Calculating the depth from pressure 
Algorithms  Seawater  
Written by Jan Schulz  
Tuesday, 03 June 2008 16:50  
Calculating the depth from pressure in seawater
ObjectiveTo identify how deep an instrument is deployed in the ocean, the ambient pressure is measured. With respect to the gravity variation with latitude and geopotential anomaly this pressure can be converted into meters depth. Saunders and Fofonoff (Saunders & Fofonoff 1976) developed an accurate equation for pressure to depth conversion using the hydrostatic equation and the KnudsenEkman equation of state. Here a function is given to compute depth in meters from pressure in decibars, latitude in degrees and geopotential anomaly in meters.
EquationThe exact formula is not convenient for routine applications due to logaritms and integrations. For practical use a fitted fourth order polynomial is used to calculate the specific volume V of a standardised ocean with a practical salinity of 35 and 0°C at depth p in decibars. The adopted equation given in the UNESCO handbook ‘Algorithms for computation of fundamental properties of seawater’ (UNESCO 1983) is:
The gravity variation with latitude Φ in degree is calculated by:
_{ } The depth z in meters can be calculated from the gravity variation g, the specific volume V and the geopotential anomaly D in J/kg:
Estimating the depth from pressure based on the Saunders and Fofonoff method (Saunders & Fofonoff 1976) results deviate by 0.08 meters at 5000 decibars and 0.44 meters at 10000 decibars (UNESCO 1983).
AlgorithmThe below algorithm in object Pascal is equal to the original Fortran code (UNESCO 1983). For the given values of pressure (decibars), latitude (degree) and geopotential anomaly (dyn meters) the function returns depth in meters. Function Depth (p, Lat, Del: Double) : Double; LiteratureSaunders P.M., Fofonoff N.P. (1976): Conversion of pressure to depth in the ocean. Deep Sea Research 23:109111. UNESCO (1983): Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science 44:155.


Last Updated on Friday, 18 March 2011 18:09 