Idealized Dynamical Core Test Cases for Weather and Climate Models

Test of the Dynamical Core of General Circulation Models : The Held-Suarez Test

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Christiane Jablonowski (cjablono@umich.edu)

Weather Prediction modeling

Test of the Dynamical Core

Workshops

The general circulation models GME, GM and IFS

Test results: The Held-Suarez Test

Partners

  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 predictions at the German Weather Services (DWD), Offenbach, Germany (in German , in English )

Forecasting by computer at the European Centre for Medium-Range Weather Forecasts (ECMWF), Reading, England

 

 

  Test of the Dynamical Core of a General Circulation Model

Atmospheric models consist of several components which describe together the state of the atmosphere. Important model components are the so-called dynamics package and the physics package which are closely, non-linearly related to each other. The dynamics contains the large-scale adiabatic part of a model (the discretized governing equations) and is explicitly resolved on the underlying grid, whereas the physics is characterized by diabatic, subgrid-scale processes. These physical processes such as radiation, friction and boundary layer interactions play an important role in the general circulation and are taken into consideration implicitly (parameterizations).

The interaction of the model components 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. Since 1994 two ways have been suggested how a dynamical core of a general circulation model can be isolated from the physics and tested on its own. These methods can be referenced as the Held-Suarez test and Boer-Denis test and are briefly explained below.

Held-Suarez Test

This test of the dynamical core has been designed by Isaac Held and Max Suarez who published the test method in 1994. A full postscript version of their article has been available on the internet and can be downloaded here:
 I.M. Held 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 is a test of the dynamical core of a general circulation model. The basic idea behind the test method is to substitute the complex physics package with simplified physics. This simplified physics (or more precisely idealized forcing) consists of  a temperature relaxation function and Rayleigh friction for the wind in lower levels. Using this forcing instead of the physics package 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. modified Held-Suarez's idealized 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:
D. L. Williamson, J. G. Olson and B.A. Boville (1998), "A Comparison of semi-Lagrangian and Eulerian tropical climate simulations", Monthly Weather Review 126:1001-1012 .

Boer-Denis Test

The second test method for a test of the dynamical core of a general circulation method has been introduced at the first 'Workshop on Dynamical Cores' in Breckenridge, Colorado, USA, in 1996. One year later this test method has been published and the abstract of G.J. Boer and B. Denis' publication can be downloaded here. The full version of their article in PDF format (900 KByte) is available on the internet as well and can be downloaded from:
G.J. Boer and B. Denis, (1997), "Numerical convergence of the dynamics of a GCM", Clim. Dyn. 13:359-374 .

The Boer-Denis test works 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.

  Joint Workshops on Numerical Methods for Global Models

Since 1996 a special 'Workshop on Test Cases for Dynamical Cores of Atmospheric General Circulation Models' has been established which is held together with the 'Workshop on Numerical Solutions of Fluid Flow in Spherical Geometry (PDEs on the Sphere)'. These dynamical core workshops are concentrated on the exchange of the results and the development of new test methods. The progress that has been made since Held-Suarez's proposal in 1994 is discussed at the PDEs on the Sphere workshops every 18 months. The workshops could possibly lead to the introduction of artificial orography in a dynamical core experiment as it has been discussed at the Gatlinburg conference in 1998.

• Breckenridge, Colorado, USA, June 1996
• Gatlinburg, Tennessee, USA, April 1998
• San Francisco, California, USA, November 1999
• Montreal, Quebec, Canada, May 2001
• Toronto, Ontario, Canada, August 2002
• Yokohama, Japan, July 2004
• Monterey, California, USA, June 2006

  Intercomparison: Three different General Circulation Models: GME, GM and IFS

Overview of the model

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 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 gives an overview of these general circulation models.The table lists the different numerical properties and provides first insight into the numerical design of each model.
 
 

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).

	GME (DWD)	GM (DWD)	IFS (ECMWF)
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	spectral triangular truncation
Horizontal resolution	ni=64 (approx. 110 km)	T106 (approx. 125 km)	T106 (approx. 125 km)
Vertical resolution	hybrid 19 levels	hybrid 19 levels	hybrid 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 3-time-level	semi-implicit 3-time-level	semi-implicit 2-time-level
Time step	400 s	900 s	2700 s
Diffusion	linear, 4th order	linear, 4th order	linear, 4th order

Comparison of the grids

The most important - and most obvious - difference of 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 newly developed DWD model GME (in German) is based on an irregular, spherical icosahedral grid (in German). This grid structure has been chosen in order to avoid the so-called 'pole problem' (convergence of the grid points near the poles) that is present in regular latitude-longitude grids.
The development of the spherical  icosahedral grid is demonstrated below. An icosahedron is a geometric figure 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 development of the icosahedral grid at the resolution ni=1, ni=2 and ni=4 (from left to right).

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

  Test results: A comparison of the dynamical cores of GME, GM and IFS

Convergence analysis: The DWD model GME

• Test design
• GME convergence analysis with respect to the horizontal resolution
• Zonal wind
• Eddy heat flux
• Eddy momentum flux
• Eddy kinetic energy

Dynamical core intercomparison: The models GME, GM and IFS

• Test design
• Comparison of the three dynamical cores
• Zonal wind
• Temperature
• Eddy heat flux
• Eddy momentum flux
• Eddy kinetic energy

Vertical high resolution experiment with the ECMWF model IFS

In January 1998 the dynamical core of the ECMWF model IFS at T63 resolution has been tested with an increased vertical resolution. Instead of the operational 31 vertical levels 50 model levels have been used to improve the vertical resolution especially in the upper atmosphere (stratosphere and lower mesosphere which lie between 11 km - approximately 50 km). The model top has been set to a pressure level of 0.1 hPa. This approach has led to interesting and new model results that are still under investigation.
The vertical high resolution dynamical core test produced a long-term oscillation in the tropical upper atmosphere that resembles the well known meteorological phenomenon of a QBO (quasi-biennial oscillation). The QBO phenomenon is characterized by a change of the major zonal wind regime in the equatorial region of the stratosphere. In nature, it is observed that easterly and westerly wind components change in a specific way approximately every 22-30 months. These wave structures have been well-met by the dynamical core test, but the model simulations are dominated by a longer time period.
This QBO-like oscillation of the IFS dynamical core has been an impressive and unexpected result. The underlying figure shows a cross section of the mean zonal wind along the equator and demonstrates the change in the zonal wind characteristics over a time period of 4800 days (approx. 13 years). Units are m/s.

Snapshots

The dynamical core tests at DWD have been initialized with artificial initial conditions and generate during the first 200-250 days of the long-term simulations a fully developed global circulation. The following snapshots provide insight into the beginning circulation on day 70. The underlying figures show the GME and GM surface pressure fields and the GME and GM temperature fields near the surface. In addition, the GME vertical velocity field demonstrates the different updraft and downdraft regions at 500hPa.
As far as the model GME is concerned it becomes obvious that the whole circulation is dominated by a wave number 5 structure which is connected to the icosahedral grid. This wave number 5 signal vanishes after model day 130 when baroclinic instability processes break the symmetry of the data.
Compare these images to those produced by I. Held, one of the authors of the dynamical core test method. He presents a snapshot of the temperature field (lower panel) and vertical motion (upper panel) in the lower troposphere (from the idealized atmospheric model (at 'T106' resolution) described in "A Proposal for the Intercomparison of the Dynamical Cores of Atmospheric General Circulation Models").

  Partners

Department of Meteorology (MIUB) at the University of Bonn, Germany (in German , in English), Advisor: Prof. Dr. Andreas Hense
 

German National Research Center for Information Technology, today's Fraunhofer Institute, Institute for Algorithms and Scientific Computing (SCAI), St.Augustin, Germany
Project/Team: Numerical Weather Forecast, Project METEO, Advisor: Dr. Wolfgang Joppich
 
 

German Weather Service DWD, Offenbach, Germany (in German , in English)
Division: Research & Development, Numerical Modelling (in German , in English)
Advisor: Dipl.-Met. Detlev Majewski
 
 

European Centre for Medium-Range Weather Forecasts ECMWF, Reading, England
Advisor: Mariano Hortal, PhD & Clive Temperton, PhD