Search

This study investigates the preservation of tracer interrelationships during advection in large-eddy simulations of an idealized deep convective cloud, which is particularly relevant to chemistry, aerosol, and cloud microphysics models. Employing the Cloud Model 1, advection is represented using third-, fifth-, and seventh-order weighted essentially non-oscillatory schemes. As a simplified analogy for cloud hydrometeors and aerosols, several inert passive tracers following linear and nonlinear relationships are initialized after the cloud reaches ∼6-km depth. Numerical mixing in the simulated turbulent convective clouds leads to significant deviations from the initial nonlinear relationships between tracers. In these simulations, a considerable fraction of the grid points where the tracers’ nonlinear relationships are altered from advection are classified as unrealistic (e.g., ∼13% for the environmental tracers on average), including errors from range-preserving unmixing and overshooting. Errors in the sum of three tracers are also relatively large, ranging between ∼1% and 16% for 5% of the grid points in and near the cloud. The magnitude of unrealistic mixing and errors in the sum of three tracers generally increase with the order of accuracy of the advection scheme. These results are consistent across model grid spacings ranging from 50 to 200 m, and across three different flow realizations for each combination of grid spacing and advection scheme tested. Tests employing a previously proposed scalar normalization procedure show substantially reduced errors in the sum of three tracers with a relatively small negative impact on other tracer relationships. This analysis, therefore, suggests efficacy of the normalization procedure when applied to turbulent three-dimensional cloud simulations. Significance Statement In nature, transporting several quantities through bulk motions of a fluid does not affect preexisting relationships between them. However, this is not always accomplished in numerical models of the atmosphere, because of intrinsic limitations in the transport algorithms employed. We aim to investigate how these errors behave in 3D realistic simulations of a cumulus cloud, where the turbulent flow constitutes a particular challenge. We show that relationships between quantities are significantly and frequently perturbed during bulk transport in the model. Moreover, our results suggest that increasing complexity of the bulk-transport algorithms (in a way that is conventionally employed for improving the representation of individual quantities) tends to worsen the representation of relationships between two or three quantities.

This paper describes and analyzes the Reed-Jablonowski (RJ) tropical cyclone (TC) test case used in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016). The intermediate complexity test case analyzes the evolution of a weak vortex into a TC in an idealized tropical environment. Simulations from 9 general circulation models (GCMs) that participated in DCMIP2016 are analyzed in this study at 50 km horizontal grid spacing, with 5 of these models also providing simulations at 25 km grid spacing for an analysis on the impact of finer grid spacing. Evolution of minimum surface pressure (MSP) and maximum 1 km azimuthally averaged wind speed (MWS), the wind-pressure relationship, radial profiles of wind speed and surface pressure, and wind composites are documented for all participating GCMs at both horizontal grid spacings. While results are generally similar between all models, some GCMs reach significantly higher storm intensities than others, ultimately impacting specific characteristics of their horizontal and vertical structure. TCs simulated at 25 km grid spacings retained these differences, but reach higher intensities and are more compact than their 50 km counterparts. These results indicate dynamical core choice is an essential factor in GCM development, and future work should be conducted to explore how specific differences within the dynamical core affect TC behavior in GCMs.

For the Community Atmosphere Model version 6 (CAM6), an adjustment is needed to conserve dry air mass. This adjustment exposes an inconsistency in how CAM6’s energy budget incorporates water—in CAM6 water in the vapor phase has energy, but condensed phases of water do not. When water vapor condenses, only its latent energy is retained in the model, while its remaining internal, potential, and kinetic energy are lost. A global fixer is used in the default CAM6 model to maintain global energy conservation, but locally the energy tendency associated with water changing phase violates the divergence theorem. This error in energy tendency is intrinsically tied to the water vapor tendency, and reaches its highest values in regions of heavy rainfall, where the error can be as high as 40 W m−2 annually averaged. Several possible changes are outlined within this manuscript that would allow CAM6 to satisfy the divergence theorem locally. These fall into one of two categories: 1) modifying the surface flux to balance the local atmospheric energy tendency and 2) modifying the local atmospheric tendency to balance the surface plus top-of-atmosphere energy fluxes. To gauge which aspects of the simulated climate are most sensitive to this error, the simplest possible change—where condensed water still does not carry energy and a local energy fixer is used in place of the global one—is implemented within CAM6. Comparing this experiment with the default configuration of CAM6 reveals precipitation, particularly its variability, to be highly sensitive to the energy budget formulation. Significance Statement This study examines and explains spurious regional sources and sinks of energy in a widely used climate model. These energy errors result from not tracking energy associated with water after it transitions from the vapor phase to either liquid or ice. Instead, the model used a global fixer to offset the energy tendency related to the energy sources and sinks associated with condensed water species. We replace this global fixer with a local one to examine the model sensitivity to the regional energy error and find a large sensitivity in the simulated hydrologic cycle. This work suggests that the underlying thermodynamic assumptions in the model should be revisited to build confidence in the model-simulated regional-scale water and energy cycles.

Effects of water mass imbalance and hydrometeor transport on the enthalpy flux and water phase on diabatic heating rate in computing the regional energy and water budget of the atmosphere over ocean are investigated. Equations of energy and water budget of the atmospheric column that explicitly consider the velocity of liquid and ice cloud particles, and rain and snow are formulated by separating water variables from dry air. Differences of energy budget equations formulated in this study from those used in earlier studies are that 1) diabatic heating rate depends on water phase, 2) diabatic heating due to net condensation of nonprecipitating hydrometeors is included, and 3) hydrometeors can be advected with a different velocity from the dry-air velocity. Convergence of water vapor associated with phase change and horizontal transport of hydrometeors is to increase diabatic heating in the atmospheric column where hydrometeors are formed and exported and to reduce energy where hydrometeors are imported and evaporated. The process can improve the regional energy and water mass balance when energy data products are integrated. Effects of enthalpy transport associated with water mass transport through the surface are cooling to the atmosphere and warming to the ocean when the enthalpy is averaged over the global ocean. There is no net effect to the atmosphere and ocean columns combined. While precipitation phase changes the regional diabatic heating rate up to 15 W m−2, the dependence of the global mean value on the temperature threshold of melting snow to form rain is less than 1 W m−2.

The transport of trace gases by the atmospheric circulation plays an important role in the climate system and its response to external forcing. Transport presents a challenge for Atmospheric General Circulation Models (AGCMs), as errors in both the resolved circulation and the numerical representation of transport processes can bias their abundance. In this study, two tests are proposed to assess transport by the dynamical core of an AGCM. To separate transport from chemistry, the tests focus on the age‐of‐air, an estimate of the mean transport time by the circulation. The tests assess the coupled stratosphere–troposphere system, focusing on transport by the overturning circulation and isentropic mixing in the stratosphere, or Brewer–Dobson Circulation, where transport time‐scales on the order of months to years provide a challenging test of model numerics. Four dynamical cores employing different numerical schemes (finite‐volume, pseudo‐spectral, and spectral‐element) and discretizations (cubed sphere versus latitude–longitude) are compared across a range of resolutions. The subtle momentum balance of the tropical stratosphere is sensitive to model numerics, and the first intercomparison reveals stark differences in tropical stratospheric winds, particularly at high vertical resolution: some cores develop westerly jets and others easterly jets. This leads to substantial spread in transport, biasing the age‐of‐air by up to 25% relative to its climatological mean, making it difficult to assess the impact of the numerical representation of transport processes. This uncertainty is removed by constraining the tropical winds in the second intercomparison test, in a manner akin to specifying the Quasi‐Biennial Oscillation in an AGCM. The dynamical cores exhibit qualitative agreement on the structure of atmospheric transport in the second test, with evidence of convergence as the horizontal and vertical resolution is increased in a given model. Significant quantitative differences remain, however, particularly between models employing spectral versus finite‐volume numerics, even in state‐of‐the‐art cores., The climatological and zonal mean zonal wind ū (m·s−1), as simulated by two different dynamical cores, (left) pseudospectral (GFDL‐PS) and (right) finite‐volume (CAM‐FV), with (top) 40 vertical levels and (bottom) 80 vertical levels. With higher vertical resolution, the pseudospectral core develops westerlies in the tropical stratosphere between 20 and 80 hPa, while the finite‐volume core consistently simulates easterlies at both vertical resolutions. Both cores have comparable horizontal resolution. The contour interval is 10 m·s−1., US National Science Foundation

Numerical general circulation models of the atmosphere are generally required to conserve mass and energy for their application to climate studies. Here we draw attention to another conserved global integral, viz. the component of angular momentum (AM) along the Earth's axis of rotation, which tends to receive less consideration. We demonstrate the importance of global AM conservation in climate simulations with the example of the Community Atmosphere Model (CAM) with the finite-volume (FV) dynamical core, which produces a noticeable numerical sink of AM. We use a combination of mathematical analysis and numerical diagnostics to pinpoint the main source of AM non-conservation in CAM–FV. We then present a method to enforce global conservation of AM, and we discuss the results in a hierarchy of numerical simulations of the atmosphere of increasing complexity. In line with theoretical expectations, we show that even a crude, non-local enforcement of AM conservation in the simulations consistently results in the mitigation of certain persistent model biases.

A new configuration of the Community Earth System Model (CESM)/Community Atmosphere Model with full chemistry (CAM-chem) supporting the capability of horizontal mesh refinement through the use of the spectral element (SE) dynamical core is developed and called CESM/CAM-chem-SE. Horizontal mesh refinement in CESM/CAM-chem-SE is unique and novel in that pollutants such as ozone are accurately represented at human exposure relevant scales while also directly including global feedbacks. CESM/CAM-chem-SE with mesh refinement down to ∼14 km over the conterminous US (CONUS) is the beginning of the Multi-Scale Infrastructure for Chemistry and Aerosols (MUSICAv0). Here, MUSICAv0 is evaluated and used to better understand how horizontal resolution and chemical complexity impact ozone and ozone precursors over CONUS as compared to measurements from five aircraft campaigns, which occurred in 2013. This field campaign analysis demonstrates the importance of using finer horizontal resolution to accurately simulate ozone precursors such as nitrogen oxides and carbon monoxide. In general, the impact of using more complex chemistry on ozone and other oxidation products is more pronounced when using finer horizontal resolution where a larger number of chemical regimes are resolved. Large model biases for ozone near the surface remain in the Southeast US as compared to the aircraft observations even with updated chemistry and finer horizontal resolution. This suggests a need for adding the capability of replacing sections of global emission inventories with regional inventories, increasing the vertical resolution in the planetary boundary layer, and reducing model biases in meteorological variables such as temperature and clouds.

Accurate representation of stratospheric trace gas transport is important for ozone modeling and climate projection. Intermodel spread can arise from differences in the representation of transport by the diabatic (overturning) circulation vs. comparatively faster adiabatic mixing by breaking waves, or through numerical errors, primarily diffusion. This study investigates the impact of these processes on transport using an idealised tracer, the age-of-air. Transport is assessed in two state-of-the-art dynamical cores based on fundamentally different numerical formulations: finite volume and spectral element. Integrating the models in free-running and nudged tropical wind configurations reveals the crucial impact of tropical dynamics on stratospheric transport. Using age-budget theory, vertical and horizontal gradients of age allow comparison of the roles of the diabatic circulation, adiabatic mixing, and the numerical diffusive flux. Their respective contribution is quantified by connecting the full 3-d model to the tropical leaky pipe framework of Neu and Plumb (1999). Transport by the two cores varies significantly in the free-running integrations, with the age in the middle stratosphere differing by about 2 years primarily due to differences in adiabatic mixing. When winds in the tropics are constrained, the difference in age drops to about 0.5 years; in this configuration, more than half the difference is due to the representation of the diabatic circulation. Numerical diffusion is very sensitive to the resolution of the core, but does not play a significant role in differences between the cores when they are run at comparable resolution. It is concluded that fundamental differences rooted in dynamical core formulation can account for a substantial fraction of transport bias between climate models.

Atmospheric modeling with element-based high-order Galerkin methods presents a unique challenge to the conventional physics–dynamics coupling paradigm, due to the highly irregular distribution of nodes within an element and the distinct numerical characteristics of the Galerkin method. The conventional coupling procedure is to evaluate the physical parameterizations ( physics) on the dynamical core grid. Evaluating the physics at the nodal points exacerbates numerical noise from the Galerkin method, enabling and amplifying local extrema at element boundaries. Grid imprinting may be substantially reduced through the introduction of an entirely separate, approximately isotropic finite-volume grid for evaluating the physics forcing. Integration of the spectral basis over the control volumes provides an area-average state to the physics, which is more representative of the state in the vicinity of the nodal points rather than the nodal point itself and is more consistent with the notion of a “large-scale state” required by conventional physics packages. This study documents the implementation of a quasi-equal-area physics grid into NCAR’s Community Atmosphere Model Spectral Element and is shown to be effective at mitigating grid imprinting in the solution. The physics grid is also appropriate for coupling to other components within the Community Earth System Model, since the coupler requires component fluxes to be defined on a finite-volume grid, and one can be certain that the fluxes on the physics grid are, indeed, volume averaged.

The Community Earth System Model 2 (CESM2) is the latest Earth System Model developed by the National Center for Atmospheric Research in collaboration with the university community and is significantly advanced in most components compared to its predecessor (CESM1). Here, CESM2's representation of the large‐scale atmospheric circulation and its variability is assessed. Further context is providedthrough comparison to the CESM1 large ensemble and other models from the Coupled Model Intercomparison Project (CMIP5 and CMIP6). This includes an assessment of the representation of jet streams and storm tracks, stationary waves, the global divergent circulation, the annular modes, the North Atlantic Oscillation, and blocking. Compared to CESM1, CESM2 is substantially improved in the representation of the storm tracks, Northern Hemisphere (NH) stationary waves, NH winter blocking and the global divergent circulation. It ranks within the top 10% of CMIP class models in many of these features. Some features of the Southern Hemisphere (SH) circulation have degraded, such as the SH jet strength, stationary waves, and blocking, although the SH jet stream is placed at approximately the correct location. This analysis also highlights systematic deficiencies in these features across the new CMIP6 archive, such as the continued tendency for the SH jet stream to be placed too far equatorward, the North Atlantic westerlies to be too strong over Europe, the storm tracks as measured by low‐level meridional wind variance to be too weak and a lack of blocking in the North Atlantic sector.

Accurate representation of tracer transport --- the movement of trace constituents by the atmospheric flow --- continues to be a challenge for climate models. Differences in the resolved circulation, biases due to physical parameterizations, and differences in the numerical representation of trace gases result in large variations in transport, even among state-of-the-art climate models. These differences result in disagreement among model projections of the evolution of stratospheric ozone throughout the 21st century particularly in the recovery of the Antarctic ozone hole. In addition to transport, the delicate momentum balance in the upper-troposphere and lower-stratosphere (UTLS) also presents a stiff challenge for model numerics, exposing the impacts of numerical dissipation, the resolution of waves, and the consequences of imperfect momentum conservation. Biases in this region impact the global circulation, e.g., influencing the extratropics jets and stratospheric polar vortices, and alter the transport and exchange of trace gases between and through the troposphere and stratosphere. In this study, we compare 2 modern dynamical cores (dycores) that employ very different numerics: the cubed sphere finite volume (CSFV) core from GFDL and the spectral element (SE) core from NCAR-CAM5. We force these dycores using identical Held-Suarez diabatic forcing in the troposphere and Polvani-Kushner diabatic forcing in the stratosphere, varying the horizontal and vertical resolution. We observe significant differences in circulation, between the two models at high vertical resolution in the lower and middle tropical stratosphere. While the finite volume core is relatively insensitive to any changes in vertical resolution, the PS and SE dycores resolve considerably different tropical stratospheric dynamics at high vertical resolution (80 levels). These models develop QBO-like westerly winds in the tropics and induce a secondary meridional circulation in the tropical stratosphere, which sets of transport between the models. Using the theoretical leaky pipe transport model we analyze and separate out the transport differences due to differences is diabatic circulation and isentropic mixing and infer that this secondary circulation strikingly modulates stratospheric tracer transport (age of air) by altering the tropical-extratropical mixing, and impacts the extratropical circulation through the subtropical jets. Implications for comprehensive atmospheric modeling are discussed.

An overview of the Community Earth System Model Version 2 (CESM2) is provided, including a discussion of the challenges encountered during its development and how they were addressed. In addition, an evaluation of a pair of CESM2 long preindustrial control and historical ensemble simulations is presented. These simulations were performed using the nominal 1° horizontal resolution configuration of the coupled model with both the “low‐top” (40 km, with limited chemistry) and “high‐top” (130 km, with comprehensive chemistry) versions of the atmospheric component. CESM2 contains many substantial science and infrastructure improvements and new capabilities since its previous major release, CESM1, resulting in improved historical simulations in comparison to CESM1 and available observations. These include major reductions in low‐latitude precipitation and shortwave cloud forcing biases; better representation of the Madden‐Julian Oscillation; better El Niño‐Southern Oscillation‐related teleconnections; and a global land carbon accumulation trend that agrees well with observationally based estimates. Most tropospheric and surface features of the low‐ and high‐top simulations are very similar to each other, so these improvements are present in both configurations. CESM2 has an equilibrium climate sensitivity of 5.1–5.3 °C, larger than in CESM1, primarily due to a combination of relatively small changes to cloud microphysics and boundary layer parameters. In contrast, CESM2's transient climate response of 1.9–2.0 °C is comparable to that of CESM1. The model outputs from these and many other simulations are available to the research community, and they represent CESM2's contributions to the Coupled Model Intercomparison Project Phase 6.

It is the purpose of this paper to provide a comprehensive documentation of the new NCAR (National Center for Atmospheric Research) version of the spectral element (SE) dynamical core as part of the Community Earth System Model (CESM2.0) release. This version differs from previous releases of the SE dynamical core in several ways. Most notably the hybrid sigma vertical coordinate is based on dry air mass, the condensates are dynamically active in the thermodynamic and momentum equations (also referred to as condensate loading), and the continuous equations of motion conserve a more comprehensive total energy that includes condensates. Not related to the vertical coordinate change, the hyperviscosity operators and the vertical remapping algorithms have been modified. The code base has been significantly reduced, sped up, and cleaned up as part of integrating SE as a dynamical core in the CAM (Community Atmosphere Model) repository rather than importing the SE dynamical core from High‐Order Methods Modeling environment as an external code.

The spectral element (SE) variable‐resolution (VR) mesh dynamical core is tested in developmental versions of the Community Earth System Model version 2 (CESM2). The SE dynamical core is tested in baroclinic wave, aquaplanet and full physics configurations to evaluate variable‐resolution simulations against uniform high and uniform low‐resolution simulations. Different physical parameterization suites are also evaluated to gauge their sensitivity to resolution. Dry dynamical core variable‐resolution cases compare well to high‐resolution tests. More recent versions of the atmospheric physics, including cloud schemes for CESM2, are less sensitive to changes in horizontal resolution. Most of the sensitivity is due to sensitivity to time step and interactions between deep convection and large‐scale condensation, which is expected from the closure methods. The resulting full physics SE‐VR model produces a similar climate to the global low‐resolution mesh and similar high‐frequency statistics in the high‐resolution region. The SE‐VR simulations are able to reproduce uniform high‐resolution results, making them an effective tool for regional climate simulations at lower computational cost. Some biases are reduced (orographic precipitation in Western United States), but biases do not necessarily go away at high resolution (e.g., summertime surface temperatures). Variable‐resolution grids are a viable alternative to traditional nesting for regional climate studies and are available in CESM2.

An algorithm to consistently couple a conservative semi-Lagrangian finite-volume transport scheme with a spectral element (SE) dynamical core is presented. The semi-Lagrangian finite-volume scheme is the Conservative Semi-Lagrangian Multitracer (CSLAM), and the SE dynamical core is the National Center for Atmospheric Research (NCAR)’s Community Atmosphere Model–Spectral Elements (CAM-SE). The primary motivation for coupling CSLAM with CAM-SE is to accelerate tracer transport for multitracer applications. The coupling algorithm result is an inherently mass-conservative, shape-preserving, and consistent (for a constant mixing ratio, the CSLAM solution reduces to the SE solution for air mass) transport that is efficient and accurate. This is achieved by first deriving formulas for diagnosing SE airmass flux through the CSLAM control volume faces. Thereafter, the upstream Lagrangian CSLAM areas are iteratively perturbed to match the diagnosed SE airmass flux, resulting in an equivalent upstream Lagrangian grid that spans the sphere without gaps or overlaps (without using an expensive search algorithm). This new CSLAM algorithm is not specific to airmass fluxes provided by CAM-SE but applies to any airmass fluxes that satisfy the Lipshitz criterion and for which the Courant number is less than one.

This paper describes the splitting supercell idealized test case used in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016). These storms are useful test beds for global atmospheric models because the horizontal scale of convective plumes is O(1 km), emphasizing non-hydrostatic dynamics. The test case simulates a supercell on a reduced-radius sphere with nominal resolutions ranging from 4 to 0.5 km and is based on the work of Klemp et al. (2015). Models are initialized with an atmospheric environment conducive to supercell formation and forced with a small thermal perturbation. A simplified Kessler microphysics scheme is coupled to the dynamical core to represent moist processes. Reference solutions for DCMIP2016 models are presented. Storm evolution is broadly similar between models, although differences in the final solution exist. These differences are hypothesized to result from different numerical discretizations, physics–dynamics coupling, and numerical diffusion. Intramodel solutions generally converge as models approach 0.5 km resolution, although exploratory simulations at 0.25 km imply some dynamical cores require more refinement to fully converge. These results can be used as a reference for future dynamical core evaluation, particularly with the development of non-hydrostatic global models intended to be used in convective-permitting regimes.

We discuss and evaluate the representation of atmospheric chemistry in the global Community Atmosphere Model (CAM) version 4, the atmospheric component of the Community Earth System Model (CESM). We present a variety of configurations for the representation of tropospheric and stratospheric chemistry, wet removal, and online and offline meteorology. Results from simulations illustrating these configurations are compared with surface, aircraft and satellite observations. Major biases include a negative bias in the high-latitude CO distribution, a positive bias in upper-tropospheric/lower-stratospheric ozone, and a positive bias in summertime surface ozone (over the United States and Europe). The tropospheric net chemical ozone production varies significantly between configurations, partly related to variations in stratosphere-troposphere exchange. Aerosol optical depth tends to be underestimated over most regions, while comparison with aerosol surface measurements over the United States indicate reasonable results for sulfate , especially in the online simulation. Other aerosol species exhibit significant biases. Overall, the model-data comparison indicates that the offline simulation driven by GEOS5 meteorological analyses provides the best simulation, possibly due in part to the increased vertical resolution (52 levels instead of 26 for online dynamics). The CAM-chem code as described in this paper, along with all the necessary datasets needed to perform the simulations described here, are available for download at www.cesm.ucar.edu.

Key developments have been made to the NCAR Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension (WACCM‐X). Among them, the most important are the self‐consistent solution of global electrodynamics, and transport of O+ in the F‐region. Other ionosphere developments include time‐dependent solution of electron/ion temperatures, metastable O+ chemistry, and high‐cadence solar EUV capability. Additional developments of the thermospheric components are improvements to the momentum and energy equation solvers to account for variable mean molecular mass and specific heat, a new divergence damping scheme, and cooling by O(3P) fine structure. Simulations using this new version of WACCM‐X (2.0) have been carried out for solar maximum and minimum conditions. Thermospheric composition, density, and temperatures are in general agreement with measurements and empirical models, including the equatorial mass density anomaly and the midnight density maximum. The amplitudes and seasonal variations of atmospheric tides in the mesosphere and lower thermosphere are in good agreement with observations. Although global mean thermospheric densities are comparable with observations of the annual variation, they lack a clear semiannual variation. In the ionosphere, the low‐latitude E × B drifts agree well with observations in their magnitudes, local time dependence, seasonal, and solar activity variations. The prereversal enhancement in the equatorial region, which is associated with ionospheric irregularities, displays patterns of longitudinal and seasonal variation that are similar to observations. Ionospheric density from the model simulations reproduces the equatorial ionosphere anomaly structures and is in general agreement with observations. The model simulations also capture important ionospheric features during storms.

Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and microphysical processes. Typically, each component is developed, at least initially, independently. Once development is mature, the components are coupled to deliver a model of the required complexity. The implementation of the coupling can have a significant impact on the model. As the error associated with each component decreases, the errors introduced by the coupling will eventually dominate. Hence, any improvement in one of the components is unlikely to improve the performance of the overall system. The challenges associated with combining the components to create a coherent model are here termed physics–dynamics coupling. The issue goes beyond the coupling between the parameterizations and the resolved fluid dynamics. This paper highlights recent progress and some of the current challenges. It focuses on three objectives: to illustrate the phenomenology of the coupling problem with references to examples in the literature, to show how the problem can be analyzed, and to create awareness of the issue across the disciplines and specializations. The topics addressed are different ways of advancing full models in time, approaches to understanding the role of the coupling and evaluation of approaches, coupling ocean and atmosphere models, thermodynamic compatibility between model components, and emerging issues such as those that arise as model resolutions increase and/or models use variable resolutions.

It is the purpose of this paper to document the NCAR global model topography generation software for unstructured grids (NCAR_Topo (v1.0)). Given a model grid, the software computes the fraction of the grid box covered by land, the grid-box mean elevation (deviation from a geoid that defines nominal sea level surface), and associated sub-grid-scale variances commonly used for gravity wave and turbulent mountain stress parameterizations. The software supports regular latitude–longitude grids as well as unstructured grids, e.g., icosahedral, Voronoi, cubed-sphere and variable-resolution grids.

This study presents a diagnosis of a multiresolution approach using the Model for Prediction Across Scales–Atmosphere (MPAS-A) for simulating regional climate. Four Atmospheric Model Intercomparison Project (AMIP) experiments were conducted for 1999–2009. In the first two experiments, MPAS-A was configured using global quasi-uniform grids at 120- and 30-km grid spacing. In the other two experiments, MPAS-A was configured using variable-resolution (VR) mesh with local refinement at 30 km over North America and South America and embedded in a quasi-uniform domain at 120 km elsewhere. Precipitation and related fields in the four simulations are examined to determine how well the VRs reproduce the features simulated by the globally high-resolution model in the refined domain. In previous analyses of idealized aquaplanet simulations, characteristics of the global high-resolution simulation in moist processes developed only near the boundary of the refined region. In contrast, AMIP simulations with VR grids can reproduce high-resolution characteristics across the refined domain, particularly in South America. This finding indicates the importance of finely resolved lower boundary forcings such as topography and surface heterogeneity for regional climate and demonstrates the ability of the MPAS-A VR to replicate the large-scale moisture transport as simulated in the quasi-uniform high-resolution model. Upscale effects from the high-resolution regions on a large-scale circulation outside the refined domain are observed, but the effects are mainly limited to northeastern Asia during the warm season. Together, the results support the multiresolution approach as a computationally efficient and physically consistent method for modeling regional climate.

This test extends the evaluation of transport schemes from prescribed advection of inert scalars to reactive species. The test consists of transporting two interacting chemical species in the Nair and Lauritzen 2-D idealized flow field. The sources and sinks for these two species are given by a simple, but non-linear, "toy" chemistry that represents combination (X + X → X2) and dissociation (X2 → X + X). This chemistry mimics photolysis-driven conditions near the solar terminator, where strong gradients in the spatial distribution of the species develop near its edge. Despite the large spatial variations in each species, the weighted sum XT = X + 2X2 should always be preserved at spatial scales at which molecular diffusion is excluded. The terminator test demonstrates how well the advection–transport scheme preserves linear correlations. Chemistry–transport (physics–dynamics) coupling can also be studied with this test. Examples of the consequences of this test are shown for illustration.

In the continued effort to understand the climate system and improve its representation in atmospheric general circulation models (AGCMs), it is crucial to develop reduced-complexity frameworks to evaluate these models. This is especially true as the AGCM community advances toward high horizontal resolutions (i.e., grid spacing less than 50 km), which will require interpreting and improving the performance of many model components. A simplified global radiative–convective equilibrium (RCE) configuration is proposed to explore the implication of horizontal resolution on equilibrium climate. RCE is the statistical equilibrium in which the radiative cooling of the atmosphere is balanced by heating due to convection. In this work, the Community Atmosphere Model, version 5 (CAM5), is configured in RCE to better understand tropical climate and extremes. The RCE setup consists of an ocean-covered Earth with diurnally varying, spatially uniform insolation and no rotation effects. CAM5 is run at two horizontal resolutions: a standard resolution of approximately 100-km grid spacing and a high resolution of approximately 25-km spacing. Surface temperature effects are considered by comparing simulations using fixed, uniform sea surface temperature with simulations using an interactive slab-ocean model. The various CAM5 configurations provide useful insights into the simulation of tropical climate as well as the model’s ability to simulate extreme precipitation events. In particular, the manner in which convection organizes is shown to be dependent on model resolution and the surface configuration (including surface temperature), as evident by differences in cloud structure, circulation, and precipitation intensity.

A recently developed cell-integrated semi-Lagrangian (CISL) semi-implicit nonhydrostatic atmospheric solver that uses the conservative semi-Lagrangian multitracer (CSLAM) transport scheme is extended to include orographic influences. With the introduction of a new semi-implicit CISL discretization of the continuity equation, the nonhydrostatic solver, called CSLAM-NH, has been shown to ensure inherently conservative and numerically consistent transport of air mass and other scalar variables, such as moisture and passive tracers. The extended CSLAM-NH presented here includes two main modifications: transformation of the equation set to a terrain-following height coordinate to incorporate orography and an iterative centered-implicit time-stepping scheme to enhance the stability of the scheme associated with gravity wave propagation at large time steps. CSLAM-NH is tested for a suite of idealized 2D flows, including linear mountain waves (dry), a downslope windstorm (dry), and orographic cloud formation.

Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems and are responsible for capturing the dynamical behavior of the Earth's atmosphere via numerical integration of the Navier–Stokes equations. These systems have existed in one form or another for over half of a century, with the earliest discretizations having now evolved into a complex ecosystem of algorithms and computational strategies. In essence, no two dynamical cores are alike, and their individual successes suggest that no perfect model exists. To better understand modern dynamical cores, this paper aims to provide a comprehensive review of 11 non-hydrostatic dynamical cores, drawn from modeling centers and groups that participated in the 2016 Dynamical Core Model Intercomparison Project (DCMIP) workshop and summer school. This review includes a choice of model grid, variable placement, vertical coordinate, prognostic equations, temporal discretization, and the diffusion, stabilization, filters, and fixers employed by each system.

For the first time a mesoscale-resolving whole atmosphere general circulation model has been developed, using the National Center for Atmospheric Research Whole Atmosphere Community Climate Model with ∼0.25° horizontal resolution and 0.1 scale height vertical resolution above the middle stratosphere (higher resolution below). This is made possible by the high accuracy and high scalability of the spectral element dynamical core from the High-Order Method Modeling Environment. For the simulated January–February period, the latitude-height structure and the magnitudes of the temperature variance compare well with those deduced from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) observations. The simulation reveals the increasing dominance of gravity waves (GWs) at higher altitudes through both the height dependence of the kinetic energy spectra, which display a steeper slope (∼−3) in the stratosphere and an increasingly shallower slope above, and the increasing spatial extent of GWs (including a planetary-scale extent of a concentric GW excited by a tropical cyclone) at higher altitudes. GW impacts on the large-scale flow are evaluated in terms of zonal mean zonal wind and tides: with no GW drag parameterized in the simulations, forcing by resolved GWs does reverse the summer mesospheric wind, albeit at an altitude higher than climatology, and only slows down the winter mesospheric wind without closing it. The hemispheric structures and magnitudes of diurnal and semidiurnal migrating tides compare favorably with observations.

A high-order incremental “remap-type” transport scheme is presented (FF-CSLAM). The scheme utilizes bi-quadratic polynomial subgrid-cell reconstruction functions based on the weighted least squares method. The integration of the reconstruction functions over flux areas, which is inherent in remap schemes, makes use of CSLAM approach of line integration. Though the formal order of the scheme is second order, yet quadratic subgrid scale polynomial reconstruction does lead to improvement in the overall accuracy of the scheme. Since the rigorous search for overlap areas between flux areas and grid cells is cumbersome, two simplifications have been suggested in the literature. The main objectives of this paper are (a) to formulate flux-form CSLAM for the icosahedral-hexagonal grid and (b) to assess the accuracy of two flux-integral simplifications.

A cell-integrated semi-Lagrangian (CISL) semi-implicit nonhydrostatic solver for the fully compressible moist Euler equations in two-dimensional Cartesian (x–z) geometry is presented. The semi-implicit CISL solver uses the inherently conservative semi-Lagrangian multitracer transport scheme (CSLAM) and a new flux-form semi-implicit formulation of the continuity equation that ensures numerically consistent transport. The flux-form semi-implicit formulation is based on a recent successful approach in a shallow-water equations (SWE) solver (CSLAM-SW). With the new approach, the CISL semi-implicit nonhydrostatic solver (CSLAM-NH) is able to ensure conservative and consistent transport by avoiding the need for a time-independent mean reference state. Like its SWE counterpart, the nonhydrostatic solver presented here is designed to be similar to typical semi-Lagrangian semi-implicit schemes, such that only a single linear Helmholtz equation solution and a single call to CSLAM are required per time step. To demonstrate its stability and accuracy, the solver is applied to a set of three idealized test cases: a density current (dry), a gravity wave (dry), and a squall line (moist). A fourth test case shows that shape preservation of passive tracers is ensured by coupling the semi-implicit CISL formulation with existing shape-preserving filters. Results show that CSLAM-NH solutions compare well with other existing solvers for the three test cases, and that it is shape preserving.

SUMMARY A new approach is proposed for constructing a fully explicit third-order mass-conservative semi-Lagrangian scheme for simulating the shallow-water equations on an equiangular cubed-sphere grid. State variables are staggered with velocity components stored pointwise at nodal points and mass variables stored as element averages. In order to advance the state variables in time, we first apply an explicit multi-step time-stepping scheme to update the velocity components and then use a semi-Lagrangian advection scheme to update the height field and tracer variables. This procedure is chosen to ensure consistency between dry air mass and tracers, which is particularly important in many atmospheric chemistry applications. The resulting scheme is shown to be competitive with many existing numerical methods on a suite of standard test cases and demonstrates slightly improved performance over other high-order finite-volume models. Copyright © 2014 John Wiley & Sons, Ltd.

Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a "minimal" set of idealized model configurations/runs/diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volume methods as well as emerging (in the context of atmospheric/oceanographic sciences) Galerkin methods. Discretization grids range from traditional regular latitude-longitude grids to more isotropic domain discretizations such as icosahedral and cubed-sphere tessellations of the sphere. The schemes are evaluated using a wide range of diagnostics in idealized flow environments. Accuracy is assessed in single- and two-tracer configurations using conventional error norms as well as novel diagnostics designed for climate and climate-chemistry applications. In addition, algorithmic considerations that may be important for computational efficiency are reported on. The latter is inevitably computing platform dependent, The ensemble of results from a wide variety of schemes presented here helps shed light on the ability of the test case suite diagnostics and flow settings to discriminate between algorithms and provide insights into accuracy in the context of global atmospheric/ocean modeling. A library of benchmark results is provided to facilitate scheme intercomparison and model development. Simple software and data-sets are made available to facilitate the process of model evaluation and scheme intercomparison.

The Community Atmosphere Model, version 4 (CAM4), was released as part of the Community Climate System Model, version 4 (CCSM4). The finite volume (FV) dynamical core is now the default because of its superior transport and conservation properties. Deep convection parameterization changes include a dilute plume calculation of convective available potential energy (CAPE) and the introduction of convective momentum transport (CMT). An additional cloud fraction calculation is now performed following macrophysical state updates to provide improved thermodynamic consistency. A freeze-drying modification is further made to the cloud fraction calculation in very dry environments (e.g., the Arctic), where cloud fraction and cloud water values were often inconsistent in CAM3. In CAM4 the FV dynamical core further degrades the excessive trade-wind simulation, but reduces zonal stress errors at higher latitudes. Plume dilution alleviates much of the midtropospheric tropical dry biases and reduces the persistent monsoon precipitation biases over the Arabian Peninsula and the southern Indian Ocean. CMT reduces much of the excessive trade-wind biases in eastern ocean basins. CAM4 shows a global reduction in cloud fraction compared to CAM3, primarily as a result of the freeze-drying and improved cloud fraction equilibrium modifications. Regional climate feature improvements include the propagation of stationary waves from the Pacific into midlatitudes and the seasonal frequency of Northern Hemisphere blocking events. A 1° versus 2° horizontal resolution of the FV dynamical core exhibits superior improvements in regional climate features of precipitation and surface stress. Improvements in the fully coupled mean climate between CAM3 and CAM4 are also more substantial than in forced sea surface temperature (SST) simulations.

A Cartesian semi-implicit solver using the Conservative Semi-Lagrangian Multitracer (CSLAM) transport scheme is constructed and tested for shallow-water (SW) flows. The SW equations solver (CSLAM-SW) uses a discrete semi-implicit continuity equation specifically designed to ensure a conservative and consistent transport of constituents by avoiding the use of a constant mean reference state. The algorithm is constructed to be similar to typical conservative semi-Lagrangian semi-implicit schemes, requiring at each time step a single linear Helmholtz equation solution and a single application of CSLAM. The accuracy and stability of the solver is tested using four test cases for a radially propagating gravity wave and two barotropically unstable jets. In a consistency test using the new solver, the specific concentration constancy is preserved up to machine roundoff, whereas a typical formulation can have errors many orders of magnitude larger. In addition to mass conservation and consistency, CSLAM-SW also ensures shape preservation by combining the new scheme with existing shape-preserving filters. With promising SW test results, CSLAM-SW shows potential for extension to a nonhydrostatic, fully compressible system solver for numerical weather prediction and climate models.

The authors evaluate the climate produced by the Community Climate System Model, version 4, running with the new spectral element atmospheric dynamical core option. The spectral element method is configured to use a cubed-sphere grid, providing quasi-uniform resolution over the sphere and increased parallel scalability and removing the need for polar filters. It uses a fourth-order accurate spatial discretization that locally conserves mass and total energy. Using the Atmosphere Model Intercomparison Project protocol, the results from the spectral element dynamical core are compared with those produced by the default finite-volume dynamical core and with observations. Even though the two dynamical cores are quite different, their simulated climates are remarkably similar. When compared with observations, both models have strengths and weaknesses but have nearly identical root-mean-square errors and the largest biases show little sensitivity to the dynamical core. The spectral element core does an excellent job reproducing the atmospheric kinetic energy spectra, including fully capturing the observed Nastrom–Gage transition when running at 0.125° resolution.

The problem of two-dimensional tracer advection on the sphere is extremely important in modeling of geophysical fluids and has been tackled using a variety of approaches. A class of popular approaches for tracer advection include ‘incremental remap’ or cell-integrated semi-Lagrangian-type schemes. These schemes achieve high-order accuracy without the need for multistage integration in time, are capable of large time steps, and tend to be more efficient than other high-order transport schemes when applied to a large number of tracers over a single velocity field. In this paper, the simplified flux-form implementation of the Conservative Semi-LAgrangian Multi-tracer scheme (CSLAM) is reformulated using quadratic curves to approximate the upstream flux volumes and Gaussian quadrature for integrating the edge flux. The high-order treatment of edge fluxes is motivated because of poor accuracy of the CSLAM scheme in the presence of strong nonlinear shear, such as one might observe in the midlatitudes near an atmospheric jet. Without the quadratic treatment of upstream edges, we observe at most second-order accuracy under convergence of grid resolution, which is returned to third-order accuracy under the improved treatment. A shallow-water barotropic instability also reveals clear evidence of grid imprinting without the quadratic correction. Consequently, these tests reveal a problem that might arise in tracer transport near nonlinearly sheared regions of the real atmosphere, particularly near cubed-sphere panel edges. Although CSLAM is used as the foundation for this analysis, the conclusions of this paper are applicable to the general class of incremental remap schemes. Copyright © 2012 John Wiley & Sons, Ltd.