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

0'

''

'

zW

xU

t

QzW

xU

t

zWw

xUwg

zp

tW

zWu

xUufV

xp

tU

,,, wWvVuUConservative variables:

Inviscid, 2-Dequations inCartesiancoordinates

Flux-Form Equations in Height Coordinates

where we have removed a hydrostatic base state

gzp

0pRpstate

equation

Flux-Form Equations in Mass Coordinate

,,

0

0pRp

gwdtd

xU

t

QxU

t

wxUwpg

tW

uxUu

xp

xp

tUInviscid, 2-D

equations without rotation:

Diagnosticrelations:

Mass and Height Cores - Comparison

- Both cores solve the unapproximated fully compressible nonhydrostatic Euler equations.

- Both cores use the same numerical integration methods:

3rd order Runge-Kutta time integration 2nd-5th 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 m a = 100 km, dx = 20 km

Mass CoordinateHeight Coordinate

5 min 10 min 15 min

Comparison of Gravity Current Simulations

HeightCoordinate

MassCoordinate

Comparison of Height and Mass Coordinates

Supercell Simulations, z = 500 m, t = 1.5 hvertical velocity (c.i.=2 m/s), rainwater (shaded, 1, 3, and 5 g/kg)

Mass Coordinate Height coordinatex = 1 km, t= 10 s

Baroclinic Wave Simulation – Surface FieldsPressure (solid, c.i.= 4 mb), temperature (dashed, c.i.= 4K), cloud field (shaded)

Mass Coordinate, 4days 12 h Height Coordinate, 4 days 6 hx = 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 respectrunning 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 theheight coordinate solver.

Message: USE THE MASS COORDINATE MODEL