| 1 |
% |
| 2 |
% [OMEGA] = B_compute_relative_vorticity(SNAPSHOT) |
| 3 |
% |
| 4 |
% For a time snapshot, this program computes the |
| 5 |
% 3D relative vorticity field from 3D |
| 6 |
% horizontal speed fields U,V (x,y,z) as: |
| 7 |
% OMEGA = ( -dVdz ; dUdz ; dVdx - dUdy ) |
| 8 |
% = ( Ox ; Oy ; ZETA ) |
| 9 |
% 3 outputs files are created. |
| 10 |
% |
| 11 |
% (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 |
| 35 |
% |
| 36 |
% Last update: |
| 37 |
% 2007/02/01 (gmaze) : Fix bug in ZETA grid and add compatibility with A-grid |
| 38 |
% |
| 39 |
|
| 40 |
% 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 |
| 78 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 79 |
global sla netcdf_UVEL netcdf_VVEL netcdf_domain netcdf_suff griddef |
| 80 |
pv_checkpath |
| 81 |
|
| 82 |
|
| 83 |
%% U,V files name: |
| 84 |
filU = strcat(netcdf_UVEL,'.',netcdf_domain); |
| 85 |
filV = strcat(netcdf_VVEL,'.',netcdf_domain); |
| 86 |
|
| 87 |
|
| 88 |
%% Path and extension to find them: |
| 89 |
pathname = strcat('netcdf-files',sla,snapshot,sla); |
| 90 |
ext = strcat('.',netcdf_suff); |
| 91 |
|
| 92 |
|
| 93 |
%% Load files and axis: |
| 94 |
ferfile = strcat(pathname,sla,filU,ext); |
| 95 |
ncU = netcdf(ferfile,'nowrite'); |
| 96 |
[Ulon Ulat Udpt] = coordfromnc(ncU); |
| 97 |
|
| 98 |
ferfile = strcat(pathname,sla,filV,ext); |
| 99 |
ncV = netcdf(ferfile,'nowrite'); |
| 100 |
[Vlon Vlat Vdpt] = coordfromnc(ncV); |
| 101 |
|
| 102 |
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 |
| 127 |
computeZETA = 1; % Compute ZETA or not ? |
| 128 |
global toshow % Turn to 1 to follow the computing process |
| 129 |
|
| 130 |
|
| 131 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 132 |
% VERTICAL COMPONENT: ZETA % |
| 133 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 134 |
|
| 135 |
% U field is on the zonal side of the c-grid and |
| 136 |
% V field on the meridional one. |
| 137 |
% So computing meridional gradient for U and |
| 138 |
% zonal gradient for V makes the relative vorticity |
| 139 |
% zeta defined on the corner of the c-grid. |
| 140 |
|
| 141 |
%%%%%%%%%%%%%% |
| 142 |
%% Dimensions of ZETA field: |
| 143 |
if toshow,disp('Dim'),end |
| 144 |
ny = length(Ulat)-1; |
| 145 |
nx = length(Vlon)-1; |
| 146 |
nz = length(Udpt); % Note that Udpt=Vdpt |
| 147 |
|
| 148 |
%%%%%%%%%%%%%% |
| 149 |
%% Pre-allocation: |
| 150 |
if toshow,disp('Pre-allocate'),end |
| 151 |
ZETA = zeros(nz,ny-1,nx-1).*NaN; |
| 152 |
dx = zeros(ny-1,nx-1); |
| 153 |
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: |
| 160 |
if computeZETA |
| 161 |
for iz = 1 : nz |
| 162 |
if toshow |
| 163 |
disp(strcat('Computing \zeta at depth : ',num2str(Udpt(iz)),... |
| 164 |
'm (',num2str(iz),'/',num2str(nz),')' )); |
| 165 |
end |
| 166 |
|
| 167 |
% Get velocities: |
| 168 |
U = ncU{4}(iz,:,:); |
| 169 |
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: |
| 182 |
% (TO DO: m_lldist accepts tables as input, so this part may be |
| 183 |
% done without x,y loop ...) |
| 184 |
for iy = 1 : ny |
| 185 |
for ix = 1 : nx |
| 186 |
if iz==1 % It's more efficient to make this test each time than |
| 187 |
% recomputing distance each time. m_lldist is a slow routine. |
| 188 |
% ZETA axis and grid distance: |
| 189 |
dx(iy,ix) = m_lldist([Vlon(ix+1) Vlon(ix)],[1 1]*Vlat(iy)); |
| 190 |
dy(iy,ix) = m_lldist([1 1]*Vlon(ix),[Ulat(iy+1) Ulat(iy)]); |
| 191 |
end %if |
| 192 |
% Horizontal gradients and ZETA: |
| 193 |
dVdx = ( V(iy,ix+1)-V(iy,ix) ) / dx(iy,ix) ; |
| 194 |
dUdy = ( U(iy+1,ix)-U(iy,ix) ) / dy(iy,ix) ; |
| 195 |
ZETA(iz,iy,ix) = dVdx - dUdy; |
| 196 |
end %for ix |
| 197 |
end %for iy |
| 198 |
end %for iz |
| 199 |
|
| 200 |
%%%%%%%%%%%%%% |
| 201 |
%% Netcdf record: |
| 202 |
|
| 203 |
% General informations: |
| 204 |
netfil = strcat('ZETA','.',netcdf_domain,'.',netcdf_suff); |
| 205 |
units = '1/s'; |
| 206 |
ncid = 'ZETA'; |
| 207 |
longname = 'Vertical Component of the Relative Vorticity'; |
| 208 |
uniquename = 'vertical_relative_vorticity'; |
| 209 |
|
| 210 |
% Open output file: |
| 211 |
nc = netcdf(strcat(pathname,sla,netfil),'clobber'); |
| 212 |
|
| 213 |
% Define axis: |
| 214 |
nc('X') = nx; |
| 215 |
nc('Y') = ny; |
| 216 |
nc('Z') = nz; |
| 217 |
|
| 218 |
nc{'X'} = 'X'; |
| 219 |
nc{'Y'} = 'Y'; |
| 220 |
nc{'Z'} = 'Z'; |
| 221 |
|
| 222 |
nc{'X'} = ncfloat('X'); |
| 223 |
nc{'X'}.uniquename = ncchar('X'); |
| 224 |
nc{'X'}.long_name = ncchar('longitude'); |
| 225 |
nc{'X'}.gridtype = nclong(0); |
| 226 |
nc{'X'}.units = ncchar('degrees_east'); |
| 227 |
nc{'X'}(:) = ZETA_lon; |
| 228 |
|
| 229 |
nc{'Y'} = ncfloat('Y'); |
| 230 |
nc{'Y'}.uniquename = ncchar('Y'); |
| 231 |
nc{'Y'}.long_name = ncchar('latitude'); |
| 232 |
nc{'Y'}.gridtype = nclong(0); |
| 233 |
nc{'Y'}.units = ncchar('degrees_north'); |
| 234 |
nc{'Y'}(:) = ZETA_lat; |
| 235 |
|
| 236 |
nc{'Z'} = ncfloat('Z'); |
| 237 |
nc{'Z'}.uniquename = ncchar('Z'); |
| 238 |
nc{'Z'}.long_name = ncchar('depth'); |
| 239 |
nc{'Z'}.gridtype = nclong(0); |
| 240 |
nc{'Z'}.units = ncchar('m'); |
| 241 |
nc{'Z'}(:) = Udpt; |
| 242 |
|
| 243 |
% And main field: |
| 244 |
nc{ncid} = ncfloat('Z', 'Y', 'X'); |
| 245 |
nc{ncid}.units = ncchar(units); |
| 246 |
nc{ncid}.missing_value = ncfloat(NaN); |
| 247 |
nc{ncid}.FillValue_ = ncfloat(NaN); |
| 248 |
nc{ncid}.longname = ncchar(longname); |
| 249 |
nc{ncid}.uniquename = ncchar(uniquename); |
| 250 |
nc{ncid}(:,:,:) = ZETA; |
| 251 |
|
| 252 |
nc=close(nc); |
| 253 |
|
| 254 |
clear x y z U V dx dy nx ny nz DVdx dUdy |
| 255 |
|
| 256 |
end %if compute ZETA |
| 257 |
|
| 258 |
|
| 259 |
%%%%%%%%%%%%%%%%%%%%%%%%% |
| 260 |
% HORIZONTAL COMPONENTS % |
| 261 |
%%%%%%%%%%%%%%%%%%%%%%%%% |
| 262 |
if toshow, disp('') |
| 263 |
disp('Now compute horizontal components of relative vorticity ...'); end |
| 264 |
|
| 265 |
% U and V are defined on the same Z grid. |
| 266 |
|
| 267 |
%%%%%%%%%%%%%% |
| 268 |
%% Dimensions of OMEGA x and y fields: |
| 269 |
if toshow,disp('Dim'),end |
| 270 |
O_nx = [length(Vlon) length(Ulon)]; |
| 271 |
O_ny = [length(Vlat) length(Ulat)]; |
| 272 |
O_nz = length(Udpt) - 1; % Idem Vdpt |
| 273 |
|
| 274 |
%%%%%%%%%%%%%% |
| 275 |
%% Pre-allocations: |
| 276 |
if toshow,disp('Pre-allocate'),end |
| 277 |
Ox = zeros(O_nz,O_ny(1),O_nx(1)).*NaN; |
| 278 |
Oy = zeros(O_nz,O_ny(2),O_nx(2)).*NaN; |
| 279 |
|
| 280 |
%%%%%%%%%%%%%% |
| 281 |
%% Computation: |
| 282 |
|
| 283 |
%% Vertical grid differences: |
| 284 |
dZ = diff(Udpt); |
| 285 |
Odpt = Udpt(1:O_nz) + dZ/2; |
| 286 |
|
| 287 |
%% Zonal component of OMEGA: |
| 288 |
if toshow,disp('Zonal direction ...'); end |
| 289 |
[a dZ_3D c] = meshgrid(Vlat,dZ,Vlon); clear a c |
| 290 |
V = ncV{4}(:,:,:); |
| 291 |
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 |
| 300 |
|
| 301 |
%% Meridional component of OMEGA: |
| 302 |
if toshow,disp('Meridional direction ...'); end |
| 303 |
[a dZ_3D c] = meshgrid(Ulat,dZ,Ulon); clear a c |
| 304 |
U = ncU{4}(:,:,:); |
| 305 |
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 |
| 314 |
|
| 315 |
clear dZ |
| 316 |
|
| 317 |
|
| 318 |
%%%%%%%%%%%%%% |
| 319 |
%% Record Zonal component: |
| 320 |
if toshow,disp('Records ...'); end |
| 321 |
|
| 322 |
% General informations: |
| 323 |
netfil = strcat('OMEGAX','.',netcdf_domain,'.',netcdf_suff); |
| 324 |
units = '1/s'; |
| 325 |
ncid = 'OMEGAX'; |
| 326 |
longname = 'Zonal Component of the Relative Vorticity'; |
| 327 |
uniquename = 'zonal_relative_vorticity'; |
| 328 |
|
| 329 |
% Open output file: |
| 330 |
nc = netcdf(strcat(pathname,sla,netfil),'clobber'); |
| 331 |
|
| 332 |
% Define axis: |
| 333 |
nc('X') = O_nx(1); |
| 334 |
nc('Y') = O_ny(1); |
| 335 |
nc('Z') = O_nz; |
| 336 |
|
| 337 |
nc{'X'} = 'X'; |
| 338 |
nc{'Y'} = 'Y'; |
| 339 |
nc{'Z'} = 'Z'; |
| 340 |
|
| 341 |
nc{'X'} = ncfloat('X'); |
| 342 |
nc{'X'}.uniquename = ncchar('X'); |
| 343 |
nc{'X'}.long_name = ncchar('longitude'); |
| 344 |
nc{'X'}.gridtype = nclong(0); |
| 345 |
nc{'X'}.units = ncchar('degrees_east'); |
| 346 |
nc{'X'}(:) = Vlon; |
| 347 |
|
| 348 |
nc{'Y'} = ncfloat('Y'); |
| 349 |
nc{'Y'}.uniquename = ncchar('Y'); |
| 350 |
nc{'Y'}.long_name = ncchar('latitude'); |
| 351 |
nc{'Y'}.gridtype = nclong(0); |
| 352 |
nc{'Y'}.units = ncchar('degrees_north'); |
| 353 |
nc{'Y'}(:) = Vlat; |
| 354 |
|
| 355 |
nc{'Z'} = ncfloat('Z'); |
| 356 |
nc{'Z'}.uniquename = ncchar('Z'); |
| 357 |
nc{'Z'}.long_name = ncchar('depth'); |
| 358 |
nc{'Z'}.gridtype = nclong(0); |
| 359 |
nc{'Z'}.units = ncchar('m'); |
| 360 |
nc{'Z'}(:) = Odpt; |
| 361 |
|
| 362 |
% And main field: |
| 363 |
nc{ncid} = ncfloat('Z', 'Y', 'X'); |
| 364 |
nc{ncid}.units = ncchar(units); |
| 365 |
nc{ncid}.missing_value = ncfloat(NaN); |
| 366 |
nc{ncid}.FillValue_ = ncfloat(NaN); |
| 367 |
nc{ncid}.longname = ncchar(longname); |
| 368 |
nc{ncid}.uniquename = ncchar(uniquename); |
| 369 |
nc{ncid}(:,:,:) = Ox; |
| 370 |
|
| 371 |
nc=close(nc); |
| 372 |
|
| 373 |
%%%%%%%%%%%%%% |
| 374 |
%% Record Meridional component: |
| 375 |
% General informations: |
| 376 |
netfil = strcat('OMEGAY','.',netcdf_domain,'.',netcdf_suff); |
| 377 |
units = '1/s'; |
| 378 |
ncid = 'OMEGAY'; |
| 379 |
longname = 'Meridional Component of the Relative Vorticity'; |
| 380 |
uniquename = 'meridional_relative_vorticity'; |
| 381 |
|
| 382 |
% Open output file: |
| 383 |
nc = netcdf(strcat(pathname,sla,netfil),'clobber'); |
| 384 |
|
| 385 |
% Define axis: |
| 386 |
nc('X') = O_nx(2); |
| 387 |
nc('Y') = O_ny(2); |
| 388 |
nc('Z') = O_nz; |
| 389 |
|
| 390 |
nc{'X'} = 'X'; |
| 391 |
nc{'Y'} = 'Y'; |
| 392 |
nc{'Z'} = 'Z'; |
| 393 |
|
| 394 |
nc{'X'} = ncfloat('X'); |
| 395 |
nc{'X'}.uniquename = ncchar('X'); |
| 396 |
nc{'X'}.long_name = ncchar('longitude'); |
| 397 |
nc{'X'}.gridtype = nclong(0); |
| 398 |
nc{'X'}.units = ncchar('degrees_east'); |
| 399 |
nc{'X'}(:) = Ulon; |
| 400 |
|
| 401 |
nc{'Y'} = ncfloat('Y'); |
| 402 |
nc{'Y'}.uniquename = ncchar('Y'); |
| 403 |
nc{'Y'}.long_name = ncchar('latitude'); |
| 404 |
nc{'Y'}.gridtype = nclong(0); |
| 405 |
nc{'Y'}.units = ncchar('degrees_north'); |
| 406 |
nc{'Y'}(:) = Ulat; |
| 407 |
|
| 408 |
nc{'Z'} = ncfloat('Z'); |
| 409 |
nc{'Z'}.uniquename = ncchar('Z'); |
| 410 |
nc{'Z'}.long_name = ncchar('depth'); |
| 411 |
nc{'Z'}.gridtype = nclong(0); |
| 412 |
nc{'Z'}.units = ncchar('m'); |
| 413 |
nc{'Z'}(:) = Odpt; |
| 414 |
|
| 415 |
% And main field: |
| 416 |
nc{ncid} = ncfloat('Z', 'Y', 'X'); |
| 417 |
nc{ncid}.units = ncchar(units); |
| 418 |
nc{ncid}.missing_value = ncfloat(NaN); |
| 419 |
nc{ncid}.FillValue_ = ncfloat(NaN); |
| 420 |
nc{ncid}.longname = ncchar(longname); |
| 421 |
nc{ncid}.uniquename = ncchar(uniquename); |
| 422 |
nc{ncid}(:,:,:) = Oy; |
| 423 |
|
| 424 |
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 |
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