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NASA NTRS1992

Search for subgrid scale parameterization by projection pursuit regression

The dependence of subgrid-scale stresses on variables of the resolved field is studied using direct numerical simulations of isotropic turbulence, homogeneous shear flow, and channel flow. The projection pursuit algorithm, a promising new regression tool for high-dimensional data, is used to systematically search through a large collection of resolved variables, such as components of the strain rate, vorticity, velocity gradients at neighboring grid points, etc. For the case of isotropic turbulence, the search algorithm recovers the linear dependence on the rate of strain (which is necessary to transfer energy to subgrid scales) but is unable to determine any other more complex relationship. For shear flows, however, new systematic relations beyond eddy viscosity are found. For the homogeneous shear flow, the results suggest that products of the mean rotation rate tensor with both the fluctuating strain rate and fluctuating rotation rate tensors are important quantities in parameterizing the subgrid-scale stresses. A model incorporating these terms is proposed. When evaluated with direct numerical simulation data, this model significantly increases the correlation between the modeled and exact stresses, as compared with the Smagorinsky model. In the case of channel flow, the stresses are found to correlate with products of the fluctuating strain and rotation rate tensors. The mean rates of rotation or strain do not appear to be important in this case, and the model determined for homogeneous shear flow does not perform well when tested with channel flow data. Many questions remain about the physical mechanisms underlying these findings, about possible Reynolds number dependence, and, given the low level of correlations, about their impact on modeling. Nevertheless, demonstration of the existence of causal relations between sgs stresses and large-scale characteristics of turbulent shear flows, in addition to those necessary for energy transfer, provides important insight into the relation between scales in turbulent flows.

Meneveau, C.↗

NASA NTRS1992

Chapman Conference on the Hydrologic Aspects of Global Climate Change, Lake Chelan, WA, June 12-14, 1990, Selected Papers

The present conference on the hydrological aspects of global climate change discusses land-surface schemes for future climate models, modeling of the land-surface boundary in climate models as a composite of independent vegetation, a land-surface hydrology parameterizaton with subgrid variability for general circulation models, and conceptual aspects of a statistical-dynamical approach to represent landscape subgrid-scale heterogeneities in atmospheric models. Attention is given to the impact of global warming on river runoff, the influence of atmospheric moisture transport on the fresh water balance of the Atlantic drainage basin, a comparison of observations and model simulations of tropospheric water vapor, and the use of weather types to disaggregate the prediction of general circulation models. Topics addressed include the potential response of an Arctic watershed during a period of global warming and the sensitivity of groundwater recharge estimates to climate variability and change.

Lettenmaier, Dennis P.↗

NASA NTRS1993

Coupled land surface/hydrologic/atmospheric models

The topics covered include the following: prototype land cover characteristics data base for the conterminous United States; surface evapotranspiration effects on cumulus convection and implications for mesoscale models; the use of complex treatment of surface hydrology and thermodynamics within a mesoscale model and some related issues; initialization of soil-water content for regional-scale atmospheric prediction models; impact of surface properties on dryline and MCS evolution; a numerical simulation of heavy precipitation over the complex topography of California; representing mesoscale fluxes induced by landscape discontinuities in global climate models; emphasizing the role of subgrid-scale heterogeneity in surface-air interaction; and problems with modeling and measuring biosphere-atmosphere exchanges of energy, water, and carbon on large scales.

Pielke, Roger↗

NASA NTRS1988

Evapotranspiration from nonuniform surfaces - A first approach for short-term numerical weather prediction

Observations of surface heterogeneity of soil moisture from scales of meters to hundreds of kilometers are discussed, and a relationship between grid element size and soil moisture variability is presented. An evapotranspiration model is presented which accounts for the variability of soil moisture, standing surface water, and vegetation internal and stomatal resistance to moisture flow from the soil. The mean values and standard deviations of these parameters are required as input to the model. Tests of this model against field observations are reported, and extensive sensitivity tests are presented which explore the importance of including subgrid-scale variability in an evapotranspiration model.

Wetzel, Peter J.↗

NASA NTRS1984

A Vertically Resolved Planetary Boundary Layer

Increase of the vertical resolution of the GLAS Fourth Order General Circulation Model (GCM) near the Earth's surface and installation of a new package of parameterization schemes for subgrid-scale physical processes were sought so that the GLAS Model GCM will predict the resolved vertical structure of the planetary boundary layer (PBL) for all grid points.

Helfand, H. M.↗

NASA NTRS1989

The length scale for sub-grid-scale parameterization with anisotropic resolution

Use of the Smagorinsky eddy-viscosity formulation and related schemes for subgrid-scale parameterization of large eddy simulation models requires specification of a single length scale, earlier related by Lilly to the scale of filtering and/or numerical resolution. An anisotropic integration of the Kolmogoroff enstrophy spectrum allows generalization of that relationship to anisotropic resolution. It is found that the Deardorff assumption is reasonably accurate for small anisotropies and can be simply improved for larger values.

Lilly, Douglas K.↗

NASA NTRS1993

A description of rainfall interception over large areas

A new scheme is developed for describing interception at spatial scales comparable to the typical resolution of climate models. The scheme is based on the Rutter model of interception and statistical description of the subgrid-scale spatial variability of canopy storage and rainfall. The interception loss simulated by the new scheme is significantly smaller than those simulated by other schemes that do not include considerations for spatial variability. The explanation of this result is partly in the enhancement of spatially averaged canopy drainage due to the large local drainage from the few buckets of large canopy storage. The relative reduction in interception loss simulated by the new scheme may explain the overestimation of interception loss by climate models that do not include the effects of spatial variability on interception processes.

Eltahir, E. A. B.↗

DOE OSTI2025

Ship‐Based Lidar Evaluation of Southern Ocean Low Clouds in the Storm‐Resolving General Circulation Model ICON and the ERA5 and MERRA‐2 Reanalyses

Global storm resolving models (GSRMs) represent the next generation of global climate models. One of them is a 5-km Icosahedral Nonhydrostatic Weather and Climate Model (ICON). Its high resolution means that parameterizations of convection and clouds, including subgrid-scale clouds, are omitted, relying on explicit simulation but necessarily utilizing microphysics and turbulence parameterizations. Standard-resolution (10–100 km) models, which use convection and cloud parameterizations, have substantial cloud biases over the Southern Ocean (SO), adversely affecting radiation and sea surface temperature. The SO is dominated by low clouds, which cannot be observed accurately from space due to overlapping clouds, attenuation, and ground clutter. We evaluated SO clouds in ICON and the ERA5 and MERRA-2 reanalyzes using approximately 2400 days of lidar observations and 2300 radiosonde profiles from 31 voyages and a Macquarie Island station during 2010–2021, compared to the model and reanalyzes using a ground-based lidar simulator. We found that ICON and the reanalyzes underestimate the total cloud fraction by about 10% and 20%, respectively. ICON and ERA5 overestimate the cloud occurrence peak at about 500 m, associated with underestimated lower tropospheric stability and overestimated lifting condensation level. The reanalyzes strongly underestimate fog and very low-level clouds, and MERRA-2 underestimates cloud occurrence at almost all heights. Outgoing shortwave radiation is overestimated in MERRA-2, implying a “too few, too bright” cloud problem. SO cloud and fog biases are a substantial issue in the analyzed model and reanalyzes and result in shortwave and longwave radiation biases.

Kuma, Peter [Stockholm Univ. (Sweden); Univ. of Ca↗

NASA NTRS1994

On the Two-Dimensionalization of Homogeneous Rotating Turbulence

Large-eddy simulation of the incompressible Navier-Stokes equations has been used to examine the long-time development of initially isotropic turbulence subjected to solid-body rotation. The simulations were carried out using a pseudo-spectral method with 128 x 128 x 512 collocation points in a computational domain that is four times larger along the rotation axis than in the other directions; subgrid-scale motions were parameterized using a spectral eddy viscosity model modified for system rotation. Simulation results show that the correlation length along the rotation am's of velocities orthogonal to the rotation vector exhibits rapid growth while the integral length-scale of velocities aligned with the rotation axis is relatively unaffected by rotation. Examination of the energy spectrum of two-dimensional, two-component motions indicates the presence of an inverse cascade of energy. System rotation also causes an alignment of vorticity along the rotation axis with relatively stronger cyclonic vorticity than anticyclonic. The onset of anisotropic effects are well characterized by Rossby numbers defined in terms of both macroscopic and microscopic quantities.

Squires, K. D.↗

NASA NTRS1993

The implementation and validation of improved land-surface hydrology in an atmospheric general circulation model

New land-surface hydrologic parameterizations are implemented into the NASA Goddard Institute for Space Studies (GISS) General Circulation Model (GCM). These parameterizations are: 1) runoff and evapotranspiration functions that include the effects of subgrid-scale spatial variability and use physically based equations of hydrologic flux at the soil surface and 2) a realistic soil moisture diffusion scheme for the movement of water and root sink in the soil column. A one-dimensional climate model with a complete hydrologic cycle is used to screen the basic sensitivities of the hydrological parameterizations before implementation into the full three-dimensional GCM. Results of the final simulation with the GISS GCM and the new land-surface hydrology indicate that the runoff rate, especially in the tropics, is significantly improved. As a result, the remaining components of the heat and moisture balance show similar improvements when compared to observations. The validation of model results is carried from the large global (ocean and land-surface) scale to the zonal, continental, and finally the regional river basin scales.

Johnson, Kevin D.↗

NASA NTRS1994

Initialization of soil-water content in regional-scale atmospheric prediction models

The purpose of this study is to demonstrate the feasibility of determining the soil-water content fields required as initial conditions for land surface components within atmospheric prediction models. This is done using a model of the hydrologic balance and conventional meteorological observations, land cover, and soils information. A discussion is presented of the subgrid-scale effects, the integration time, and the choice of vegetation type on the soil-water content patterns. Finally, comparisons are made between two The Pennsylvania State University/National Center for Atmospheric Research mesoscale model simulations, one using climatological fields and the other one using the soil-moisture fields produced by this new method.

Smith, Christopher B.↗

DOE OSTI2025

Understanding drivers and uncertainty in projected African precipitation

We investigate the drivers of projected summer precipitation changes and their uncertainties across Africa in the second half of the 21st century under the SSP2-4.5 and SSP5-8.5 scenarios using CMIP6 models. Our results reveal distinct regional precipitation changes, particularly under SSP5-8.5, with robust increases of 75%, 24%, and 17% over the Sahara, South Eastern Africa, and South Central Africa, respectively, and a decline of up to 5% over West Southern Africa (WSAF). In most regions, precipitation increases are driven by enhanced vertical thermodynamic processes associated with temperature-induced moisture increases and enhanced moisture convergence. In contrast, the WSAF decrease is associated with vertical dynamic processes driven by a weakening of the Hadley circulation’s ascending branch. Model uncertainty accounts for over 85% of total projection uncertainty across all regions and is largely due to subgrid-scale parameterizations. Overall, this study enhances our understanding of climate change impacts on African precipitation.

Taguela, Thierry N↗

NASA NTRS1993

Inertial transfers in the helical decomposition

The directions of the triadic energy transfers assumed in a previous paper agree with the spectral closures, in a similarity range, if the exponent of the power-law energy spectrum is less than unity. The helical interactions showing a strong local energy transfer when the triad is nonlocal, sum up to a reverse cascade unless the spectrum falls off faster than a -7/3 power of the wave number. The energy cascades from each type of helical interaction are calculated for a -5/3 inertial range using the eddy damped quasinormal Markovian model. One type of interaction is responsible for 86 percent of the cascade. The contributions of the two classes of helical interactions to the subgrid-scale eddy viscosity are presented, together with the contributions from the forward and reverse cascading interactions. An application of the assumption on the triadic energy transfers to turbulence under rapid rotation gives a simple argument for the tendency toward nonlinear two-dimensionalization of the flow.

Waleffe, Fabian↗

NASA NTRS1976

Spectral and spatial energetics of the GISS model atmosphere

A calculation of the spectral and spatial energetics of the Goddard Institute for Space Studies (GISS) 9-level model of the global atmosphere is given. Results are presented from a model simulation of January 1973 and compared with previous model studies and an observational analysis for the Northern Hemisphere. The spectral analysis permits detailed study of those physical processes of scale larger than the grid spacing and allows indirect conclusions concerning unresolved subgrid-scale processes. Major conclusions for larger-than-grid-scale processes are that (1) the GISS model with a relatively coarse resolution of 4 deg latitude by 5 deg longitude produces significant nonlinear energy transfers; and (2) baroclinic conversion is large near planetary wave-number 6, but both the GISS model and another orographic model show a less peaked structure than nonorographic models and observations. A linear fit to the kinetic energy spectrum yields a power law of -2.6 in the wavenumber region 8 to 15. For subgrid-scale processes, the turbulence theory result of very small energy flux cascade is obtained.

Tenenbaum, J.↗

DOE OSTI2025

JHTDB-wind: a web-accessible large-eddy simulation database of a wind farm with virtual sensor querying

This paper introduces JHTDB-wind (https://turbulence.idies.jhu.edu/datasets/windfarms, last access: 11 November 2025), a publicly accessible database containing large-eddy simulation (LES) data from wind farms. Building on the framework of the Johns Hopkins Turbulence Database (JHTDB), which hosts direct numerical simulation (DNS) and some LES datasets of canonical turbulent flows, JHTDB-wind stores the 4D space–time history of the flow and provides users the ability to access and query the data via a web-based virtual sensor interface. The initial dataset comprises LES results from a large wind farm with 10×6 turbines, modeled using a filtered actuator line method, under conventionally neutral atmospheric conditions. These data comprise 1 h (hour) of flow field data (velocity, pressure, potential temperature deviation, subgrid-scale (SGS) eddy viscosity, and turbine forces, approximately 15 TB (terabytes) and wind turbine data – including both turbine-level operational quantities and blade-level aerodynamic quantities (approximately 1.3 TB) – stored in Zarr and Parquet formats, respectively. Data retrieval is facilitated by the giverny Python package, allowing remote users to query the database in Python or MATLAB (C and Fortran support are available for flow field data). This paper details the simulation setup and demonstrates data access through examples that analyze wind farm flow structures and turbine performance. The framework is extensible to future datasets, including the JHTDB-wind diurnal cycle simulation analyzed in Xiao et al. (2025).

17 WIND ENERGY↗

NASA NTRS1977

Numerical simulation of the Gulf Stream and Mid-Ocean eddies

Oceanographic field measurements have revealed intense, transient mesoscale motions in many parts of the world ocean. The circulation of the western North Atlantic, considered in the present study as a rectangular basin, is simulated with a primitive equation model that has five levels and a horizontal grid size of 37 km. The model ocean is driven by a 2.5 gyre pattern of steady zonal wind stress and by a Newtonian-type surface heating. Two cases are considered: the first uses a Laplacian formulation for the subgrid-scale lateral diffusions of heat and momentum; the second uses a highly scale-selective biharmonic formulation for these diffusions. An analysis of the heat transport, in the biharmonic experiment, shows that the horizontal transport of heat by eddies is much larger than the subgrid-scale horizontal heat diffusion. In the Gulf Stream region, the eddy heat transport is comparable to the effect of a lateral diffusion coefficient of 10 to the 7th sq cm/s.

Semtner, A. J., Jr.↗

NASA NTRS1974

The GISS model of the global atmosphere

A description and numerical results are presented for a global atmospheric circulation model developed at the Goddard Institute for Space Studies (GISS). The model version described is a 9-level primitive-equation model in sigma coordinates. It includes a realistic distribution of continents, oceans and topography. Detailed calculations of energy transfer by solar and terrestrial radiation make use of cloud and water vapor fields calculated by the model. The model hydrologic cycle includes two precipitation mechanisms: large-scale supersaturation and a parameterization of subgrid-scale cumulus convection. Results are presented both from a comparison of the 13th to the 43rd days (January) of one integration with climatological statistics, and from five short-range forecasting experiments. In the extended integration, the near-equilibrium January-mean model atmosphere exhibits an energy cycle in good agreement with observational estimates, together with generally realistic zonal mean fields of winds, temperature, humidity, transports, diabatic heating, evaporation, precipitation, and cloud cover.

Somerville, R. C. J.↗

NASA NTRS1993

Development and analysis of prognostic equations for mesoscale kinetic energy and mesoscale (subgrid scale) fluxes for large-scale atmospheric models

Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes generated by such subgrid-scale landscape discontinuities in large-scale atmospheric models.

Avissar, Roni↗