Introduction to the Hands-on Component of DCMIP and the DCMIP-2025 Test Cases

Christiane Jablonowski¹, Timothy Andrews¹, Owen Hughes¹, Nicholas Androski¹, and Joshua Elms²

1: Department of Climate and Space Sciences and Engineering�University of Michigan, Ann Arbor, USA

2: Department of Earth and Atmospheric Sciences, Indiana University, Bloomington, USA

DCMIP-2025 Summer School, Boulder, CO, June/2/2025

Overview of DCMIP-2025 & DCMIP Test Case Suite

• 3 dycores embedded in NCAR’s Community Atmosphere Model (CAM) + ML:
• DoE/NCAR’s Spectral Element (SE) model
• NCAR’s Model for Prediction Across Scales (MPAS)
• NOAA’s Finite-Volume Cubed Sphere (FV3), Geophysical Fluid Dynamics Laboratory
• 3 ML weather prediction emulators:�Spherical FourCastNet (NVIDIA), GraphCast (Google), and Pangu (Huawei Cloud)
• 4 science themes:
• Dry mountain-generated inertia gravity waves (hydrostatic)
• Dry mesoscale mountain-generated processes and vortices (hydrostatic)
• Gap flow
• Vortex shedding (von-Karman vortex streets)
• Physics-dynamics coupling: Squall line test with simple rain (nonhydro)
• Idealized ML test ideas including baroclinic wave and Hakim and Masanam (2024)

Dynamical Cores in NCAR’s CAM framework

SE: local spectral

• equiangular cubed- sphere grid
• A grid staggering

FV3: finite-volume (FV)

• equi-edge cubed-sphere grid
• D grid staggering

MPAS: FV & finite differ.

• centroidal Voronoi tessellations (similar to hexagonal grid)
• C grid

SE and FV3 can be run as hydrostatic or non-hydrostatic models, MPAS is non-hydrostatic

Cubed-sphere figures from Santos (2024)

Review of DCMIP and the DCMIP Wiki Page

• Let us take a look at the DCMIP webpage:�https://sites.google.com/umich.edu/dcmip-2025

Reminder: Signatures of 2D Topographic Gravity Waves

Dudhia (Mon. Wea. Rev., 1993)

inertia-gravity waves

hydrostatic GW

non-hydrostatic GW

QG flow

potential flow

Vertical velocity (cm/s)

Science Theme 1: Topographic Inertia-Gravity Waves

• Dry mountain-generated inertia gravity waves (hydrostatic, with Coriolis forces)

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Based upon the initial conditions specified by Hughes and Jablonowski (HJ 2023) for the baroclinic wave test case (Ullrich et al., 2014) with added topography (originally with the peak surface height of 2000 m).

Theme 1: New Design Choices Based on HJ2023

• Introduction of a stratosphere in the temperature field
• Rayleigh friction (RF) sponge layer in the upper 10 km
• Higher (peak height 4 km) and steeper mountain ridge than HJ2023
• New vertical grid spacings: L88 (max Δz = 800 m), L120 (max Δz = 400 m), L207 (max Δz = 200 m)

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Initial conditions: temperature and static stability (squared Brunt-Vaisala frequency N²)

kink in N²

• Characteristics of the initial conditions: vertical wavelength is vastly reduced in upper levels
• Provides test of the vertical grid spacing and its impact on the topographic waves

Theme 1: Characteristics of the Mountain Waves

• Topographic waves are depicted by the potential temperature contours and horizontal divergence (colors), 4 km mountain peak
• Δz = 200 m resolves additional wave signatures, converged

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Δz = 800 m

Δz = 200 m

Spectral Element (110 km)

Spectral Element (110 km)

Meridional cross sections of potential temperature (contours) and horizontal divergence (colors) at 35ºN

Theme 1: SE Mountain Waves at Day 3.75

Δz = 800 m

Δz = 200 m

FV3 (C96, 100 km)

FV3 (C96, 100 km)

• Topographic waves are depicted by the potential temperature contours and horizontal divergence (colors), 4 km mountain peak
• Noisy wave patterns, Δz = 200 m reinforces the noise, needs closer evaluation

Theme 1: FV3 Mountain Waves at Day 3.75

Meridional cross sections of potential temperature (contours) and horizontal divergence (colors) at 35ºN

Δz = 200 m

Δz = 200 m

FV3 (100 km)

Meridional cross sections at 35º N

Theme 1: Use Ri Number as a Turbulence Indicator

SE (110 km)

Theme 2: Mesoscale Mountain-Generated Flows

Dry, hydrostatic (Nd/U >>1), mountain-generated processes

• Case 2a: Gap flow
• Case 2b: Vortex shedding

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These both use:

• A X=20 small Earth, so the radius is approx 319 km.
• Isothermal atmosphere of 288 K, constant static stability of N=0.018 1/s
• Solid body rotation of u = U cos(lat), with U=10 m/s
• Model top of 30 km
• A stretched vertical grid with Δz = 300 m over the mountain
• A 15 km Rayleigh friction layer to damp the vertically-propagating gravity waves
• Topography with peak height of 1.5 km

Observed surface geopotential

Theme 2a: Inspiration for the Gap Flow Test Scenario

• Analytic ridge mountain profile with gap at the equator (shown on next slide), well resolved

• h₀ is the mountain peak height, default is h₀ = 1500 m
• e_i control the shape of the mountain, �default is 10
• d_i are length scales, note the Earth’s radius a is now a/X(=20)
• Default settings are�x_lon = 40 km, x_lat = 300 km, x_gap = 50 km
• Explore what happens with a shorter or wider gap or higher mountain?

Theme 2a: Topographic Profile of the Gap Flow Test

Vertical profiles of the mountain height (m), with 1 degree dycores (Δx = 5.5 km spacing)

Rule-of-thumb : 3+ points over a feature of interest (well-resolved)

Note the asymmetry in MPAS (Voronoi) vs SE (cubed-sphere).

Theme 2a: Topographic Profile of the Gap Flow Test

SE

MPAS

• Normalized zonal wind perturbations at z = 300 m with westerly incoming flow hitting the mountain: dry SE (1º-degree, X=20) model with Δx = 5.5 km and Δz = 300 m
• Flow accelerates through the gap, gets blocked in front of the mountain barrier (in white)

with Coriolis force

Theme 2a: Gap Flow Results for SE

without Coriolis force

Coriolis forces confine the spatial extent of the flow pattern

More gap acceleration and less reverse flow

Normalized zonal wind perturbations at z = 300 m

Temperature perturbations at z = 300 m

with Δx = 5.5 km and Δz = 300 m

Theme 2a: Gap Flow Intercomparison, No Rotation

• Dycore intercomparisons without the Coriolis force: SE, FV3 and MPAS at day 0.25

Differences need to be further explored and understood

MPAS develops asymmetries on hexagonal grid: gap is not straight but curvy, will benefit from higher resolution

Normalized zonal wind perturbations at z = 300 m

Temperature perturbations at z = 300 m

with Δx = 5.5 km and Δz = 300 m

Theme 2a: Gap Flow Intercomparison with Rotation

• Dycore intercomparisons with the Coriolis force: SE, FV3 and MPAS at day 0.25

MPAS develops asymmetries on hexagonal grid: gap is not straight but curvy, will benefit from higher resolution

Note the difference in the lee vortices, with the Coriolis force!

Theme 2a: Gap flow modifications

• Topographical modifications (NOT MPAS):
• Change the mountain and gap widths
• Vary the mountain height h (changes Froude number)
• More changes to the Froude number Fr = U/(Nh):
• Change the flow speed U
• Change the isothermal temperature and thereby the static stability N (Brunt-Vaisala frequency)
• Change the vertical resolution over the mountain
• Move the gap off from the equator
• Switch Coriolis forces on/off
• Dycore specific, e.g. transport scheme, diffusion settings

• Meso-scale flow phenomena
• Impact of mountains on small islands:�Shedding vortices �(von Karman vortex street)

Theme 2b: Inspiration for the Vortex Shedding Test

Madeira

Gran Canaria

• Von Karman vortex streets: inspiration from Madeira and Gran Canaria

Theme 2b: Inspiration for the Vortex Shedding Test

Round shape: approximate Gran Canaria as a Gaussian mountain with a similar height/diameter (H/D) aspect ratio seen in observations

Madeira:�Oval shape

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Theme 2b: SE Vortex Shedding Results

r: great circle distance�d: half width

Theme 2b: �Vortex Shedding Intercomparison

• No Coriolis force
• T pertubations at z = 300 m at day 1 from SE, FV3, and MPAS with 2.75 km grid spacings
• Very different flow patterns impacted by diffusion characteristics
• SE: most regular pattern
• FV3 is very sensitive to diffusion settings.
• MPAS will have differences from Voronoi mesh.

Theme 2b: �Vortex Shedding Intercomparison

• No Coriolis force
• Normalized zonal wind pertubations at z = 300 m at day 1 from SE, FV3, and MPAS with 2.75 km grid spacings
• Very different flow patterns impacted by diffusion characteristics

Theme 2b: Vortex modifications

• Topographical modifications (NOT MPAS):
• Change the half-width d of the round Gaussian mountain (Gran Canaria)
• Change to an oval shape mountain (mimicking Madeira)
• Change the peak height
• A decisive parameter is the mountain ratio: Height/Diameter
• Change the Froude number: flow speed and Brunt-Vaisala frequency (via T₀)
• Change the vertical resolution over the mountain
• Move the mountain to a different latitude (and Southern hemisphere!)
• Switch Coriolis forces on/off
• Test impact of dycore-dependent dissipation mechanisms
• Do any of these affect the frequency of the vortex shedding?

• Squall line: A linearly-organized zone of convection
• Common in the US east of the Rockies
• Brings enhanced winds and precipitation
• Extends around O(10 km)-O(100 km)
• Commonly develops a bow-like shape
• Requires:
• Static Instability (high initial CAPE)
• Low-level vertical wind shear
• Provides a test bed for several model design aspects
• Requires non-hydrostatic dynamical core: large vertical accelerations produced by unstable parcels
• Requires km-scale resolution
• Tests the physics-dynamics interplay at the grid scale

NEXRAD reflectivity

Theme 3: Inspiration for the Squall Line Test Case

• based on the Klemp et al. (2015) supercell test case (also used for DCMIP-2016)
• hydrostatic & cyclostrophic balanced initial state
• uses a reduced-radius, non-rotating earth with reduction factor of X=60�(Δx = 1.85 km grid spacing for a 1-degree base grid)
• uses low-level zonal wind shear of 12 m/s from the surface to 2.5 km. At the surface, wind is -5 m/s.
• Idealized thermodynamic sounding with high CAPE (~2200 J/kg) comparable to severe Oklahoma squall lines

Theme 3: Squall Line Initial Conditions

Equatorial zonal wind and thermodynamic sounding profiles based on Klemp et. al (2015).

Theme 3: Squall Line Trigger

• Use many bubble perturbations instead of just one (supercell) to trigger the squall line
• E.g. 9 warm, low level thermal bubble perturbations
• 3 km horizontal radius, 1.5 km vertical radius
• 6 km spacing

3K thermal ”bubble” perturbations based upon DCMIP 2016’s supercell test case (Zarzycki et al. 2016) originally proposed by Klemp et al 2015.

Theme 3: Kessler Microphysics with Radar Reflectivity

• Model moisture physics with Kessler microphysics: a simple, warm-rain water scheme
• Additional derived radar reflectivity (Z) output variable
• Common measurement by weather radars to track precipitating systems like squall lines
• We use the Marshall-Palmer relationship between rain rate and Z measured in a logarithmic scale (dBZ)
• Gives a 3D field that indicates where precipitation is occurring

Snapshots at 2.5 km with SEne30 (Δx = 1.85 km) using 40 vertical levels (L40) with Δz = 500 m, 9 warm bubbles are used as triggers

bow echo

Theme 3: Squall Line Circulation Intercomparisons

cubed-sphere grid imprinting

Radar reflectivity at 2.5 km

t = 3 hours

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1-degree horizontal resolution

500 m vertical resolution

MPAS

FV3

SE

Theme 3: Squall Line Circulation Intercomparisons

cubed-sphere grid imprinting

• Bow echo present in each
• Each exhibit considerable variation
• The structure is highly sensitive to the diffusion settings used in each model.

MPAS

FV3

SE

asymmetric about the equator

Theme 3: Squall Line Modifications

• Diffusion and the sponge layer
• SE, FV3, and MPAS each have a variety of different options (FV3 and MPAS especially)
• How do these affect model convergence, numerical stability, and grid imprinting?
• FV3 in the current setup has significant grid imprinting. Can different FV3 diffusion options mitigate this?
• Warm bubbles: How do the properties of the bubble triggers affect the squall line?
• Change the number
• Change the spacing between bubbles
• Change the size/strength of each bubble
• Center the squall line asymmetric with the equator
• Background environment: How do the properties of the environment affect the squall?
• Change the strength or size of the shear
• Modify the initial surface temperature or tropopause temperature

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• Benefits of ML weather emulators?
• Speed: SFNO simulates one year 5000x faster than IFS¹
• Accuracy: GraphCast has lower error in 10-day Z500 fcst than HRES-IFS²

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• Can we trust them?
• For numerical weather prediction: yes, their forecasts verify
• For modeling the present climate: probably, they capture extremes, etc. well³
• For modeling other climate states: not yet, and let’s discuss

Theme 4: Idealized Machine Learning Testbed

Motivating question:� Can we trust, or not, ML weather emulators: esp. for climate emulation?

Planned tests and sub-questions:

• ERA5 initial conditions
• Look for conservation of mass
• Steady-state conditions (baroclinic wave initial state without a perturbation)¹
• How quickly/realistically does the model state return to ERA5-like?
• Baroclinic wave and tropical cyclone seed embedded in a smooth background flow (e.g. seasonal means derived from ERA5)²
• How does their growth depend on perturbation magnitude/location?
• Is the observed behavior realistic?
• Steady-state conditions with perturbation¹
• Same as above, but further out-of-sample

Theme 4: Idealized Machine Learning Testbed

1: Bouvier et al. (2023)

2: Hakim and Masanam (2024)

• Focus on three weather emulators from NVIDIA’s Earth-2 MIP framework:
1. FourCastNet v2 (NVIDIA)
2. GraphCast (Google)
3. Pangu-Weather (Huawei Cloud)

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• All models (M) are trained on ERA5 state vectors (x) to do:

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• No way to simplify physics, turn on/off components, etc.

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Theme 4: Idealized Machine Learning Testbed

• Surface pressure is force of gravity accelerating column of air into surface area A

p = (M*g) / A

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• Area (A) static
• Gravity (g) static
• Conservation of Mass states M static
• ∴ Pressure (p) should be static

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• Run long simulations, observe trend in global mean surface

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Theme 4: Conservation of Mass

• Initial condition (see fig.) in:
• Geostrophic balance
• Hydrostatic balance

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• How rapidly/realistically does model return from steady-state to ERA5-like?

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• Analyze model response to varying:
• intensity/location of jet
• surface temperature
• moisture profile

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Theme 4:

Steady-State Maintenance

From Bouvier et al. 2024, Fig. 5:

• Zonal wind speed in ms^-1 (black contours)
• Temperature in K (red contours)
• Dynamical tropopause at 2 PVU (blue contours)

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Model: fcnv2_sm (73 channel)

Emulation results from Joshua Elms (Indiana University) with FourCastNet: steady-state initial condition (baroclinic wave)

Observation: Steady-state initial conditions break right away in FourCastNet v2, try new approach

• Initial condition: 40 year DJF time-mean
• Model stepping
• Instead of naive approach:
• Use Hakim and Masanam (2024) method (right)�to remove steady-state tendency of the model (dx)
• Benefit: isolates the model response to perturbation

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Theme 4: Idealized baroclinic wave development

Hakim and Masanam (2024) figure 3d:

Geopotential heights (z) and wind (V)

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Gray: DJF mean geopotential h (60 m)

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Red/Blue: height anomalies (20 m, pos/neg)

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Green arrow: anomalous wind vectors (V - V̅)

Theme 4: Idealized baroclinic wave development

• Clear baroclinic wave from Pangu-Weather (see figure)�
• What about other two models? �
• Analyze model response to varying:
• intensity/location of perturbation
• initial condition �(DJF vs. JAS, etc.)

Summary

• DCMIP-2025 will survey three NCAR CAM dynamical cores and two ML emulators
• Dynamical core evaluations will focus on the impact of topography and the physics-dynamics interplay
• DCMIP includes morning lectures and hands-on afternoon modeling sessions at NCAR
• Goals:
• Teach you (about 50 students and early-career scientists) and the community at large how dynamical cores are built and coupled to physics
• Provide a hands-on learning opportunity using three standard dycores at NCAR
• Inspire further scientific explorations of the physical flow patterns
• Establish an enhanced testbed for dynamical cores and new idealized testbeds for ML approaches
• Explore the physical characteristics of ML approaches
• Lectures will be live streamed and recorded on NCAR’s YouTube channel: https://www.youtube.com/@NCAR_CGD
• Our communication tool is the DCMIP webpage: https://sites.google.com/umich.edu/dcmip-2025

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