Climate diagnosis increasingly involves understanding the evolution of relatively weak signals in a high-order chaotic system of strongly interacting components. Assessing the sensitivity of the full system to perturbations (or errors) is problematic: forward "brute force" calculations are too expensive, and backward "adjoint" calculations assume linearity. Fortunately, for many specific problems it is not necessary to consider the full complexity of climate interactions; diagnosis with simpler models can be very useful. The simplification usually involves restricting the focus to component subsystems (atmosphere, ocean, land, cryosphere etc) or using models that emphasize "dynamics" over "physics" or vice versa. In growing recognition of climate sensitivity to the details of atmospheric physics, attention is increasingly turning toward diagnostic models with complex physics and simplified dynamics. Single column models (SCMs) that consider complex diabatic interactions within a single atmospheric column are the best and most extreme examples of these, and the focus of this study.

SCMs provide an efficient modeling framework in which the vertical profiles of temperature and humidity evolve in response to diabatic interactions within the column and advection by the large scale circulation. The advective tendencies are either prescribed or neglected. This decoupling of the column physics from its large-scale environment, while apparently necessary to make an SCM workable at all, can nevertheless lead to rapid spurious error growth in SCM experiments, especially in the tropics.

An SCM framework that couples the vertical advective tendencies to the column physics is developed here. Conceptually, the column is viewed as being embedded in a region of uniform background winds, temperature and humidity, which allows all fluctuating advection terms to be specified in terms of vertical velocity, temperature, and humidity. The vertical velocity at any instant is given by a formula that links the vertical temperature advection to the history of the SCM-generated diabatic heating rates upto that instant. The parameters in this coupling formula are obtained empirically from a separate dry linear Primitive Equation (PE) model forced by steady idealized diabatic heating

The ability of this dynamical coupling formula to determine local vertical velocities from the history of local diabatic heating rates is tested in a linear PE model forced by oscillating 3-dimensional heating fields. The formula works surprisingly well over a wide range of spatial and temporal heating scales, even passing the hard test of correctly reproducing the phase shift and amplication of the response for near-resonant heating. This success suggests that to obtain the correct advective tendencies, detailed knowledge of the vertical and temporal structure of the diabatic forcing is necessary, but that of its horizontal structure is not.

The single column model with vertical velocities coupled to the local temperature and humidity in this manner effectively eliminates the spurious SCM instabilities alluded to above. It is argued that future SCM diagnoses of GCM physics would benefit from such a coupling. Such a dynamically interactive SCM would also be useful in increasing the realism of simple "Box"-type models of climate variability.