daily averaged tropical precipitation and lower tropospheric instability in E3SM is inconsistent with observations, a bias that could potentially impact the simulation of intraseasonal disturbances.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Interactive Gas Chemistry for Enhanced Science Capabilities of the Energy Exascale Earth System Model Version 3

Atmospheric chemistry plays a crucial role in Earth system models (ESMs), controlling atmospheric composition and radiative balance; it is highly interactive with the physical climate, biogeochemical cycles, and human systems. However, it often imposes computational challenges in an ESM. Here we develop a full troposphere‐stratosphere interactive chemistry module for the US Department of Energy's Energy Exascale Earth System Model (E3SM). We intentionally build a streamlined module based on E3SM version 2 that interacts with other components and maintains all of major chemical and chemistry‐climate feedbacks. The module incorporates a new, highly efficient tracer advection scheme; linearization of stratospheric chemistry; and abridged tropospheric chemical mechanism with 28 reactive tracers. This new model, E3SM‐chem, can readily perform century‐long climate simulations of ozone, methane, and nitrous oxide based on emission scenarios as well as provide hourly budgets for the gas‐phase radicals that drive aerosol chemistry. We evaluate E3SM‐chem with an atmosphere‐only simulation as in the recent climate model intercomparison project (CMIP6) finding results similar to the other CMIP6 models. For the present‐day, E3SM‐chem matches the standard measurement metrics for stratospheric and tropospheric ozone, surface air quality, other key reactive gases like carbon monoxide, and the methane lifetime. Overall, E3SM‐chem maintains the climate fidelity of the baseline model while adding at most 20% to the computational cost of the atmosphere model. Hence, interactive chemistry can be a default configuration for long climate simulations at resolutions of 1° or finer, which is crucial for producing self‐consistent chemistry‐climate feedbacks that alter the climate system.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

The Energy Exascale Earth System Model Version 3: 1. Overview of the Atmospheric Component

This paper describes the atmospheric component of the US Department of Energy's Energy Exascale Earth System Model (E3SM) version 3. Significant updates have been made to the atmospheric physics compared to earlier versions. Specifically, interactive gas chemistry has been implemented, along with improved representations of aerosols and dust emissions. A new stratiform cloud microphysics scheme more physically treats ice processes and aerosol‐cloud interactions. The deep convection parameterization has been largely improved with sophisticated microphysics for convective clouds, making model convection sensitive to large‐scale dynamics, and incorporating the dynamical and physical effects of organized mesoscale convection. Improvements in aerosol wet removal processes and parameter re‐tuning of key aerosol and cloud processes have improved model aerosol radiative forcing. The model's vertical resolution has increased from 72 to 80 layers with the extra eight layers added in the lower stratosphere to better simulate the Quasi‐Biennial Oscillation. These improvements have enhanced E3SM's capability to couple aerosol, chemistry, and biogeochemistry and reduced some long‐standing biases in simulating tropical variability. Compared to its predecessors, the model shows a much stronger signal for the Madden‐Julian Oscillation, Kelvin waves, mixed Rossby‐gravity waves, and eastward inertia‐gravity waves. Aerosol radiative forcing has been considerably reduced and is now better aligned with community best estimates, leading to significantly improved skill in simulating historical temperature records. Its simulated mean‐state climate is largely comparable to E3SMv2, but with some notable degradation in shortwave cloud radiative effect, precipitable water, and surface wind stress, which will be addressed in future updates.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Numerical Water Tracers in the Atmospheric Component of the Energy Exascale Earth System Model: Implementation and Changes in Moisture Origin

Numerical water tracers are implemented in the Energy Exascale Earth System Model version 2. Simulations performed with the water‐tag‐enabled model for both pre‐industrial and future greenhouse gas concentrations reveal a marked increase in the role of mid‐latitude and southern subtropical regions as exporters of atmospheric moisture—to the extratropical upper troposphere and the tropical free troposphere. For the latter, the northward shift of the Intertropical Convergence Zone increases cross‐hemispheric transport of subtropical water vapor to the Northern Hemisphere. In the polar regions, most of the lower tropospheric moistening instead arises from increases in local evaporation. These findings illustrate the utility of the water tags, underscore critical changes in global hydrologic cycle, and provide insight into atmospheric dynamics under future climate scenarios. For applications when a global grid is desired, we additionally propose a novel statistical reconstruction, based on copula modeling, of the joint distribution of origin of water vapor, which reduces the number of tracers from order $\mathcal{O}\left({n}^{2}\right)$to order $\mathcal{O}(n)$, substantially ameliorating the considerable computational cost of water tracers. This statistical reconstruction is particularly beneficial to the interpretation of the relationship between latitude and longitude of origin of moisture over the tropical oceans and in the lower troposphere over land.

copula modeling↗