A Numerical Study of the Initiation of Cumulus Clouds over Mountainous Terrain

Abstract

The initiation of cumulus clouds over mountainous terrain is investigated by means of a numerical model. Two-dimensional motion is simulated over a mountain and valley. Changes at the mountain surface of both temperature and water vapor initiate the motion. The equations are similar to Ogura's (1963) but include an extra buoyancy term due to water vapor. Five cases have been numerically integrated. Cases 1 and 4 are included to demonstrate the dynamic effect of water vapor by comparison with a previously integrated “dry model.” Case 1, which allows evaporation at the mountain surface, causes the upslope motion to develop at a 20 per cent faster rate than the dry case. Case 4, which allows no evaporation at the surface, augments the motion over that of the dry case by approximately 10 per cent. A comparison of the results with Braham and Draginis' (1960) observation of potential temperature and water vapor over the Santa Catalinas shows some similarities but indicates that the numerical model has eddy mixing effects that are too small. Case 2 is included to model cloud initiation on a typical Tucson summer day with run in the mountains. The initial environmental stability is greater than in Case 1 (2.8C km⁻¹ potential temperature change compared to 1.0C km⁻¹ for Case 1), but the water vapor content in Case 2 is greater. The effect is to slow the development of the slope winds and the development of the cloud. Cloud initiation occurs after approximately two hours from the assumed initial equilibrium conditions. The cloud development extends over 30 min. The position of the stream function center with respect to the cloud outline is crucial to the shape and evolution of the cloud. A second stream function center rising beneath the first initiates a second growth surge in the cloud. Case 3 is included to show the effect of decreasing the mountain slope from 45° to approximately 26°. The mountain ridge is 300 m lower than in the other cases. Environmental conditions are the same as those in Case 1. The motion develops slightly slower, a cloud forming 100 m lower and 9 min later (at 72 min) than in Case 1. Case 5 has the same initial conditions as Case 2 but has an eddy mixing coefficient of 40 m sec⁻¹, ten times greater than that in the other cases. The larger diffusion coefficients result in a broader upslope flow and a later cloud initiation than in Case 2. The results are compared with photogrammetric data presented by Orville (1965).