On the Forcing of the Radial-vertical Circulation within Cyclones-Part 1: Concepts and Equations

お? Following the theoretical result of Eliassen, the Sawyer-Eliassen equation for frontal circulations and the equation for forcing the meridional circulation within a circumpolar vortex are extended in isentropic coordinates to describe the forcing of the azimuthally averaged mass-weighted radial-vertical circulation within translating extratropical and tropical cyclones. Several physical processes which are not evident in studies employing isobaric coordinates are isolated in this isentropic study. These processes include the effects of pressure torque, inertial torque and storm translation that are associated with the asymmetric structure in isentropic coordinates. This isentropic study also includes the effects of eddy angular momentum transport, diabatic heating and frictional torque that are common in both isentropic and isobaric studies. All of the processes are modulated by static, inertial and baroclinic stabilities. Consistent with the theoretical result of Eliassen, the numerical solution from this isentropic study shows that the roles of torque, diabatic heating and hydrodynamic stability in forcing the radial-vertical circulation within stable vortices are that 1) positive (negative) torque which results in the counterclockwise (clockwise) rotation of vortices also forces the outflow (inflow) branch of the radial-vertical circulation, 2) diabatic heating (cooling) forces the ascent (descent) branch of the radial-vertical circulation and 3) for given forcing, the weaker hydrodynamic stability results in a stronger radial-vertical circulation. It is the net inflow or convergence (net outflow or divergence), vertical motions and the associated redistribution of properties that favor the evolution of vortices with colorful weather events. Numerical solutions of this isentropic study are given in companion articles. The relatively important contribution of various physical processes to the forcing of the azimuthally-averaged mass-weighted radial-vertical circulation within different translating cyclones and in their different stages of development will be investigated.

SOME DIAGNOSTICS IN NONLINEAR REPRODUCTIVE DISPERSION MODELS

This article discusses the problem of the detection of influential cases in nonlinear reproductive dispersion models (NRDM). A diagnostic based on case\|deletion approach in estimating equations is proposed. The relationships between the generalized leverage defined by Wei et al. in 1998, statistical curvature, and the local influence of the response vector perturbations are investigated in NRDM. Two numerical examples are given to illustrate the results.