Test Case 3: Squall line

Description

Squall lines are important phenomena associated with convective activity in storms. This test mimics the formation and movement of a squall line by initializing a line of warm temperature bubbles along a line of constant longitude. This test has similarities to the supercell test from the previous DCMIP in 2016 (Zarzycki et al. 2019) but uses many warm bubbles instead of a single 'supercell' (see below). The supercell test from DCMIP 2016 was primarily based upon the work of Klemp et al. (2015).

Figure 1: Initial bubble perturbation for small Earth scale factor of X=60, initialized on a 1-degree cubed sphere grid. This configuration uses 9 bubbles (pert_num/n_bub), a horizontal half width of 5 km (r_h/pert_rh), a vertical half width of 1.5 km (r_z/pert_rz), 10 km spacing between each bubble (delta s/pert_spacing).

A key feature of this test case is that it focuses on nonhydrostatic dynamics. Hence, nonhydrostatic versions of each dycore are used: the StormSPEED branch for SE, the nonhydrostatic solver for FV3, and MPAS, which is already nonhydrostatic. A small Earth is used to ensure a nonhydrostatic regime, where the horizontal length scale is comparable to the vertical length scale. This is not the case for 1 or 0.5 degree resolutions on a regular sized Earth, as the horizontal grid spacings are 110 km (1 degree) or 55 km (0.5 degrees) and the vertical grid spacings in this test are 0.5 km. A higher resolution horizontal grid on a km-scale comparable to the vertical would require an excessive amount of computational resources for this ideal test. A small Earth factor of X=60 is used in this test, which makes for horizontal spacings of ~1.8 km (1 degree) and ~ 0.9 km (0.5 degrees). Smaller Earths have been used in literature, such as X=120 in Klemp et al. (2015), but this makes the physics timestep size too small for CAM.

This test includes moist physics, whereas the test cases 1 and 2 are for dry dynamical cores. A Kessler physics model is implemented, which is a simple microphysics scheme that tracks changes to water vapour, cloud water, and rain water components. For more details on Kessler Physics see the Appendix of Hughes & Jablonowski (2023). An additional radar reflectivity routine is implemented, which follows the Marshall-Palmer power law relation with precipitation rate. Radar reflectivity, Z, is a measurement of the backscattered light from water droplets made by weather radars. It gives an indication of the amount of precipitation at a given point in the atmosphere and scales strongly with the size of the water droplet. Since it can take on a wide range of values, it is typically reported in a decible-like log base-10 unit referred to as dBZ. This measure is often used in weather reports when discussing the size and structure of precipitating systems like squall lines.

The initial condition is in hydrostatic balance. The test is run without the Coriolis force, so instead of geostrophic balance, the initialisation enforces a cyclostrophic balance between the pressure gradients and centrifugal forces. There is a background shear flow and a temperature profile that leads to a large amount of convection available potential energy (CAPE) of ~ 2000 m^2/s^2 . An iterative method is required to compute the initial condition, which makes it more computationally expensive than cases 1 and 2.

Modifications: All dynamical cores:

All the following modifications involve changes in the parameters for the squall line initial condition routine. To make modifications, change the variable of interest in the ic_squall.f90 file that can be found in your $CASE_DIRECTORY/SourceMods/src.cam/ directory. Any modifications made to this file will require a rebuild of the model. This can be done by first cleaning the build with ./case.build --clean-all followed with a qcmd -A UMIC0107 -- ./case.build command. Note that rebuild may take awhile, sometimes as much as 10 minutes.

1. Change the temperature of the bubbles (pert_dtheta).
2. Change the number of bubbles (pert_num), the spacing of bubbles (pert_spacing) and the vertical/horizontal radius (pert_rz/pert_rh) of each bubble.

For example, other squall line test cases, such as Carley et al. 2023, have used 7 bubbles with 40 km spacing.

1. Break the hemispheric symmetry of the bubbles (pert_latc).
2. Change the background velocity such as the magnitude of shear (U_s), the height of the shear layer (z_s), or the velocity at the surface (U_c).
3. Change the size of the velocity transition layer between the linear low level shear and upper level constant velocity. How does it impact grid imprinting?
4. Change the thermal background such as the temperature at the surface (theta0), the temperature at the tropopause (theta_tr/T_tr), the altitude of the tropopause (z_tr).
5. Change the time step. Do the models display temporal convergence of the expected order?
6. Increase the horizontal resolution. Do the models converge as expected?
7. Change the resolution used to produced the initial conditions (nz and nphi). The initialization routine uses an iteration procedure on a an initial grid of size nz (height) and nphi (latitude). The initial data is then computed by interpolating onto the actual horizontal and vertical grid supplied by the model. Does the resolution of this initial grid impact the results?

Modifications: Dycore specific

The biggest source of variability between models is likely to come from the difference in how each model treats diffusion. Each model has various settings to control how viscosity is treated and the characteristics of the sponge layer. The values used for SE and FV3 were largely chosen to achieve numerical stability and reduce the effects of grid imprinting. Initial testing also demonstrated that the inclusion of a Rayleigh friction sponge layer on the MPAS produce a squall line more similar to the SE and FV3 models. The following changes involve changes of dycore specific namelist variables within the user_nl_cam file. Unlike the previous modifications to the ic_squall.f90 file, changes to user_nl_cam do not require a rebuild.

SE:

See the SE namelist options here.

Change the hyperviscosity diffusion coefficients. In the default setup, se_nu = se_nu_div = se_nu_p. Are any of them more beneficial for maintaining the numerical stability?

Changes to diffusion may require changes in the time steps (se_tstep, se_dt_remap_factor, se_dt_tracer_factor). It can be tricky to get these right. I recommend making XML changes to reduce STOP_N and JOB_WALLCLOCK_TIME to make short test runs if you're running into errors.

Change the strength of the sponge layer (nu_top) or turn it off completely.
Change the number of vertical levels for the sponge layer. This is controlled by the model_init_mod.F90 file in SourceMods/src.cam.

FV3:

See the FV3 namelist options here.

FV3 has a lot of grid-imprinting but also a lot of different diffusion settings. Which diffusion settings mitigate grid-imprinting the best?

Modify the choice of horizontal transport scheme, using the hord namelist parameters.
Modify the order of hyperviscosity diffusion. The 1-degree case uses 6th order while the 0.5-degree case uses 4th order to achieve numerical stability. Other fv3 squall line tests in the literature have used an 8th order diffusion scheme.
Introduce a Smagorinsky-like Laplacian diffusion through the fv3_dddmp. Other fv3 squall line tests in the literature have used a value of 0.2.
In some cases, vorticity damping can help to keep simulations stable if the horizontal transport scheme is not very diffusive. You can turn on vorticity damping with fv3_do_vort_damp and control the coefficient with fv3_vtdm4. What is the impact of introducing vorticity damping?
Introduce Laplacian damping to the main region of the domain (not the sponge layers) with fv3_d2_bg. Does introducing additional diffusion along with the hyperviscosity diffusion help with diffusion and mitigate grid imprinting? Does it effect the updraft and precipitation structure of the squall?
There are three different types of sponge layers that can be activated in FV3: Rayleigh friction sponge (controlled by fv3_rf_cutoff and fv3_tau), a Laplacian diffusion sponge (controlled by fv3_d2_bg_k1 and fv3_d2_bg_k2) and a 2dx filter sponge (controlled by fv3_n_sponge). The Rayleigh friction sponge is currently the only sponge layer applied, to match the Rayleigh friction sponge used in MPAS and in supercell ideal test cases in the literature. Do the other sponge layers produce similar squall line structure. Do they help mitigate grid imprinting?

MPAS:

Like FV3, MPAS also has many options for the transport scheme and diffusion settings. See MPAS for more details on all the available options. For this squall line test case, default transport and diffusion settings were used, except for the sponge layer. Changing the transport and diffusion options and their effects on squall structure or grid imprinting has yet to be tested!

Modify the horizontal or vertical advection schemes.
Modify the diffusion settings, such as introducing Lapalacian or fourth-order hyperviscosity options or modifying the Smagorinsky settings.
Modify the strength or size of the Rayleigh friction sponge layer. There are separate settings for vertical and horizontal momentum damping.

Below are some of the settings used by the supercell test case included within MPAS that differ from the current squall line setup for DCMIP 2025:

mpas_split_dynamics_transport = false (versus true)

mpas_number_of_sub_steps = 6 (versus 2)

mpas_dynamics_split_steps = 1 (versus 3)

mpas_h_mom_eddy_visc2 = 500.0 (versus 0.0)

mpas_v_mom_eddy_visc2 = 500.0 (versus 0.0)

mpas_h_theta_eddy_visc2 = 500.0 (versus 0.0)

mpas_v_theta_eddy_visc2 = 500.0 (versus 0.0)

mpas_horiz_mixing = '2d_fixed' (versus '2d_smagorinsky')

mpas_coef_3rd_order = 0.25 (versus 1.0)

mpas_mix_full = false (versus true)

mpas_zd = 20000.0 (versus 15000.0)

mpas_xnutr = 0.0 (versus 0.2)

References:

Carley, J., Wicker, L., Jablonowski, C., Clark, A., Nelson, J., Jirak, I., & Viner, K. (2023). Mitigation Efforts to Address Rapid Refresh Forecast System (RRFS) v1 Dynamical Core Performance Issues and Recommendations for RRFS v2. https://doi.org/10.25923/ccgj-7140

Hughes, O. K., & Jablonowski, C. (2023). A mountain-induced moist baroclinic wave test case for the dynamical cores of atmospheric general circulation models. Geoscientific Model Development, 16(22), 6805-6831.

Klemp, J., Skamarock, W., & Park, S.-H. (2015). Idealized global nonhydrostatic atmospheric test cases on a reduced-radius sphere. Journal of Advances in Modeling Earth Systems, 7 (3), 1155–1177.

Zarzycki, C. M., plus heaps.... (2019). DCMIP2016: The splitting supercell test case.Geoscientific Model Development, 12 (3), 879–892. https://doi.org/10.5194/gmd-12-879-2019

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