# gsw_geo_strf_PISH

`Pressure intergrated steric height PISH (75-term equation)`

## USAGE:

`geo_strf_PISH = gsw_geo_strf_PISH(SA,CT,p,p_ref)`

## DESCRIPTION:

```Calculates pressure-integrated steric height PISH as the integral of
pressure multiplied by specific volume anomaly from the pressure p of
the “bottle” to the reference pressure p_ref, divided by the constant
value of the gravitational acceleration, 9.7963 m s^-2, this being the
gravitational acceleration averaged over the surface of the global ocean
(see page 46 of Griffies, 2004).  ```
```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.```
```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
expression for specific volume of 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).  For dynamical oceanography we may
take the 75-term rational function expression for specific volume as
essentially reflecting the full accuracy of TEOS-10.  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 PISH.`

## 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_PISH = Pressure intergrated steric height           [ kg s^2 ]
The output geo_strf_PISH has dimensions 1xN, where N is the number of
profiles in the input data.
Note. If p_ref exceeds the pressure of the deepest “bottle” on a
vertical profile, then the pressure-integrated steric height is
returned as NaN.```

## 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_PISH = gsw_geo_strf_PISH(SA,CT,p,p_ref)`
`geo_strf_PISH =`
`  5.766680282284854e+06`

## AUTHOR:

`Paul Barker, Trevor McDougall and Tom Haine [ 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).```
```Griffies, S. M., 2004: Fundamentals of Ocean Climate Models. Princeton,
NJ: Princeton University Press, 518 pp + xxxiv.```
```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. (3.31.4) and section 3.31 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`