function vapor_over_ice_sphere,T,rad
   
;-----------------------------------------------------------------------------
; Compute the ratio of saturation vapor pressure over an ice sphere (Ea,i) 
; over the ambient saturation vapor pressure over a plane ice surface (Esat,i).
;
; In:
;   T......temperature, K
;   rad....ice particle radius, nm
;
; Out:
;   Svi....saturation vapor pressure ratio, Svi = Ea,i / Esat,i
;
; Source: Mark Hervig
;-----------------------------------------------------------------------------
   

;- some constants

   R   = 8.314       ; gas constant, J/mol/K
   Mww = 18.0        ; molecular weight of H2O, g/mol
   Sti = 0.12        ; surface tension of ice in the presence of air, J/m2
   Di  = 0.916       ; ice density, g/cm3
   
;- the vapor pressure ratio, according to eqn 6-38 in Pruppacher & Klett,
;  "Microphysics of Clouds and Precipitation"

   Svi = exp(1e3 * 2.* Mww * Sti / ( R * T * Di * rad) )
   
;- done

   return,Svi
   
   end