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<br />where -= ~~, in these calculations Wo is assumed 0 at the surface, <br /> <br />dp = 100 mb. Above 400 mb, a top boundary condition is imposed which <br /> <br />assumes that the tropopause acts as a material boundary, forcing verti- <br />cal motion to approach zero. This top boundary condition changes the <br />value of (isign) from plus to minus when p < 400 mb, thereby producing <br />upward motion in the case of divergence above 400 mb and downward motion <br />in the case of convergence above this level. Integration is performed <br />from Po = 900 mb to Pn = 200 mb in all detailed case analyses. Sensi- <br />tivity of vertical motion analyses to integration from top Po = 200 mb <br />to Pn = 900 mb were performed to determine the impact of this method <br />particularly in cases having strong upper-level forcing. Results are <br />presented in Appendix B. In this study, however, all integrations were <br />performed from 900 to 200 mb unless otherwise stated, because errors in <br />upper-level winds are carried downward in the later integration method, <br />and the most reliable winds were generally observed from 900 to 400 mb. <br />Note that no adjustment was made to the vertical motion as suggested by <br />O'Brien (1970) in an effort to maintain computational simplicity. <br /> <br />Horizontal advection is computed in the form: <br /> <br />(S2 - SI) <br />Vp \" p S = U.QS + V AS - u + v <br />EX Ay - AX <br /> <br />(S2 - SI) <br />6.y <br /> <br />( 11) <br /> <br />Where u and v are the average wind components over the grid spacing <br /> <br />and <br /> <br />S2 - SI <br />AX <br /> <br />and S2 - SI <br />6y <br /> <br />are the gradients of a scalar quantity S <br /> <br />across the grid interval AX and6.Y; generally set to AX =Ay = 0.20 <br /> <br />46 <br />