  Recent advancements in evaluating matrix-exponential functions have opened
the doors to the practical use of exponential time-integration methods in
numerical weather prediction (NWP). The success of exponential methods in
shallow water simulations has led to the question of whether they can be
beneficial in a 3D atmospheric model. In this paper, we take the first step
forward by evaluating the behavior of exponential time-integration methods in
the Navy's compressible deep-atmosphere nonhydrostatic global model
(NEPTUNE-Navy Environmental Prediction sysTem Utilizing a Nonhydrostatic
Engine). Simulations are conducted on a set of idealized test cases designed to
assess key features of a nonhydrostatic model and demonstrate that exponential
integrators capture the desired large and small-scale traits, yielding results
comparable to those found in the literature. We propose a new upper boundary
absorbing layer independent of reference state and shown to be effective in
both idealized and real-data simulations. A real-data forecast using an
exponential method with full physics is presented, providing a positive outlook
for using exponential integrators for NWP.
