Tables 49-51 217 



RELATION BETWEEN GEOPOTENTIAL AND GEOMETRIC HEIGHT 1 



Definition of geopotential. — The geopotential or gravity potential at any point is the 

 potential energy, due to gravity, of unit mass at the point. Conventionally, geopotential is 

 taken to be zero at mean sea level, in large part because mean sea level is a horizontal or 

 level surface, and therefore has no component of gravity tangent to it. 



If 



g = acceleration of gravity, cm. sec." 2 , 



Z = geometric height above mean sea level, cm., 



$ = geopotential, cm. 2 sec." 2 



then 



z 



*=l gdZ (l) 



which is numerically equivalent to the work done against gravity in lifting unit mass from 

 mean sea level to a point at elevation Z. The cgs unit of geopotential is the cm. 2 sec. -2 , 

 equivalent to the erg gram. -1 



Prof. V. Bjerknes 2 made use of the term "dynamic height" in referring to the geo- 

 potential of a point, because the latter is preferable to geometric height in meteorology 

 as a representation of the vertical coordinate of the point. Professor Bjerknes proposed 

 as the unit of geopotential the so-called geodynamic meter (gdm.) or dynamic meter, for 

 short. By definition 1 geodynamic meter = 10 m. a sec." 2 = 10 5 cm. 2 sec." 2 



At the meeting of the International Commission for the Exploration of the Upper Air 8 

 held in London, 1925, a resolution was adopted to the effect that heights in all forms and 

 publications of the International Commission are to be represented as geopotentials in 

 terms of the geodynamic meter as the unit. This unit was officially sanctioned until 1947 

 when -the Aerological Commission of the International Meteorological Organization met 

 in Toronto. At the Toronto meeting of the Aerological Commission 4 a new unit of geo- 

 potential was adopted for official use in aerological work. This was given the name 

 geopotential meter (gpm.), and defined by the relation 1 geopotential meter = 0.98 

 dynamic meter. It follows that 1 gpm. = 0.98 gdm. = 9.8 m. 2 sec." 2 = 98,000 cm. 2 sec." 2 



Accordingly, if 



g = acceleration of gravity, m. sec." 2 , 

 Z = geometric height, m., 

 <£ = geopotential, gpm. 



*=h\ 9 dZ (2) 



The unit of geopotential in English measures was given the name geopotential foot 

 (gpft.) ; its relation to the geopotential meter is 1 gpft. = 0.3048 gpm. 



The geopotential meter was chosen as the unit of geopotential because the geometric 

 height in meters and the geopotential in geopotential meters are approximately equal in 

 the lower atmosphere, where g is approximately 980 cm. sec." 2 



Pressure altitudes in the standard atmosphere are actually in terms of a special unit of 

 geopotential. For the NACA Standard Atmosphere the unit called the meter is actually 

 0.980665 gdm., and for the ICAN Standard Atmosphere it is actually 0.98062 gdm. ( See 

 Tables 63 and 64.) 



Computation. — To integrate equation (2), using Newton's inverse-square law of gravi- 

 tation, let 



g$ = actual acceleration of gravity at mean sea level at the given latitude <P, 



m. see." 2 , 

 g = acceleration of gravity, in m. sec." 3 , at elevation Z meters and latitude <p, 

 R = appropriate value of radius of earth at given latitude, in meters, 



then 



g = g*R 2 /(R + Z)' (3) 



1 Harrison, L. P., unpublished manuscript, 1949. 



"Bjerknes, V., et al., Dynamical meteorology and hydrography, vol. 1, Washington, 1910. 

 * International Commission for the Exploration of the Upper Air. Report of the meeting in London, 

 April 16-22, 1925. Meteorol. Off. Publ. No. 281, London, 1925. 



4 I. M. O. Aerological Commission, abridged final report, Publ. 62, Lausanne, 1949. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



