# 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 using the MRST-PCHIP method of Barker and McDougall (2020). 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 =

16.829126675036644 14.454693755102685 10.727894578402342 7.699845274649316 3.578081589449148 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 =

12.172172845782585 9.797739925848624 6.070940749148281 3.042891445395256 -1.078872239804912 -4.656953829254061

## AUTHOR:

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

## VERSION NUMBER:

3.06.12 (29th July, 2021)

## REFERENCES:

Barker, P.M., and T.J. McDougall, 2020: Two interpolation methods using multiply-rotated piecewise cubic hermite interpolating polynomials.J. Atmosph. Ocean. Tech.,37, pp. 605-619. http://dx.doi.org/10.1175/JTECH-D-19-0211.1

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