Generation of inertia-gravity waves in idealized baroclinic-wave life cycles: Explicit vs. semi-implicit time stepping in a finite-volume solver for the pseudo-incompressible equations

Inertia–gravity waves (IGWs) emitted from jets and fronts are ubiquitous in the atmosphere and have a significant impact on atmospheric processes (Plougonven and Zhang, 2014). Since the mechanism responsible for the spontaneous emission of IGWs during the evolution of an initially balanced flow remain poorly understood, their representation in numerical weather prediction models is challenging (de la Cámara and Lott, 2015). Better understanding of this IGW source mechanism based on idealized numerical simulations is crucial to improve the accuracy of the forecasts. In this study, idealized baroclinic-wave life cycle experiments on the f-plane are performed to investigate spontaneous emission, using a finite-volume solver for the pseudo-incompressible equations (Rieper et al., 2013). In particular, the implementation of a semi-implicit time stepping scheme, along the lines of Smolarkiewicz and Margolin (1997) and Benaccio and Klein (2019), but adjusted to our staggered grid, permits longer simulation runs with much larger domains. A novelty is the implementation of a simple Newtonian heating function based on Held and Suarez (1994), which is used for forcing a baroclinically unstable temperature profile and allows the background state to vary in time (O’Neill and Klein, 2014). The results of the model with semi-implicit time stepping scheme will be documented and compared to an explicit Runge-Kutta scheme. The analysis may serve as a basis for the development and validation of a parameterization scheme for GWs emitted from jets and fronts.

References:

Benaccio, T., and R. Klein, 2019: A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics. Mon. Wea. Rev., 147, 4221-4240.
de la Cámara, A., and F. Lott, 2015: A parameterization of gravity waves emitted by fronts and jets. Geophys. Res. Lett., 42, 2071-2078.
Held, I.M., and M.J. Suarez, 1994: A Proposal for the Intercomparison of the Dynamical Cores of Atmospheric General Circulation Models. Bull. Amer. Meteor. Soc., 75, 1825-1830.
O’Neill, W.P., and R. Klein, 2014: A moist pseudo-incompressible model. Atmos. Res., 142, 133-141. Plougonven R., and F. Zhang, 2014: Internal gravity waves from atmospheric jets and fronts. Rev. Geophys., 52, 33-76.
Rieper, F., Hickel, S., and U. Achatz, 2013: A conservative integration of the pseudo-incompressible equations with implicit turbulence parameterization. Mon. Wea. Rev., 141, 861-886. Smolarkiewicz, P.K., and L.G. Margolin, 1997: On forward-in-time differencing for fluids: an Eulerian/semi-Langrangian nonhydrostatic model for stratified flows. Atmosphere-Ocean, 35, 127- 152.