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<br />t: <br /> <br />tain of smooth form <br /> <br />co <br /> <br />11< <br /> <br />Co = ha J <br /> <br />exp (-ak) cos k x dk = <br /> <br />2 <br />a h <br />2 + 2 <br />a x <br /> <br />(10) <br /> <br />where <br /> <br />C = amplitude of ground perturbation <br />h = maximum height of ground perturbation <br />a = half width, in the x distance (where C = .~) <br />k = wave number <br /> <br />A solution for the perturbation above a mountain is obtained by setting k = O. <br />For such an approximation (broad mountain solution) the amplitude of the <br />streamline displacement over an ideal mountain is given by <br /> <br />ah <br />a2 + x2 <br />and the corresponding equation for the perturbation vertical motion is:: <br /> <br />C = <br />z <br /> <br />(a cos If (z) z-x sin If (z) z) <br /> <br />(11) <br /> <br />w = -2a X hu (a cos If (z) z-x sin If (z) z) - ahu sin If(z) z 1[12) <br />(a2 + x2)2 (a2+x2) <br /> <br />~ <br /> <br />The solution to equation.(5) is periodic in the vertical with a wave length <br />equal to 211 / If (z). Figure 18 is the output of the airflow section of the <br />model for actual mountain wind profile data for 29 January 1969, 1900 MST, <br />" and the mountain profile used f9r the Park Range. <br />'( '7"16 rOl ".11111 l1Hrrfllldy <br /> <br />The limitations and the validity of the lineari.zed theory of mountain airflow <br />used in this model have been discussed by several investigators (Queney <br />48,"~orby 1954). From these analyses it can be concluded that equations <br />andCVare a valid first approximation to two-dimensional flow over a smooth <br />mountain range. Results will obviously not be valid for individual areas over <br />rough terrain or ne9;!J:h~__ID.Qll:g.tain."slo~.e.. Verification of the airflow over a <br />given range should be obtained with aircraft and balloon measurements. It <br />seems clear tpat adjustments in the mountain parameters will be necessary <br />to "calibrate" the model for a given area. <br /> <br /> <br />3. 1. 2 Condensation of Orographic Clouds <br /> <br />" <br /> <br />Using the perturbation vertical velocities obtained with the airflow model, <br />calculation of condensed water can next be considered. The rate of forma- <br />tion of liquid water (assuming no supersaturation) can be given as <br /> <br />dQ <br />c <br />dz <br /> <br />= w dq <br />~ s <br />dz <br /> <br />(13) <br /> <br />~ <br /> <br />41 <br />