CGD's Dr. David Williamson

Abstract

A deterministic initial value test case for dry dynamical cores of atmospheric general circulation models is presented that assesses the evolution of an idealized baroclinic wave in the Northern Hemisphere. The initial zonal state is quasi-realistic and completely defined by analytic expressions which are a steady-state solution of the adiabatic inviscid primitive equations with pressure-based vertical coordinates. A two-component test strategy first evaluates the ability of the discrete approximations to maintain the steady-state solution. Then an overlaid perturbation is introduced which triggers the growth of a baroclinic disturbance over the course of several days.

The test is applied to four very different dynamical cores at varying horizontal and vertical resolutions. In particular, the NASA/NCAR Finite Volume dynamics package, the NCAR spectral transform Eulerian and the semi-Lagrangian dynamical cores of the Community Atmosphere Model CAM3 are evaluated. In addition, the icosahedral finite-difference model GME of the German Weather Service (DWD) is tested. These hydrostatic dynamical cores represent a broad range of numerical approaches and, at very high resolutions, provide independent referenc e solutions. The paper discusses the convergence-with-resolution characteristics of the schemes and evaluates the uncertainty of the high resolution reference solutions.

Figure caption: RMS differences of the surface pressure differences (in hPa) of the growing perturbation for each horizontal resolution compared to the highest horizontal resolution of the same model with 26 levels: (a) NCAR Eulerian, (b) NCAR semi-Lagrangian, (c) NASA/NCAR Finite Volume and (d) German Weather Service (DWD) GME model.

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Williamson, D. L. and J. G. Olson, 2007: A comparison of forecast errors in CAM2 and CAM3 at the ARM Southern Great Plains Site, Journal of Climate, 20, 4572-4585.

Abstract

We compare short forecast errors and the balance of terms in the moisture and temperature prediction equations which lead to those errors for the Community Atmosphere Model versions 2 and 3 (CAM2 and CAM3) at T42 truncation. The comparisons are made for an individual model column from global model forecasts at the ARM Southern Great Plains site for the April 1997 and June/July 1997 Intensive Observing Periods. The goal is to provide insight into parameterization errors in the CAM which ultimately should lead to improvements in the way processes are modeled. The atmospheric initial conditions are obtained from ECMWF reanalyses (ERA40). The land initial conditions are spun up to be consistent with those analyses. We identify the differences between the model formulations that are responsible for the major differences in the forecast errors and/or parameterization behaviors. We perform a sequence of experiments, accumulating the changes from CAM3 back toward CAM2 to demonstrate the effect of the differences in formulations.

In June/July 1997 the CAM3 temperature and moisture forecast errors were larger than those of CAM2. The terms identified as being responsible for the differences are 1) the convective time scale assumed for the Zhang-McFarlane deep convection, 2) the energy associated with the conversion between water and ice of the rain associated with the Zhang-McFarlane convection parameterization, and 3) the dependence of the rainfall evaporation on cloud fraction. In April 1997 the CAM2 and CAM3 temperature and moisture forecast errors are very similar, but different tendencies arising from modifications to one parameterization component are compensated by responding changes in another component to yield the same total moisture tendency. The addition of detrainment of water in CAM3 by the Hack shallow convection to the prognostic cloud water scheme is balanced by a responding difference in the advective tendency. A halving of the time scale assumed for the Hack shallow convection was compensated by a responding change in the prognostic cloud water. Changes to the cloud fraction parameterization affect the radiative heating which in turn modifies the stability of the atmospheric column and affects the convection. The resulting changes in convection tendency are balanced by responding changes in the prognostic cloud water parameterization tendency.

Figure caption: Mean day 1 forecast temperature (a) and specific humidity (b) errors for CAM3 (solid), CAM2 (short dash) and an intermediate model, EXPJ1 (long dash) for the June/July 1997 IOP.

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Williamson, D. L., 2007: The Evolution of Dynamical Cores for Global Atmospheric Models. Journal of the Meteorological Society of Japan, 85B, 241-269.

Abstract

The evolution of global atmospheric model dynamical cores from the first developments in the early 1960s to present day is reviewed. Numerical methods for atmospheric models are not straightforward because of the so-called {\it pole problem}. The early approaches include methods based on composite meshes, on quasi-homogeneous grids such as spherical geodesic and cubed sphere, on reduced grids, and on a latitude-longitude grid with short time steps near the pole, none of which were entirely successful. This resulted in the dominance of the spectral transform method after it was introduced. Semi-Lagrangian semi-implicit methods were developed which yielded significant computational savings and became dominant in Numerical Weather Prediction. The need for improved physical properties in climate modeling led to developments in shape preserving and conservative methods. Today the numerical methods development community is extremely active with emphasis placed on methods with desirable physical properties, especially conservation and shape preservation, while retaining the accuracy and efficiency gained in the past. Much of the development is based on quasi-uniform grids. Although the need for better physical properties is emphasized in this paper, another driving force is the need to develop schemes which are capable of running efficiently on computers with thousands of processors and distributed memory.

Test cases for dynamical core evaluation are also briefly reviewed. These range from well defined deterministic tests to longer term statistical tests with both idealized forcing and complete parameterization packages but simple geometries. Finally some aspects of coupling dynamical cores to parameterization suites are discussed.

Figure caption: Examples of grids that have been used for global atmospheric model dynamical cores.