| 1 |
% |
| 2 |
% [] = C_COMPUTE_POTENTIAL_VORTICITY(SNAPSHOT,[WANTSPLPV]) |
| 3 |
% |
| 4 |
% This file computes the potential vorticity Q from |
| 5 |
% netcdf files of relative vorticity (OMEGAX, OMEGAY, ZETA) |
| 6 |
% and potential density (SIGMATHETA) as |
| 7 |
% Q = OMEGAX . dSIGMATHETA/dx + OMEGAY . dSIGMATHETA/dy + (f+ZETA).dSIGMATHETA/dz |
| 8 |
% |
| 9 |
% The optional flag WANTSPLPV is set to 0 by defaut. If turn to 1, |
| 10 |
% then the program computes the simple PV defined by: |
| 11 |
% splQ = f.dSIGMATHETA/dz |
| 12 |
% |
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% Note that none of the fields are defined on the same grid points. |
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% So, I decided to compute Q on the same grid as SIGMATHETA, ie. the |
| 15 |
% center of the c-grid. |
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% |
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% 06/07/2006 |
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% gmaze@mit.edu |
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% |
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|
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function [] = C_compute_potential_vorticity(snapshot,varargin) |
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|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%% Setup |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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global sla netcdf_domain netcdf_suff |
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pv_checkpath |
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|
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%% Flags to choose which term to compute (by default, all): |
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FLpv1 = 1; |
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FLpv2 = 1; |
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FLpv3 = 1; |
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if nargin==2 % case of optional flag presents: |
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if varargin{1}(1) == 1 % Case of the simple PV: |
| 36 |
FLpv1 = 0; |
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FLpv2 = 0; |
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FLpv3 = 2; |
| 39 |
end |
| 40 |
end %if |
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|
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%% Optionnal flags: |
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global toshow % Turn to 1 to follow the computing process |
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|
| 45 |
|
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%% NETCDF files: |
| 47 |
|
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% Path and extension to find them: |
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pathname = strcat('netcdf-files',sla,snapshot,sla); |
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ext = strcat('.',netcdf_suff); |
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|
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% Names: |
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if FLpv3 ~= 2 % We don't need them for splPV |
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filOx = strcat('OMEGAX' ,'.',netcdf_domain); |
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filOy = strcat('OMEGAY' ,'.',netcdf_domain); |
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filOz = strcat('ZETA' ,'.',netcdf_domain); |
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end %if |
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filST = strcat('SIGMATHETA','.',netcdf_domain); |
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|
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% Load files and coordinates: |
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if FLpv3 ~= 2 % We don't need them for splPV |
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ferfile = strcat(pathname,sla,filOx,ext); |
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ncOx = netcdf(ferfile,'nowrite'); |
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[Oxlon Oxlat Oxdpt] = coordfromnc(ncOx); |
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ferfile = strcat(pathname,sla,filOy,ext); |
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ncOy = netcdf(ferfile,'nowrite'); |
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[Oylon Oylat Oydpt] = coordfromnc(ncOy); |
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ferfile = strcat(pathname,sla,filOz,ext); |
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ncOz = netcdf(ferfile,'nowrite'); |
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[Ozlon Ozlat Ozdpt] = coordfromnc(ncOz); |
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end %if |
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ferfile = strcat(pathname,sla,filST,ext); |
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ncST = netcdf(ferfile,'nowrite'); |
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[STlon STlat STdpt] = coordfromnc(ncST); |
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|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% Then, compute the first term: OMEGAX . dSIGMATHETA/dx % |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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if FLpv1 |
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|
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%%%%% |
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%% 1: Compute zonal gradient of SIGMATHETA: |
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|
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% Dim: |
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if toshow,disp('dim'),end |
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nx = length(STlon) - 1; |
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ny = length(STlat); |
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nz = length(STdpt); |
| 90 |
|
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% Pre-allocate: |
| 92 |
if toshow,disp('pre-allocate'),end |
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dSIGMATHETAdx = zeros(nz,ny,nx-1)*NaN; |
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dx = zeros(1,nx).*NaN; |
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STup = zeros(nz,nx); |
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STdw = zeros(nz,nx); |
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|
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% Zonal gradient of SIGMATHETA: |
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if toshow,disp('grad'), end |
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for iy = 1 : ny |
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if toshow |
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disp(strcat('Computing dSIGMATHETA/dx at latitude : ',num2str(STlat(iy)),... |
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'^o (',num2str(iy),'/',num2str(ny),')' )); |
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end |
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[dx b] = meshgrid( m_lldist(STlon(1:nx+1),[1 1]*STlat(iy)), STdpt ) ; clear b |
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STup = squeeze(ncST{4}(:,iy,2:nx+1)); |
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STdw = squeeze(ncST{4}(:,iy,1:nx)); |
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dSTdx = ( STup - STdw ) ./ dx; |
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% Change horizontal grid point definition to fit with SIGMATHETA: |
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dSTdx = ( dSTdx(:,1:nx-1) + dSTdx(:,2:nx) )./2; |
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dSIGMATHETAdx(:,iy,:) = dSTdx; |
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end %for iy |
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|
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|
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%%%%% |
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%% 2: Move OMEGAX on the same grid: |
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if toshow,disp('Move OMEGAX on the same grid as dSIGMATHETA/dx'), end |
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|
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% Change vertical gridding of OMEGAX: |
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Ox = ncOx{4}(:,:,:); |
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Ox = ( Ox(2:nz-1,:,:) + Ox(1:nz-2,:,:) )./2; |
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% And horizontal gridding: |
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Ox = ( Ox(:,2:ny-1,:) + Ox(:,1:ny-2,:) )./2; |
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|
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%%%%% |
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%% 3: Make both fields having same limits: |
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%% (Keep points where both fields are defined) |
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Ox = squeeze(Ox(:,:,2:nx)); |
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dSIGMATHETAdx = squeeze( dSIGMATHETAdx (2:nz-1,2:ny-1,:) ); |
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|
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%%%%% |
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%% 4: Last, compute first term of PV: |
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PV1 = Ox.*dSIGMATHETAdx ; |
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|
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% and define axis fron the ST grid: |
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PV1_lon = STlon(2:length(STlon)-1); |
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PV1_lat = STlat(2:length(STlat)-1); |
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PV1_dpt = STdpt(2:length(STdpt)-1); |
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|
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clear nx ny nz dx STup STdw iy dSTdx Ox dSIGMATHETAdx |
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end %if FLpv1 |
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|
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|
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|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% Compute the second term: OMEGAY . dSIGMATHETA/dy % |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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if FLpv2 |
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|
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%%%%% |
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%% 1: Compute meridional gradient of SIGMATHETA: |
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|
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% Dim: |
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if toshow,disp('dim'), end |
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nx = length(STlon) ; |
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ny = length(STlat) - 1 ; |
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nz = length(STdpt) ; |
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|
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% Pre-allocate: |
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if toshow,disp('pre-allocate'), end |
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dSIGMATHETAdy = zeros(nz,ny-1,nx).*NaN; |
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dy = zeros(1,ny).*NaN; |
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STup = zeros(nz,ny); |
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STdw = zeros(nz,ny); |
| 166 |
|
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% Meridional gradient of SIGMATHETA: |
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% (Assuming the grid is regular, dy is independent of x) |
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[dy b] = meshgrid( m_lldist([1 1]*STlon(1),STlat(1:ny+1) ), STdpt ) ; clear b |
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for ix = 1 : nx |
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if toshow |
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disp(strcat('Computing dSIGMATHETA/dy at longitude : ',num2str(STlon(ix)),... |
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'^o (',num2str(ix),'/',num2str(nx),')' )); |
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end |
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STup = squeeze(ncST{4}(:,2:ny+1,ix)); |
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STdw = squeeze(ncST{4}(:,1:ny,ix)); |
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dSTdy = ( STup - STdw ) ./ dy; |
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% Change horizontal grid point definition to fit with SIGMATHETA: |
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dSTdy = ( dSTdy(:,1:ny-1) + dSTdy(:,2:ny) )./2; |
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dSIGMATHETAdy(:,:,ix) = dSTdy; |
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end %for iy |
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|
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%%%%% |
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%% 2: Move OMEGAY on the same grid: |
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if toshow,disp('Move OMEGAY on the same grid as dSIGMATHETA/dy'), end |
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|
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% Change vertical gridding of OMEGAY: |
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Oy = ncOy{4}(:,:,:); |
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Oy = ( Oy(2:nz-1,:,:) + Oy(1:nz-2,:,:) )./2; |
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% And horizontal gridding: |
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Oy = ( Oy(:,:,2:nx-1) + Oy(:,:,1:nx-2) )./2; |
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|
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%%%%% |
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%% 3: Make them having same limits: |
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%% (Keep points where both fields are defined) |
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Oy = squeeze(Oy(:,2:ny,:)); |
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dSIGMATHETAdy = squeeze( dSIGMATHETAdy (2:nz-1,:,2:nx-1) ); |
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|
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%%%%% |
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%% 4: Last, compute second term of PV: |
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PV2 = Oy.*dSIGMATHETAdy ; |
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|
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% and defined axis fron the ST grid: |
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PV2_lon = STlon(2:length(STlon)-1); |
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PV2_lat = STlat(2:length(STlat)-1); |
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PV2_dpt = STdpt(2:length(STdpt)-1); |
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|
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|
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clear nx ny nz dy STup STdw dy dSTdy Oy dSIGMATHETAdy |
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end %if FLpv2 |
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|
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|
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|
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|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% Compute the third term: ( f + ZETA ) . dSIGMATHETA/dz % |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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if FLpv3 |
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|
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%%%%% |
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%% 1: Compute vertical gradient of SIGMATHETA: |
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|
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% Dim: |
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if toshow,disp('dim'), end |
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nx = length(STlon) ; |
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ny = length(STlat) ; |
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nz = length(STdpt) - 1 ; |
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|
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% Pre-allocate: |
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if toshow,disp('pre-allocate'), end |
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dSIGMATHETAdz = zeros(nz-1,ny,nx).*NaN; |
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ST = zeros(nz+1,ny,nx); |
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dz = zeros(1,nz).*NaN; |
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|
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% Vertical grid differences: |
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dz = diff(STdpt); |
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[a dz_3D c] = meshgrid(STlat,dz,STlon); clear a c |
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|
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% Vertical gradient: |
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if toshow,disp('Vertical gradient of SIGMATHETA'), end |
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ST = ncST{4}(:,:,:); |
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dSIGMATHETAdz = ( ST(2:nz+1,:,:) - ST(1:nz,:,:) ) ./ dz_3D; |
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clear dz_3D ST |
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|
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% Change vertical gridding: |
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dSIGMATHETAdz = ( dSIGMATHETAdz(1:nz-1,:,:) + dSIGMATHETAdz(2:nz,:,:) )./2; |
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|
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if FLpv3 == 1 % Just for full PV |
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|
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%%%%% |
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%% 2: Move ZETA on the same grid: |
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if toshow,disp('Move ZETA on the same grid as dSIGMATHETA/dz'), end |
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Oz = ncOz{4}(:,:,:); |
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% Change horizontal gridding: |
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Oz = ( Oz(:,:,2:nx-1) + Oz(:,:,1:nx-2) )./2; |
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Oz = ( Oz(:,2:ny-1,:) + Oz(:,1:ny-2,:) )./2; |
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|
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end %if FLpv3=1 |
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|
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%%%%% |
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%% 3: Make them having same limits: |
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%% (Keep points where both fields are defined) |
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if FLpv3 == 1 |
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Oz = squeeze(Oz(2:nz,:,:)); |
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end %if |
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dSIGMATHETAdz = squeeze( dSIGMATHETAdz (:,2:ny-1,2:nx-1) ); |
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|
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|
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%%%%% |
| 271 |
%% 4: Last, compute third term of PV: |
| 272 |
% and defined axis fron the ST grid: |
| 273 |
PV3_lon = STlon(2:length(STlon)-1); |
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PV3_lat = STlat(2:length(STlat)-1); |
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PV3_dpt = STdpt(2:length(STdpt)-1); |
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|
| 277 |
% Planetary vorticity: |
| 278 |
f = 2*(2*pi/86400)*sin(PV3_lat*pi/180); |
| 279 |
[a f c]=meshgrid(PV3_lon,f,PV3_dpt); clear a c |
| 280 |
f = permute(f,[3 1 2]); |
| 281 |
|
| 282 |
% Third term of PV: |
| 283 |
if FLpv3 == 2 |
| 284 |
% Compute simple PV, just with planetary vorticity: |
| 285 |
PV3 = f.*dSIGMATHETAdz ; |
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else |
| 287 |
% To compute full PV: |
| 288 |
PV3 = (f+Oz).*dSIGMATHETAdz ; |
| 289 |
end |
| 290 |
|
| 291 |
|
| 292 |
|
| 293 |
clear nx ny nz dz ST Oz dSIGMATHETAdz f |
| 294 |
end %if FLpv3 |
| 295 |
|
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|
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|
| 298 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 299 |
% Then, compute potential vorticity: |
| 300 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 301 |
if toshow,disp('Summing terms to get PV:'),end |
| 302 |
% If we had computed the first term: |
| 303 |
if FLpv1 |
| 304 |
if toshow,disp('First term alone'),end |
| 305 |
PV = PV1; |
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PV_lon=PV1_lon;PV_lat=PV1_lat;PV_dpt=PV1_dpt; |
| 307 |
end |
| 308 |
% If we had computed the second term: |
| 309 |
if FLpv2 |
| 310 |
if exist('PV') % and the first one: |
| 311 |
if toshow,disp('Second term added to first one'),end |
| 312 |
PV = PV + PV2; |
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else % or not: |
| 314 |
if toshow,disp('Second term alone'),end |
| 315 |
PV = PV2; |
| 316 |
PV_lon=PV2_lon;PV_lat=PV2_lat;PV_dpt=PV2_dpt; |
| 317 |
end |
| 318 |
end |
| 319 |
% If we had computed the third term: |
| 320 |
if FLpv3 |
| 321 |
if exist('PV') % and one of the first or second one: |
| 322 |
if toshow,disp('Third term added to first and/or second one(s)'),end |
| 323 |
PV = PV + PV3; |
| 324 |
else % or not: |
| 325 |
if toshow,disp('Third term alone'),end |
| 326 |
PV = PV3; |
| 327 |
PV_lon=PV3_lon;PV_lat=PV3_lat;PV_dpt=PV3_dpt; |
| 328 |
end |
| 329 |
end |
| 330 |
|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 333 |
% Record: |
| 334 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 335 |
if toshow,disp('Now reccording PV file ...'),end |
| 336 |
|
| 337 |
% General informations: |
| 338 |
if FLpv3 == 1 |
| 339 |
netfil = strcat('PV','.',netcdf_domain,'.',netcdf_suff); |
| 340 |
units = 'kg/s/m^4'; |
| 341 |
ncid = 'PV'; |
| 342 |
longname = 'Potential vorticity'; |
| 343 |
uniquename = 'potential_vorticity'; |
| 344 |
else |
| 345 |
netfil = strcat('splPV','.',netcdf_domain,'.',netcdf_suff); |
| 346 |
units = 'kg/s/m^4'; |
| 347 |
ncid = 'splPV'; |
| 348 |
longname = 'Simple Potential vorticity'; |
| 349 |
uniquename = 'simple_potential_vorticity'; |
| 350 |
end %if |
| 351 |
|
| 352 |
% Open output file: |
| 353 |
nc = netcdf(strcat(pathname,sla,netfil),'clobber'); |
| 354 |
|
| 355 |
% Define axis: |
| 356 |
nc('X') = length(PV_lon); |
| 357 |
nc('Y') = length(PV_lat); |
| 358 |
nc('Z') = length(PV_dpt); |
| 359 |
|
| 360 |
nc{'X'} = 'X'; |
| 361 |
nc{'Y'} = 'Y'; |
| 362 |
nc{'Z'} = 'Z'; |
| 363 |
|
| 364 |
nc{'X'} = ncfloat('X'); |
| 365 |
nc{'X'}.uniquename = ncchar('X'); |
| 366 |
nc{'X'}.long_name = ncchar('longitude'); |
| 367 |
nc{'X'}.gridtype = nclong(0); |
| 368 |
nc{'X'}.units = ncchar('degrees_east'); |
| 369 |
nc{'X'}(:) = PV_lon; |
| 370 |
|
| 371 |
nc{'Y'} = ncfloat('Y'); |
| 372 |
nc{'Y'}.uniquename = ncchar('Y'); |
| 373 |
nc{'Y'}.long_name = ncchar('latitude'); |
| 374 |
nc{'Y'}.gridtype = nclong(0); |
| 375 |
nc{'Y'}.units = ncchar('degrees_north'); |
| 376 |
nc{'Y'}(:) = PV_lat; |
| 377 |
|
| 378 |
nc{'Z'} = ncfloat('Z'); |
| 379 |
nc{'Z'}.uniquename = ncchar('Z'); |
| 380 |
nc{'Z'}.long_name = ncchar('depth'); |
| 381 |
nc{'Z'}.gridtype = nclong(0); |
| 382 |
nc{'Z'}.units = ncchar('m'); |
| 383 |
nc{'Z'}(:) = PV_dpt; |
| 384 |
|
| 385 |
% And main field: |
| 386 |
nc{ncid} = ncfloat('Z', 'Y', 'X'); |
| 387 |
nc{ncid}.units = ncchar(units); |
| 388 |
nc{ncid}.missing_value = ncfloat(NaN); |
| 389 |
nc{ncid}.FillValue_ = ncfloat(NaN); |
| 390 |
nc{ncid}.longname = ncchar(longname); |
| 391 |
nc{ncid}.uniquename = ncchar(uniquename); |
| 392 |
nc{ncid}(:,:,:) = PV; |
| 393 |
|
| 394 |
nc=close(nc); |
| 395 |
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