Re: Geostrophic velocity

[Mick Spillane <Mick.Spillane@xxxxxxxx>]

On Wed, 4 Aug 2004, Mohammed Al Saafani wrote:
> I'm trying to calculate the dynamic height and geostrophic velocity
> using the "dynamic_height.jnl" supported with ferret, but my problem
> that my section is perpendicular to the coast line (making angle with
> lat and also with lon). I had created the section using the example in
> chapter 8 with "sorti and reshape:" to get section with longitude and
> depth, in that latitude is still a variable which was not recognized in
> calculating GEO_U and GEO_Uz in "dynamic_height.jnl" since latitude is
> not a dimension in this case. Its like calculating the geostrophic
> velocity for along track stations.

Hello Mohammed,

!!! See the remark at the end if you are dealing with a situation where
your original data is on an east-west/north-south grid!!!

	I looked at the script dynamic_height.jnl which, as you say, is
based on an east-west/north-south grid. The variable dyn_ht does not
depend on the horizontal grid and should work with any section data.
There are however two problems in the geostrophic variable calculations :

  1) the Coriolis parameter ( 1.458424E-4*SIN(Y/57.29578) in the original)

  2) the horizontal gradient (for example DYN_HT[X=@DDC])

The first of these is easily fixed - just replace Y with the actual
latitude along your section.  The second is a bit trickier. As the script
stands the horizontal derivatives assume that X and Y are in units of
longitude and latitude so that @ddc will return gradients in units of
"per meter".
	In the example in the manual where a section is extracted by
defining XLON and YLAT and using "samplexy", the section axis is abstract
I.  One would need to introduce great circle distances along the section
to properly represent the station spacing.

Here is a snippet I used in a situation where I needed great circle
separations

! computes greatcircle distance (in km) from lon,lat in degrees
let d2r=atan(1.)/45
let lat1=d2r*lat ; lat2=d2r*lat[i=@shf:1]
let lon1=d2r*lon ; lon2=d2r*lon[i=@shf:1]
let ds=111.11*acos(sin(lat1)*sin(lat2)+cos(lat1)*cos(lat2)*cos(lon2-lon1))

These may give you some ideas for how to write a geostrophic calculation
routine for a rotated coordinate system. Perhaps some other user has
already dealt with the issue.

Good luck,
Mick

PS: One other thought comes to mind if you (or other users) were starting
with data on a east-west/north-south grid!
	If you used the existing dynamic_height script on the original
temp and salt, wouldn't it be better (and correct) to samplexy the
resulting geostrophic velocity components to the skewed section, rather than
samplexy'ing the temp and salt to the section and then applying
dynamic_height to the slanttemp and slantsalt variables?