## Dissertations from ProQuest

#### Title

The behavior of a class of minimal models of the atmospheric general circulation

1988

Article

#### Degree Name

Doctor of Philosophy (Ph.D.)

#### Department

Meteorology and Physical Oceanography

#### First Committee Member

Lee E. Branscome, Committee Chair

#### Abstract

Minimal criteria are established which a numerical model of the atmosphere must meet in order to qualify as a "General Circulation Model". The ability of a class of low-order, two-layer, $\beta$-plane channel models to meet these criteria is investigated. At least the first and third meridional modes are required in order to achieve qualitatively correct heat and momentum balances. To produce a realistic energy spectrum, wave-wave interactions provided a cascade mechanism for redistributing energy and enstrophy among all the waves. It is necessary to explicitly resolve at least one wave which is linearly stable for the chosen set of external parameter values. This guarantees that a spurious energy build-up does not occur at the shortest resolved scales.A (3,3) model (i.e., three waves resolved in both horizontal directions) has the optimal resolution for the selected model geometry and formulation. Model behavior changes only quantitatively for resolutions greater than this, but changes qualitatively for lower resolutions. This result has implications for theories of multiple equilibria or weather regimes.A parameter study was conducted on a (2,2) version of the model which included zonally asymmetric bottom topography, since very pronounced weather regimes had previously been found for this case. When the forcing and dissipation time scales were lengthened to more realistic values, the weather regimes vanished. Instead, either a chaotic flow or a single-wave equilibrium flow emerged, depending on the ratio of the forcing and dissipative parameters.Stationary wave budget studies were conducted when topography was included in the (3,3) and higher order models. The heat and vorticity budgets were dominated by the "linear" or wave-mean flow interaction terms. The "nonlinear" or wave-wave interaction terms were smaller, always acted to oppose the sense of the corresponding linear term, and had the effect of smoothing out the stationary wave in the height and vorticity fields. An investigation of these topographic cases revealed little evidence of multiple equilibria or weather regimes. However, the (5,5) model, which has a more realistic energy spectrum than the (3,3) model when topography is included, exhibited a significant amount of low-frequency variability and many strong, long-lived anomalies. (Abstract shortened with permission of author.)

#### Keywords

Physics, Atmospheric Science