Characteristics of Atmospheric Transport Using Three Numerical Formulations for Atmospheric Dynamics in a Single GCM Framework
Authors: Rasch Philip J. , Coleman Danielle B. , Mahowald Natalie , Williamson David L. , Lin Shian-Jiann , Boville Byron A. , Hess Peter 
Published: June 2006

Abstract
This study examines the sensitivity of a number of important archetypical tracer problems to the numerical method used to solve the equations of tracer transport and atmospheric dynamics. The tracers' scenarios were constructed to exercise the model for a variety of problems relevant to understanding and modeling the physical, dynamical, and chemical aspects of the climate system. The use of spectral, semi-Lagrangian, and finite volume (FV) numerical methods for the equations is explored. All subgrid-scale physical parameterizations were the same in all model simulations.
The model behavior with a few short simulations with passive tracers is explored, and with much longer simulations of radon, SF6, ozone, a tracer designed to mimic some aspects of a biospheric source/sink of CO2, and a suite of tracers designed around the conservation laws for thermodynamics and mass in the model.
Large differences were seen near the tropopause in the model, where the FV core shows a much reduced level of vertical and meridional mixing. There was also evidence that the subtropical subsidence regions are more isolated from Tropics and midlatitudes in the FV core than seen in the other model simulations. There are also big differences in the stratosphere, particularly for age of air in the stratosphere and ozone. A comparison with estimated age of air from CO2 and SF6 measurements in the stratosphere suggest that the FV core is behaving most realistically.
A neutral biosphere (NB) test case is used to explore issues of diurnal and seasonal rectification of a tracer with sources and sinks at the surface. The sources and sinks have a zero annual average, and the rectification is associated with temporal correlations between the sources and sinks, and transport. The test suggests that the rectification is strongly influenced by the resolved-scale dynamics (i.e., the dynamical core) and that the numerical formulation for dynamics and transport still plays a critical role in the distribution of NB-like species. Since the distribution of species driven by these processes have a strong influence on the interpretation of the “missing sink” for CO2 and the interpretation of climate change associated with anthropogenic forcing herein, these issues should not be neglected.
The spectral core showed the largest departures from the predicted nonlinear relationship required by the equations for thermodynamics and mass conservations. The FV and semi-Lagrangian dynamics (SLD) models both produced errors a factor of 2 lower. The SLD model shows a small but systematic bias in its ability to maintain this relationship that was not present in the FV simulation.
The results of the study indicate that for virtually all of these problems, the model numerics still have a large role in influencing the model solutions. It was frequently the case that the differences in solutions resulting from varying the numerics still exceed the differences in the simulations resulting from significant physical perturbations (like changes in greenhouse gas forcing). This does not mean that the response of the system to physical changes is not correct. When results are consistent using different numerical formulations for dynamics and transport it lends confidence to one's conclusions, but it does indicate that some caution is required in interpreting the results.
The results from this study favor use of the FV core for tracer transport and model dynamics. The FV core is, unlike the others, conservative, less diffusive (e.g., maintains strong gradients better), and maintains the nonlinear relationships among variables required by thermodynamic and mass conservation constraints more accurately.