Tropopause Height Calculator

The tropopause marks the top of the convectively stirred part of the atmosphere, where the steady decline of temperature with height gives way to an isothermal or warming stratosphere. This tool locates it by the simplest physical route: if the troposphere cools at a roughly constant rate gamma from a surface temperature T0, the height at which temperature reaches the observed tropopause value Tt is (T0 - Tt) / gamma. Pressure at that level follows from the hydrostatic barometric relation P = P0 (Tt/T0)^(g / (gamma R)), where the exponent is close to 5.26 for the standard 6.5 K per km lapse rate with R = 287.06 J per kg per K. Typical outcomes bracket the answer. A mid latitude tropopause sits near 10 to 12 km with a temperature around 215 to 220 K and pressure near 200 to 250 hPa, while a tropical tropopause reaches 16 to 18 km, is far colder at 190 to 195 K, and lies near 100 hPa. The latitude estimate included here, roughly 17 minus 8 times the square of the sine of latitude in km, captures that equator-to-pole contrast. The method has clear limits. Real lapse rates are not constant with height, the WMO thermal definition requires the lapse rate to fall to 2 K per km with that condition sustained through the next 2 km rather than a simple temperature crossing, and near the jet streams double tropopauses and tropopause folds make any single height ill defined.

Until the end of the nineteenth century the atmosphere was assumed to keep cooling upward indefinitely. Instrumented free balloons overturned that. Leon Teisserenc de Bort, working from his observatory at Trappes near Paris, and Richard Assmann in Berlin both reported in 1902 that above roughly 11 km the temperature stopped falling. Teisserenc de Bort proposed the names troposphere for the churning lower layer and stratosphere for the stratified layer above it, and the boundary between them came to be called the tropopause. Once radiosondes made soundings routine, a reproducible definition became necessary. The World Meteorological Organization adopted the thermal criterion in 1957, defining the first tropopause as the lowest level where the lapse rate falls to 2 degrees C per km provided the average lapse rate over the next 2 km does not exceed that value, and allowing explicitly for a second tropopause aloft. Dynamical meteorology later added the potential vorticity definition, commonly placed between 1.5 and 3.5 PVU, which handles tropopause folds and jet stream structure better at middle and high latitudes. Long observational records have since been used to track change: Dian Seidel and William Randel, publishing in the Journal of Geophysical Research in 2006, documented a rising global tropopause consistent with tropospheric warming and stratospheric cooling.