Idealized Dynamical Core Test Cases for Weather and Climate Models

Test of the Dynamical Core of General Circulation Models:
Short deterministic and long climate simulations

Professor Christiane Jablonowski (

850 hPa temperature of the baroclinic wave at day 9

Weather Prediction modeling

Tests of the Dynamical Core

Workshops and DCMIP

DCMIP snapshots

Held-Suarez Test: The models GME, GM and IFS

Held-Suarez Test Results


Curriculum VitaeHomeAdaptive grids

  A few comments on weather prediction modeling

Weather prediction models or generally speaking atmospheric general circulation models are the discrete, numerical representatives of the underlying governing physical laws. The following two web sites provide first insight into the concepts of a weather prediction model and give some hints concerning its complex structures.
  • Numerical weather prediction models at the German Weather Services (DWD), Offenbach, Germany
  • Modelling and Prediction at the European Centre for Medium-Range Weather Forecasts (ECMWF), Reading, England

    Top of the page

      Tests of the Dynamical Core of a General Circulation Model (GCM)

    Atmospheric models consist of several components which describe the state of the atmosphere. Important model components are the dynamics package, the so-called dynamical core, and the physics package which strongly interacts with the dynamical core in a non-linear fashion. The dynamical core contains the large-scale adiabatic part of a model (the discretized equations of motion) and is explicitly resolved on the underlying grid, whereas the physics is characterized by diabatic, subgrid-scale processes. These physical processes such as radiation, clouds, friction and boundary layer interactions play an important role in the general circulation. However, their characterisic spatial scales are too small to be resoved on a typical GCM grid with grid spacings of order 50 km or wider. Therefore, the overall effects of the small-scale processes are estimated via so-called physical parameterizations. These are often derived empirically.

    The interaction of the model components in a full GCM makes it difficult or even impossible to decide which phenomena are caused by which model component. Each attempt to gather information on a specific model component - so for example information on the dynamical core of a model - is influenced by the impact of the physical parameterizations. This difficulty is alleviated when testing the dynamical core in isolation. This can ve viewed as a 'unit test before coupling the dynamics to the physics parametrization suite. Dry dynamical core tests give valuable information about the characteristics of the numerical discretizations, such as the diffusive behavior, and are especially useful as a begugging tool during the model development phases. In addition, dynamical cores can be intercompared which provides information about the uncertainties in the numerical solutions.

    Two groups of dynamical core tests need to be distinguished. First, dynamical cores can be tested with short deterministic test cases which typically cover a simulation period of about 10-30 days. Second, dynamical cores can be tested in a climate mode that assesses the statistics of the model simulations. These runs span a multi-year time period and are typically run with simple prescribed forcings (Rayleigh friction and Newtonian temperature relaxation) that replace the complex physics suite. Two such dry 'climate' forcings have been suggested in the literature. They are known as the Held-Suarez test and the Boer-Denis test which are briefly described below. We extended these dry test paradigms and developed a moist variant of the Held-Suarez test in Thatcher and Jablonowski (2016).

    Deterministic Dynamical Core Tests

    Short deterministic test cases for dynamical cores have become prominient over the last decade and our research group has played a paramount role in defining them. The key to their widespread use is that they need to be 'easy-to-implement'. Short dynamical core test cases start from prescribed initial conditions that are ideally provided in analytic form. The simulations are run in a 'forecast mode' for 10-30 day time periods and are either compared to analytic solutions (if available) or high-resolution reference solutions. Examples of dry dynamical core test cases are the Jablonowski-Williamson steady-state and baroclinic wave test (Jablonowski and Williamson, QJ 2006; Williamson et al., MWR 2009; Lauritzen et al., JAMES 2010), 3D advection, Rossby-Haurwitz waves, mountain-generated Rossby waves or gravity waves (Jablonowski et al. 2008, Ullrich and Jablonowski, JCP 2012). We also suggest a moist tropical cyclone test case in aqua-planet mode that can either be run in a full-physics or simple-physics setup (Reed and Jablonowski, JAMES 2012). These simulations are initialized with a weak axisymmetric vortex that is embedded into tropical environmental conditions (Reed and Jablonowski, MWR 2011). The vortex then evolves into a tropical cyclone over 10 simulation days. This collection and examples of the model simulations are provided in:

    Additional information is available on the following web pages that provide

    Held-Suarez Test

    This test of the dynamical core has been designed by Isaac Held (GFDL, Princeton) and Max Suarez (NASA) who published the test method in 1994. The article is available online from AMS:
     Held, I. M. and M. J. Suarez (1994): A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models, Bull. Am. Meteorol. Soc. 73, 1825-1830 .

    The Held-Suarez test evaluates the dry dynamical core without any topography in a climate mode. 1200-day integrations are required that allow the assessment of climate statistics like the zonal-mean time-mean general ciculation and the Eddy fluxes. The basic idea behind the test method is to replace the complex physics package with simple forcing functions. These idealized forcings consist of a Newtonian temperature relaxation towards a prescribed thermal equilibrium temperature and Rayleigh friction for the wind at lower levels. Using these forcings a dynamical core can be tested on its own or can be compared with other dynamical cores because the dynamically induced circulation is no longer influenced by interactions with the physical parameterizations.

    A variation of the Held-Suarez test has been developed by D. L. Williamson, J. G. Olson and B.A. Boville, NCAR, Boulder, USA, in 1998 and is here referenced as the Held-Suarez-Williamson test. Williamson et al. (1998) modified the Held-Suarez temperature forcing function in the upper atmosphere (above 100hPa) to test the model behavior in the stratosphere and mesosphere. This change becomes important when using vertical high resolution models since the Held-Suarez forcing provides an isothermal, stable temperature profile in the upper atmosphere which keeps the stratosphere and mesosphere passive.
    The Held-Suarez-Williamson test method has been published in:
    Williamson, D. L., J. G. Olson and B.A. Boville (1998), "A Comparison of semi-Lagrangian and Eulerian tropical climate simulations", Monthly Weather Review 126:1001-1012 .

    Thatcher and Jablonowski: A moist variant of the Held-Suarez Test

    We developed a moist extension of the Held-Suarez test which is described in the online article:
     Thatcher, D. R. and C. Jablonowski (2016): A moist aquaplanet variant of the Held-Suarez test for atmospheric model dynamical cores, Geosci. Model Dev., Vol. 9, 1263-1292 .

    This moist idealized test case (MITC) was inspired by the Held–Suarez (HS) test and the simplified moist physics package described in Reed and Jablonowski (JAMES, 2012). This moist variant of the HS test sheds light on the nonlinear dynamics–physics moisture feedbacks without the complexity of full-physics parameterization packages. In particular, it adds simplified moist processes to the HS forcing to model large-scale condensation, boundary-layer mixing, and the exchange of latent and sensible heat between the atmospheric surface and an ocean-covered planet. In Thatcher and Jablonowski (2016) we demonstrate (via a variety of dynamical cores of the National Center for Atmospheric Research (NCAR)’s Community Atmosphere Model (CAM)) that the inclusion of the moist idealized physics package leads to climatic states that closely resemble aquaplanet simulations with complex physical parameterizations. This establishes that the MITC approach generates reasonable atmospheric circulations and can be used for a broad range of scientific investigations. In our paper we provide examples of two application areas. First, the test case reveals the characteristics of the physics–dynamics coupling technique and reproduces coupling issues seen in full-physics simulations. In particular, we show that sudden adjustments of the prognostic fields due to moist physics tendencies can trigger undesirable large-scale gravity waves, which can be remedied by a more gradual application of the physical forcing. Second, the moist idealized test case can be used to intercompare dynamical cores. These examples demonstrate the versatility of the MITC approach and we make further suggestions of other application areas. The new moist variant of the HS test can be considered a test case of intermediate complexity.

    Boer-Denis Test

    Another method to test the dry dynamical core in a 'climate mode' was introduced by Boer and Denis (1997). All details are provided in their article
    Boer, G. J. and B. Denis, (1997), "Numerical convergence of the dynamics of a GCM", Clim. Dyn. 13:359-374 .

    The Boer-Denis test is similar to the Held-Suarez test. The physics package is replaced with an idealized forcing mechanism. These forcing functions are based on two prescribed temperature and heating profiles as well as a friction term that slows down the wind at lower levels.

    Top of the page

      Forum for Dynamical Core Test Cases:
         Workshops and the Dynamical Core Model Intercomparison Project (DCMIP)

    Ideas for new dynamical core test cases and the results of model intercomparisons are discussed at the 'Partial Differential Equations on the Sphere (PDEs on the Sphere)' workshops that take place every 18-24 months. The list of the PDEs on the Sphere Workshops since 1998 can be found below. In addition, I am one of the founders of the 'Dynamical Core Model Intercomparison Project (DCMIP)' which is based on our experience with three summer schools. In 2008, we conducted a hands-on model intercomparison workshop and summer school at NCAR that focused on dry dynamical core tests (Jablonowski et al. 2008). In the summer of 2012, we conducted the DCMIP-2012 summer school with a focus on non-hydrostatic dynamical cores and their interactions with simplified moisture processes. In the summer of 2016, the DCMIP-2016 summer school put even more emphasis on the interaction between nonhydrostatic dynamical cores and simplified physics processes.

    Links to the Dynamical Core Model Intercomparison Project (DCMIP) and Summer Schools:
    The DCMIP test case suites:
    PDEs on the Sphere Workshops
    Top of the page

      Snapshots of dry dynamical core test cases and the DCMIP intercomparison from 2008

    3D advection with prescribed winds:

    Figure: Selected results of the dynamical core intercomparison project conducted during the 2008 NCAR ASP summer school. The names of the dynamical cores are specified in the headers. The figure shows a cross section of an advected slotted ellipse after 12 days that was transported up and down and around the sphere via an analytically prescribed 3D wind field. The initial condition and reference solution can be used to assess the characteristics of the advection schemes in the participating models denoted by the acronyms. The horizontal grid spacings are approximately 110 km with 60 levels in the vertical direction (vertical grid spacing is 250 m).

    Baroclinic wave:

    Figure: Surface pressure field at day 9 of the baroclinic instability test case simulated with 9 different dynamical cores. The tests starts with balanced initial conditions that are overlaid by a Gaussian hill perturbation. The grid imprint of the cubed-sphere and icosahedral grids can be seen in the Southern Hemisphere (GEOS-FVCUBE, GME, ICON, OLAM). Spectral ringing appears in CAM-EUL and HOMME. The baroclinic wave test is documented in Jablonowski and Williamson (QJ, 2006) and in the Jablonowski and Williamson NCAR Technical Report TN-469+STR (2006).

      Held-Suarez Test and Model Intercomparison: Models GME, GM and IFS

    Overview of the models

    The dynamical cores of three different general circulation models have been tested using the proposal of Held-Suarez. The models involved in this investigation are global weather prediction models that are or have been used operationally at the German Weather Center (DWD, Offenbach, Germany) and the European Centre for Medium-Range Weather Forecasts (ECMWF, Reading, England). The table below provides an overview of these GCMs and their numerical designs.
    GME (DWD)
    GM (DWD)
    Model type Grid point model Spectral model Spectral model
    Grid Spherical icosahedral grid Gaussian grid Reduced Gaussian grid
    Horizontal discretization finite differences, 2nd order spectral
    triangular truncation
    triangular truncation
    Horizontal resolution  ni=64 (approx. 110 km) T106 (approx. 125 km) T106 (approx. 125 km)
    Vertical resolution hybrid
    19 levels
    19 levels
    31 levels
    Model top 10 hPa 10 hPa 10 hPa
    Prognostic variables
    (dry model)
    zonal wind u
    meridional wind v
    temperature T
    surface pressure ps
    relative vorticity
    horizontal divergence
    temperature T
    natural logarithm (ps)
    relative vorticity
    horizontal divergence
    temperature T
    natural logarithm (ps)
    Advection scheme Eulerian Eulerian Semi-Lagrange
    Time stepping scheme semi-implicit
    Time step 400 s 900 s 2700 s
    Diffusion linear, 4th order linear, 4th order linear, 4th order
    Numerical properties of the global weather prediction models GME Version 1.7 (DWD model), GM Version 1.15 (DWD model) and IFS cycle 18 (ECMWF model).

    Comparison of the grids

    An important - and most obvious - difference between the three models is the different underlying grid structure. In contrast to the two spectral models GM (DWD) and IFS (ECMWF) that use a quasi-regular Gaussian or reduced Gaussian grid, the DWD model GME is based on an irregular, spherical icosahedral grid. This grid structure has been chosen in order to avoid the so-called 'pole problem' (convergence of the meridians near the poles) that is present in regular latitude-longitude grids.
    The design of the spherical icosahedral grid is demonstrated below. An icosahedron is a geometric construct that consists of 20 identical triangles which touch the surrounding sphere at 12 points. This grid represents an icosahedral grid at the resolution ni=1 and can now be continuously refined. Each refinement step divides each side of the icosahedral triangles into two, so that the number of refinements 'ni' can be used to indicate the grid resolution. The following figures illustrate the structure of the icosahedral grid at the resolution ni=1, ni=2 and ni=4 (from left to right).

    Icosahedral grid (ni=1)Icosahedral grid (ni=2)Icosahedral grid (ni=4)

    In contrast, a Gaussian grid represents a quasi regular latitude-longitude grid and its principle grid structure is shown in the figure below.

    Gaussian grid

    Top of the page

      Held-Suarez test results: A comparison of the dynamical cores of GME, GM and IFS

    Most of the results depicted here are presented in

    Jablonowski, C. (1998): Test der Dynamik zweier globaler Wettervorhersagemodelle des Deutschen Wetterdienstes: Der Held-Suarez Test, Diploma Thesis, Metorological Institute of the University of Bonn, Germany, September 1998, 151 pp.

    The document is written in German and the translated title reads 'Test of the Dynamics of two global Weather Prediction Models of the German Weather Service: The Held-Suarez Test'. While the text might be hard to read for a non-German speaker, the figures are self-explanatory and can easily be compared to other sources in the literature.

    Convergence analysis: The DWD model GME

      Collaborators and Partners

    UM logo

    University of Michigan alumni
    Collaborators: Paul A. Ullrich (UC Davis), Kevin Reed (Stony Brook University), James Kent (U.K. Met Office, U.K.), Colin Zarzycki (Penn State University)

    NCAR logo

    National Center for Atmospheric Research (NCAR), Boulder, CO, USA
    Collaborators: David L. Williamson, Peter H. Lauritzen, Ram D. Nair

    Sandia logo

    Sandia National Laboratories (SNL), Albuquerque, NM, USA
    Collaborator: Mark A. Taylor


    Top of the pageCurriculum VitaeHomeAdaptive grids

    Last updated March/24/2021