Exner function

The Exner function is an important parameter in <a href="/facts/Atmospheric_model/j7epJxSw">atmospheric modeling</a>. The Exner function can be viewed as non-dimensionalized pressure and can be defined as:

Π
        =
        
          
            (
            
              
                p
                
                  p
                  
                    0
                  
                
              
            
            )
          
          
            
              R
              
                d
              
            
            
              /
            
            
              c
              
                p
              
            
          
        
        =
        
          
            T
            θ
          
        
      
    
    {\displaystyle \Pi =\left({\frac {p}{p_{0}}}\right)^{R_{d}/c_{p}}={\frac {T}{\theta }}}

where 
 
 
 
 
 p
 
 0
 
 
 
 
 {\displaystyle p_{0}}
 
 is a standard reference surface pressure, usually taken as 1000 <a href="/facts/HPa/Am1To2Qm">hPa</a>; 
 
 
 
 
 R
 
 d
 
 
 
 
 {\displaystyle R_{d}}
 
 is the <a href="/facts/Specific_gas_constant/RUXszrMH">specific gas constant</a> for dry air; 
 
 
 
 
 c
 
 p
 
 
 
 
 {\displaystyle c_{p}}
 
 is the <a href="/facts/Table_of_specific_heat_capacities/LhKdTqVN">specific heat capacity of dry air</a> at constant pressure; 
 
 
 
 T
 
 
 {\displaystyle T}
 
 is the <a href="/facts/Absolute_temperature/JXeJJPa6">absolute temperature</a>; and 
 
 
 
 θ
 
 
 {\displaystyle \theta }
 
 is the <a href="/facts/Potential_temperature/nwTn25SC">potential temperature</a>. It is named after <a href="/facts/Felix_Maria_von_Exner-Ewarten/Twsh6nDx">Felix Maria von Exner-Ewarten</a>.

<ul><li>Pielke, Roger A. Mesoscale Meteorological Modeling. Orlando: Academic Press, Inc., 1984.</li>
<li>U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service. National Weather Service Handbook No. 1 - Facsimile Products. Washington, DC: Department of Commerce, 1979.</li></ul>

Exner function open-in-new

Exner function