#dycore

[openclimate]

Comparison of Finite Volume and Spectral Dynamical Cores in CESM

These are two papers led by G. Bala.

Simulated climate near steep topography: Sensitivity to numerical methods for atmospheric transport.

Abstract

We present the sensitivity of the simulated climate near steep topographical regions when the numerical method for atmospheric transport in the Community Climate System Model (CCSM3) is changed from spectral to a finite volume (FV) transport. Our analysis of the circulation and precipitation shows significant local improvement in three aspects: 1) The Gibbs oscillations present in the cloudiness and shortwave radiative forcing fields in the spectral simulation are absent in the FV simulation. 2) The alongshore component of wind stress in the western coastal regions of North and South America increases in the FV simulation. This tends to reduce the persistent biases in sea surface temperature through enhanced oceanic upwelling. 3) The FV simulation shows improvement in the wet-dry contrast of orographically forced precipitation. These local improvements have impact on continental and larger scales and are critical to the confident use of information from climate predictions in adaptation to climate change.

Evaluation of a CCSM3 Simulation with a Finite Volume Dynamical Core for the Atmosphere at 1 degree  Latitude by 1.25 degree  Longitude Resolution

Abstract

A simulation of the present-day climate by the Community Climate System Model version 3 (CCSM3) that uses a Finite Volume (FV) numerical method for solving the equations governing the atmospheric dynamics is presented. The simulation is compared to observations and to the well-documented simulation by the standard CCSM3, which uses the Eulerian spectral method for the atmospheric dynamics. The atmospheric component in the simulation herein uses a 1degree latitude x 1.25 degree longitude grid, which is a slightly finer resolution than the T85-grid used in the spectral transform. As in the T85 simulation, the ocean and ice models use a nominal 1-degree grid. Although the physical parameterizations are the same and the resolution is comparable to the standard model, substantial testing and slight retuning were required to obtain an acceptable control simulation. There are significant improvements in the simulation of the surface wind stress and sea surface temperature. Improvements are also seen in the simulations of the total variance in the tropical Pacific, the spatial pattern of ice thickness distribution in the Arctic, and the vertically integrated ocean circulation in the Antarctic Circumpolar Current. The results herein demonstrate that the FV version of the CCSM coupled model is a state-of-the-art climate model whose simulation capabilities are in the class of those used for Intergovernmental Panel on Climate Change (IPCC) assessments. The simulated climate is very similar to that of the T85 version in terms of its biases, and more like the T85 model than the other IPCC models.

These are author’s personal copies.

[openclimate]

An object-based evaluation method is applied to the simulated orographic precipitation for the idealized experimental setups using the National Center of Atmospheric Research (NCAR) Community Atmosphere Model (CAM) with the finite volume (FV) and Eulerian spectral transform dynamical cores with varying resolutions. The method consists of the application of k-means cluster analysis to the precipitation features to determine their spatial boundaries and the calculation of the semivariograms (SVs) for the isolated features for evaluation.

The quantitative analysis revealed differences between the simulated precipitation by the FV and Eulerian spectral transform models that are not visually apparent. The simulated large-scale precipitation features of the idealized test cases provide analogs to orographic precipitation features observed in simulations of Atmospheric Model Intercomparison Project (AMIP) models. The spatial boundaries of these features (determined by k-means clustering) for Eulerian spectral T85 and T170 resolutions revealed the level of merger between the two large-scale features simulated because of each peak in the double mountain idealized setup. Both FV 1 degree and 0.5 degree resolutions were able to simulate the dryer region between the two mountains. The SVs of precipitation for the single and double mountain setups show close agreement between FV 1 degree, FV 0.5 degree, and Eulerian spectral T170 resolutions; however, Eulerian spectral T85 simulated the precipitation in lower intensity, indicating the qualitative difference in resolutions previously determined to be equivalent. Such close agreement was not observed in the more realistic idealized setup.

Paper is author’s personal copy.

[openclimate]

To assess the impact of dynamical formulation on climate simulations, a semi-Lagrangian and an Eulerian dynamical core have been used for 5-yr climate simulations with the same physical parameterizations. The comparison of the climate simulations is focused on various eddy statistics (the study of time-mean states from the simulations has been published in a previous paper). Significant differences between the two simulations are evident. Generally, the stationary eddy variances are stronger in the semi-Lagrangian simulation while the transient eddy variances are stronger in the Eulerian simulation. Compared to the data assimilated by the Goddard Earth Observing System data assimilation system, the semi-Lagrangian simulation is closer to the assimilation in many aspects than the Eulerian simulation, even though the Eulerian model was used in the data assimilation.

The paper shows that rather than corrupting the ability to diagnose model performance with a parallel data assimilation, quantitative rigor can be advanced because the model environment is more controlled. The two dynamical cores have been run for the idealized Held-Suarez tests to help understand the differences found in the climate simulations. The eddy statistics from the Held-Suarez tests are weaker and more diffused in the semi-Lagrangian than the Eulerian core. The transformed Eulerian mean diagnostics reveal that less wave activity propagates from the lower and middle troposphere into the upper troposphere in the semi-Lagrangian core. The residual circulation driven by eddy forcing is weaker in the semi-Lagrangian core than in the Eulerian core. Consequently, the semi-Lagrangian simulation is closer to the radiative equilibrium state than the Eulerian simulation. These diagnostics show that the different treatment of small-scale processes in the model (e.g., diffusion) profoundly impacts the simulation of the general circulation.

Paper is author’s personal copy.

[openclimate]

Abstract: The effective resolution of a numerical scheme describes the smallest spatial scale (largest wave number) that is completely resolved by that scheme. Using dispersion relation analysis allows the effective resolution of a numerical scheme for the advection equation to be calculated. The advection equation is a fundamental building block of dynamical cores of atmospheric and ocean models, and this analysis provides an indication of the effective resolution of the numerical methods used by dynamical cores. Using a variety of finite-difference schemes, the effect on effective resolution of using explicit diffusion and hyper-diffusion terms is examined. The choice of order-of-accuracy, and the time-stepping of the numerical scheme is also investigated with regard to effective resolution. Finally, we apply this analysis to methods that are commonly used in dynamical cores of atmospheric general circulation models, namely semi-Lagrangian and finite-volume methods. Paper is author's personal copy.

[openclimate]

Abstract: Numerical models of fluid flows calculate the resolved flow at a given grid resolution. The smallest wave resolved by the numerical scheme is deemed the effective resolution. Advection schemes are an important part of the numerical models used for computational fluid dynamics. For example, in atmospheric dynamical cores they control the transport of tracers. For linear schemes solving the advection equation, the effective resolution can be calculated analytically using dispersion analysis. Here, a numerical test is developed that can calculate the effective resolution of any scheme (linear or non-linear) for the advection equation.

The tests are focused on the use of non-linear limiters for advection schemes. It is found that the effective resolution of such non-linear schemes is very dependent on the number of time steps. Initially, schemes with limiters introduce large errors. Therefore, their effective resolution is poor over a small number of time steps. As the number of time steps increases the error of non-linear schemes grows at a smaller rate than that of the linear schemes which improves their effective resolution considerably. The tests highlight that a scheme that produces large errors over one time step might not produce a large accumulated error over a number of time steps. The results show that, in terms of effective-resolution, there is little benefit in using higher than third-order numerical accuracy with traditional limiters. The use of weighted essentially non-oscillatory (WENO) schemes, or relaxed and quasi-monotonic limiters, which allow smooth extrema, can eliminate this reduction in effective resolution and enable higher than third-order accuracy.

Paper is author’s personal copy.

[openclimate]

ABSTRACT An object-based evaluation method to quantify biases of general circulation models (GCMs) is introduced using the National Center of Atmospheric Research (NCAR) Community Atmosphere Model (CAM). Idealized experiments with different topography are designed to reproduce the spatial characteristics of precipitation biases that were present in Atmospheric Model Intercomparison Project simulations using the CAM finite volume (FV) andCAMEulerian spectral dynamical cores. Precipitation features are identified as “objects” to understand the causes of the differences between CAM FV and CAM Eulerian spectral dynamical cores. Three different mechanisms of precipitation were simulated in idealized experiments: stable upslope ascent, local surface fluxes, and resolved downstream waves. The results indicated stronger sensitivity of theCAM Eulerian spectral dynamical core to resolution. The application of spectral filtering to topography is shown to have a large effect on the CAM Eulerian spectral model simulation. The removal of filtering improved the results when the scales of the topography were resolvable. However, it reduced the simulation capability of the CAM Eulerian spectral dynamical core because of Gibbs oscillations, leading to unusable results. A clear perspective about models biases is provided from the quantitative evaluation of objects extracted from these simulations and will be further discussed in part II of this study.

Paper is author’s personal copy.

[openclimate]

Abstract: Ertel’s potential vorticity (PV) is used as a diagnostic tool to give a direct comparison between the treatment of PV in the dynamics and the integration of PV as a passive tracer, yielding a systematic evaluation of a model’s consistency between the dynamical core’s integration of the equations of motion and its tracer transport algorithm. Several quantitative and qualitative metrics are considered to measure the consistency, including error norms and grid-independent probability density functions. Comparisons between the four dynamical cores of the National Center for Atmospheric Research’s (NCAR) Community Atmosphere Model version 5.1 (CAM) are presented. We investigate the consistency of these dynamical cores in an idealized setting: the presence of a breaking baroclinic wave. For linear flow, before the wave breaks, the consistency for each model is good. As the flow becomes nonlinear, the consistency between dynamic PV and tracer PV breaks down, especially at small scales. Large values of dynamic PV are observed that do not appear in the tracer PV. The results indicate that the spectral-element (CAM-SE) dynamical core is the most consistent of the dynamical cores in CAM, however the consistency between dynamic PV and tracer PV is related to and sensitive to the diffusive properties of the dynamical cores.

Paper is author’s personal copy.

[openclimate]

ABSTRACT The dynamical core of an atmospheric general circulation model is engineered to satisfy a delicate balance between numerical stability, computational cost, and an accurate representation of the equations of motion. It generally contains either explicitly added or inherent numerical diffusion mechanisms to control the buildup of energy or enstrophy at the smallest scales. The diffusion fosters computational stability and is sometimes also viewed as a substitute for unresolved subgrid-scale processes. A particular form of explicitly added diffusion is horizontal divergence damping.

In this paper a von Neumann stability analysis of horizontal divergence damping on a latitude-longitude grid is performed. Stability restrictions are derived for the damping coefficients of both second- and fourth- order divergence damping. The accuracy of the theoretical analysis is verified through the use of idealized dynamical core test cases that include the simulation of gravity waves and a baroclinic wave. The tests are applied to the finite-volume dynamical core of NCAR’s Community Atmosphere Model version 5 (CAM5). Investigation of the amplification factor for the divergence damping mechanisms explains how small-scale meridional waves found in a baroclinic wave test case are not eliminated by the damping.

(Paper is author’s personal copy.