Analysis of convective motions based on the Mean Air Flow as Lagrangian dynamics approximation

A new technique, referred to as the Mean Air Flow As Lagrangian dynamics Approximation (MAFALDA) for analyzing convective motions, is introduced here and applied to study the thermodynamic cycle in moist convection. In this technique, the convective mass transport is sorted in terms of the equivalent potential temperature, and an isentropic streamfunction for convective motions is defined. This sorting method emphasizes the fact that moist convection is characterized by the ascent of warm, moist air parcels with high entropy, and the subsidence of colder and dryer air parcels with lower entropy. Furthermore, by averaging of the vertical velocity at a constant value of the equivalent potential temperature, one can filter out gravity wave motions and isolate the irreversible convective overturning. The conditional averaging methodology can also be applied to other variables to determine the mean vertical velocity and various thermodynamic properties of the different air parcels associated with the convective transport.

The isentropic averaging is used to construct a set of idealized thermodynamic cycles and aims at capturing the various thermodynamic transformations associated with convective motions. In effect, fixed values of the streamfunction are interpreted as parcel trajectories. The isentropic averaging also makes it possible to determine the values of the thermodynamic variables, such as temperature, humidity, cloud water and Gibbs free energy along these idealized trajectories. The technique is then applied to reconstruct the thermodynamic cycles in a set of radiative-convective equilibrium simulations run with a high resolution cloud resolving model. It is shown that the bulk of the convective mass transport associated with shallow and intermediate convection is very inefficient at converting internal energy into kinetic energy. The net production of kinetic energy, in this case, is less than one tenth of what would be expected for a Carnot cycle. In contrast, the deeper convective motions, which account for less than 10 percent of the convective mass transport, are markedly more efficient and account for more than two thirds of the total production of kinetic energy.

The MAFALDA technique is a new way to diagnose the thermodynamic transformations in complex numerical simulations of turbulent convection. It allows to reconstruct the thermodynamic properties of a set of 'mean' air parcels based solely on the basic dynamical and thermodynamical variables, without requiring any detailed knowledge of the numerical parameterization within the model. Therefore MAFALDA can be used both to investigate the physical behavior of convection and to directly compare different numerical models results.