224 Table 52 



GEOPOTENTIAL COMPUTATIONS 



Resolution 78, I. M. O. Twelfth Conference of Directors (Washington, 1947) states: 

 The Conference decides: 



(1) that the geopotential used in upper air reports and analyses shall be expressed in 

 terms of geopotential meters (gpm.), or geopotential feet (gpft.) ; 



(2) that the geopotential meter shall be defined as being equal to 0.98 of the dynamic 

 meter so that the value of the geopotential shall, for practical purposes, be numerically 

 equal to the height expressed in meters. 



The geopotential $ of a point at height Z above mean sea level is the work which must 

 be done against gravity in raising a unit mass from sea level to height Z 



*= \ gds (1) 



where g is the local acceleration of gravity at the height s. Similarly, the difference in 

 geopotential A* between levels si and Si is 



{Si 

 gds (2) 



If po is the pressure at mean sea level and p the pressure at height Z, from the hydro- 

 static equation 



* = R T'mv loge — , in cgs units, (3) 



P 



where R is the gas constant for dry air and T'mv is the mean adjusted virtual temperature 1 

 (°K.) between p and p. Similarly if pi and pi are the pressures at Si and Si respectively 



A* = R T'mv loge — , in cgs units. (4) 



pi 



If A$o is the geopotential difference between levels having pressures pi and pi for a 

 mean temperature of the layer of 0°C. (273.16 °K.) and t'mv is the actual mean adjusted 

 virtual temperature of the layer in °C. 



A$ = A3>„ + A$o -^ (5) 



where T a = 273.16 °K. and 



AS ) o = .R Tolog e £i, in cgs units. (6) 



pi 



Expressing geopotential differences in terms of the geopotential meter, gpm. (1 gpm. = 

 98000 ergs g. -1 = 98000 cm. 2 sec." a = 0.98 dynamic meter), equations (4) and (6) become 



A# = 67.442 T' m v log 10 £• = 67.442 (273.16 + t'mv) log 10 h. (4a) 



pi pi 



A$ = 18422.5 log™^ (6a) 



Pi 



Table 52 A gives A$ in geopotential meters between a given pressure and the nearest 

 standard pressure surface above it. Table 52 B gives A* in geopotential meters between 

 successive standard pressure surfaces as a function of t'mv. Table 52 C gives A$o in geo- 

 potential meters between a given pressure and the nearest standard pressure surface 



below it. Table 52 D gives values of A<£ ~- to be used in connection with the values 



/ 



obtained from Tables 52 A and 52C to determine A* in accordance with equation (5). 

 To evaluate geopotential in terms of geopotential meters : 



1. Determine the geopotential of the surface level. (This quantity is approximately 

 numerically equal to the elevation in meters of the surface level above mean sea 

 level; for exact value see Table 50.) 



1 See Table 72 for definition of mean adjusted virtual temperature. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



