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Show tain of smooth form co exp (-ak) cos k x dk = where ' a = = = k = wave number h 2 h a2 + X2 .a (10) amplitude of ground perturbation maximum height of ground perturbation half width, in the x distance (where C = £) 2 A solution for the perturbation above a mountain is obtained by setting k = 0. iFor such an approximation (broad mountain solution) the amplitude of the :(s treamline displacement over an ideal mountain is given by ah (a cos If (z) z -x sin /f (z) z) (11) smd the corresponding equation for the perturbation vertical motion is: 1 Ii w = -2a X hu (a cos /f (z) z-x sin /f (z) z) - ahu sin /f(z) z (a2 + x2) -2 (12) (a2 +x2) The solution to equation . (5) is periodic in the vertical with a wave length equal to 211 I /f (z). Figure 18 is the output of the airflow section of the model for actual mountairi •wind profile data for 29 January 1969, 1900 MST, and the mountain profile used for the Park Range. 11 1 The limitations and the validity of the linearized theory of mountain airflow used in this model have been discussed by several investigators (Queney 1948, Corby 1954). From these analyses it can be concluded that equations 5 and 6 are a valid first approximation to two-dimensional flow over a smooth ilm ountain range. Results will obviously not be valid for individual areas over rough terrain or near the mountain slope. Verification of the airflow over a given range should be obtained with aircraft and balloon measurements . It seems clear that adjustments in the mountain parameters will be necessary 1 'to "calibrate 11 the model for a given area. ll ii 13. 1. 2 1 Condensation of Orographic Clouds Us ing the perturbation vertical velocities obtained with the a i rflow model, c alculation of condensed water can next be consider ed. The rate of for m a 1tion of liquid water (assuming no supersaturation) can be given a s dQ C = dz w dq - S dz 41 (13) |