The Vertical Momentum Budget of Shallow Cumulus Convection: Insights From a Lagrangian Perspective

Abstract

Abstract A Lagrangian Particle Dispersion Model is embedded into large eddy simulations to diagnose the responses of shallow cumulus convection to a small‐amplitude large‐scale temperature perturbation. The Lagrangian framework allows for a decomposition of the vertical momentum budget and diagnosis of the forces that regulate cloudy updrafts. The results are used to shed light on the parameterization of vertical velocity in convective schemes, where the treatment of the effects of entrainment as well as buoyancy‐induced and mechanically induced pressure gradients remains highly uncertain. We show that both buoyancy‐induced and mechanically induced pressure gradients are important for the vertical momentum budget of cloudy updrafts, whereas the entrainment dilution term is relatively less important. Based on the analysis of the dominant force balance, we propose a simple model to derive the perturbation pressure gradient forces. We further illustrate that the effective buoyancy and dynamic perturbation pressure can be approximated to a good extent using a simple cylindrical updraft model given the cloud radius. This finding has the potential for improving the parameterization of vertical velocity in convective schemes and the development of a unified scheme for cumulus convection.

Keywords

• Lagrangian
• vertical velocity
• perturbation pressure
• simple model
• convective schemes