Model for Prediction Across Scales MPAS

1
Model for Prediction Across Scales (MPAS)

• Joe Klemp, Bill Skamarock (NCAR)
• Todd Ringler (Los Alamos National Laboratory)
• John Thuburn (University of Exeter, UK)

2
Future Weather/Climate Atmospheric Dynamic Core

• Problems with lat-lon coordinate for global
  models
• Pole singularities require special filtering
• Polar filters do not scale well on massively
  parallel computers
• Highly anisotropic grid cells at high latitudes

• Consideration of alternative spatial
  discretizations

Priority Requirements

• Efficient on existing and proposed supercomputer
  architectures
• Scales well on massively parallel computers
• Well suited for cloud (nonhydrostatic) to global
  scales
• Capability for local grid refinement and
  regional domains
• Conserves at least mass and scalar quantities

3
Why a Hexagonal Grid?
to circumvent the pole problem !
Grids designed to remove the pole singularity
icosahedral grid (hexagons)
cubed sphere
icosahedral grid (triangles)

• Finite-volume formulation
• Hexagonal grid is most isotropic (wave
  propagation).
• Pentagons are easier to handle than corners of
  cube.
• Hexagonal grid permits larger explicit time steps

4
Isotropy in Linear Advection Simulations
t 70,000 s, ?t 200 s, ?x 5 km
5
Accuracy and Isotropy of Second Order Diffusion

Normalized second order Laplacian
6
Why a C-Grid?
Since the 1960s, virtually all nonhydrostatic
cloud and mesoscale models have used a C-grid.
1-D wave equation
Linear gravity-wave dispersion
C-grid staggering
A-grid staggering
C grid
A grid
The C-grid provides twice the resolution of the A
grid, and avoids the parasitic mode
7
C-Grid - SWL Linear Stability Limits
Wave Propagation CFL limit (rel)
Advection CFL limit (rel)
Equivalent Grid Size
Rectangular Grid
Triangular Grid
Hexagonal Grid
8
Hexagonal C-Grid ProblemNon-Stationary
Geostrophic Mode
Traditional Coriolis velocity evaluation
9
Hexagonal C-Grid ProblemNon-Stationary
Geostrophic Mode
New Coriolis velocity evaluation (Thuburn, JCP)
10
Generalization for Irregular Hexagons
In discrete analogue of vorticity equation
(?t-f?a), the divergence ?a on the Delaunay
triangulation must be identical to the divergence
?A on the Voronoi hexagons used in the height
equation (ht-H?A)
where
divergence ?A in hexagon A
divergence ?a in triangle ABC
Construct tangential velocities from weighted sum
of (10) normal velocities on edges of adjacent
hexagons.
All weights w je depend only local area ratios
RAa, etc.
11
Shallow Water Test Case 2 Steady Zonal Flow
(Todd Ringler, LANL)
12
Shallow Water Test Case 2 Steady Zonal Flow
(Todd Ringler, LANL)
13
Shallow-Water Test Case 5 Flow over an Isolated
Mountain
Potential vorticity conserved to roundoff. Total
energy conserved to time-truncation error.
40962 cells, dx 120 km 2nd order
differencing RK4 time differencing
(Todd Ringler, LANL)
14
Limited-Area Cloud Model on Hexagonal C-Grid
Splitting Supercell at 2 hours
Finite-Volume Fluxes on Hexagonal C-Grid

• Research Progress
• Constructed a 3-D limited-area hexagonal-grid
  cloud model based on WRF/ARW numerics to evaluate
  performance.
• Documented that hexagonal-grid cloud simulations
  are at least as accurate and computationally more
  efficient than those on a conventional
  rectangular grid.

1 km Hexagonal Grid Simulation
15
3-D Supercell Simulation 500 m Horizontal Grid

Rectangular Grid
Hexagonal Grid
Vertical velocity contours at 1, 5, and 10 km
(c.i. 3 m/s)
30 m/s vertical velocity surface shaded in
red Rainwater surfaces shaded as transparent
shells Perturbation surface temperature shaded on
baseplane
16
Selective Grid Refinement
Adjustment of grid cells to specified density
function
(Michael Duda, MMM)

• Lili Ju (Univ. South Carolina)
• Max Gunzberger (FSU)
• Todd Ringler (LANL)

17
Selective Mesh Refinement Based on Terrain Height

spherical centroidal voronoi tessellation
(Michael Duda, MMM)
18
Summary

• We have solved the non-stationary
  geostrophic-mode problem for the irregular
  hexagonal C grid (for any Voronoi grid).
• The global hexagonal C-grid SW solver
• Accuracy similar to other state-of-the-art
  solvers.
• Conserves PV to machine roundoff.
• Conserves total energy to time-truncation error.
• Robust - explicit filtering not needed in SW test
  cases 2 and 5, and it is stable for long
  integrations.
• Unstructured grid permits selective grid
  refinement
• The regional hexagonal C-grid cloud model
• Accuracy similar to state-of-the-art rectangular
  grid models.
• Slightly greater efficiency compared to
  rectangular grid models.
• Future Nonhydrostatic global hexagonal C-grid
  solver.