Horizontal Mesh

Omega uses the MPAS mesh specification. The names of the mesh variables have been retained, with the caveat that they now begin with a capital letter (e.g. angleEdge becomes AngleEdge).

The Mesh class is meant to be a container for all mesh variables local to a decomposed sub-domain that can be easily passed among the dycore routines. It depends on a given Decomp and reproduces the cell/edge/vertex totals and connectivity information from that class. The Mesh class also creates parallel I/O decompositions that are used to read in the additional mesh variables, which are not required for Decomp.

Currently, the Mesh class reads in every field required by the MPAS mesh specification except those read by Decomp. The input contents are defined by the HorzMeshIn FieldGroup. Refer to the specification for the definition, units, and dimensions of each field.

These are all read using the input IOStream HorzMeshIn

  IOStreams:
    HorzMeshIn:
      UsePointerFile: false
      Filename: OmegaMesh.nc
      Mode: read
      Precision: double
      Freq: 1
      FreqUnits: OnStartup
      UseStartEnd: false
      Contents:
        - HorzMeshIn

Only the Filename should be changed by the user to point to the relevant input mesh file. The mesh Filename is sometimes overridden by the driver routine in the case of unit tests using an optional argument to the decomposition.

In addition, some mesh metadata are read from the file and stored as mesh variables. These include OnSphere (or on_a_sphere for backcompatibility), IsPeriodic (is_periodic), SphereRadius (sphere_radius), XPeriod (x_period), and YPeriod (y_period). The two flags OnSphere and IsPeriodic are stored as YES/NO strings in the metadata but as boolean flags in the code. For a spherical mesh, SphereRadius must match the Earth radius from the Physical Constants Dictionary (REarth in GlobalConstants.h) to a relative tolerance of \(10^{-8}\); the model aborts otherwise. See the MPAS mesh specification for how to bring older meshes into compliance.

In the future, the Mesh class will optionally compute internally those fields the specification marks as could be computed internally — the areas, lengths, angles, and weights needed for the TRiSK discretization.

Horizontal mixing mesh scaling

Omega scales horizontal viscosity and diffusivity with the local mesh size. This scaling is enabled by default and is controlled by the following configuration option:

  HorzMesh:
    MeshScalingEnable: true

The reference width is the global median cell width, computed during mesh initialization. Each cell’s width is defined as the diameter of a circle with the same area as the cell.

At each edge, an effective cell width is computed from the mean area of the two adjacent cells. The Laplacian mixing coefficient is multiplied by the ratio of this width to the reference width, and the biharmonic mixing coefficient by the cube of that ratio. The parameters ViscDel2, ViscDel4, EddyDiff2 and EddyDiff4 therefore specify the mixing coefficients at the median resolution. Their values may need adjustment when changing to a mesh with a different median cell width.

On a mesh with equal cell areas, both scaling factors are one. Setting MeshScalingEnable to false also sets both factors to one, giving spatially uniform mixing coefficients.

The initialization log reports whether mesh scaling is enabled, the median cell width and the range of both scaling factors over interior edges.

MPAS-Ocean in E3SM references its mixing coefficients to the finest cells of the mesh, where its scaling factors are one, rather than to the median cell. To reproduce the MPAS-Ocean mixing on a given mesh, multiply the MPAS-Ocean Laplacian coefficients by \(W_{med}/W_{ref}\) and the biharmonic coefficients by \((W_{med}/W_{ref})^3\). Here \(W_{med}\) is the median cell width and \(W_{ref}\) is the nominal finest resolution of the mesh (for example, 30 km for EC30to60E2r2). The table below lists the converted viscosities for some E3SM meshes.

Mesh	\(W_{med}\) (km)	\(W_{ref}\) (km)	Parameter	Omega	MPAS-Ocean
EC30to60E2r2	35.92	30.00	ViscDel2 (m\(^2\)/s)	1197	1000
			ViscDel4 (m\(^4\)/s)	2.06e11	1.20e11
RRS18to6v3	8.77	6.00	ViscDel4 (m\(^4\)/s)	9.99e9	3.20e9
RRSwISC6to18E3r5	8.48	6.00	ViscDel4 (m\(^4\)/s)	9.03e9	3.20e9