1 |
% |
% |
2 |
% [] = B_COMPUTE_RELATIVE_VORTICITY(SNAPSHOT) |
% [OMEGA] = B_compute_relative_vorticity(SNAPSHOT) |
3 |
% |
% |
4 |
% For a time snapshot, this program computes the |
% For a time snapshot, this program computes the |
5 |
% 3D relative vorticity field from 3D |
% 3D relative vorticity field from 3D |
6 |
% horizontal speed fields U,V (x,y,z) as: |
% horizontal speed fields U,V (x,y,z) as: |
7 |
% OMEGA = ( -dVdz ; dUdz ; dVdx - dUdy ) |
% OMEGA = ( -dVdz ; dUdz ; dVdx - dUdy ) |
8 |
% = ( Ox ; Oy ; ZETA ) |
% = ( Ox ; Oy ; ZETA ) |
9 |
% 3 output files are created. |
% 3 outputs files are created. |
10 |
% |
% |
11 |
% 06/07/2006 |
% (U,V) must have same dimensions and by default are defined on |
12 |
|
% a C-grid. |
13 |
|
% If (U,V) are defined on an A-grid (coming from a cube-sphere |
14 |
|
% to lat/lon grid interpolation for example), ie at the same points |
15 |
|
% as THETA, SALTanom, ... the global variable 'griddef' must |
16 |
|
% be set to 'A-grid'. Then (U,V) are moved to a C-grid for the computation. |
17 |
|
% |
18 |
|
% ZETA is computed at the upper-right corner of the C-grid. |
19 |
|
% OMEGAX and OMEGAY are computed at V and U locations but shifted downward |
20 |
|
% by 1/2 grid. In case of a A-grid for (U,V), OMEGAX and OMEGAY are moved |
21 |
|
% to a C-grid according to the ZETA computation. |
22 |
|
% |
23 |
|
% |
24 |
|
% Files names are: |
25 |
|
% INPUT: |
26 |
|
% ./netcdf-files/<SNAPSHOT>/<netcdf_UVEL>.<netcdf_domain>.<netcdf_suff> |
27 |
|
% ./netcdf-files/<SNAPSHOT>/<netcdf_VVEL>.<netcdf_domain>.<netcdf_suff> |
28 |
|
% OUPUT: |
29 |
|
% ./netcdf-files/<SNAPSHOT>/OMEGAX.<netcdf_domain>.<netcdf_suff> |
30 |
|
% ./netcdf-files/<SNAPSHOT>/OMEGAY.<netcdf_domain>.<netcdf_suff> |
31 |
|
% ./netcdf-files/<SNAPSHOT>/ZETA.<netcdf_domain>.<netcdf_suff> |
32 |
|
% |
33 |
|
% 2006/06/07 |
34 |
% gmaze@mit.edu |
% gmaze@mit.edu |
35 |
% |
% |
36 |
|
% Last update: |
37 |
|
% 2007/02/01 (gmaze) : Fix bug in ZETA grid and add compatibility with A-grid |
38 |
|
% |
39 |
|
|
40 |
function [] = B_compute_relative_vorticity(snapshot) |
% On the C-grid, U and V are supposed to have the same dimensions and are |
41 |
|
% defined like this: |
42 |
|
% |
43 |
|
% y |
44 |
|
% ^ ------------------------- |
45 |
|
% | | | | | | |
46 |
|
% | ny U * U * U * U * | |
47 |
|
% | | | | | | |
48 |
|
% | ny -- V --- V --- V --- V -- |
49 |
|
% | | | | | | |
50 |
|
% | U * U * U * U * | |
51 |
|
% | | | | | | |
52 |
|
% | -- V --- V --- V --- V -- |
53 |
|
% | | | | | | |
54 |
|
% | U * U * U * U * | |
55 |
|
% | | | | | | |
56 |
|
% | -- V --- V --- V --- V -- |
57 |
|
% | | | | | | |
58 |
|
% | 1 U * U * U * U * | |
59 |
|
% | | | | | | |
60 |
|
% | 1 -- V --- V --- V --- V -- |
61 |
|
% | |
62 |
|
% | 1 nx |
63 |
|
% | 1 nx |
64 |
|
%--|-------------------------------------> x |
65 |
|
% | |
66 |
|
% |
67 |
|
% On the A-grid, U and V are defined on *, so we simply shift U westward by 1/2 grid |
68 |
|
% and V southward by 1/2 grid. New (U,V) have the same dimensions as original fields |
69 |
|
% but with first col for U, and first row for V set to NaN. Values are computed by |
70 |
|
% averaging two contiguous values. |
71 |
|
% |
72 |
|
|
73 |
|
function varargout = B_compute_relative_vorticity(snapshot) |
74 |
|
|
75 |
|
|
76 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
77 |
% Setup |
% Setup |
78 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
79 |
global sla netcdf_UVEL netcdf_VVEL netcdf_domain netcdf_suff |
global sla netcdf_UVEL netcdf_VVEL netcdf_domain netcdf_suff griddef |
80 |
pv_checkpath |
pv_checkpath |
81 |
|
|
82 |
|
|
90 |
ext = strcat('.',netcdf_suff); |
ext = strcat('.',netcdf_suff); |
91 |
|
|
92 |
|
|
93 |
%% Load files: |
%% Load files and axis: |
94 |
ferfile = strcat(pathname,sla,filU,ext); |
ferfile = strcat(pathname,sla,filU,ext); |
95 |
ncU = netcdf(ferfile,'nowrite'); |
ncU = netcdf(ferfile,'nowrite'); |
96 |
[Ulon Ulat Udpt] = coordfromnc(ncU); |
[Ulon Ulat Udpt] = coordfromnc(ncU); |
101 |
|
|
102 |
clear ext ferfile |
clear ext ferfile |
103 |
|
|
104 |
|
%% Load grid definition: |
105 |
|
global griddef |
106 |
|
if length(griddef) == 0 |
107 |
|
griddef = 'C-grid'; % By default |
108 |
|
end |
109 |
|
switch lower(griddef) |
110 |
|
case {'c-grid','cgrid','c'} |
111 |
|
% Nothing to do here |
112 |
|
case {'a-grid','agrid','a'} |
113 |
|
disp('Found (U,V) defined on A-grid') |
114 |
|
% Move Ulon westward by 1/2 grid point: |
115 |
|
Ulon = [Ulon(1)-abs(diff(Ulon(1:2))/2) ; (Ulon(1:end-1)+Ulon(2:end))/2]; |
116 |
|
% Move V southward by 1/2 grid point: |
117 |
|
Vlat = [Vlat(1)-abs(diff(Vlat(1:2))/2); (Vlat(1:end-1)+Vlat(2:end))/2]; |
118 |
|
% Now, (U,V) axis are defined as if they came from a C-grid |
119 |
|
% (U,V) fields are moved to a C-grid during computation... |
120 |
|
otherwise |
121 |
|
error('The grid must be: C-grid or A-grid'); |
122 |
|
return |
123 |
|
end %switch griddef |
124 |
|
|
125 |
|
|
126 |
%% Optionnal flags |
%% Optionnal flags |
127 |
computeZETA = 1; % Compute ZETA or not ? |
computeZETA = 1; % Compute ZETA or not ? |
128 |
global toshow % Turn to 1 to follow the computing process |
global toshow % Turn to 1 to follow the computing process |
144 |
ny = length(Ulat)-1; |
ny = length(Ulat)-1; |
145 |
nx = length(Vlon)-1; |
nx = length(Vlon)-1; |
146 |
nz = length(Udpt); % Note that Udpt=Vdpt |
nz = length(Udpt); % Note that Udpt=Vdpt |
|
ZETA_lon = Ulon(1:nx); |
|
|
ZETA_lat = Vlat(1:ny); |
|
147 |
|
|
148 |
%%%%%%%%%%%%%% |
%%%%%%%%%%%%%% |
149 |
%% Pre-allocation: |
%% Pre-allocation: |
152 |
dx = zeros(ny-1,nx-1); |
dx = zeros(ny-1,nx-1); |
153 |
dy = zeros(ny-1,nx-1); |
dy = zeros(ny-1,nx-1); |
154 |
|
|
155 |
|
ZETA_lon = Ulon(2:nx+1); |
156 |
|
ZETA_lat = Vlat(2:ny+1); |
157 |
|
|
158 |
%%%%%%%%%%%%%% |
%%%%%%%%%%%%%% |
159 |
%% Compute relative vorticity for each z-level: |
%% Compute relative vorticity for each z-level: |
160 |
if computeZETA |
if computeZETA |
161 |
for iz=1:nz |
for iz = 1 : nz |
162 |
if toshow |
if toshow |
163 |
disp(strcat('Computing \zeta at depth : ',num2str(Udpt(iz)),... |
disp(strcat('Computing \zeta at depth : ',num2str(Udpt(iz)),... |
164 |
'm (',num2str(iz),'/',num2str(nz),')' )); |
'm (',num2str(iz),'/',num2str(nz),')' )); |
167 |
% Get velocities: |
% Get velocities: |
168 |
U = ncU{4}(iz,:,:); |
U = ncU{4}(iz,:,:); |
169 |
V = ncV{4}(iz,:,:); |
V = ncV{4}(iz,:,:); |
170 |
|
switch lower(griddef) |
171 |
|
case {'a-grid','agrid','a'} |
172 |
|
% Move U westward by 1/2 grid point: |
173 |
|
% (1st col is set to nan, but axis defined) |
174 |
|
U = [ones(ny+1,1).*NaN (U(:,1:end-1) + U(:,2:end))/2]; |
175 |
|
% Move V southward by 1/2 grid point: |
176 |
|
% (1st row is set to nan but axis defined) |
177 |
|
V = [ones(1,nx+1).*NaN; (V(1:end-1,:) + V(2:end,:))/2]; |
178 |
|
% Now, U and V are defined as if they came from a C-grid |
179 |
|
end |
180 |
|
|
181 |
% And now compute the vertical component of relative vorticity: |
% And now compute the vertical component of relative vorticity: |
182 |
% (TO DO: m_lldist accepts tables as input, so this part may be |
% (TO DO: m_lldist accepts tables as input, so this part may be |
195 |
ZETA(iz,iy,ix) = dVdx - dUdy; |
ZETA(iz,iy,ix) = dVdx - dUdy; |
196 |
end %for ix |
end %for ix |
197 |
end %for iy |
end %for iy |
|
|
|
198 |
end %for iz |
end %for iz |
199 |
|
|
200 |
%%%%%%%%%%%%%% |
%%%%%%%%%%%%%% |
278 |
Oy = zeros(O_nz,O_ny(2),O_nx(2)).*NaN; |
Oy = zeros(O_nz,O_ny(2),O_nx(2)).*NaN; |
279 |
|
|
280 |
%%%%%%%%%%%%%% |
%%%%%%%%%%%%%% |
281 |
%% Horizontal components: |
%% Computation: |
282 |
|
|
283 |
%% Vertical grid differences: |
%% Vertical grid differences: |
284 |
dZ = diff(Udpt); |
dZ = diff(Udpt); |
287 |
%% Zonal component of OMEGA: |
%% Zonal component of OMEGA: |
288 |
if toshow,disp('Zonal direction ...'); end |
if toshow,disp('Zonal direction ...'); end |
289 |
[a dZ_3D c] = meshgrid(Vlat,dZ,Vlon); clear a c |
[a dZ_3D c] = meshgrid(Vlat,dZ,Vlon); clear a c |
290 |
V = ncV{4}(:,:,:); |
V = ncV{4}(:,:,:); |
291 |
Ox = - ( V(2:O_nz+1,:,:) - V(1:O_nz,:,:) ) ./ dZ_3D; |
switch lower(griddef) |
292 |
|
case {'a-grid','agrid','a'} |
293 |
|
% Move V southward by 1/2 grid point: |
294 |
|
% (1st row is set to nan but axis defined) |
295 |
|
V = cat(2,ones(O_nz+1,1,O_nx(1)).*NaN,(V(:,1:end-1,:) + V(:,2:end,:))/2); |
296 |
|
% Now, V is defined as if it came from a C-grid |
297 |
|
end |
298 |
|
Ox = - ( V(2:O_nz+1,:,:) - V(1:O_nz,:,:) ) ./ dZ_3D; |
299 |
clear V dZ_3D % For memory use |
clear V dZ_3D % For memory use |
300 |
|
|
301 |
%% Meridional component of OMEGA: |
%% Meridional component of OMEGA: |
302 |
if toshow,disp('Meridional direction ...'); end |
if toshow,disp('Meridional direction ...'); end |
303 |
[a dZ_3D c] = meshgrid(Ulat,dZ,Ulon); clear a c |
[a dZ_3D c] = meshgrid(Ulat,dZ,Ulon); clear a c |
304 |
U = ncU{4}(:,:,:); |
U = ncU{4}(:,:,:); |
305 |
Oy = ( U(2:O_nz+1,:,:) - U(1:O_nz,:,:) ) ./ dZ_3D; |
switch lower(griddef) |
306 |
|
case {'a-grid','agrid','a'} |
307 |
|
% Move U westward by 1/2 grid point: |
308 |
|
% (1st col is set to nan, but axis defined) |
309 |
|
U = cat(3,ones(O_nz+1,O_ny(2),1).*NaN,(U(:,:,1:end-1) + U(:,:,2:end))/2); |
310 |
|
% Now, V is defined as if it came from a C-grid |
311 |
|
end |
312 |
|
Oy = ( U(2:O_nz+1,:,:) - U(1:O_nz,:,:) ) ./ dZ_3D; |
313 |
clear U dZ_3D % For memory use |
clear U dZ_3D % For memory use |
314 |
|
|
315 |
clear dZ |
clear dZ |
316 |
|
|
317 |
|
|
318 |
%%%%%%%%%%%%%% |
%%%%%%%%%%%%%% |
319 |
%% Record Zonal component: |
%% Record Zonal component: |
320 |
if toshow,disp('Records ...'); end |
if toshow,disp('Records ...'); end |
422 |
nc{ncid}(:,:,:) = Oy; |
nc{ncid}(:,:,:) = Oy; |
423 |
|
|
424 |
nc=close(nc); |
nc=close(nc); |
425 |
|
close(ncU); |
426 |
|
close(ncV); |
427 |
|
|
428 |
|
% Outputs: |
429 |
|
OMEGA = struct(... |
430 |
|
'Ox',struct('value',Ox,'dpt',Odpt,'lat',Vlat,'lon',Vlon),... |
431 |
|
'Oy',struct('value',Oy,'dpt',Odpt,'lat',Ulat,'lon',Vlon),... |
432 |
|
'Oz',struct('value',ZETA,'dpt',Udpt,'lat',ZETA_lat,'lon',ZETA_lon)... |
433 |
|
); |
434 |
|
switch nargout |
435 |
|
case 1 |
436 |
|
varargout(1) = {OMEGA}; |
437 |
|
end |