ATM Grid Resolution Summary

Atmosphere Grid Trivia. Note about the "NE" variable.  This is the name of a Fortran variable and also used in CIME XML files to refer to cubed sphere grids.  It is meaningless jargon to most people.  For written documents we recommend referring to grids by their resolution in km.  For the quasi-uniform cubed-sphere grid, average grid spacing at the equator is a good measure of the resolutions.

For cubed sphere grids (CAM-SE Grid Overview ), NE is the Number of spectral Elements along each cube face.  Thus the total number of elements N = 6 NE^2.

For regionally refined grids, internally in the code NE=0 and the number of elements N is read in from the Exodus RRM mesh file.  RRM grids can be any quadrilateral tiling of the sphere and may not be based on cubed-sphere grids.  

For any spectral element grid with N elements, the number of unique points (physics columns) is (np-1)^2 * N + 2, where each element contains a np x np tensor product of  Gauss-Lobatto points.  

What is the “resolution” of E3SM when using the physgrid (i.e. pg2)?

For example, a ne256pg2 case has dynamics on the “np4” grid (approx. grid spacing of dx~13km) and physics on the “pg2” grid (approx. grid spacing of dx~19.5km). So the grid spacing of physics is roughly 1.5x that of dynamics. The effective resolution of the dynamics is often assumed to be 3*dx or 4*dx because the scales between 3*dx and 1*dx (i.e. wave lengths from 6*dx to 2*dx) are heavily dissipated by the model and thus do not contain much energy. Thus, the effective resolution of ne256np4 is dx~39km at best.

The E3SM “pg2” physics grid is designed to exploit the fact that dynamics doesn’t contain much information at the 1*dx to 3*dx scales. The dynamics will update the state on the np4 grid, which is then mapped to the pg2 grid. The physics tendencies are then computed on the pg2 grid and interpolated back to the np4 dynamics grid before being applied to update the np4 state variables. Extensive testing has shown that we get nearly the same result if we run the physics on the “pg2” grid, as we would if we ran the physics on the “np4” grid (see Hannah et al. 2021).

Thus, the “actual” resolution of the model is a tricky and nuanced topic, but we often need to shorthand to colloquially describe the resolution of the model for context when comparing to other models. There are three schools of thought on how we should navigate this.

#1 - Resolution => smallest grid spacing (i.e. np4)

Using the smallest grid spacing is consistent with how most people refer to other models that use a single grid. The notion of “effective resolution” is already somewhat of an ambiguous concept - so this approach argues that the smallest grid spacing is a more “concrete” measure of the “resolution”. The recipient of this information is free to form their own idea about what the effective resolution really is.

#2 - Resolution => largest grid spacing (i.e. pg2)

Despite the importance of the dynamics, most users of the model only interact with the output or surface coupling tendencies, which happen to be on the pg2 grid. We often refer to modern high-resolution grids based on what we think they can represent, such as “storm resolving” or “cloud resolving” or “cloud permitting”. When using the pg2 grid the circulations that make up an updraft are represented on the dynamics grid - but the actual feature of interest whose existence strongly relies on microphysical processes (i.e. cloud/storm) is arguably only represented by the physics grid. Therefore, this approach of references the largest grid spacing provides a more intuitive sense of the scale that convective processes are being represented

#3 - Resolution => effective resolution of dynamics

The third approach is to recognize that in reality neither np4 or pg2 grid can actual represent the features of interest due to the roll off of the power spectrum. This is often defined as the scales in the KE power spectra where the energy starts to roll off from the expected k^-5/3 scaling. (e.g. see https://e3sm.atlassian.net/wiki/spaces/NGDNA/pages/2269971049) But this rolloff point is computed differently by different people and thus hard to compare models via their reported effective resolution. This is the least popular option because it involves a subjective choice of how the effective resolution is determined. So one person’s 39km resolution is another persons 52km resolution. Also, it is rare to hear a model with a single grid described by its effective resolution for the same reason, and comparing effective resolutions across different types of grids (i.e. spectral vs finite volume) adds to the ambiguity of the comparison.

What resolution is “comparable” to a given pg2 grid?

The above discussion is focused more around the semantics involved with describing the specific grid configuration of the atmosphere component of E3SM (EAM). But what if you want to run another model such as MPAS-A or WRF or CESM and use a “comparable” grid spacing to a given E3SM case?

The best approach for this scenario is to use the dynamics grid spacing. From Hannah et al. (2021) we know that the model solution when using pg2 is comparable to what we get when physics calculations are done on the np4 grid (i.e. ne30pg2 vs ne30np4), which is why the cost savings from using pg2 are so appealing. But for any other model that does not use separate grids for dynamics and physics it would not make sense to match the spacing of the pg2 grid because this would unfairly degrade the resolved scales of the dynamics. Thus, the optimal strategy is to match the approximate grid spacing of the np4 grid when comparing between models.

*All reported resolutions are average distances based on a third order cubed sphere spectral element domain using 4x4 Gauss-Labotto points (np=4).

**Standard vertical resolution for E3SM is 72 vertical levels.

For cubed sphere grids with np=4:

For quick reference, one RRM grid being tested ne0np4_northamericax4v1 has 14454 elements and 130088 physics columns.

Now that we are moving to the physgrid (i.e. pg2) it is useful to have a table that compares various aspects of typical pg2 and np4 grids. 

For the formulas, note that NP is normally 4 (ex. ne30np4) and NPG is normally 2 (ex. ne30pg2)