Bergman, J. W., and P. D. Sardeshmukh, 2004: Dynamic stabilization of atmospheric single column models. J. Climate, 17, 1004-1021.
Single Column Models (SCMs) provide an economical framework for assessing the sensitivity of atmospheric temperature and humidity to natural and imposed perturbations, and also for developing improved representations of diabatic processes in weather and climate models. Their economy is achieved at the expense of ignoring interactions with the circulation dynamics; thus advection by the large-scale flow is either prescribed or neglected. This artificial decoupling of the diabatic and adiabatic tendencies can often cause rapid error growth in SCM integrations, especially in the Tropics where large-scale vertical advection is important. As a result, SCMs can quickly develop highly unrealistic thermodynamic structures, making it pointless to study their subsequent evolution.
This paper suggests one way around this fundamental difficulty through a simple coupling of the diabatic and adiabatic tendencies. In essence, the local vertical velocity at any instant is specified by a formula that links the local vertical temperature advection to the evolution of SCM-generated diabatic heating rates up to that instant. This vertical velocity is then used to determine vertical humidity advection, and also horizontal temperature and humidity advection under an additional assumption that the column is embedded in a uniform environment. The parameters in the formula are estimated in a separate set of calculations, from the approach to equilibrium of a linearized global primitive-equation model forced by steady heat sources. As a test, the parameterized dynamics are used to predict the linear model's local response to oscillating heat sources, and found to perform remarkably well over a wide range of space and time scales. In a second test, the parameterization is found to capture important aspects of a general circulation model's vertical advection and temperature tendencies and their lead-lag relationships with diabatic heating fluctuations at convectively active locations in the Tropics.
When implemented in the NCAR SCM, the dynamically coupled SCM shows a clear improvement over its uncoupled counterpart for tropical conditions observed during the Tropical Ocean Global Atmosphere Coupled OceanAtmosphere Response Experiment (TOGA COARE). Coupling effectively stabilizes the SCM. As a result, short-term prediction errors are substantially reduced, the ensemble spread is reduced in ensemble runs, and the SCM is able to maintain realistic thermodynamic structures in extended runs. Such a dynamically coupled SCM should therefore be more useful not only for isolating physical parameterization errors in weather and climate models, but also for economical simulations of regional climate variability.