The addition of heat to a stratified airstream with application to the dynamics of orographic rain

Abstract

SUMMARYThe response of a stratified airstream to combined thermal and orographic forcing is investigated theoretically using the linearized hydrostatic equations of motion. The magnitude of the heating aloft is computed from observed rainfall rates. The elevated heating is shown to produce vertically propagating waves whose amplitude, relative to the mountain waves, is determined by the parameter gQb/cpTUaNh (symbols Appendix I). For typical wind speeds and rainfall rates the thermally generated waves will equal or exceed the orographically generated waves. These waves produce large vertical variations in the wave momentum flux at the levels where heat is being added and alter, or even reverse, the mountain drag. In hydrostatic flow, the phase relationship between the heating rate and the induced vertical displacements is found, unexpectedly, to be negative. In the vicinity of the heating, air parcels are displaced downwards. This result can be explained by wave propagation ideas but not by parcel arguments. This helps to explain why mountain wave amplitudes are sometimes reduced in moist atmospheres. The broad heat-induced descent may act to limit the amount of condensation-precipitation occurring in a stable middle-level orographic cloud. Other types of orographic precipitation involving embedded convection in stratus layers, low level feeder clouds, or deep cumulus convection may not be adversely effected by the heat-induced descent.

Understanding Hector: The Dynamics of Island Thunderstorms

“…In this section we examine a linear model of flow over an isolated heat source in order to gain insight into the effects of that heating. The linear response of an airflow to prescribed heating has been examined by a number of authors (e.g., Malkus and Stern 1953;Raymond 1972;Smith and Lin 1982;Lin 1986). In this study, we follow the work of Lin (1986) who developed a model of the three-dimensional response to an isolated heat source.…”

Orographic–convective flows, wave reflection, and gravity-wave momentum fluxes in a two-layer hydrostatic atmosphere

“…We consider the finite-depth convective forcing which extends from z ¼ h 1 ¼ 1 km to z ¼ h 2 ¼ 11 km vertically and has the half-width of heating a c ¼ 10 km and b c ¼ 5a c . Smith and Lin (1982) and Chun andBaik (1998, 2002), respectively, in which orographically and convectively forced mesoscale flows and momentum fluxes are discussed.…”

“…The parameter c 3 ¼ (N S /N T ){R 1 2 þ R 2 2 -2R 1 R 2 cos(h 1 -h 2 þ 2h H0 )} is related to the wave transmission through the tropopause. When N T ¼ N S and s ¼ 0, M m is equal to the momentum flux given in Smith and Lin (1982) in which uniform basicstate wind speed and static stability are considered. The convectively forced momentum flux component can be written as…”

“…In a single-layer atmospheric setting, Smith and Lin (1982) and Lin and Smith (1986) showed that the linear combination of orographically and convectively forced flows determine total flows in the region where orographic precipitation occurs. Davies and Sch ar (1986) considered diabatic heat released from non-precipitating clouds accompanied by mountain lee waves in a single-layer atmosphere.…”

“…An overview of gravity-wave drag parameterizations is given in Kim et al, (2003). Smith and Lin (1982) presented an analytic expression for the vertical flux of the horizontal momentum in the case of uniform basic-state wind speed and static stability. Their expression contains a momentum flux cross term which results from the non-linear interaction between orographically and convectively forced flows.…”