Abstract

We describe a promising alternative approach to modelling moist convection and cloud development in the atmosphere. Rather than using a conventional grid‐based approach, we use Lagrangian “parcels” to represent key dynamical and thermodynamical variables. In the prototype model considered, parcels carry vorticity, mass, specific humidity, and liquid‐water potential temperature. In this first study, we ignore precipitation, and many of these parcel “attributes” remain unchanged (i.e. are materially conserved). While the vorticity does change following the parcel motion, the vorticity tendency is readily computed and, crucially, unwanted numerical diffusion can be avoided. The model, called “Moist Parcel‐In‐Cell” (MPIC), is a hybrid approach which uses both parcels and a fixed underlying grid for efficiency: advection (here moving parcels) is Lagrangian whereas inversion (determining the velocity field) is Eulerian. The parcel‐based representation of key variables has several advantages: (a) it allows an explicit subgrid representation; (b) it provides a velocity field which is undamped by numerical diffusion all the way down to the grid scale; (c) it does away with the need for eddy viscosity parametrizations and, in their place, it provides for a natural subgrid parcel mixing; (d) it is exactly conservative (i.e. there can be no net loss or gain of any theoretically conserved attribute); and (e) it dispenses with the need to have separate equations for each conserved parcel attribute; attributes are simply labels carried by each parcel. Moreover, the latter advantage increases as more attributes are added, such as the distributions of microphysical properties, chemical composition and aerosol loading.

Highlights

  • Clouds, convection and moist processes generally pose serious challenges for modelling the Earth’s climate and weather (e.g. Holloway et al, 2014; Bony et al, 2015)

  • We do not attempt to model every aspect of this process, but only intend to demonstrate a viable computational approach that could lead to a step change in modelling atmospheric convection in general

  • In the results presented below using the Moist Parcel-In-Cell” (MPIC) model, we find that the discrepancy between parcel and grid densities is negligible over cloud development time-scales when using the recommended default numerical settings

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Summary

INTRODUCTION

Convection and moist processes generally pose serious challenges for modelling the Earth’s climate and weather (e.g. Holloway et al, 2014; Bony et al, 2015). Aerosols feed back on the cloud physics by acting as condensation nuclei and modifying the distributions of cloud particles For these reasons, a sophisticated cloud-resolving model capable of studying cloud–chemistry–climate processes may need to carry cloud microphysical spectra, aerosol spectra and a number of interacting chemical species on its grids. A sophisticated cloud-resolving model capable of studying cloud–chemistry–climate processes may need to carry cloud microphysical spectra, aerosol spectra and a number of interacting chemical species on its grids These additional attributes place enormous demands on computational resources – involving both the cost of dynamical transport and that of additional processes such as chemical reactions – and are included at the expense of the resolution needed to capture cloud fine structure.

PHYSICAL SETTING AND MATHEMATICAL FRAMEWORK
THE NUMERICAL ALGORITHM
The parcel vorticity equation
Parcel interpolation
The inversion problem
Filtering
Parcel splitting and mixing
Time stepping
NUMERICAL TESTS AND PARAMETER SETTINGS
Time step loop
Initialization
Default numerical parameter settings
Description of the flow evolution
Dependence on maximum parcel stretch
Dependence on minimum parcel volume fraction
Dependence on time step
Incompressibility
Dependence on resolution
4.10 Comparison with MONC
Findings
CONCLUSIONS
Full Text
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