A Proposed Test Suite for Atmospheric Model Dynamical Cores Christiane Jablonowski University of Michigan, Ann Arbor, MI Contact Information: Christiane Jablonowski 1) The Idea A) 3D advection experimentsD) Mountain-induced Rossby wave train 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 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. 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. 2) The proposal 3) Tests cases for moist dynamical cores 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. 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 are also feasible. 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). 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 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). 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). 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. Moist dynamical core test cases are an important intermediate step towards full GCM evaluations. A variety of moist test cases are suggested: 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. G) Climate assessments including moisture: A variant of the Held- Suarez 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 aqua- planet 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 aqua- planet simulations is under way. 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 ( 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. References Boer, G. J. and B. Denis, 1997: Numerical Convergence of the Dynamics of a GCM. Clim. Dyn., 13, Frierson, D., I. M. Held and P. Zurita-Gotor, 2006: A Gray-Radiation Aquaplanet Moist GCM. Part I: Static Stability and Eddy Scale. J. Atmos. Sci., J. Atmos. Sci., 63, Galewsky, J., A. Sobel and I. Held, 2005: Diagnosis of Subtropical Humidity Dynamics Using Tracers of Last Saturation. J. Atmos. Sci., 62, Giraldo, F. X. and T. E. Rosmond, 2004: A Scalable Spectral Element Eulerian Atmospheric Model (SEE-AM) for NWP: Dynamical Core Tests. Mon. Wea. Rev., 132, Held, I. M. and M. J. Suarez, 1994: A proposal for the Intercomparison of the Dynamical Cores of Atmospheric General Circulation Models. Bulletin of the Amer. Meteor. Soc., 75(10), Jablonowski, C. and D. L. Williamson, 2006a: A Baroclinic Wave Test Case for Dynamical Cores of General Circulation Models: Model Intercomparisons. NCAR Technical Note NCAR/TN-469+STR, pp. 89 Jablonowski, C. and Williamson, D.L. 2006b: A Baroclinic Instability Test Case for Atmospheric Model Dynamical Cores. Quart. J. Roy. Met. Soc., Vol. 132, No. 622, October Part C, in press Monaco, A. V. and R. T. Williams, 1975: An Atmospheric Global Prediction Model Using a Modified Arakawa Differencing Scheme. Technical Report NPS-51WU75041, Dept. of Meteorology, Naval Postgraduate School, Monterey, CA Neale, R. B. and B. J. Hoskins, 2001: A Standard Test for AGCMs Including their Physical Parameterizations: I: The Proposal. Atm. Sci. Let., 1 Polvani, L. M. and R. Saravanan, 2000: The Three-Dimensional Structure of Breaking Rossby Waves in the Polar Wintertime Stratosphere. J. Atmos. Sci., 57, Polvani, L. M., R. K. Scott, and S. J. Thomas, 2004: Numerically Converged Solutions of the Global Primitive Equations for Testing the Dynamical Cores at Atmospheric GCMs. Mon. Wea. Rev., 132, Schär, C., D. Leuenberger, O. Fuhrer, D. Luethi, and C. Girard, 2002: A New Terrain-Following Vertical Coordinate Formulation for Atmospheric Prediction Models. Mon. Wea. Rev.,130, Smolarkiewicz, P. K., L. G. Margolin, and A. A. Wyszogrodzki, 2001: A Class of Nonhydrostatic Global Models. J. Atmos. Sci., 58, Tomita, H. and M. Satoh, 2004: A New Dynamical Framework of Nonhydrostatic Global Model Using the Icosahedral Grid. Fluid Dyn. Res., 34, Willamson, D. L., J. B. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, 1992: A Standard Test Set for Numerical Approximations to the Shallow Water Equations in Spherical Geometry. J. Comp. Phys., 102, B) Steady-state test case C) Baroclinic Waves E) 3D Rossby Haurwitz wave 4) Non-hydrostatic dynamical cores Fig. 2: Steady-state initial conditions that are an analytic solution to the inviscid primitive equations. Models should maintain the steady- state for at least 10 days. Global error norms can be assessed. Source: Schär et al., MWR 2002 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. 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