WV being half the density of air ie twice as buoayant, you may see the power of its uplift to and past the points of radiative escape. Points we ponder. Brett

]]>Yes SOD, another interesting paper. These papers mostly deal with the time step which is just one element of the numerical error. On coarse grids, spatial discretization errors are quite large. You have posted on some of these issues and how much higher resolution produces different answers.

]]>What is an aquaplanet simulation?

In an aqua-planet the earth is covered with water and has no mountains. The sea surface temperature (SST) is specied, usually with rather simple geometries such as zonal symmetry. The ‘correct’ solutions of aqua-planet tests are not known.

However, it is thought that aqua-planet studies might help us gain insight into model differences, understand physical processes in individual models, understand the impact of changing parametrizations and dynamical cores, and understand the interaction between dynamical cores and parametrization packages. There is a rich history of aqua-planet experiments, from which results relevant to this paper are discussed below.

They found that running different “mechanisms” for the same parameterizations produced quite different precipitation results. In investigating further it appeared that the time step was the key change.

Their conclusion:

]]>When running the Neale and Hoskins (2000a) standard aqua-planet test suite with two versions of the CCM3, which differed in the formulation of the dynamical cores, we found a strong sensitivity in the morphology of the time averaged, zonal averaged precipitation.

The two dynamical cores were candidates for the successor model to CCM3; one was Eulerian and the other semi-Lagrangian.

They were each configured as proposed for climate simulation application, and believed to be of comparable accuracy.

The major difference was computational efficiency. In general, simulations with the Eulerian core formed a narrow single precipitation peak centred on the equator, while those with the semi-Lagrangian core produced more precipitation farther from the equator accompanied by a double peak straddling the equator with a minimum centred on the equator..

..We do not know which simulation is ‘correct’. Although a single peak forms with smaller time steps, the simulations do not converge with the smallest time step considered here. The maximum precipitation rate at the equator continues to increase..

..The significance of the time truncation error of parametrizations deserves further consideration in AGCMs forced by real-world conditions.

For any who haven’t seen it here’s the reference mentioned in the previous comment. It’s an interesting paper because it is a phenomena that has been largely ignored previously and since. 😦

It is the steady state version of the phenomena documented in Teixiera et al SOD quotes from about.

https://arc.aiaa.org/doi/abs/10.2514/1.J052676?journalCode=aiaaj

]]>That’s all I could find as well SOD. I did fine what appears to be his Ph. D. thesis that looked interesting. It may be more along the lines of your interest in clouds.

]]>Yes, It’s an interesting paper. It continues to surprise me how scientists ignore the well known multiple solution characteristic of nonlinear systems. It was totally ignored in CFD until a paper from the GGNS team on multiple solutions of RANS. Google “numerical evidence of multiple solutions for the Reynolds’ Averaged NAvier-Stokes Equations.” This paper shows that particularly on coarser grids, there can be quite a few of these multiple solutions. And unsurprisingly, this paper which seems very important to me has seen very little followup. There is a lot of focus on how to “tweak” the simulations to get the “right” solution and just ignoring those combinations of parameters that give a “wrong” solution. The issue here is a cultural belief that “if I run the code right, I will get the right answer.” These cultural prejudices are virtually impossible to address in my experience.

]]>Cheedela et al. 2010 is referenced but all I can find (it looks like it’s the right paper) is an abstract:

]]>One of the papers cited is – Time Step Sensitivity of Nonlinear Atmospheric Models: Numerical Convergence, Truncation Error Growth, and Ensemble Design, Teixeira et al 2007.

On the Lorenz equations:

]]>Figure 3a shows the evolution of X for r =19 for three different time steps (10

^{-2}, 10^{-3}, and 10^{-4}LTU).In this regime the solutions exhibit what is often referred to as transient chaotic behavior (Strogatz 1994), but after some time all solutions converge to a stable fixed point.

Depending on the time step used to integrate the equations, the values for the fixed points can be different, which means that the climate of the model is sensitive to the time step.

In this particular case, the solution obtained with 0.01 LTU converges to a positive fixed point while the other two solutions converge to a negative value.

To conclude the analysis of the sensitivity to parameter r, Fig. 3b shows the time evolution (with r =21.3) of X for three different time steps. For time steps 0.01 LTU and 0.0001 LTU the solution ceases to have a chaotic behavior and starts converging to a stable fixed point.

However, for 0.001 LTU the solution stays chaotic, which shows that different time steps may not only lead to uncertainty in the predictions after some time, but may also lead to fundamentally different regimes of the solution.

These results suggest that time steps may have an important impact in the statistics of climate models in the sense that something relatively similar may happen to more complex and realistic models of the climate system for time steps and parameter values that are currently considered to be reasonable.