A simple analytical expression for indexing the orographic precipitation rate over high mountains is presented. The formula is based upon the assumption that the moisture convergence in the mountainous boundary layer approximately equals the precipitation. Realistic precipitation distributions are obtained when numerical advection is permitted for the Himalayas, Equadorian Andes and the Sierra Nevada Mountains in California. In the latter case the simulated distributions compete well with a fully two-dimensional precipitation model for some unusual stormy events. Following the model results over high mountains, it is suggested that for the distribution of precipitation, particularly over the high mountains, the detailed microphysical processes may play a lesser essential role than that for small to medium size mountains.
The elevation of maximum orographic precipitation zm, is investigated and an analytical expression for zm is derived for a bell-shaped mountain. This expression predicts zm values that are in general agreement with observations. The elevation of maximum precipitation zm is found to always be shifted to lower levels than the point of the steepest slope. It is also shown that an upper limit for zm exists. This upper limit is independent of the mountain height and is determined mainly by the moisture scale height and the tropospheric wide height.
In addition to the two maxima of precipitation over the Himalayas that have been observed in the foothills and at about 2–2.4 km, a third unknown maxima is predicted by the theory. This unobserved maxima is predicted over the Great Himalayan Range at the height of 4 km. Such a maxima, if it exists, could not be detected due to the lack of enough observations at high elevations.