This paper describes the splitting supercell idealized test case
used in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016).
These storms are useful test beds for global atmospheric models because the
horizontal scale of convective plumes is O(1 km), emphasizing
non-hydrostatic dynamics. The test case simulates a supercell on a
reduced-radius sphere with nominal resolutions ranging from 4 to 0.5 km and is based
on the work of

Supercells are strong, long-lived convective cells containing deep,
persistent rotating updrafts that operate on spatial scales O(10 km). They
can persist for many hours and frequently produce large hail, tornados,
damaging straight-line winds, cloud-to-ground lightning, and heavy rain

The supercell test applied in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016)

Previous work regarding the role of model numerics in simulating extreme
weather features has generally focused on limited area domains

The supercell test here emphasizes resolved, non-hydrostatic dynamics. In this regime, the effective grid spacing is very similar to the horizontal scale of convective plumes. Further, the addition of simplified moist physics injects energy near the grid scale in a conditionally unstable atmosphere, which imposes significant stress on model numerics. The supercell test case therefore sheds light on the interplay of the dynamical core and subgrid parameterizations and highlights the impact of both implicit and explicit numerical diffusion on model solutions. It also demonstrates credibility of a global modeling framework to simulate extreme phenomena, essential for future weather and climate simulations.

List of constants used for the supercell test.

The test case is defined as follows. The setup employs a non-rotating
reduced-radius sphere with scaling factor

All simulations are integrated for 120 min. Outputs of the full
three-dimensional prognostic fields as well as all variables pertaining to
the microphysical routines were stored for post-processing at least every
15 min. Four different horizontal resolutions were specified: 4, 2, 1, and
0.5

The mean atmospheric state is designed such that it consists of large
instability (convective available potential energy (CAPE) of approximately
2200 m

The definition of this test case relies on hydrostatic and cyclostrophic wind
balance, written in terms of Exner pressure

The wind velocity is analytically defined throughout the domain. Meridional
and vertical wind is initially set to zero. The zonal wind is obtained from

The equatorial profile is determined through numerical iteration. Potential
temperature at the Equator is specified via

It is assumed that the saturation mixing ratio is given by

Pressure and temperature at the Equator are obtained by iterating on
hydrostatic balance with initial state

This iteration procedure generally converges to machine epsilon after
approximately 10 iterations. The equatorial moisture profile is then extended
through the entire domain:

Once the equatorial profile has been constructed, the virtual potential
temperature through the remainder of the domain can be computed by iterating
on Eq. (

Participating modeling centers and associated dynamical cores that submitted results for the splitting supercell test.

Again, approximately 10 iterations are needed for convergence to machine
epsilon. Once virtual potential temperature has been computed throughout the
domain, Exner pressure throughout the domain can be obtained from
Eq. (

To initiate convection, a thermal perturbation is introduced into the initial
potential temperature field:

Initial state for the supercell test. All plots are latitude–height
slices at 0

Same
as Fig.

An additional iterative step is then required to bring the potential
temperature perturbation into hydrostatic balance. Without this additional
iteration, large vertical velocities will be generated as the flow rapidly
adjusts to hydrostatic balance since the test does not possess strong
non-hydrostatic characteristics at initialization. Plots showing the initial
state of the supercell are shown in Figs.

The test case is designed such that the thermal perturbation will induce a
convective updraft immediately after initialization. As rainwater is
generated by the microphysics, reduced buoyancy and a subsequent downdraft at
the Equator in combination with favorable vertical pressure gradients near
the peripheral flanks of the storm will cause it to split into two
counter-rotating cells that propagate transversely away from the Equator
until the end of the test

As noted in

Models that contributed supercell test results during DCMIP2016 are listed in
Table

Due to the multitude of differing implicit and explicit diffusion in the
participating models, some groups chose to apply variations in how either
horizontal or vertical diffusion were treated in this test case. Deviations
from the above-specified diffusion are as follows. CSU applied uniform
three-dimensional second-order diffusion with coefficients of

The following section describes the results of the supercell test case during DCMIP2016, both from a intermodel time evolution perspective and intramodel sensitivity to model resolution and ensuing convergence. Note that there is no analytic solution for the test case, but features specific to supercells should be observed and are subsequently discussed. It is not the intent of this paper to formally explore the precise mechanisms for model spread or define particular solutions as superior but rather to publish an overview set of results from a diverse group of global, non-hydrostatic models to be used for future development endeavors. Future work employing this test case in a more narrow sense can isolate some of the model design choices that impact supercell simulations.

Figure

Time evolution of cross-sections of 5 km vertical velocity
(m s

All model solutions show bulk similarities. With respect to vertical
velocity, a single, horseshoe-shaped updraft is noted at 30 min in all
models, although the degree to which the maximum updraft velocities are
centered on the Equator vary. A corresponding downdraft is located
immediately to the east of the region of maximum positive vertical velocity.
This downdraft is single-lobed (e.g., ACME-A) or double-lobed (e.g., GEM) in
all simulations. Separation of the initial updraft occurs by 60 min across
all models, although variance begins to develop in the meridional deviation
from the Equator of the splitting supercell. Models such as NICAM, FV

Structural differences also begin to emerge at 60 min. For example, FVM,
GEM, ACME-A, and TEMPEST all exhibit three local maxima in vertical velocity:
two large updrafts mirrored about the Equator with one small maximum still
located over Equator centered near the initial perturbation. Similar behavior
is noted in the

While the aggregate response of a single updraft eventually splitting into
poleward-propagating symmetric storms about the Equator is well matched
between the configurations, notable differences exist, particularly towards
the end of the runs. At 120 min, FVM, GEM, ACME-A, OLAM, and MPAS all show
two discrete supercells approximately 30

The relative smoothness of the storms as measured by the vertical velocity
and rainwater fields also varies between models, particularly at later
times. ACME-A, FVM, GEM, OLAM, and MPAS produce updrafts that are relatively
free of additional, small-scale local extrema in the vicinity of the core of
the splitting supercell. Conversely, CSU, FV

Resolution sensitivity of cross-sections of 5 km vertical velocity
(m s

Maximum domain updraft velocity (m s

Figure

As resolution increases (left to right), models show increasing horizontal
structure in both the vertical velocity and rainwater fields. Updraft
velocity generally increases with resolution, particularly going from 4 to
2 km, implying that the supercell is underresolved at 4 km resolution. This
is supported by previous mesoscale simulations investigating supercells in
other frameworks

At the highest resolutions, there is a distinct group of models that exhibit
more small-scale structure, particularly in vertical velocity, at

Same as Fig.

While Fig.

The maximum updraft velocity as a function of resolution for particular model
configurations varies quite widely. NICAM produces the weakest supercell,
with velocities around 30 m s

Same as Fig.

As in Fig.

As in Fig.

Figure

In addition to Figs.

As a metric, IKE is less sensitive to grid-scale velocities and is also a
more holistic measure of storm-integrated intensity. This is shown in
Fig.

While the formal supercell test case definition during DCMIP2016 specified
0.5 km grid spacing as the finest resolution for groups to submit, it is
clear that full convergence has not been reached for some of the modeling
groups (e.g., Sect.

For TEMPEST and FVM, results indicate solution differences are markedly smaller between 0.5 and 0.25 km than between 1 and 0.5 km, implying the test is not fully converged at 0.5 km for these models. Therefore, 0.25 km may be a better target for a reference grid spacing going forward.

It is worth noting that the reference solution in

Non-hydrostatic dynamics are required for accurate representation of supercells. The results from this test case show that clear differences and uncertainties exist in storm evolution when comparing identically initialized dynamical cores at similar nominal grid resolutions. Intramodel convergence in bulk, integrated quantities appears to generally occur at approximately 0.5 km grid spacing. However, intermodel differences are quite large even at these resolutions. For example, maximum updraft velocity within a storm between two models may vary by almost a factor of 2 even at the highest resolutions assessed at DCMIP2016.

Structural convergence is weaker than bulk-integrated metrics. Two-dimensional horizontal cross-sections through the supercells at various times show that some models are well converged between 1 and 0.5 km, while results from other models imply that finer resolutions are needed to assess whether convergence will occur with a particular test case formulation and model configuration. Interestingly, in some cases, maximum bulk quantities converge faster than snapshots of cross-sections.

We postulate that these differences and uncertainties likely stem from not
only the numerical discretization and grid differences outlined in

Given the lack of an analytic solution, we emphasize that the goal of this paper is not to define particular supercells as optimal answers. Rather, the main intention of this test at DCMIP2016 was to produce a verifiable database for models to use as an initial comparison point when evaluating non-hydrostatic numerics in dynamical cores. Pushing grid spacings to 0.25 km and beyond to formalize convergence would be a useful endeavor in future application of this test, either at the modeling center level or as part of future iterations of DCMIP. Variable-resolution or regionally refined dynamical cores may reduce the burden of such simulations, making them more palatable for researchers with limited computing resources.

We acknowledge that, as groups continue to develop non-hydrostatic modeling techniques, small changes in the treatment of diffusion in the dynamical core will likely lead to changes in their results from DCMIP2016. We recommend modeling centers developing or optimizing non-hydrostatic dynamical cores to perform this test and compare their solutions to the baselines contained in this paper as a check of sanity relative to a large and diverse group of next-generation dynamical cores actively being developed within the atmospheric modeling community.

Information on the availability of source code for the
models featured in this paper can be found in

CMZ prepared the text and corresponding figures in this paper.
PAU assisted with formatting of the test case description in
Sect.

The authors declare that they have no conflict of interest.

DCMIP2016 is sponsored by the National Center for Atmospheric Research Computational Information Systems Laboratory, the Department of Energy Office of Science (award no. DE-SC0016015), the National Science Foundation (award no. 1629819), the National Aeronautics and Space Administration (award no. NNX16AK51G), the National Oceanic and Atmospheric Administration Great Lakes Environmental Research Laboratory (award no. NA12OAR4320071), the Office of Naval Research and CU Boulder Research Computing. This work was made possible with support from our student and postdoctoral participants: Sabina Abba Omar, Scott Bachman, Amanda Back, Tobias Bauer, Vinicius Capistrano, Spencer Clark, Ross Dixon, Christopher Eldred, Robert Fajber, Jared Ferguson, Emily Foshee, Ariane Frassoni, Alexander Goldstein, Jorge Guerra, Chasity Henson, Adam Herrington, Tsung-Lin Hsieh, Dave Lee, Theodore Letcher, Weiwei Li, Laura Mazzaro, Maximo Menchaca, Jonathan Meyer, Farshid Nazari, John O'Brien, Bjarke Tobias Olsen, Hossein Parishani, Charles Pelletier, Thomas Rackow, Kabir Rasouli, Cameron Rencurrel, Koichi Sakaguchi, Gökhan Sever, James Shaw, Konrad Simon, Abhishekh Srivastava, Nicholas Szapiro, Kazushi Takemura, Pushp Raj Tiwari, Chii-Yun Tsai, Richard Urata, Karin van der Wiel, Lei Wang, Eric Wolf, Zheng Wu, Haiyang Yu, Sungduk Yu, and Jiawei Zhuang. We would also like to thank Rich Loft, Cecilia Banner, Kathryn Peczkowicz and Rory Kelly (NCAR), Carmen Ho, Perla Dinger, and Gina Skyberg (UC Davis), and Kristi Hansen (University of Michigan) for administrative support during the workshop and summer school. The National Center for Atmospheric Research is sponsored by the National Science Foundation. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the US Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. Edited by: Simone Marras Reviewed by: two anonymous referees