# gsw_geo_strf_dyn_height

`dynamic height anomaly (75-term equation)`

## 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 (Roquet et 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 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.```

## 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`