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code obtained from faulks.lcs.mit.edu:/scratch/adcroft/cubed_sphere |
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|
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path('/home/dimitri/matlab/adcroft/bin',path); |
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tic |
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[dxg,dyg,dxf,dyf,dxc,dyc,dxv,dyu,Ec,Eu,Ev,Ez,latC,lonC,latG,lonG,... |
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Q11,Q22,Q12, TUu,TUv,TVu,TVv ]=gengrid_fn(576,4,'conf','c',0,0); |
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toc |
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|
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timings nireas faulks |
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gengrid_fn(576,2,'conf','c',0,0) 47.9 60.0 |
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gengrid_fn(576,4,'conf','c',0,0) 163.9 |
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|
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current 80S-80N, 1/4-deg isotropic grid: |
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1440 * 1088 = 1566720 grid points |
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27.7987 km at Equator, 4.8272 km at 80N |
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|
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tripolar grid: |
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2304 grid boxes around Equator |
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2*pi*6371/2304 = 17.3742 km grid at Equator |
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switch to bipolar is at 60N where grid is 17.3742*cos(60) = 8.6871 km |
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at North Pole grid size is 17.3742/pi = 5.5304 km |
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smallest distance in Canadian Archipelago is approximately 17.3742/6 = 2.8957 km |
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worst aspect ratio is approximately 3 |
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number of grid points in sperical polar region is 2304*960 = 2211840 |
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number of grid points in bipolar grid is 1152*1152 = 1327104 |
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total number of grid points is 3538944 |
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advantages, grid is perfectly orthogonal |
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there are no singularities |
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no modifications to sea-ice thermodynamics |
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|
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by comparison |
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the cubed sphere with 2304 grid boxes around Equator |
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using Alistair's eq 16 has: |
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576*576*6 = 1990656 grid points (56% of tripolar grid, 127% of 1/4-deg grid) |
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largest distance is 22.9683 (132% of tripolar grid) |
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smallest distance is 3.2633 (112% of tripolar grid, 68% of 1/4-deg grid) |
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worst aspect ratio is 1.6162 (53% of tripolar grid) |
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but orthogonality is not as good as that of tripolar grid |
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and sea-ice dynamics need some work |
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also for the tripolar grid, removing land point will |
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result in much more dramatic reduction in number of grid |
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points because the three singularities are over land. |
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|
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|
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|
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table |
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first row is min, max, and mean of dxg and dyg |
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second row is min, max, and mean of dxg./dyg |
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third row is min, max, and mean of angles, excluding cube corners |
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|
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conf, nratio=4 |
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2.1460 18.0293 15.9182 |
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0.9172 1.0903 1.0000 |
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89.9978 98.5344 90.0562 |
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|
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conf, nratio=2 |
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2.1460 18.0293 15.9182 |
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0.9167 1.0909 1.0000 |
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89.9978 98.5344 90.0562 |
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|
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q=0, nratio=4 |
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2.2544 17.5336 15.9487 |
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0.9172 1.0903 1.0006 |
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89.9977 98.5344 90.0554 |
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|
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q=0, nratio=2 |
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2.2544 17.4069 15.9468 |
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0.9167 1.0909 1.0006 |
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89.9977 98.5344 90.0554 |
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|
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q=1, nratio=4 (has NaNs) |
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13.6379 67.1398 16.1959 |
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0.2031 4.9226 1.0552 |
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89.9972 98.5343 90.0497 |
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|
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q=1, nratio=2 |
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13.6310 67.1393 16.1925 |
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0.2031 4.9238 1.0551 |
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89.9972 98.5343 90.0497 |
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|
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q=1/2, nratio=4 |
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2.8990 21.0171 16.0604 |
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0.6992 1.4302 1.0137 |
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89.9974 98.5344 90.0527 |
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|
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q=1/2, nratio=2 |
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2.8958 21.0001 16.0613 |
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0.6999 1.4287 1.0136 |
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89.9974 98.5344 90.0527 |
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|
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q=7/8, nratio=4 (has NaNs) |
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13.6379 67.1398 16.1959 |
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0.2031 4.9226 1.0552 |
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89.9972 98.5343 90.0497 |
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|
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q=7/8, nratio=2 |
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13.6310 67.1393 16.1925 |
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0.2031 4.9238 1.0551 |
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89.9972 98.5343 90.0497 |
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|
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q=i3, nratio=4 |
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13.1144 65.1937 16.1921 |
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0.2092 4.7807 1.0549 |
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89.9972 98.5343 90.0497 |
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|
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q=i3, nratio=2 |
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12.4259 62.6094 16.1915 |
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0.2179 4.5899 1.0546 |
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89.9973 98.5343 90.0498 |
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|
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tan, nratio=4 |
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3.2633 22.9683 16.0912 |
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0.6188 1.6162 1.0203 |
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89.9974 98.5344 90.0519 |
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|
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tan, nratio=2 |
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3.2633 22.9683 16.0912 |
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0.6188 1.6162 1.0203 |
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89.9974 98.5344 90.0519 |
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|
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tan2, nratio=4 |
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2.2237 17.7883 15.9327 |
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0.9174 1.0900 1.0001 |
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89.9978 98.5344 90.0558 |
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|
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tan2, nratio=2 |
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2.2237 17.7883 15.9327 |
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0.9169 1.0906 1.0001 |
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89.9978 98.5344 90.0558 |
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|
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new, nratio=4 |
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2.5095 18.8618 15.9191 |
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0.8889 1.1250 1.0000 |
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89.9978 98.5344 90.0561 |
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|
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new, nratio=2 |
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2.8863 20.9484 15.9201 |
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0.8000 1.2500 1.0002 |
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89.9978 98.5344 90.0561 |
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|
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gengrids % Does it all |
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gengrids_fn(nx,nratio,projection,orientation,plotfigs,writedata) |
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[dxg,dyg,dxf,dyf,dxc,dyc,dxv,dyu,Ec,Eu,Ev,Ez,latC,lonC,latG,lonG,... |
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Q11,Q22,Q12, TUu,TUv,TVu,TVv ]=gengrid_fn(24,2,'conf','c',1,0); |
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|
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[X,Y,Z,x,y]=read_scubdat(fn,n); % Read SCUB0002.DAT file |
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[X,Y,Z]=map_xy2xyz(x,y); % Map (x,y) -> (X,Y,Z) |
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[X,Y,Z]=gmap_xy2xyz(x,y); % Map (x,y) -> (X,Y,Z) |
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[lon,lat]=map_xyz2lonlat(X,Y,Z); % Map (X,Y,Z) -> (lon,lat) |
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[X,Y,Z]=map_lonlat2xyz(lon,lat); % Map (lon,lat) -> (X,Y,Z) |
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[lat,lon]=calc_geocoords(lx,ly,tile) % Map (x,y) -> (lat,lon) |
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[X,Y,Z]=rotate_about_xaxis(lX,lY,lZ,angle); % Rotate about X axis |
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[X,Y,Z]=rotate_about_yaxis(lX,lY,lZ,angle); % Rotate about Y axis |
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[X,Y,Z]=rotate_about_zaxis(lX,lY,lZ,angle); % Rotate about Z axis |
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V=coord2vector(XG,YG,ZG); % Convert [X,Y,Z] to vector V |
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|
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angle=angle_between_coords(X1,Y1,Z1,X2,Y2,Z2); % Angles between coords |
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angle=angle_between_vectors(V1,V2); % Angles between vectors V1,V2 |
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excess=excess_of_quad(V1,V2,V3,V4); % Excess of quadrilateral |
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|
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q=rescale_coordinate(q,'q=i3'); % Re-scale single coordinate |
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[dx,dy,E]=calc_fvgrid(lx,ly); % Calculate F.V. grid info |
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dxg=conf_dx(q); % Calculate conformal dxg |
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[dxg,dxc,dxf,dxv]=reduce_dx(dx,nratio); % Sum fine-grid dx -> dxg,... |
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[Ec,Ez,Ev]=reduce_E(dx,nratio); % Sum fine-grid E -> Ec,... |
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|
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a=bari(b); % Two point average in I dir. |
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a=barj(b); % Two point average in J dir. |
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write_tiles('LATC',lat) % Write tiled files |
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displaytiles(lat) % Display tiles in comp. layout |
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plotcube(X,Y,Z,C) % Display tiles as 3-D sphere |
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merccube(lonG,latG,C) % Display tiles Mercator proj. |
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