NCAR Release of CAM‐SE in CESM2.0: A Reformulation of the Spectral Element Dynamical Core in Dry‐Mass Vertical Coordinates With Comprehensive Treatment of Condensates and Energy

Abstract

It is the purpose of this paper to provide a comprehensive documentation of the new NCAR (National Center for Atmospheric Research) version of the spectral element (SE) dynamical core as part of the Community Earth System Model (CESM2.0) release. This version differs from previous releases of the SE dynamical core in several ways. Most notably the hybrid sigma vertical coordinate is based on dry air mass, the condensates are dynamically active in the thermodynamic and momentum equations (also referred to as condensate loading), and the continuous equations of motion conserve a more comprehensive total energy that includes condensates. Not related to the vertical coordinate change, the hyperviscosity operators and the vertical remapping algorithms have been modified. The code base has been significantly reduced, sped up, and cleaned up as part of integrating SE as a dynamical core in the CAM (Community Atmosphere Model) repository rather than importing the SE dynamical core from High‐Order Methods Modeling environment as an external code.

A Total Energy Error Analysis of Dynamical Cores and Physics‐Dynamics Coupling in the Community Atmosphere Model (CAM)

“…CAM‐SE is formulated using a terrain‐following hybrid‐sigma vertical coordinate η but the coordinate levels are defined in terms of dry air mass per unit area ( M ( d ) ) instead of total air mass; η ( d ) (see Lauritzen et al, , for details). In such a coordinate system it is convenient to define the tracer state in terms of a dry mixing ratio instead of moist mixing ratio where ρ ( d ) is the mass of dry air per unit volume of moist air and ρ ( ℓ ) is the mass of the water substance of type ℓ per unit volume of moist air.…”

“…Define associated heat capacities at constant pressure . We refer to condensates as being thermodynamically and inertially active if they are included in the thermodynamic equation and momentum equations; for example, if the thermodynamic equation is formulated in terms of temperature, the energy conversion term includes a generalized heat capacity which is a function of the condensates and their associated heat capacities (see, e.g., section 2.3 in Lauritzen et al, ). Similarly, the weight of the condensates is included in the pressure field and pressure gradient force.…”

“…The pseudo‐code in Figure defines the acronyms in terms of where in the CAM‐SE algorithm the TE vertical integrals are computed and output. For details on the CAM‐SE algorithm please see Lauritzen et al ().…”

“…Here we focus on versions of the Community Atmosphere Model (CAM) that use the spectral‐element (SE; Lauritzen et al, ) and finite‐volume (FV; Lin, ) dynamical cores. These dynamical cores couple with physics in a time‐split manner; that is, physics receives a state updated by dynamics (see Williamson, , for a discussion of time‐split versus process split PDC in the context of CAM).…”

“…In spectral transform models it is customary to add the energy change due to explicit diffusion on momentum back as heating (referred to as frictional heating), so that the diffusion of momentum does not affect the TE budget (see, e.g., p.71 in Neale et al, ). This is also done in CAM‐SE (Lauritzen et al, ).…”