# gsw_geo_strf_dyn_height

dynamic height anomaly (75-term equation)

## Contents

## USAGE:

geo_strf_dyn_height = gsw_geo_strf_dyn_height(SA,CT,p,p_ref)

## DESCRIPTION:

Calculates dynamic height anomaly as the integral of specific volume anomaly from the pressure p of the "bottle" to the reference pressure p_ref.

Hence, geo_strf_dyn_height is the dynamic height anomaly with respect to a given reference pressure. This is the geostrophic streamfunction for the difference between the horizontal velocity at the pressure concerned, p, and the horizontal velocity at p_ref. Dynamic height anomaly is the geostrophic streamfunction in an isobaric surface. The reference values used for the specific volume anomaly are SSO = 35.16504 g/kg and CT = 0 deg C. This function calculates specific volume anomaly using the computationally efficient 75-term expression for specific volume (Roquetet al., 2015).

This function evaluates the pressure integral of specific volume using SA and CT interpolated with respect to the intergral of bouyancy frequency N2 using the method of Barker et al. (2017). This "curve fitting" method uses a Piecewise Cubic Hermite Interpolating Polynomial to produce a smooth curve with minimal artificial watermasses between the observed data points.

Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougallet al.(2003). The GSW library function "gsw_infunnel(SA,CT,p)" is avaialble to be used if one wants to test if some of one's data lies outside this "funnel".

Click for a more detailed description of dynamic height anomaly. |

## INPUT:

SA = Absolute Salinity [ g/kg ] CT = Conservative Temperature [ deg C ] p = sea pressure [ dbar ] ( i.e. absolute pressure - 10.1325 dbar ) p_ref = reference pressure [ dbar ] ( i.e. reference absolute pressure - 10.1325 dbar )

SA & CT need to have the same dimensions. p may have dimensions Mx1 or 1xN or MxN, where SA & CT are MxN. p_ref needs to be a single value, it can have dimensions 1x1 or Mx1 or 1xN or MxN.

## OUTPUT:

geo_strf_dyn_height = dynamic height anomaly [ m^2/s^2 ]

## EXAMPLE 1:

SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;] CT = [28.8099; 28.4392; 22.7862; 10.2262; 6.8272; 4.3236;] p = [ 10; 50; 125; 250; 600; 1000;] p_ref = 1000

geo_strf_dyn_height = gsw_geo_strf_dyn_height(SA,CT,p,p_ref)

geo_strf_dyn_height =

17.434370534476397 15.077272863514917 11.353433025780669 7.942688032614864 3.608928554434066 0

## EXAMPLE 2:

SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;] CT = [28.8099; 28.4392; 22.7862; 10.2262; 6.8272; 4.3236;] p = [ 10; 50; 125; 250; 600; 1000;] p_ref = 500

geo_strf_dyn_height = gsw_geo_strf_dyn_height(SA,CT,p,p_ref)

geo_strf_dyn_height =

12.723940504666212 10.366842833704730 6.643002995970482 3.232258002804677 -1.101501475376121 -4.710430029810187

## AUTHOR:

Paul Barker and Trevor McDougall [ help@teos-10.org ]

## VERSION NUMBER:

3.06 (15th May, 2017)

## REFERENCES:

Barker, P.M., T.J. McDougall and S.J. Wotherspoon, 2017: An interpolation method for oceanographic data.J. Atmosph. Ocean. Tech.(To be submitted).

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of seawater - 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp. Available from the TEOS-10 web site. See Eqn. (3.7.3) and section 3.27 of this TEOS-10 Manual.

McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater.J. Atmosph. Ocean. Tech.,20, pp. 730-741.

Roquet, F., G. Madec, T.J. McDougall and P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard.Ocean Modelling,90, pp. 29-43. http://dx.doi.org/10.1016/j.ocemod.2015.04.002

The software is available from http://www.TEOS-10.org