# gsw_geo_strf_dyn_height_pc

dynamic height anomaly for piecewise constant profiles (75-term equation)

## Contents

## USAGE:

[geo_strf_dyn_height_pc, p_mid] = gsw_geo_strf_dyn_height_pc(SA,CT,delta_p)

## DESCRIPTION:

Calculates dynamic height anomaly as the integral of specific volume anomaly from the the sea surface pressure (0 Pa) to the pressure p. This function, gsw_geo_strf_dyn_height_pc, is to used when the Absolute Salinity and Conservative Temperature are piecewise constant in the vertical over sucessive pressure intervals of delta_p (such as in a forward "z-coordinate" ocean model). "geo_strf_dyn_height_pc" is the dynamic height anomaly with respect to the sea surface. That is, "geo_strf_dyn_height_pc" is the geostrophic streamfunction for the difference between the horizontal velocity at the pressure concerned, p, and the horizontal velocity at the sea surface. Dynamic height anomaly is the geostrophic streamfunction in an isobaric surface. The reference values used for the specific volume anomaly are SA = SSO = 35.16504 g/kg and CT = 0 deg C. The output values of geo_strf_dyn_height_pc are given at the mid-point pressures, p_mid, of each layer in which SA and CT are vertically piecewice constant(pc). This function calculates specific volume anomaly using the computationally-efficient 75-term expression for specific volume (Roquet et al., 2015)

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 McDougall et 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 for piecewise constant profiles. |

## INPUT:

SA = Absolute Salinity [ g/kg ] CT = Conservative Temperature [ deg C ] delta_p = difference in sea pressure between the deep and [ dbar ] shallow extents of each layer in which SA and CT are vertically constant delta_p must be positive.

Note. Sea pressure is absolute pressure minus 10.1325 dbar.

SA & CT need to have the same dimensions. delta_p may have dimensions Mx1 or 1xN or MxN, where SA & CT are MxN.

## OUTPUT:

geo_strf_dyn_height_pc = dynamic height anomaly [ m^2/s^2 ] p_mid = mid-point pressure in each layer [ dbar ]

## EXAMPLE:

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;] delta_p = [ 10; 40; 75; 125; 350; 400;]

[geo_strf_dyn_height_pc, p_mid] = ... gsw_geo_strf_dyn_height_pc(SA,CT,delta_p)

geo_strf_dyn_height_pc =

-0.300346215853487 -1.755165998114308 -4.423531083131365 -6.816659136254657 -9.453175257818430 -12.721009624991439

p_mid =

1.0e+002 *

0.050000000000000 0.300000000000000 0.875000000000000 1.875000000000000 4.250000000000000 8.000000000000000

## AUTHOR:

Trevor McDougall & Claire Roberts-Thomson. [ help@teos-10.org ]

## VERSION NUMBER:

3.06 (15th May, 2017)

## REFERENCES:

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 Eqns. (3.32.2) and (A.30.6) of this TEOS-10 Manual.

McDougall, T. J. and A. Klocker, 2010: An approximate geostrophic streamfunction for use in density surfaces. Ocean Modelling, 32, 105-117. See section 8 of this paper.

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, P.M. Barker, 2015: Accurate polynomial expressions for the density and specifc volume of seawater using the TEOS-10 standard. Ocean Modelling.

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