## Abstract

This paper investigates the factors that determine the equilibrium state, and in particular the height and structure of the tropopause, in an idealized primitive equation model forced by Newtonian cooling in which the eddies can determine their own depth. Previous work has suggested that the midlatitude tropopause height may be understood as the intersection between a radiative and a dynamical constraint. The dynamical constraint relates to the lateral transfer of energy, which in midlatitudes is largely effected by baroclinic eddies, and its representation in terms of mean-flow properties. Various theories have been proposed and investigated for the representation of the eddy transport in terms of the mean flow, including a number of diffusive closures and the notion that the flow evolves to a state marginally supercritical to baroclinic instability. The radiative constraint expresses conservation of energy and so must be satisfied, although it need not necessarily be useful in providing a tight constraint on tropopause height.

This paper explores whether and how the marginal criticality and radiative constraints work together to produce an equilibrated flow and a tropopause that is internal to the fluid. The paper investigates whether these two constraints are consistent with simulated variations in the tropopause height and in the mean state when the external parameters of an idealized primitive equation model are changed. It is found that when the vertical redistribution of heat is important, the radiative constraint tightly constrains the tropopause height and prevents an adjustment to marginal criticality. In contrast, when the stratification adjustment is small, the radiative constraint is only loosely satisfied and there is a tendency for the flow to adjust to marginal criticality. In those cases an alternative dynamical constraint would be needed in order to close the problem and determine the eddy transport and tropopause height in terms of forcing and mean flow.

*Corresponding author address:*Pablo Zurita-Gotor, Departamento de Geofísica y Meteorología, Universidad Complutense, Facultad de Ciencias Físicas, Madrid 28040, Spain. E-mail: pzurita@alum.mit.edu