Atmospheric Adjustment to Generalized Forcing

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A theoretical investigation of atmospheric adjustment to generalized forcings will be carried out by the Principal Investigator. Atmospheric adjustment is defined as the response of a moist compressible atmosphere to a prescribed forcing. Immediately after an instantaneous forcing of arbitrary shape, the atmosphere will, in general, be in a state of geostrophic and hydrostatic imbalance. The study of atmospheric adjustment describes the subsequent tendency of the air to achieve a state of geostrophic and hydrostatic balance. It is an extension of the classic problem of geostrophic adjustment to include the effects of compressibility and to allow for nonhydrostatic and moist processes. The forcings studied will be completely general and include momentum, mass, thermal, and moisture forcings. The impact of the time scale of the forcing will also be assessed. Thus, the research will provide insight into the fundamental workings of the atmosphere. The solutions also will shed light on the dynamics of clouds, mesoscale convective systems, and other nonhydrostatic circulations driven by moist convection. Although both heating and moistening correspond to an addition of buoyancy to the air mass, there is a fundamental difference. An addition of heat can be transformed to other forms of energy that can be propagated away; an addition of water must be conserved and cannot be transformed (in the absence of phase changes) and propagated out of the system.A suite of linear problems will be used to examine the full effects of compressibility in the adjustment to generalized forcings. Initial value and Fourier transform techniques will be used to solve for the linear time-dependent problems analytically. The energetics will be examined and the partitioning of the energy between the acoustic, gravity, and Lamb modes and the balanced final state will be assessed. These solutions provide a benchmark to test the dynamical cores of mesoscale, cloud, and forecasting models.These analytic solutions of the linearized adjustment problem will be supplemented by numerical investigations. These numerical studies will address the effect of nonlinearities on the atmospheric response and enable solutions with a more realistic base-state atmosphere. The research also will develop an anelastic model that eliminates the acoustic and Lamb waves. This new model will be an advance over existing models in that it will conserve mass, moisture, and energy. Numerical experiments will document the merits of these anelastic equations in comparison to the fully compressible equations. Thus in addition to providing insight into the dynamics of the atmosphere the research will help to benchmark and develop nonhydrostatic models, which are the foundation for numerical weather forecast models.