BACKGROUND 183 



(1) A barotropic level (level of nondivergence) exists at some pressure 

 level greater than 500 mbar. 



(2) The horizontal wind velocity divergence changes sign at the level 

 of nondivergence (LND). 



(3) The vertical velocity vector in the troposphere is proportional to 

 that at the LND. 



(4) The vertical velocity vector (a) vanishes at the surface of the earth 

 and (b) approaches zero at the outer reaches of the atmosphere. 



Commencing with the equation of continuity, 



l^+F-Vp + pV-F + l (pW) = 0, (5.1) 



where p is the density of air, V is the horizontal del operator, V Is the 

 horizontal wind velocity vector, W is the vertical wind speed, and z is the 

 vertical coordinate; and employing horizontal velocity divergence in the 

 natural coordinate system of the form 



F = f^ + . f . (5.2) 



ds dn 



Moler and Holden derive for the magnitude of the vertical vector at the 

 LND, upon employing the vorticity equation. 



(TF)lnd = 



p 



^ (I) (11) 



1 "" 



_7LND ^ dt J LND S dS 



(III) 



LND i OZ J 



(5.3) 



where f is the vertical component of the absolute vorticity. Moler and 

 Holden reason that of the labeled integrals (I) decreases in proportion 

 to the height above the LND and is « (II) at 300 mbar. Since W « V, 

 (III) makes only a small contribution. The expression for (IF)lnd be- 

 comes 



W.No = - i f" Vf^(f-f)dz, (5.4) 



P 7 LND f ds \dx dy/ 



