Flux-conservative thermodynamic equations in a mass-weighted framework

Abstract

A B S T R A C TA set of equations, ready for discretization, is presented for the purely thermodynamic part of atmospheric energetics along a vertical column. Considerations of kinetic energy budgets and detailed turbulence laws are left for further study. The equations are derived in a total mass-based framework, both for the vertical coordinate system and for the conservation laws. This results in the use of the full barycentric velocity as the vector of advection. Under these conditions, the equations are derived from first principles on the basis of an a priori defined set of simplifying hypotheses. The originality of the resulting set of equations is twofold. First, even in the presence of a full prognostic treatment of cloud and precipitation processes, there exists a flux-conservative form for all relevant budgets, including that of the thermodynamic equation. Secondly, the form of the state law that is obtained for the multiphase system allows the flux-conservative form to be kept when going from the hydrostatic primitive equations system to the fully compressible system and projecting then the heat source/sink on both temperature and pressure tendencies.

Multiscale Performance of the ALARO-0 Model for Simulating Extreme Summer Precipitation Climatology in Belgium

“…The ALARO-0 model utilizes 1) the Action de Recherche Petite Echelle Grande Echell (ARPEGE) Calcul Radiatif avec Nebulosite (ACRANEB) scheme for radiation (Ritter and Geleyn 1992, recast in a Net Exchanged Rate framework), 2) a semi-Lagrangian horizontal diffusion scheme (SLHD) (Vana et al 2008), 3) some pseudoprognostic turbulent kinetic energy (pTKE) scheme (i.e., a Louis-type scheme for stability dependencies, but with memory, advection, and autodiffusion of the overall intensity of turbulence), and 4) a statistical sedimentation scheme for precipitation within a prognostic-type scheme for microphysics ). The physics package of the ALARO-0 model is coupled to the dynamics of the ALADIN model (Bubnova et al 1995) via a physics-dynamics interface based on a flux-conservative formulation of the equations proposed by Catry et al (2007).…”

Dynamical kernel of the Aladin–NH spectral limited‐area model: Revised formulation and sensitivity experiments

“…The heat source Q may be optionally applied at constant volume as for example in (5)-(6), or at constant pressure (Catry et al, 2007). In this latter case, as discussed in BHBG95, the source in the T equation simply becomes (Q/Cp) and the source associated with heating vanishes in theq equation.…”

The Central European limited‐area ensemble forecasting system: ALADIN‐LAEF

“…The main modifications from ALADIN-25 are in large-scale precipitation, turbulent transport and radiation. For resolved cloudiness and precipitation, a prognostic type parametrization ALARO is used (Catry et al, 2007;Geleyn et al, 2008;Gerard et al, 2009), a pseudo-prognostic turbulent scheme JFG06 is introduced (Geleyn et al, 2006, pers. comm.…”