TRR 181 Seminar "How white is the sky?" by Prof. Nedjeljka Žagar (Universität Hamburg)

The TRR 181 seminar is held by Prof. Dr. Nedjeljka Žagar (Universität Hamburg) on February 24, 11am.

How white is the sky?

Abstract

This talk will discuss the kinetic energy spectra of vertical motions in the atmosphere. In contrast to the kinetic energy spectra of the horizontal motion, that are known to be red, the kinetic energy spectra of the vertical motions are poorly understood.  First of all, the vertical velocity is not an observed quantity of the global observing system. Dynamical cores of several global numerical weather prediction (NWP) models that are used to produce reanalyses are hydrostatic, meaning that the vertical velocity is a diagnostic quantity usually derived from the mass continuity equation. In climate research, diagnostic of vertical velocity and the computation of the Lorenz energy cycle are commonly carried out in the system with the pressure vertical coordinate, where vertical velocity is defined as the material derivative of the pressure. This   system is applied here for the derivation of vertical velocities of the Rossby and inertia-gravity waves. 

Vertical velocities associated with the Rossby and gravity waves are commonly treated separately using the quasi-geostrophic omega equations and polarization relations for the stratified Boussinesq fluid in the (x,z) plane, respectively. A separate treatment of the Rossby and gravity wave regimes makes it challenging to compare energies of their vertical motions and vertical momentum fluxes.  A unified treatment and interactions can be carried out by non-hydrostatic numerical prediction models but their understanding requires the toolkit of theory. In particular, the Rossby and gravity wave regimes are difficult to separate in the tropics and their frequency gap, present in the extra tropical case, is filled with the Kelvin and mixed Rossby-gravity waves. 

I will derive an analytical expression for the vertical velocity of the Rossby and gravity waves using the normal-mode function framework in the hydrostatic atmosphere that can be considered applicable up to the horizontal scales around 10 km.  The new framework is applied to the global analyses and spectra of kinetic energy of vertical motions are discussed for latitude and altitude bands.