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Short ‐ term time step convergence in a climate model

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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.

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Similar to Figure 2 but for moist simulations conducted with subgrid‐scale physics parameterization. Dots: average log10(RMSE) of six ensemble simulations. Vertical bars: ensemble standard deviation of log10(RMSE). “Full Model”: standard CAM5‐SE configuration with real‐world land‐sea mask and topography. All other simulations: SE dynamical core (Dyn) plus one parameterization in an aqua‐planet setup. “St Cld”: stratiform cloud macrophysics and microphysics; “Sh Cu” and “Dp Cu”: shallow and deep cumulus convection; “Rad”: radiation. “CAM5 mac+mic” in Figure 3b and “Dyn + St Cld” in Figure 3a refer to the same group of simulations. “CAM5 mac+mic, no precip”: similar to “CAM5 mac+mic”, but without the formation and sedimentation of rain and snow. “CAM5 mac only”: CAM5 cloud macrophysics scheme was switched on but the stratiform cloud microphysics was turned off. “CAM4 mac+mic”: stratiform cloud parameterizations from CAM4. “Smpl Cond”: simplified representation of large‐scale condensation following Reed and Jablonowski [2012]. The entire 3‐D domain was included in the calculation of the RMSE.
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jame20146-fig-0003: Similar to Figure 2 but for moist simulations conducted with subgrid‐scale physics parameterization. Dots: average log10(RMSE) of six ensemble simulations. Vertical bars: ensemble standard deviation of log10(RMSE). “Full Model”: standard CAM5‐SE configuration with real‐world land‐sea mask and topography. All other simulations: SE dynamical core (Dyn) plus one parameterization in an aqua‐planet setup. “St Cld”: stratiform cloud macrophysics and microphysics; “Sh Cu” and “Dp Cu”: shallow and deep cumulus convection; “Rad”: radiation. “CAM5 mac+mic” in Figure 3b and “Dyn + St Cld” in Figure 3a refer to the same group of simulations. “CAM5 mac+mic, no precip”: similar to “CAM5 mac+mic”, but without the formation and sedimentation of rain and snow. “CAM5 mac only”: CAM5 cloud macrophysics scheme was switched on but the stratiform cloud microphysics was turned off. “CAM4 mac+mic”: stratiform cloud parameterizations from CAM4. “Smpl Cond”: simplified representation of large‐scale condensation following Reed and Jablonowski [2012]. The entire 3‐D domain was included in the calculation of the RMSE.

Mentions: The added complexity of parameterized subgrid‐scale physics may lead to larger uncertainties in the estimated convergence rate. Therefore, ensemble simulations with six members were performed using independent atmospheric states for the initial conditions. The ensemble‐mean temperature error and the standard deviation of the six members are shown in Figure 3 with thick dots and vertical bars, respectively.


Short ‐ term time step convergence in a climate model
Similar to Figure 2 but for moist simulations conducted with subgrid‐scale physics parameterization. Dots: average log10(RMSE) of six ensemble simulations. Vertical bars: ensemble standard deviation of log10(RMSE). “Full Model”: standard CAM5‐SE configuration with real‐world land‐sea mask and topography. All other simulations: SE dynamical core (Dyn) plus one parameterization in an aqua‐planet setup. “St Cld”: stratiform cloud macrophysics and microphysics; “Sh Cu” and “Dp Cu”: shallow and deep cumulus convection; “Rad”: radiation. “CAM5 mac+mic” in Figure 3b and “Dyn + St Cld” in Figure 3a refer to the same group of simulations. “CAM5 mac+mic, no precip”: similar to “CAM5 mac+mic”, but without the formation and sedimentation of rain and snow. “CAM5 mac only”: CAM5 cloud macrophysics scheme was switched on but the stratiform cloud microphysics was turned off. “CAM4 mac+mic”: stratiform cloud parameterizations from CAM4. “Smpl Cond”: simplified representation of large‐scale condensation following Reed and Jablonowski [2012]. The entire 3‐D domain was included in the calculation of the RMSE.
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getmorefigures.php?uid=PMC5016774&req=5

jame20146-fig-0003: Similar to Figure 2 but for moist simulations conducted with subgrid‐scale physics parameterization. Dots: average log10(RMSE) of six ensemble simulations. Vertical bars: ensemble standard deviation of log10(RMSE). “Full Model”: standard CAM5‐SE configuration with real‐world land‐sea mask and topography. All other simulations: SE dynamical core (Dyn) plus one parameterization in an aqua‐planet setup. “St Cld”: stratiform cloud macrophysics and microphysics; “Sh Cu” and “Dp Cu”: shallow and deep cumulus convection; “Rad”: radiation. “CAM5 mac+mic” in Figure 3b and “Dyn + St Cld” in Figure 3a refer to the same group of simulations. “CAM5 mac+mic, no precip”: similar to “CAM5 mac+mic”, but without the formation and sedimentation of rain and snow. “CAM5 mac only”: CAM5 cloud macrophysics scheme was switched on but the stratiform cloud microphysics was turned off. “CAM4 mac+mic”: stratiform cloud parameterizations from CAM4. “Smpl Cond”: simplified representation of large‐scale condensation following Reed and Jablonowski [2012]. The entire 3‐D domain was included in the calculation of the RMSE.
Mentions: The added complexity of parameterized subgrid‐scale physics may lead to larger uncertainties in the estimated convergence rate. Therefore, ensemble simulations with six members were performed using independent atmospheric states for the initial conditions. The ensemble‐mean temperature error and the standard deviation of the six members are shown in Figure 3 with thick dots and vertical bars, respectively.

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