Vertical velocity field computation package


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Vertical velocity computation package


1. Generalities

This page provides a simple package to compute vertical velocities from a known density field and a known geostrophic field. The scientific background, based on the Omega equation can be found for example in:

  1. Hoskins, B.J., Draghici, I., and Davies, H. (1978). A new look at the omega equation. Quart. J. Roy. Meteor. Soc., 104:31-38.
  2. Tintore, J., Damia, G., and Alonso, S. (1991). Mesoscale Dynamics and Vertical Motion in the Alboran Sea. American Meteorological Society, 21:811-823.
  3. Viudez, A., Tintore, J., and Haney, R. (1996). Circulation in the Alboran sea as determined by quasi-synoptic hydrographic observations. Part I: Three-dimensional structure of the two anticyclonic gyres. Journal of Physical Oceanography, 26:684-705.
Solving the omega equation involves the following steps:
  1. - analysis of hydrographic T,S data on a regular grid (see details in the README FILE)
  2. - computation of density from a state equation
  3. - computation of geostrophic velocity field with a given level of no motion
  4. - omega equation inversion
Boundary conditions for the omega equation are imposed as follows: w=0 everywhere (bottom and open sea).

Units are 'kg/m3' for density, 'm/s' for horizontal geostrophic velocity. Results for vertical velocity are provided in m/day.

2. Contents

The following package contains the omega source code and a test example.


To install the source, download the file, uncompress the file with

'gunzip omega.tar.gz'

and extract the files with

'tar xvf omega.tar'

If your computer does not know 'tar' or 'gunzip', try the following package

and uncompress it with


The single source file 'omega.f' contains the computation routines Compile it with the following command:

'f77 -O omega.f -o omega.a'

File 'omega' is a korn shell script. It pipes every information to the omega code.

The files 'alboran.sal.*' and 'alboran.tem.*' in the directory 'data' are the data files (example of the survey 1 of the Omega-1 cruise).

To run the computation, simply type


The resulting file 'omega.W' should be equal (or very close) to file ''. The result at level 26 (101m depth) should look like the postscript file


3. Format description

To understand the way the data is stored, please refer to the figure below. The file are stored in a 3D array (matrix) with 3 indexes I, J, K, going from 1 to IMAX, 1 to JMAX, 1 to KMAX. The origin is located at the 'bottom left deepest corner'.

Output loops are nested as follows: DO K=1,NZ DO J=1,NY WRITE(55,541) (W(I,J,K),I=1,NX) ENDDO ENDDO 541 FORMAT(8F10.5) There are KMAX horizontal slices from the bottom (K=1) to the surface (K=KMAX). Increasing I's go from W to E and increasing J's go from S to N. Of course, you are free to write your own I/O routines: just mind the computation format.



Last modified March 5th, 1999
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