Leaky Rigid Lid: New Dissipative Modes in the Troposphere

4 An effective boundary condition is derived for the top of the troposphere, based on a wave 5 radiation condition at the tropopause. This boundary condition, which can be formulated 6 as a pseudo-differential equation, leads to new vertical dissipative modes. These modes can 7 be computed explicitly in the classical setup of a hydrostatic, non-rotating atmosphere with 8 a piecewise constant Brunt-Väisälä frequency. 9 In the limit of an infinitely strongly stratified stratosphere, these modes loose their dis10 sipative nature and become the regular baroclinic tropospheric modes under the rigid-lid 11 approximation. For realistic values of the stratification, the decay time-scales for the first 12 few modes range from an hour to a week, suggesting that the time-scale for many atmo13 spheric phenomena may be set up by the rate of energy loss through upwards propagating 14 waves. 15