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<br /> <br />t V2,q2,02 <br />{ t&P2 <br /> <br />22 <br /> <br />Vo,qo,Oo <br /> <br />} V"q ,,0, <br />t&P, <br /> <br />2, <br /> <br /> <br />t&Po <br /> <br />20 <br />Xo <br /> <br />x, <br /> <br />X2 <br /> <br />~: Symbolic two-dimensional flow <br />across a barrier. <br /> <br />1 r ~ <br />r 0 , 1 = PwAX L (q 0 + Qo) g <br /> <br />~] <br />- (ql+Qd g <br /> <br />where: <br /> <br />ro) 1 = average precipitation rate OVI!r <br />the distance AX <br /> <br />q = 1 ayer mean water vapor specif'i c <br />humidity <br /> <br />Q = layer mean cloud water (liquid <br />or solid) specific humidity <br /> <br />AP = layer thickness (in pressure <br />units) <br /> <br />v = mean horizontal velocity of <br />1 ayer <br /> <br />g = gravity <br /> <br />Pw = density of water (I g cm-3) <br /> <br />For two-dimensional, steady-state, <br />hydrostatic flow, the continuity equatil)n <br />can be written (assuming water substance <br />changes negligible): <br /> <br />APO Vo = AP1Vl = AP2V2 <br />--- <br />g g g <br /> <br />Therefore (2) can be written, in general <br /> <br />~[ <br />rI,I+1 = (qI+QI) <br />pAXg <br /> <br />(qI+1+QI+1 )] <br /> <br />where <br /> <br />dqs <br />qI+l - qy = ~ AhI,Y+1 <br /> <br />dqs/dz was defined in (1) and Ahr 1+1 is <br />the parcel vertical displacement 6etween <br />point I and Y+l and AhI,I+1 can be written <br />as <br /> <br />AhI,I+1 = d(zI+1 - ZY) <br /> <br />where' <br /> <br />d = 1 _ (1 _ AhT)(PO - PI) <br />Aho Po - PT <br /> <br />is the vertical displacement factor <br />depending on the degree of stability and <br />moisture of the parcel. <br /> <br />If we define: <br /> <br />qy - qY+l = ACy,Y+l <br /> <br />(5) <br /> <br />( 2) <br /> <br />as condensation per unit mass, occurring as <br />the parcel moves from point I to point 1+1, <br />and specify that a constant fraction E of <br />the sum of condensate formed and "imported" <br />precipitates over AX, the remaining cloud <br />water, QY+1 at point 1+1 is: <br /> <br />QY+1 = {1-E)Qy + (1-E)ACI,I+1 (6) <br /> <br />Now, substituting (5) and (6) into (2) <br />yields: <br /> <br />rI 1+1 = VpOAPo E [QI + ACI 1+1] (7) <br />, W{gAX) , <br /> <br />The tl!rm [Qy + ACI 1+1] can be either <br />>0 (condensation)'or , 0 (evaporation). <br />In the latter case, rI,I+l = O. <br /> <br />The model uses, a$ input: <br /> <br />. Rawinsonde data analyzed and <br />interpolated for 15 evenly <br />spaced pressure layers. <br /> <br />. A fine mesh topography grid of <br />35 x 45 points with AX = 10.0 km <br />(see Fig. 2). <br /> <br />. The stations' coordinates for <br />which estimates of precipitation <br />are to be made. <br /> <br />( 3) <br /> <br /> <br />. <br /> <br />. <br /> <br />. <br /> <br />(4) <br /> <br />I · <br />- <br />. <br />! . <br />8 <br /> <br />. <br /> <br />. <br /> <br />Ff~. 2: Model topography obtained using <br />a 0 km grid interval. <br />