Nonlinear Instability and Error Growth in Northern Hemisphere Three-Dimensional Flows: Cyclogenesis, Onset-of-Blocking and Mature Anomalies

Abstract

The nonlinear interactions of an initial small amplitude instability mode with a three-dimensional climatological flow (for Northern Hemisphere, January 1978), an which it is growing are studied in a multilevel nonlinear primitive equation model incorporating spherical geometry. Numerical experiments in which there is either constant or no forcing are considered. For the forced runs the forcing is such that the climatological flow is an exact steady state solution which, however, is unstable when perturbed by the normal mode disturbance. For the unforced runs, we examine the divergence of two ?forecasts,? one of which has the climatological flow as initial conditions and the other, the climatological flow perturbed by the instability solution. The structural changes that occur in the total and disturbance streamfunctions and kinetic energies and in the disturbance momentum and heat fluxes are examined. The initially small-scale shallow disturbance increases in wale and penetrates into the upper troposphere as nonlinear effects become increasingly important during the integrations. Similar vertical penetrations occur for the disturbance kinetic energies and heat and momentum fluxes giving more realistic distributions than does the initial three-dimensional instability mode. For both forced and free runs, the formation of mature anomalies is preceded by the upstream development of westward tilting high-low dipoles. The results are compared with observations of the development of mature anomalies and with theoretical predictions based on three dimensional instability theory. It is found that there is qualitative agreement between the observations, three-dimensional instability theory and the numerical integrations.