Baroclinic Instability and Wave-Wave Interactions in Quasi-geostrophic Error Growth

Abstract

A two-level quasi-geostrophic beta-plane channel model with a smooth lower surface is used to study the dynamics of the growth of errors, with particular attention paid to the roles of wave-wave interactions via-a-vis those of baroclinic instability. The model has 16 zonal wavenumbers and 6 meridional modes on a midlatitude channel of width 5000 km and length 28 306 km. For a cross-channel ?radiative equilibrium? temperature drop of 61°K and a radiative time constant of 20 days, the model produces a zonally averaged temperature drop of 30°K. The energy spectrum shows a peak at zonal wavenumber 4 to 5 due to baroclinic instability, and a planetary wave peak due solely to nonlinear interactions which extract energy from the unstable scales. Three predictability experiments were performed, involving sample sizes of 110 to 220 forecasts of length 30 days. With the initial error in the smallest scales (with 1% of climatological variance), the error spectrum develops a peak in the unstable scales (zonal wavenumbers 4 to 6) within the first few days. This peak is the result of the interactions of stable waves, and is not due directly to baroclinic instability. By day 15 in the forecast, baroclinic instability becomes the dominant mechanism for error energy creation in the unstable scales, but the stable wave-wave interactions do not approach their equilibrium configuration as an energy sink for the unstable waves until after day 20. A distinct planetary wave peak in the error spectrum doe not appear until day 25. Nonlinear interactions involving one stable and one unstable wave are an important source of planetary wave error energy for most of the forecast. With the initial errors in the most unstable scales (Experiment 2), the model exhibits more vigorous baroclinic instability. This leads to instability overtaking nonlinearity as the principal source of time-integrated total (wave) error energy four days earlier than in the previous experiment Paradoxically the planetary wave peak (due solely to wave-wave interactions) appears earlier than in the first experiment. This is due to enhanced forcing of the planetary wave by interactions of the large initial error in the unstable waves with stable waves, and to reduced forcing of the unstable waves by wave-wave interactions early in the forecast. Interactions of the unstable waves with initial errors in the planetary wave lead to the appearance of an error energy peak in intermediate scales in a third experiment. These latter waves dominate the time-integrated error spectrum until instability catches up (at day 10) and produces large errors in the unstable scales.