A Diagnostic Equation for Tendency of Lapse-Rate-Tropopause Heights and its Application

The tropopause is the boundary between the troposphere and stratosphere, and is normally defined by the temperature lapse rate. Previous studies have noted that synoptic-scale and planetary-scale disturbances bring about lapse-rate-tropopause (LRT) height fluctuations on time scales from several days to several years. In the present study, a diagnostic expression for the tendency of LRT height is derived by assuming that the LRT can be characterized as a discontinuity in the vertical gradient of the potential temperature. In addition, the contribution from each term in the thermodynamic equation to the LRT height is quantified. The derived equation is validated by examining the time variation of the LRT height associated with baroclinic waves in an idealized numerical calculation, that of the zonal mean LRT height in GPS radio-occultation data, and that of the LRT height in reanalysis data. Using the derived equation, the factors of the seasonal cycle of the Arctic tropopause are quantitatively investigated.