em_hill2d_x at dx=400m — spurious upper-domain structure not present in analytic solution

[Ojesutofunmi]

Hello WRF community,
I am running the em_hill2d_x idealized case at dx=400m (reduced from the standard dx=2km) for a model comparison study, and I am having difficulty reproducing the analytic solution cleanly at the higher resolution. The link to the test case: NWPdesign. Attached is the plot that compares the w′ field at dx=2km and dx=400m against the analytic solution.
Setup:

• WRF 4.6.0, em_hill2d_x
• dx=400m, dt=4s, e_we = 201, ztop = 30 km
• damp_opt=3, zdamp=10km, dampcoef = 0.1
• khdif=0, kvdif=0
• diff_opt=2, hybrid_opt=2
• periodic_x/y boundaries
• Run duration: 5 hours

Namelist:
&domains
time_step = 4,
time_step_fract_num = 0,
time_step_fract_den = 1,
max_dom = 1,
s_we = 1,
e_we = 201,
s_sn = 1,
e_sn = 3,
s_vert = 1,
e_vert = 121,
dx = 400,
dy = 400,
ztop = 30000.,
/
&physics
mp_physics = 0,
ra_lw_physics = 0,
ra_sw_physics = 0,
radt = 0,
sf_sfclay_physics = 0,
sf_surface_physics = 0,
bl_pbl_physics = 0,
bldt = 0,
cu_physics = 0,
cudt = 0,
/
&fdda
/
&dynamics
hybrid_opt = 2,
rk_ord = 3,
diff_opt = 2,
km_opt = 1,
damp_opt = 3,
zdamp = 10000.,
dampcoef = .1,
khdif = 0,
kvdif = 0,
smdiv = 0.1,
emdiv = 0.01,
epssm = 0.1,
time_step_sound = 6,
h_mom_adv_order = 5,
v_mom_adv_order = 3,
h_sca_adv_order = 5,
v_sca_adv_order = 3,
non_hydrostatic = .true.,
mix_full_fields = .false.,
moist_adv_opt = 0,
scalar_adv_opt = 0,
/
&bdy_control
periodic_x = .true.,
periodic_y = .true.,
symmetric_xs = .false.,
symmetric_xe = .false.,
symmetric_ys = .false.,
symmetric_ye = .false.,
open_xs = .false.,
open_xe = .false.,
open_ys = .false.,
open_ye = .false.,
/
&grib2
/
&namelist_quilt
nio_tasks_per_group = 0,
nio_groups = 1,
/
&ideal
ideal_case = 1
/
Problem: At dx = 2 km, the w′ field matches the analytic linear hydrostatic solution well. At dx=400 m with the same basic configuration, the upper domain (above ~7km) develops a spurious large-scale structure that does not exist in the analytic solution. This persists across many configurations tested.

What I have tried:

• diff_opt = 1, 2, 3
• e_vert = 121, 241, 301
• zdamp = 10000–15000m
• khdif = 0–10, kvdif = 0–50
• dampcoef = 0.1–0.2
• smdiv = 0.01–0.2
• diff_6th_opt = 2, diff_6th_factor = 0.12 (tested, did not resolve the issue)

None of these produced a clean match to the analytic solution at dx=400m.

Question: Has anyone successfully run em_hill2d_x at dx = 400 m or finer and obtained a clean w′ field that matches the analytical solution? Is there a recommended namelist configuration for this resolution?
Thank you in advance.

Note on attachments: I was unable to attach the comparison plot due to a temporary upload issue on the forum ("temporary directory missing"). I am happy to share the images directly if anyone is willing to assist: please feel free to reply or send a private message, and I will send them over.

 

[Ming Chen]

I believe you can change the resolution to a smaller value. However, the issue is not that simple as just change the grid size.
First, the domain physical size is determined based on the grid size. Second, the terrain height is hard-coded, and I am not sure whether it should be modified for a smaller domain as in your case. Third, the dynamic options may not work well for the resolution of 400m. This resolution is not high enough for LES, yet it is not coarse enough for the application of various schemes.
The above comments are just my personal opinions. But I don't have many experiences on this topic. Please refer to the literature for more information.