Poster presented:
Jablonowski, C. (2006): A Proposed Test Suite for Atmospheric Model Dynamical Cores, 11th Annual CCSM Workshop, Breckenridge, CO, June/20-22/2006
Jablonowski, C. (2006): A Proposed Test Suite for Atmospheric Model Dynamical Cores, Eos Trans. AGU, 87(52), Fall Meet. Suppl., Abstract A41D-0062
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Contact Information:
Christiane Jablonowski
E-mail: cjablono@umich.edu
A Proposed Test Suite for Atmospheric Model Dynamical Cores
Christiane Jablonowski
University of Michigan, Ann Arbor, MI
1) The Idea
Tests of atmospheric General Circulation Models (GCMs) and, in particular, tests
of their dynamical cores are important steps towards future model improvements.
They reveal the influence of an individual model design on climate and weather
simulations and indicate whether the circulation is described representatively by
the numerical approach.
Testing a global 3D atmospheric model is not straightforward. In the absence of
non-trivial analytic solutions, the model evaluations most commonly rely on
intuition, experience and model intercomparisons. In addition, GCM simulation
statistics are typically compared to global reanalysis data while numerical weather
forecasts are compared to local observations. Such approaches are not applicable
to pure dynamical core assessments that isolate the dynamics package from the
physical parameterizations. In general, three different sets of equations are most
commonly used in dynamical cores. These include the hydrostatic primitive
equations as well as the non-hydrostatic shallow-atmosphere and non-hydrostatic
deep-atmosphere equation sets.
As modeling groups now move towards the next generation of dynamical cores a
standard test suite for hydrostatic and non-hydrostatic dynamics packages on the
sphere if highly desirable. This poster contributes to this effort. It suggests a
collection of dynamical core test cases with varying complexity.
A) 3D advection experiments
D) Mountain-induced Rossby wave train
Moist dynamical core test cases are an important intermediate step
towards full GCM evaluations. A variety of moist test cases are
suggested:
Source: Schär et al., MWR 2002
F) An idealized tropical cyclone test case with simplified moisture
processes is under development (Jablonowski et al.). This test case
starts from numerically balanced initial conditions with a prescribed
vortex in tropical regions. A flat ocean-covered surface is assumed. The
goal is to spin up a tropical cyclone which is driven by latent heating
from large-scale condensation processes. A simplified boundary layer
scheme is under consideration. If needed, a convective
parameterization will be applied.
Fig. 1: Advection of a tracer around the sphere with prescribed
nondivergent wind fields and idealized topography. A 3D version of
the 2D Schär et al. 2002 approach is under development. The initial
state is the analytic solution after one revolution. Here, three snapshots
of the tracer distribution at times t1, t2, t3 are shown.
B) Steady-state test case
2) The proposal
Fig. 4: Pressure field at 4 km of a Rossby wave train at day 15. The
wave is triggered by an idealized mountain as indicated by the contour
lines. The contour interval is 200 m. This Witch-of-Agnesi mountain
profile follows Tomita and Satoh (2004). Other more confined mountain
shapes as in Smolarkiewicz et al. 2001 are also feasible.
The following test suite for dynamical cores on the sphere is proposed:
A) 3D advection experiments: The test evaluates the 3D advection scheme in
isolation. Using prescribed wind fields the tracer advection around the sphere in
presence of idealized orography is assessed. A formulation based on the 2D
Schär et al. 2002 approach is under development.
B) Steady-state test case: The test starts from balanced initial conditions that are a
analytical solution of the hydrostatic primitive equations. A two component test
strategy (B & C) first evaluates the ability of the discrete approximations to
maintain the steady-state solution (Jablonowski and Williamson 2006a,b).
C) Evolution of a baroclinic wave: Starting from test B, an overlaid Gaussian hill
perturbation is introduced. This triggers the growth of a baroclinic disturbance
over the course of several days (see references above). A similar test has also
been suggested by Polvani et al. (2004).
3) Tests cases for moist dynamical cores
G) Climate assessments including moisture: A variant of the HeldSuarez test including moisture has been proposed by Galewsky et al.
(2005). Here, the moisture is added in form of tracer constituents.
Furthermore, Frierson et al. (2006) suggested a gray-radiation aquaplanet experiment with simplified physics. In contrast, the full physics
package is utilized in the alternative aqua-planet test case by Neale and
Hoskins (2001). Meanwhile, a model intercomparison project for aquaplanet simulations is under way.
4) Non-hydrostatic dynamical cores
Special test cases for non-hydrostatic dynamical cores need to be
considered. Examples include traveling acoustic and gravity waves on
a non-rotating sphere as well as 3D mountain-wave assessments.
E) 3D Rossby Haurwitz wave
Modeling groups are invited to test and adjust the
proposed test suite using their dynamical cores. The future
goal is to formulate a standard test suite for hydrostatic
and non-hydrostatic dynamical cores on the sphere that
will be broadly accepted by the community.
Feedback on the existing test cases and suggestions for
new test cases are highly appreciated (email:
cjablono@umich.edu). In addition, proposals for
standardized diagnostics are welcome. Overall, the idea is
to develop an easy-to-use set of tools for dynamical cores
on the sphere that increase in complexity and is relevant to
atmospheric phenomena.
Such an approach will enable the community to compare
the dynamical cores in an objective manner.
Fig. 2: Steady-state initial conditions that are an analytic solution to
the inviscid primitive equations. Models should maintain the steadystate for at least 10 days. Global error norms can be assessed.
C) Baroclinic Waves
D) Mountain-induced Rossby wave train: The test starts from balanced initial
conditions that are an analytical solution of the hydrostatic or non-hydrostatic
equation set. An idealized mountain then triggers the evolution of a Rossby
wave train over the course of 15 days. Similar tests have been applied by
Smolarkiewicz et al. (2001) and Tomita and Satoh (2004). It is a 3D extension
of the standard shallow water test 5 (Williamson et al. 1992).
E) 3D Rossby-Haurwitz wave with wavenumber 4: The test starts from
analytical initial conditions that prescribe a wavenumber 4 pattern in the
atmosphere (Monaco and Williams 1975; Giraldo and Rosmond 2004). During
the simulation the pattern moves from east to west without change of shape.
The test is a 3D extension of the standard shallow water test 6 (Williamson et al.
1992).
References
F) Idealized tropical cyclone with simplified moisture processes: The test adds
simplified moisture processes to the dynamical core. It assesses the evolution of
an idealized tropical cyclone that is driven by latent heat release. (Jablonowski,
Held and Garner, in preparation).
G) Long-term climate assessments: Two idealized climate benchmarks for dry
dynamical cores have been suggested by Held and Suarez (1994) and Boer and
Denis (1997). Here, the physics parameterizations are replaced by simple
forcing functions. In addition, aqua-planet simulations for full GCMs have been
proposed (Neale and Hoskins 2001). The latter prescribe an ocean-covered
surface and therefore test the GCM with simplified boundary conditions.
5) The Invitation
Fig. 3: 850hPa temperature field (in K) of an idealized
baroclinic wave at model day 9. The initially smooth
temperature field develops strong gradients associated with
warm and cold frontal zones. Wave breaking events set in
shortly hereafter. High-resolution reference solutions of
this test case along with their uncertainties are assessed in
Jablonowski and Williamson (2006a,b).
Fig. 5: (a) Surface pressure, (b) zonal wind, (c) meridional wind and (d) temperature fields near the
surface (lowest model level) at day 10. This Rossby-Haurwitz wave with wavenumber 4 pattern moves
from east to west without change of shape. The initial flow field is an analytic solution of the nonlinear
barotropic vorticity equation. The fields are extended to 3D. Here a variant of the Giraldo and
Rosmond (2004) formulation is used (Jablonowski, under development) where the orography field is
set to zero. In addition, the meridional wind formulation follows Monaco and Williams (1975).
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