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Short ‐ term time step convergence in a climate model

View Article: PubMed Central - PubMed

ABSTRACT

This paper evaluates the numerical convergence of very short (1 h) simulations carried out with a spectral‐element (SE) configuration of the Community Atmosphere Model version 5 (CAM5). While the horizontal grid spacing is fixed at approximately 110 km, the process‐coupling time step is varied between 1800 and 1 s to reveal the convergence rate with respect to the temporal resolution. Special attention is paid to the behavior of the parameterized subgrid‐scale physics. First, a dynamical core test with reduced dynamics time steps is presented. The results demonstrate that the experimental setup is able to correctly assess the convergence rate of the discrete solutions to the adiabatic equations of atmospheric motion. Second, results from full‐physics CAM5 simulations with reduced physics and dynamics time steps are discussed. It is shown that the convergence rate is 0.4—considerably slower than the expected rate of 1.0. Sensitivity experiments indicate that, among the various subgrid‐scale physical parameterizations, the stratiform cloud schemes are associated with the largest time‐stepping errors, and are the primary cause of slow time step convergence. While the details of our findings are model specific, the general test procedure is applicable to any atmospheric general circulation model. The need for more accurate numerical treatments of physical parameterizations, especially the representation of stratiform clouds, is likely common in many models. The suggested test technique can help quantify the time‐stepping errors and identify the related model sensitivities.

No MeSH data available.


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Dependence of the temperature RMSE (in K, cf. equation (1)) on the physics‐dynamics coupling time step Δt (in s) in 1 h dry adabatic simulations that were conducted with the SE dynamical core using real‐world land‐sea mask and topography. The Lagrangian and Eulerian vertical discretization schemes are referred to as “LGN” and “EUL”, respectively. Simulations with the standard hyperviscosity are denoted by “vis”, and those without viscosity by “inv”. Colored dots show the temperature RMSE calculated over all grid cells of the horizontal mesh and all levels of the vertical grid. Dashed lines are linear fits between log10(RMSE) and log10(Δt). The convergence rates are given in parenthesis. We note that the results in this figure were obtained without physics parameterization, but the errors are plotted against the physics‐dynamics coupling time step Δt for consistency with other figures. The entire 3‐D domain was included in the calculation of the RMSE.
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jame20146-fig-0002: Dependence of the temperature RMSE (in K, cf. equation (1)) on the physics‐dynamics coupling time step Δt (in s) in 1 h dry adabatic simulations that were conducted with the SE dynamical core using real‐world land‐sea mask and topography. The Lagrangian and Eulerian vertical discretization schemes are referred to as “LGN” and “EUL”, respectively. Simulations with the standard hyperviscosity are denoted by “vis”, and those without viscosity by “inv”. Colored dots show the temperature RMSE calculated over all grid cells of the horizontal mesh and all levels of the vertical grid. Dashed lines are linear fits between log10(RMSE) and log10(Δt). The convergence rates are given in parenthesis. We note that the results in this figure were obtained without physics parameterization, but the errors are plotted against the physics‐dynamics coupling time step Δt for consistency with other figures. The entire 3‐D domain was included in the calculation of the RMSE.

Mentions: Four configurations of the SE dynamical core were tested which used different combinations of the vertical discretization methods (floating Lagrangian (“LGR”) versus Eulerian (“EUL”)) and the hyperviscosity setting (inviscid without diffusion (“inv”) versus standard diffusion (“vis”)). The convergence properties of these combinations are shown in Figure 2. The figure displays the temperature RMSE versus the process‐coupling time step Δt in a double‐logarithmic diagram. Recall that the dynamics time steps are shorter than Δt as shown in Table 1, but Δt is plotted here for consistency with other figures. The dashed lines are linear fits between the actual data points which are denoted by colored dots. The convergence rates are noted in parentheses.


Short ‐ term time step convergence in a climate model
Dependence of the temperature RMSE (in K, cf. equation (1)) on the physics‐dynamics coupling time step Δt (in s) in 1 h dry adabatic simulations that were conducted with the SE dynamical core using real‐world land‐sea mask and topography. The Lagrangian and Eulerian vertical discretization schemes are referred to as “LGN” and “EUL”, respectively. Simulations with the standard hyperviscosity are denoted by “vis”, and those without viscosity by “inv”. Colored dots show the temperature RMSE calculated over all grid cells of the horizontal mesh and all levels of the vertical grid. Dashed lines are linear fits between log10(RMSE) and log10(Δt). The convergence rates are given in parenthesis. We note that the results in this figure were obtained without physics parameterization, but the errors are plotted against the physics‐dynamics coupling time step Δt for consistency with other figures. The entire 3‐D domain was included in the calculation of the RMSE.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC5016774&req=5

jame20146-fig-0002: Dependence of the temperature RMSE (in K, cf. equation (1)) on the physics‐dynamics coupling time step Δt (in s) in 1 h dry adabatic simulations that were conducted with the SE dynamical core using real‐world land‐sea mask and topography. The Lagrangian and Eulerian vertical discretization schemes are referred to as “LGN” and “EUL”, respectively. Simulations with the standard hyperviscosity are denoted by “vis”, and those without viscosity by “inv”. Colored dots show the temperature RMSE calculated over all grid cells of the horizontal mesh and all levels of the vertical grid. Dashed lines are linear fits between log10(RMSE) and log10(Δt). The convergence rates are given in parenthesis. We note that the results in this figure were obtained without physics parameterization, but the errors are plotted against the physics‐dynamics coupling time step Δt for consistency with other figures. The entire 3‐D domain was included in the calculation of the RMSE.
Mentions: Four configurations of the SE dynamical core were tested which used different combinations of the vertical discretization methods (floating Lagrangian (“LGR”) versus Eulerian (“EUL”)) and the hyperviscosity setting (inviscid without diffusion (“inv”) versus standard diffusion (“vis”)). The convergence properties of these combinations are shown in Figure 2. The figure displays the temperature RMSE versus the process‐coupling time step Δt in a double‐logarithmic diagram. Recall that the dynamics time steps are shorter than Δt as shown in Table 1, but Δt is plotted here for consistency with other figures. The dashed lines are linear fits between the actual data points which are denoted by colored dots. The convergence rates are noted in parentheses.

View Article: PubMed Central - PubMed

ABSTRACT

This paper evaluates the numerical convergence of very short (1 h) simulations carried out with a spectral‐element (SE) configuration of the Community Atmosphere Model version 5 (CAM5). While the horizontal grid spacing is fixed at approximately 110 km, the process‐coupling time step is varied between 1800 and 1 s to reveal the convergence rate with respect to the temporal resolution. Special attention is paid to the behavior of the parameterized subgrid‐scale physics. First, a dynamical core test with reduced dynamics time steps is presented. The results demonstrate that the experimental setup is able to correctly assess the convergence rate of the discrete solutions to the adiabatic equations of atmospheric motion. Second, results from full‐physics CAM5 simulations with reduced physics and dynamics time steps are discussed. It is shown that the convergence rate is 0.4—considerably slower than the expected rate of 1.0. Sensitivity experiments indicate that, among the various subgrid‐scale physical parameterizations, the stratiform cloud schemes are associated with the largest time‐stepping errors, and are the primary cause of slow time step convergence. While the details of our findings are model specific, the general test procedure is applicable to any atmospheric general circulation model. The need for more accurate numerical treatments of physical parameterizations, especially the representation of stratiform clouds, is likely common in many models. The suggested test technique can help quantify the time‐stepping errors and identify the related model sensitivities.

No MeSH data available.


Related in: MedlinePlus