  This paper presents the development of a deep-atmosphere, nonhydrostatic
dynamical core (DyCore) targeted towards ground-thermosphere atmospheric
prediction. This DyCore is based on a novel formulation of the specific
internal energy equation (SIEE), which, unlike standard potential temperature
formulations, is valid for variable composition atmospheres. Two versions of a
SIEE are derived from basic principles. The first version, which uses a
product-rule (PR) continuity equation, contains an additional compressible term
and does not conserve mass. The second version, which does not use the
product-rule (No-PR) in the continuity equation, contains two compressible
terms and conserves mass to machine precision regardless of time truncation
error. The pressure gradient and gravitational forces in the momentum balance
equation are formulated in a manner appropriate for HA applications and the
spectral element method (SEM) is used with Implicit-Explicit (IMEX) and
Horizontally Explicit Vertically Implicit (HEVI) time-integration. These new
equation sets were implemented in two U. S. Navy atmospheric models: the
Nonhydrostatic Unified Model of the Atmosphere (NUMA) and the Navy
Environmental Prediction sysTem Using a Nonhydrostatic Core (NEPTUNE).
Numerical results using a nonhydrostatic and hydrostatic baroclinic
instability, a balanced zonal flow, and HA mountain wave experiments are shown.
These results are compared to existing deep-atmosphere dynamical cores,
indicating that the proposed discretized IEE equation sets are viable
next-generation ground-to-thermosphere DyCores.
