126 Table 40 



gradient wind 



The equation for the gradient wind speed V in cgs units is, 



v=rt 



where 



(-'+V 1+ ^> (1) 



r — "radius of curvature" of the trajectory = R tan a (see Table 166), 

 / = Coriolis parameter 2w sin <j> (« = angular velocity of rotation of the earth, 

 # = latitude), 

 V„ = geostrophic wind speed (see Tables 37-39). 



Equation (1) can be rewritten in the following form 



v= 3600 I l(_ 1 ^ _4Vg_\ (2) 



2 \ \ 3600 r\) 



for any of the following consistent combinations of units: 



a. V and V „ in miles per hour, r in statute miles, 



b. " " " " knots, r in nautical miles, 



c. " " " " kilometers per hour, r in kilometers. 



V is a function of the parameter rf and of the geostrophic wind speed V t only. In applying 

 equations (1) and (2) the following sign convention is necessary: for cyclonic curvature 

 rf > 0, for anticyclonic curvature rf < 0. 



Table 40 A gives values of the parameter rf as a function of latitude, 0, and r. Table 

 40 B gives values of V for cyclonic curvature and Table 40 C for anticyclonic curvature 

 as a function of the parameter rf and the geostrophic wind speed V „. 



To find the gradient wind speed at a given point : 



1. Determine the latitude <t> and the value r of the trajectory. (Table 166 indicates 



a method for finding r on a polar stereographic map projection; for other 

 projections an estimate must be made.) 



2. From Table 40 A find the parameter rf. (This parameter is linear in r so that 



values for other radii than those given may be readily determined from the table, 

 e.g., if r — 2300, add the values for r — 2000 and r = 300.) 



3. Determine the geostrophic wind speed V„ at the given point (see Tables 37-39). 



(V a and r must be in one of the consistent combinations of units given above.) 



4. Enter Table 40 B (cyclonic case) or Table 40 C (anticyclonic case) with the 



arguments rf and V „. The corresponding tabular value is the gradient wind V 

 in the same units as V„. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



