A method is proposed to evaluate the coupled mass, momentum and thermal energy budget equations for a deep valley under two-dimensional, steady-state flow conditions. The method requires the temperature, down- valley wind and valley width fields to be approximated by simple analytical functions. The vertical velocity field is calculated using the mass continuity equation. Advection terms in the momentum and energy equations are then calculated using finite differences computed on a vertical two-dimensional grid that runs down the valley's axis. The pressure gradient term in the momentum equation is calculated from the temperature field by means of the hydrostatic equation. The friction term is then calculated as a residual in the xmomentum equation, and the diabatic cooling term is calculated as a residual in the thermal energy budget equation.
The method is applied to data from an 8-km-long segment of Colorado's; Brush Creek Valley on the night of 30–31 July 1982. Pressure decreased with distance down the peak on horizontal surfaces, with peak horizontal pressure gradients of 0.04 hPa km−1. The valley mass budget indicated that subsidence was required in the valley to support calculated mean along-valley mass flux divergence. Peak subsidence rates on the order of 0.10 m s−1 were calculated. Subsiding motions in the valley produced negative vertical down-valley momentum fluxes in the upper valley atmosphere, but produced positive down-valley momentum fluxes below the level of the jet. Friction, calculated as a residual in the x momentum equation, was negative, as expected on physical grounds. and attained reasonable quantitative values.
The strong subsidence field in the stable valley atmosphere produced subsidence warming that was only partly counteracted by down-valley cold air advection. Strong diabatic cooling was therefore required in order to account for the weak net cooling of the valley atmosphere during the nighttime period when tethered balloon observations were made.