Limits...
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.


Related in: MedlinePlus

Schematic convergence pathways of three time stepping schemes. Curves B and C denote two schemes that have the same order of accuracy but different magnitudes of error. Line A represents a lower‐order scheme. Further details are discussed in section 1.
© Copyright Policy - creativeCommonsBy-nc-nd
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5016774&req=5

jame20146-fig-0001: Schematic convergence pathways of three time stepping schemes. Curves B and C denote two schemes that have the same order of accuracy but different magnitudes of error. Line A represents a lower‐order scheme. Further details are discussed in section 1.

Mentions: If the atmospheric model under consideration is a numerically consistent discretization of a well‐posed continuous problem, then the discretization error with respect to the reference solution is expected to level off as the time step is reduced to a sufficiently small value. This is schematically shown in Figure 1 by the blue and green curves which reach a lower bound related to, for example, the accumulation of rounding error discussed by Rosinski and Williamson [1997]. In practice, it is often unnecessary to seek a solution to this level of accuracy. The required time step size could easily produce a model that is too expensive to run from a computational viewpoint; hence an error tolerance can be defined through physical reasoning. Once the error of a particular solution falls below that tolerance (see open circles in Figure 1), a “physically reasonable convergence” is achieved, and the quality of the solution becomes practically equivalent to that of the reference solution. The choice of the tolerance depends on the physical quantity in question, and might vary for different scientific investigations. Our study focuses on the numerical convergence. Therefore, the tolerance is established as a concept but is not extensively discussed with respect to the physical flow characteristics.


Short ‐ term time step convergence in a climate model
Schematic convergence pathways of three time stepping schemes. Curves B and C denote two schemes that have the same order of accuracy but different magnitudes of error. Line A represents a lower‐order scheme. Further details are discussed in section 1.
© Copyright Policy - creativeCommonsBy-nc-nd
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5016774&req=5

jame20146-fig-0001: Schematic convergence pathways of three time stepping schemes. Curves B and C denote two schemes that have the same order of accuracy but different magnitudes of error. Line A represents a lower‐order scheme. Further details are discussed in section 1.
Mentions: If the atmospheric model under consideration is a numerically consistent discretization of a well‐posed continuous problem, then the discretization error with respect to the reference solution is expected to level off as the time step is reduced to a sufficiently small value. This is schematically shown in Figure 1 by the blue and green curves which reach a lower bound related to, for example, the accumulation of rounding error discussed by Rosinski and Williamson [1997]. In practice, it is often unnecessary to seek a solution to this level of accuracy. The required time step size could easily produce a model that is too expensive to run from a computational viewpoint; hence an error tolerance can be defined through physical reasoning. Once the error of a particular solution falls below that tolerance (see open circles in Figure 1), a “physically reasonable convergence” is achieved, and the quality of the solution becomes practically equivalent to that of the reference solution. The choice of the tolerance depends on the physical quantity in question, and might vary for different scientific investigations. Our study focuses on the numerical convergence. Therefore, the tolerance is established as a concept but is not extensively discussed with respect to the physical flow characteristics.

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