Leaky rigid lid: New dissipative modes in the troposphere

An effective boundary condition is derived for the top of the troposphere, based on a wave radiation condition at the tropopause. This boundary condition, which can be formulated as a pseudodifferential equation, leads to new vertical dissipative modes. These modes can be computed explicitly in the classical setup of a hydrostatic, nonrotating atmosphere with a piecewise constant Brunt-Väisälä frequency. In the limit of an infinitely strongly stratified stratosphere, these modes lose their dissipative nature and become the regular baroclinic tropospheric modes under the rigid-lid approximation. For realistic values of the stratification, the decay time scales of the first few modes for mesoscale disturbances range from an hour to a week, suggesting that the time scale for some atmospheric phenomena may be set up by the rate of energy loss through upward-propagating waves.