1. 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.

2. The Need for Test Cases
Test for the correctness of coding, and the appropriateness of approximations (anelasticity, linearizations in the continuous or discrete equations, etc.).
Test robustness, accuracy, and efficiency of the solver.
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

3. Guiding Principles
Tests should be easy to configure (b.c’s, initializations).
Tests should be easy to evaluate (analytical solutions, converged numerical solutions, obvious solution features, simple diagnostics).
Tests should require only minimal physics (dissipation, very simple moist physics).
Tests should test something in the solver.
Test set should be a minimal set.

4. Proposed Test Set Adiabatic flow with no terrain
Inertia gravity waves in a periodic channel
Density current
Adiabatic flow with terrain
Resting atmosphere
Potential flow over a mountain
2D mountain waves – hydrostatic and nonhydrostatic,
linear and nonlinear
3D mountain waves
Schaer (MWR 2002; Klemp et al 2003) mountain wave test
Moist Convection (squall-lines?, supercells?)

5. 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)

6. Density Current Reference Solution (50 meter grid)
Potential Temperature (c.i. = 1 K) 4 3
height (km) 2 1 3 6 9 12 15 18
horizontal distance (km)

7. Density Current Test 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)

8. Density Current Test 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)

9. WRF-mass model

10. Density Current Verification
Density current speed (location at end time).
Minima and maxima for momentum, temperature.
Eddy structure.
Symmetry (for translating solution; U > 0).
What Does This Test in a Model?
Coding (time integration, nonlinear terms).
Nonlinear behavior.
Efficiency and robustness
Different timesteps, spatial resolution
Translation

11. Shaer Test Case (MWR 2002; Klemp et al 2003)
Linear Analytic Solution
where

12. 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

13. 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

14. MC2 simulation from
MAP case IOP2B
(from Benoit et al 2002)
MC2 with original
Galchen coordinate
transformation.
MC2 with SL calculation of W and with SLEVE vertical coordinate
(Schar et al 2002)

15. Shaer Test Case (MWR 2002; Klemp et al 2003)
Verification:
Solution structure and amplitude
What Does This Test in a Model
Metric 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

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

17. Supercell simulation, vertical velocity and rainwater
WRF-mass model, time = 1.5 h, z = 1500 m
domain – (x,y,z) = (90,90,20) km
Uni-directional shear; x,y periodic boundaries

18. time =1.5 h, z = 1500 m

20. 2D squall line simulation

21. Proposed Test Set Adiabatic flow with no terrain
Inertia gravity waves in a periodic channel
Density current
Adiabatic flow with terrain
Resting atmosphere
Potential flow over a mountain
2D mountain waves – hydrostatic and nonhydrostatic,
linear and nonlinear
3D mountain waves
Schaer (MWR 2002; Klemp et al 2003) mountain wave test
Moist Convection (squall-lines?, supercells?)