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Recent advancements in evaluating matrix-exponential functions have openedthe doors to the practical use of exponential time-integration methods innumerical weather prediction (NWP). The success of exponential methods inshallow water simulations has led to the question of whether they can bebeneficial in a 3D atmospheric model. In this paper, we take the first stepforward by evaluating the behavior of exponential time-integration methods inthe Navy's compressible deep-atmosphere nonhydrostatic global model(NEPTUNE-Navy Environmental Prediction sysTem Utilizing a NonhydrostaticEngine). Simulations are conducted on a set of idealized test cases designed toassess key features of a nonhydrostatic model and demonstrate that exponentialintegrators capture the desired large and small-scale traits, yielding resultscomparable to those found in the literature. We propose a new upper boundaryabsorbing layer independent of reference state and shown to be effective inboth idealized and real-data simulations. A real-data forecast using anexponential method with full physics is presented, providing a positive outlookfor using exponential integrators for NWP.

Exponential time integration for 3D compressible atmospheric models