# Re: [ferret_users] converting depth cordinated into density (sigma) cordinate

```If you really want to convert pressure to depth, see the paper by

```
Saunders P.M., Fofonoff N.P. (1976): Conversion of pressure to depth in the ocean. Deep-Sea Res. 23:109-111.
```
Here is a code snippet to do that conversion in Ferret:

! Input for pressure-to-depth conversion
let lat = -30       ! latitude in degrees (30S, same result as 30N)
let P = 10000       ! hydrostatic pressure in decibars

! Saunders & Fofonoff algorithm to compute depth (m) from pressure (db)
let alat = abs(lat)
let a = sin(alat / 57.29578)
let xx = a * a
let gr = 9.780318 * (1.0 + (5.2788E-3 + 2.36E-5 * xx) * xx) + 1.092E-6 * P
let depthterm = (((-1.82E-15 * P + 2.279E-10) * P - 2.2512E-5) * P + 9.72659) * P
let depth = depthterm / gr
list depth

```
The corresponding code in Fortran is available in a 1983 report from UNESCO (see page 28):
```
```
UNESCO (1983): Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science 44:1-55.
```
http://unesdoc.unesco.org/images/0005/000598/059832eb.pdf

Cheers,

Jim

On Wed, 18 Jan 2017, binny ra wrote:

```
```Hi Ryo, Ansley and Ferreters

As of now its very difficult for me to get Z axis in meters from Z axis of dbars but what I can do is this:-

suppose I am having two NC files
salt_pressure.nc          !! salinity in unit of dbars axis
salt_meter.nc               !! salinity in units of meter axis

so can I do like this to get salinity in the Z axis of units of meter

let salt_new_meter=salt_pressure[gz=salt_meter]

so in this way I am replacing the Z axis of dbars from Z axis of meters. Is this the way I can use to get my
desired results ?

regards, binny

On Wed, Jan 18, 2017 at 1:09 PM, Ryo Furue <furue@xxxxxxxxxx> wrote:
Hi Binny, Ansley, and ferret users,

On Wed, Jan 18, 2017 at 5:32 AM, Ansley C. Manke
<ansley.b.manke@xxxxxxxx> wrote:

> The method would be the same. You need an expression that relates the units
> of Z axis to the other; it doesn't matter what is being converted to what.

I agree, but one issue that may not be obvious when you want to
convert to the z axis, is how to find the "z field".  In the
z-to-sigma (z-to-density) conversion of the 3D variable salt

ZAXREPLACE( salt, sigma, z[gz=axden]) ,

you need the 3D variable sigma(x,y,z).  To convert a 3D variable
salt(x,y,p) to the z axis, one needs the 3D "z field" z3d(x,y,p),
which is the depth of the isobaric surface p at (x,y). If you have
such a variable, then the conversion would be

ZAXREPLACE(salt, z3d, z[gz=z_axis]) .

You can compute z3d using the hydrostatic relation dp/dz = - rho z if
you know density.

HAVING SAID THAT, is this really what you are after, Binny?

Normally, pressure-to-z conversion is just to "re-interpret" the
vertical axis: You equate 10 dbar to 10 meters, for example. If this
re-interpretation is fine, all you need is

define axis/z= . . . ./units=meters  z_axis
let salt_in_z = salt_in_p[gz=z_axis@ASN]

See
http://ferret.pmel.noaa.gov/Ferret/documentation/users-guide/Grids-Regions/GRIDS#_VPINDEXENTRY_663
for the @ASN transformation.  There is an example down the webpage.

Regards,

Ryo

```
```
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CEA-CNRS-UVSQ

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