Mass Coordinate WRF Dynamical Core - Eulerian geometric height coordinate (z) core (in framework, parallel, tested in idealized, NWP applications) - Eulerian mass coordinate (hydrostatic pressure) core (in framework, parallel, tested in idealized, NWP applications) - Semi-Lagrangian hybrid coordinate core (under development, see Jim Purser’s talk) - Eulerian hybrid coordinate core (under development) WRF dynamical core development efforts (Working Group 1) four cores have been or are being developed

Conservative variables: Inviscid, 2-D equations in Cartesian coordinates Flux-Form Equations in Height Coordinates where we have removed a hydrostatic base state state equation

Flux-Form Equations in Mass Coordinate Inviscid, 2-D equations without rotation: Diagnostic relations:

Mass and Height Cores - Comparison - Both cores solve the unapproximated fully compressible nonhydrostatic Euler equations. - Both cores use the same numerical integration methods: 3 rd order Runge-Kutta time integration 2 nd -5 th order advection operators C-grid Split – explicit acoustic/gravity wave integration - The two cores produce nearly identical (and equally accurate) solutions in the idealized test cases and for several months of daily 48h forecasts (using the same physics). Both are equally efficient.

2-D Mountain Wave Simulation a = 1 km, dx = 200 ma = 100 km, dx = 20 km Mass Coordinate Height Coordinate

5 min 10 min15 min Comparison of Gravity Current Simulations Height Coordinate Mass Coordinate

Comparison of Height and Mass Coordinates

Supercell Simulations, z = 500 m, t = 1.5 h vertical velocity (c.i.=2 m/s), rainwater (shaded, 1, 3, and 5 g/kg) Mass Coordinate Height coordinate  x = 1 km,  t= 10 s

Baroclinic Wave Simulation – Surface Fields Pressure (solid, c.i.= 4 mb), temperature (dashed, c.i.= 4K), cloud field (shaded) Mass Coordinate, 4days 12 h Height Coordinate, 4 days 6 h  x = 100 km,  t= 10 min

Mass and Height Cores - Differences Upper boundary condition: - Height coordinate core uses a rigid lid (w = 0) condition or uses a radiation condition (w /= 0) - Mass coordinate core uses a constant or specified pressure, in both cases this upper surface is a material surface. Consequences – when the atmosphere is heated the pressure increases in the height coordinate model, the atmosphere expands in the mass coordinate model; the latter is physically more realistic. caveat: a radiation condition is still needed to prevent reflection of vertically propagating gravity waves.

Mass and Height Cores - Differences Hydrostatic option: The nonhydrostatic mass coordinate solver reverts to a standard sigma-coordinate hydrostatic solver with a simple switch. Efficient integration of the gravity wave terms in the hydrostatic model is retained (via a split-explicit integration). There is no simple hydrostatic option for the height coordinate core.

The Mass Coordinate WRF Core – It’s Here!!! There is little difference between the cores with respect running the cores and using the results. We are supporting the mass coordinate core as the dynamics solver for community use. Nesting and 3DVAR will appear for the mass-coordinate solver; these capabilities will not be developed for the height coordinate solver. Message: USE THE MASS COORDINATE MODEL