Standardized Test Set for Nonhydrostatic Dynamical Cores of NWP Models

Bill Skamarock (NCAR), Jim Doyle (ONR), Peter Clark, Nigel Wood (MetOffice)

Objective: Compile a set of test cases to verify the correctness and examine the robustness of nonhydrostatic solvers (not full NWP models). Publish this test set (journal article, web page, etc.) to facilitate community use.

Today: Propose a test set, invite community input – comments, additions, deletions, etc.

The Need for Test Cases

1. Test for the correctness of coding, and the appropriateness of approximations (anelasticity, linearizations in the continuous or discrete equations, etc.).

2. Test robustness, accuracy, and efficiency of the solver.

3. Documentation:

• What solver components are tested by a particular test?

• Solution: analytical, numerically converged, subjective?

• Setup of tests and interpretation of results

• Fine points and issues

Guiding Principles

1. Tests should be easy to configure (b.c’s, initializations).

2. Tests should be easy to evaluate (analytical solutions, converged numerical solutions, obvious solution features, simple diagnostics).

3. Tests should require only minimal physics (dissipation, very simple moist physics).

4. Tests should test something in the solver.

5. Test set should be a minimal set.

Proposed Test Set

Adiabatic flow with no terrain

Inertia gravity waves in a periodic channelDensity current

Adiabatic flow with terrain

Resting atmosphere

2D mountain waves – hydrostatic and nonhydrostatic,linear and nonlinear

Potential flow over a mountain

3D mountain wavesSchaer (MWR 2002; Klemp et al 2003) mountain wave test

Moist Convection (squall-lines?, supercells?)

Density Current Test Case (Straka et al, IJNMF, 1993)

2D channel (x , z ; 51.2 x 6.4 km)Initial state: theta = 300 K (neutral) + perturbation (max = 16.2 K)Eddy viscosity = 75 m**2/s (constant)

0 3 6 9 12 15 180

1

2

3

4

horizontal distance (km)

heig

ht (

km)

Density Current Reference Solution (50 meter grid)Potential Temperature (c.i. = 1 K)

Density CurrentTest Case

WRF-mass model,50 m solution (reference)100, 200 and 400 m solns.

Advection:5th order (horizontal)3rd order (vertical)RK3 time integration

Timesteps:1 s (50 m)1 s (100 m) (stab > 3 s)2 s (200 m)4 s (400 m)

Density CurrentTest Case

WRF-mass model,50 m solution (reference)100, 200 and 400 m solns.

Advection:2nd order (horizontal)2nd order (vertical)RK3 time integration

Timesteps:1 s (50 m)1 s (100 m) (stab > 3 s)2 s (200 m)4 s (400 m)

WRF-mass model

Density Current Verification

1. Density current speed (location at end time).

2. Minima and maxima for momentum, temperature.

3. Eddy structure.

4. Symmetry (for translating solution; U > 0).

What Does This Test in a Model?

1. Coding (time integration, nonlinear terms).

2. Nonlinear behavior.

3. Efficiency and robustness

• Different timesteps, spatial resolution

• Translation

x

a

xHxh 2

2

2

cosexp)(

Shaer Test Case (MWR 2002; Klemp et al 2003)

1

1

10

01.0

5000

4000

250

msU

sN

metersa

meters

metersH

where Linear Analytic Solution

Schaer Test Case

Leapfrog model

dx = 500 m, dz = 300 m

4th order for advection and metric term for omega

4th order advection and 2nd order metric term for omega

Schaer Test Case

COAMPS

dx = 1000 m, dz = 300 m

4th order advection and metric term for omega

4th order advection and 2nd order metric term for omega

MC2 simulation from MAP case IOP2B(from Benoit et al 2002)

MC2 with originalGalchen coordinatetransformation.

MC2 with SL calculation of W and with SLEVE vertical coordinate(Schar et al 2002)

Shaer Test Case (MWR 2002; Klemp et al 2003)

Verification:Solution structure and amplitude

What Does This Test in a ModelMetric terms – pressure gradients, divergence operators and advection (comp of omega)Steady-state solution: not a test of time integration methods (except in SL models).

Special Needs?

Boundary conditions – wave radiation in horizontal, absorbing layer aloft

Convection: Supercell

Tests full nonlinear model.Needs: moist physics (Kessler)Will work with periodic x,y boundaries, constant 2nd order dissipation

Supercell simulation, vertical velocity and rainwaterWRF-mass model, time = 1.5 h, z = 1500 m

domain – (x,y,z) = (90,90,20) kmUni-directional shear; x,y periodic boundaries

time =1.5 h, z = 1500 m

2D squall line simulation

Proposed Test Set

Adiabatic flow with no terrain

Inertia gravity waves in a periodic channelDensity current

Adiabatic flow with terrain

Resting atmosphere

2D mountain waves – hydrostatic and nonhydrostatic,linear and nonlinear

Potential flow over a mountain

3D mountain wavesSchaer (MWR 2002; Klemp et al 2003) mountain wave test

Moist Convection (squall-lines?, supercells?)