undef with unpack in dtype netcdf

Don Hooper hoop at COLORADO.EDU
Thu Mar 10 16:13:05 EST 2005


Jennifer,

With regard to NetCDF conventions, the picture isn't perfectly clear.
Unidata's documentation is unclear because, packed variables have two
types:  the packed type and the unpacked type.  However, their doc doesn't
seem to go into that distinction, and just talks about "the type of the
variable".  I would presume that they mean the type displayed by ncdump,
and hence the packed type.  Generally, that's how folks do missing_value
and _FillValue.  This is handy when the packed type is an integer one, as
one can do exact comparisions for equality, rather than the threshold type
you described GrADS doing for floating point values.  However, the application
is then left to decide what value to replace missings with during unpacking.
Actually NetCDF conventions, like CF, I *think* specifically require these
attributes to be of the packed type, but I don't feel like wading through
those web pages right now.  %}

I dunno if any of this helps....

-Hoop, who's getting used to having his main contribution be as a bad example....
> From owner-gradsusr at LIST.CINECA.IT  Thu Mar 10 13:13:54 2005
>
> Hi, Diane --
> First, a clarification of terminology:
> > undef -1.e+34f missing_value
> In this undef entry, you've provided a "file-wide" undef value of
> -1e+34 and an "undef attribute name". When you provide the attribute
> name, this tells GrADS that variables in the file may have different
> undef values and it needs to retrieve those along with the data when it
> does the I/O. Then, each variable is tested against its own missing
> value. If data are determined to be missing, then the missing value is
> changed to the file-wide undef, so that after I/O all variables appear
> to have the same undef value. This makes it possible to compare
> variables with different undefs without confusing GrADS.  If no undef
> attribute name is given, the file-wide undef is used for each variable,
> and the missing value attribute is not retrieved during I/O.
>
> I believe your issue has to do with whether the missing value attribute
> corresponds to a packed or unpacked data value. The way it has been
> implemented in the dtype netcdf interface is the latter: GrADS unpacks
> first, then does a "fuzzy" test to see if data values are within
> epsilon of the missing value -- if so, then they are assigned the
> file-wide undef.
>
> Since the missing value in your data set corresponds to a packed data
> value, then I suggest trying this as a solution: put the unpacked value
> of the undef as your file-wide undef without the undef attribute name:
>    undef -10.0017
>
> I have no idea what the NetCDF convention is for missing_value and
> _FillValue -- whether these are meant to correspond to packed or
> unpacked values. Anyone else know the answer to this?
>
> Jennifer
>
>
> On Mar 10, 2005, at 2:17 PM, Diane Stokes wrote:
>
> > Hi,
> >
> > I'm running GrADS 1.9b3 on AIX:
> >
> > Config: v1.9b3 32-bit big-endian readline sdf/xdf netcdf lats printim
> >
> >
> > I'm trying to help someone here read a netcdf file, using the new
> > "dtype
> > netcdf" entry in the data descriptor file.  This data includes a packed
> > variable, temp.
> >
> > The data descriptor file and output from ncdump -c are attached.
> >
> > When I include the "upack" line in the descriptor file, temp displays
> > correctly *except* for the fact that the missing points are not masked
> > out.  GrADS sees these values as -10.0017.
> >
> > If I remove the "undef" line, the missing values are seen as -32768 and
> > are masked out correctly, but, of course, the wrong values are
> > displayed
> > for the temperature (because they haven't been unpacked).
> >
> > Is the problem that GrADS is expecting -32768 but seeing -10.0017?  Or
> > might it be a roundoff issue, eg, GrADS is expecting -10, but seeing
> > -10.0017?  Either way, any suggestions?
> >
> > We could use sdfopen to read one file, but we are templating a time
> > series of files.  We have to use "dtype netcdf" instead to avoid core
> > dumps.
> >
> > Maskout will work in the meantime, but that is not an ideal solution.
> >
> >
> >
> > *ALSO*, I can display the non-packed packed variables version using
> > gradsnc.  I get, eg:
> >
> > ga-> d eta_t
> > Warning: Scale Factor Attribute Value Not Retrieved ... setting to 1.0
> > Warning: Offset Attribute Value Not Retrieved ... setting to 0.0
> > Contouring: -1.8 to 0.6 interval 0.3
> >
> > But with gradshdf, I get:
> >
> > ga-> d eta_t
> > ncattget: ncid 4: Attribute not found
> >
> > and GrADS exits. (No core dump).
> >
> > I'll start a new thread with this one if you like, but then you'd get
> > another copy of the same ncdump -c output.
> >
> >   Thanks in advance for any help.
> >      Diane
> >
> > --
> > Diane Stokes
> > Environmental Modeling Center
> > National Weather Service/NOAA
> >
> > DSET /ptmp/wx20wn/SIMU_OUT/TS/%y4%m201.ocean_month.nc
> > dtype netcdf
> > options template
> > undef -1.e+34f missing_value
> > unpack scale_factor add_offset
> > title operational godas time_mean files
> > *
> >
> > XDEF 360 LINEAR 0.5 1.0
> > YDEF 200 LEVELS -74.5  -73.5  -72.5  -71.5  -70.5  -69.5  -68.5  -67.5
> >  -66.5
> >     -65.5  -64.5  -63.5  -62.5  -61.5  -60.5  -59.5  -58.5  -57.5
> > -56.5
> >     -55.5  -54.5  -53.5  -52.5  -51.5  -50.5  -49.5  -48.5  -47.5
> > -46.5
> >     -45.5  -44.5  -43.5  -42.5  -41.5  -40.5  -39.5  -38.5  -37.5
> > -36.5
> >     -35.5  -34.5  -33.5  -32.5  -31.5  -30.5  -29.50046  -28.50319
> >     -27.51137  -26.52855  -25.5582  -24.60365  -23.66805  -22.75435
> >     -21.86525  -21.00319  -20.17032  -19.36844  -18.59905  -17.86328
> >     -17.16186  -16.4952  -15.86328  -15.26573  -14.70179  -14.17033
> >     -13.66988  -13.19861  -12.75437  -12.33475  -11.93702  -11.55824
> >     -11.19526  -10.84474  -10.50324  -10.16717  -9.833385  -9.500055
> >     -9.166725  -8.833395  -8.500065  -8.166735  -7.833405  -7.500075
> >     -7.166745  -6.833415  -6.500085  -6.166755  -5.833425  -5.500095
> >     -5.166765  -4.833435  -4.500105  -4.166775  -3.833445  -3.500115
> >     -3.166785  -2.833455  -2.500125  -2.166795  -1.833465  -1.500135
> >     -1.166805  -0.833475  -0.500145  -0.166815  0.166515  0.499845
> > 0.833175
> >     1.166505  1.499835  1.833165  2.166495  2.499825  2.833155
> > 3.166485
> >     3.499815  3.833145  4.166475  4.499805  4.833135  5.166465
> > 5.499795
> >     5.833125  6.166455  6.499785  6.833115  7.166445  7.499775
> > 7.833105
> >     8.166435  8.499765  8.833095  9.166425  9.499755  9.833085
> > 10.16687
> >     10.50294  10.84444  11.19496  11.55794  11.93672  12.33445
> > 12.75407
> >     13.19831  13.66958  14.17003  14.70149  15.26543  15.86298  16.4949
> >     17.16156  17.86298  18.59875  19.36814  20.17002  21.00289
> > 21.86495
> >     22.75405  23.66775  24.60335  25.5579  26.52825  27.51107  28.50289
> >     29.50016  30.4997  31.4997  32.4997  33.4997  34.4997  35.4997
> > 36.4997
> >     37.4997  38.4997  39.4997  40.4997  41.4997  42.4997  43.4997
> > 44.4997
> >     45.4997  46.4997  47.4997  48.4997  49.4997  50.4997  51.4997
> > 52.4997
> >     53.4997  54.4997  55.4997  56.4997  57.4997  58.4997  59.4997
> > 60.4997
> >     61.4997  62.4997  63.4997  64.4997
> >
> > ZDEF 40 levels 5  15  25  35  45  55  65  75  85  95  105  115  125
> > 135  145  155
> >     165  175  185  195  205  215  225  238.4779  262.2945  303.0287
> >     366.7978  459.091  584.6193  747.187  949.5881  1193.53  1479.588
> >     1807.187  2174.619  2579.091  3016.798  3483.029  3972.294
> > 4478.478
> >
> > TDEF 14 LINEAR 16jan0001 1mo
> >
> > vars 6
> > eta_t    0 t,y,x   ssh
> > temp    40 t,z,y,x   temp
> > salt    40 t,z,y,x   salt
> > mld      0 t,y,x   mld
> > sfc_hflux      0 t,y,x   heat flux
> > pme      0 t,y,x   precip-evap
> > endvars
> >
> > netcdf 00010101.ocean_month {
> > dimensions:
> >         xt_ocean = 360 ;
> >         yt_ocean = 200 ;
> >         Time = UNLIMITED ; // (1 currently)
> >         nv = 2 ;
> >         zt_ocean = 40 ;
> >         zt_edges_ocean = 41 ;
> >         zw_ocean = 40 ;
> >         zw_edges_ocean = 41 ;
> > variables:
> >         float xt_ocean(xt_ocean) ;
> >                 xt_ocean:long_name = "tcell longitude" ;
> >                 xt_ocean:units = "degrees_E" ;
> >                 xt_ocean:cartesian_axis = "X" ;
> >         float yt_ocean(yt_ocean) ;
> >                 yt_ocean:long_name = "tcell latitude" ;
> >                 yt_ocean:units = "degrees_N" ;
> >                 yt_ocean:cartesian_axis = "Y" ;
> >         double Time(Time) ;
> >                 Time:long_name = "Time" ;
> >                 Time:units = "days since 0001-01-01 00:00:00" ;
> >                 Time:cartesian_axis = "T" ;
> >                 Time:calendar_type = "JULIAN" ;
> >                 Time:calendar = "JULIAN" ;
> >                 Time:bounds = "Time_bounds" ;
> >         float nv(nv) ;
> >                 nv:long_name = "vertex number" ;
> >                 nv:units = "none" ;
> >                 nv:cartesian_axis = "N" ;
> >         float zt_ocean(zt_ocean) ;
> >                 zt_ocean:long_name = "tcell depth" ;
> >                 zt_ocean:units = "meters" ;
> >                 zt_ocean:cartesian_axis = "Z" ;
> >                 zt_ocean:positive = "down" ;
> >                 zt_ocean:edges = "zt_edges_ocean" ;
> >         float zt_edges_ocean(zt_edges_ocean) ;
> >                 zt_edges_ocean:long_name = "tcell depth edges" ;
> >                 zt_edges_ocean:units = "meters" ;
> >                 zt_edges_ocean:cartesian_axis = "Z" ;
> >                 zt_edges_ocean:positive = "down" ;
> >         float zw_ocean(zw_ocean) ;
> >                 zw_ocean:long_name = "ucell depth" ;
> >                 zw_ocean:units = "meters" ;
> >                 zw_ocean:cartesian_axis = "Z" ;
> >                 zw_ocean:positive = "down" ;
> >                 zw_ocean:edges = "zw_edges_ocean" ;
> >         float zw_edges_ocean(zw_edges_ocean) ;
> >                 zw_edges_ocean:long_name = "ucell depth edges" ;
> >                 zw_edges_ocean:units = "meters" ;
> >                 zw_edges_ocean:cartesian_axis = "Z" ;
> >                 zw_edges_ocean:positive = "down" ;
> >         float eta_t(Time, yt_ocean, xt_ocean) ;
> >                 eta_t:long_name = "surface height on T cells" ;
> >                 eta_t:units = "meter" ;
> >                 eta_t:valid_range = -10.f, 10.f ;
> >                 eta_t:missing_value = -10.f ;
> >                 eta_t:cell_methods = "time: mean" ;
> >                 eta_t:time_avg_info =
> > "average_T1,average_T2,average_DT" ;
> >         short temp(Time, zt_ocean, yt_ocean, xt_ocean) ;
> >                 temp:long_name = "Potential temperature" ;
> >                 temp:units = "deg_C" ;
> >                 temp:valid_range = -32767s, 32767s ;
> >                 temp:missing_value = -32768s ;
> >                 temp:packing = 4 ;
> >                 temp:scale_factor = 0.001678518f ;
> >                 temp:add_offset = 45.f ;
> >                 temp:cell_methods = "time: mean" ;
> >                 temp:time_avg_info =
> > "average_T1,average_T2,average_DT" ;
> >         short salt(Time, zt_ocean, yt_ocean, xt_ocean) ;
> >                 salt:long_name = "Salinity" ;
> >                 salt:units = "psu" ;
> >                 salt:valid_range = -32767s, 32767s ;
> >                 salt:missing_value = -32768s ;
> >                 salt:packing = 4 ;
> >                 salt:scale_factor = 0.001678518f ;
> >                 salt:add_offset = 45.f ;
> >                 salt:cell_methods = "time: mean" ;
> >                 salt:time_avg_info =
> > "average_T1,average_T2,average_DT" ;
> >         float wt(Time, zw_ocean, yt_ocean, xt_ocean) ;
> >                 wt:long_name = "vertical velocity T-points" ;
> >                 wt:units = "m/sec" ;
> >                 wt:valid_range = -10.f, 10.f ;
> >                 wt:missing_value = -10.f ;
> >                 wt:cell_methods = "time: mean" ;
> >                 wt:time_avg_info = "average_T1,average_T2,average_DT" ;
> >         float mld(Time, yt_ocean, xt_ocean) ;
> >                 mld:long_name = "mixed layer depth" ;
> >                 mld:units = "m" ;
> >                 mld:valid_range = 0.f, 1000000.f ;
> >                 mld:missing_value = 0.f ;
> >                 mld:cell_methods = "time: mean" ;
> >                 mld:time_avg_info = "average_T1,average_T2,average_DT"
> > ;
> >         float sfc_hflux(Time, yt_ocean, xt_ocean) ;
> >                 sfc_hflux:long_name = "surface heat flux" ;
> >                 sfc_hflux:units = "Watts/m^2" ;
> >                 sfc_hflux:valid_range = -10000.f, 10000.f ;
> >                 sfc_hflux:missing_value = -1.e+10f ;
> >                 sfc_hflux:cell_methods = "time: mean" ;
> >                 sfc_hflux:time_avg_info =
> > "average_T1,average_T2,average_DT" ;
> >         float pme(Time, yt_ocean, xt_ocean) ;
> >                 pme:long_name = "precip-evap (liquid, frozen,
> > evaporation)" ;
> >                 pme:units = "m/sec" ;
> >                 pme:valid_range = -10.f, 10.f ;
> >                 pme:missing_value = -1.e+10f ;
> >                 pme:cell_methods = "time: mean" ;
> >                 pme:time_avg_info = "average_T1,average_T2,average_DT"
> > ;
> >         double average_T1(Time) ;
> >                 average_T1:long_name = "Start time for average period"
> > ;
> >                 average_T1:units = "days since 0001-01-01 00:00:00" ;
> >         double average_T2(Time) ;
> >                 average_T2:long_name = "End time for average period" ;
> >                 average_T2:units = "days since 0001-01-01 00:00:00" ;
> >         double average_DT(Time) ;
> >                 average_DT:long_name = "Length of average period" ;
> >                 average_DT:units = "days" ;
> >         double Time_bounds(Time, nv) ;
> >                 Time_bounds:long_name = "Time axis boundaries" ;
> >                 Time_bounds:units = "days" ;
> >
> > // global attributes:
> >                 :filename = "ocean_month.nc" ;
> >                 :title = "indian ocean exp" ;
> > data:
> >
> >  xt_ocean = 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5,
> > 11.5,
> >     12.5, 13.5, 14.5, 15.5, 16.5, 17.5, 18.5, 19.5, 20.5, 21.5, 22.5,
> > 23.5,
> >     24.5, 25.5, 26.5, 27.5, 28.5, 29.5, 30.5, 31.5, 32.5, 33.5, 34.5,
> > 35.5,
> >     36.5, 37.5, 38.5, 39.5, 40.5, 41.5, 42.5, 43.5, 44.5, 45.5, 46.5,
> > 47.5,
> >     48.5, 49.5, 50.5, 51.5, 52.5, 53.5, 54.5, 55.5, 56.5, 57.5, 58.5,
> > 59.5,
> >     60.5, 61.5, 62.5, 63.5, 64.5, 65.5, 66.5, 67.5, 68.5, 69.5, 70.5,
> > 71.5,
> >     72.5, 73.5, 74.5, 75.5, 76.5, 77.5, 78.5, 79.5, 80.5, 81.5, 82.5,
> > 83.5,
> >     84.5, 85.5, 86.5, 87.5, 88.5, 89.5, 90.5, 91.5, 92.5, 93.5, 94.5,
> > 95.5,
> >     96.5, 97.5, 98.5, 99.5, 100.5, 101.5, 102.5, 103.5, 104.5, 105.5,
> > 106.5,
> >     107.5, 108.5, 109.5, 110.5, 111.5, 112.5, 113.5, 114.5, 115.5,
> > 116.5,
> >     117.5, 118.5, 119.5, 120.5, 121.5, 122.5, 123.5, 124.5, 125.5,
> > 126.5,
> >     127.5, 128.5, 129.5, 130.5, 131.5, 132.5, 133.5, 134.5, 135.5,
> > 136.5,
> >     137.5, 138.5, 139.5, 140.5, 141.5, 142.5, 143.5, 144.5, 145.5,
> > 146.5,
> >     147.5, 148.5, 149.5, 150.5, 151.5, 152.5, 153.5, 154.5, 155.5,
> > 156.5,
> >     157.5, 158.5, 159.5, 160.5, 161.5, 162.5, 163.5, 164.5, 165.5,
> > 166.5,
> >     167.5, 168.5, 169.5, 170.5, 171.5, 172.5, 173.5, 174.5, 175.5,
> > 176.5,
> >     177.5, 178.5, 179.5, 180.5, 181.5, 182.5, 183.5, 184.5, 185.5,
> > 186.5,
> >     187.5, 188.5, 189.5, 190.5, 191.5, 192.5, 193.5, 194.5, 195.5,
> > 196.5,
> >     197.5, 198.5, 199.5, 200.5, 201.5, 202.5, 203.5, 204.5, 205.5,
> > 206.5,
> >     207.5, 208.5, 209.5, 210.5, 211.5, 212.5, 213.5, 214.5, 215.5,
> > 216.5,
> >     217.5, 218.5, 219.5, 220.5, 221.5, 222.5, 223.5, 224.5, 225.5,
> > 226.5,
> >     227.5, 228.5, 229.5, 230.5, 231.5, 232.5, 233.5, 234.5, 235.5,
> > 236.5,
> >     237.5, 238.5, 239.5, 240.5, 241.5, 242.5, 243.5, 244.5, 245.5,
> > 246.5,
> >     247.5, 248.5, 249.5, 250.5, 251.5, 252.5, 253.5, 254.5, 255.5,
> > 256.5,
> >     257.5, 258.5, 259.5, 260.5, 261.5, 262.5, 263.5, 264.5, 265.5,
> > 266.5,
> >     267.5, 268.5, 269.5, 270.5, 271.5, 272.5, 273.5, 274.5, 275.5,
> > 276.5,
> >     277.5, 278.5, 279.5, 280.5, 281.5, 282.5, 283.5, 284.5, 285.5,
> > 286.5,
> >     287.5, 288.5, 289.5, 290.5, 291.5, 292.5, 293.5, 294.5, 295.5,
> > 296.5,
> >     297.5, 298.5, 299.5, 300.5, 301.5, 302.5, 303.5, 304.5, 305.5,
> > 306.5,
> >     307.5, 308.5, 309.5, 310.5, 311.5, 312.5, 313.5, 314.5, 315.5,
> > 316.5,
> >     317.5, 318.5, 319.5, 320.5, 321.5, 322.5, 323.5, 324.5, 325.5,
> > 326.5,
> >     327.5, 328.5, 329.5, 330.5, 331.5, 332.5, 333.5, 334.5, 335.5,
> > 336.5,
> >     337.5, 338.5, 339.5, 340.5, 341.5, 342.5, 343.5, 344.5, 345.5,
> > 346.5,
> >     347.5, 348.5, 349.5, 350.5, 351.5, 352.5, 353.5, 354.5, 355.5,
> > 356.5,
> >     357.5, 358.5, 359.5 ;
> >
> >  yt_ocean = -74.5, -73.5, -72.5, -71.5, -70.5, -69.5, -68.5, -67.5,
> > -66.5,
> >     -65.5, -64.5, -63.5, -62.5, -61.5, -60.5, -59.5, -58.5, -57.5,
> > -56.5,
> >     -55.5, -54.5, -53.5, -52.5, -51.5, -50.5, -49.5, -48.5, -47.5,
> > -46.5,
> >     -45.5, -44.5, -43.5, -42.5, -41.5, -40.5, -39.5, -38.5, -37.5,
> > -36.5,
> >     -35.5, -34.5, -33.5, -32.5, -31.5, -30.5, -29.50046, -28.50319,
> >     -27.51137, -26.52855, -25.5582, -24.60365, -23.66805, -22.75435,
> >     -21.86525, -21.00319, -20.17032, -19.36844, -18.59905, -17.86328,
> >     -17.16186, -16.4952, -15.86328, -15.26573, -14.70179, -14.17033,
> >     -13.66988, -13.19861, -12.75437, -12.33475, -11.93702, -11.55824,
> >     -11.19526, -10.84474, -10.50324, -10.16717, -9.833385, -9.500055,
> >     -9.166725, -8.833395, -8.500065, -8.166735, -7.833405, -7.500075,
> >     -7.166745, -6.833415, -6.500085, -6.166755, -5.833425, -5.500095,
> >     -5.166765, -4.833435, -4.500105, -4.166775, -3.833445, -3.500115,
> >     -3.166785, -2.833455, -2.500125, -2.166795, -1.833465, -1.500135,
> >     -1.166805, -0.833475, -0.500145, -0.166815, 0.166515, 0.499845,
> > 0.833175,
> >     1.166505, 1.499835, 1.833165, 2.166495, 2.499825, 2.833155,
> > 3.166485,
> >     3.499815, 3.833145, 4.166475, 4.499805, 4.833135, 5.166465,
> > 5.499795,
> >     5.833125, 6.166455, 6.499785, 6.833115, 7.166445, 7.499775,
> > 7.833105,
> >     8.166435, 8.499765, 8.833095, 9.166425, 9.499755, 9.833085,
> > 10.16687,
> >     10.50294, 10.84444, 11.19496, 11.55794, 11.93672, 12.33445,
> > 12.75407,
> >     13.19831, 13.66958, 14.17003, 14.70149, 15.26543, 15.86298,
> > 16.4949,
> >     17.16156, 17.86298, 18.59875, 19.36814, 20.17002, 21.00289,
> > 21.86495,
> >     22.75405, 23.66775, 24.60335, 25.5579, 26.52825, 27.51107,
> > 28.50289,
> >     29.50016, 30.4997, 31.4997, 32.4997, 33.4997, 34.4997, 35.4997,
> > 36.4997,
> >     37.4997, 38.4997, 39.4997, 40.4997, 41.4997, 42.4997, 43.4997,
> > 44.4997,
> >     45.4997, 46.4997, 47.4997, 48.4997, 49.4997, 50.4997, 51.4997,
> > 52.4997,
> >     53.4997, 54.4997, 55.4997, 56.4997, 57.4997, 58.4997, 59.4997,
> > 60.4997,
> >     61.4997, 62.4997, 63.4997, 64.4997 ;
> >
> >  Time = 15.5 ;
> >
> >  nv = 1, 2 ;
> >
> >  zt_ocean = 5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105, 115, 125, 135,
> > 145,
> >     155, 165, 175, 185, 195, 205, 215, 225, 238.4779, 262.2945,
> > 303.0287,
> >     366.7978, 459.091, 584.6193, 747.187, 949.5881, 1193.53, 1479.588,
> >     1807.187, 2174.619, 2579.091, 3016.798, 3483.029, 3972.294,
> > 4478.478 ;
> >
> >  zt_edges_ocean = -0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110,
> > 120, 130,
> >     140, 150, 160, 170, 180, 190, 200, 210, 220, 231.7389, 250.3862,
> >     282.6616, 334.9132, 412.9444, 521.8552, 665.9031, 848.3875,
> > 1071.559,
> >     1336.559, 1643.388, 1990.903, 2376.855, 2797.944, 3249.913,
> > 3727.662,
> >     4225.386, 4736.739 ;
> >
> >  zw_ocean = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130,
> > 140, 150,
> >     160, 170, 180, 190, 200, 210, 220, 231.7389, 250.3862, 282.6616,
> >     334.9132, 412.9444, 521.8552, 665.9031, 848.3875, 1071.559,
> > 1336.559,
> >     1643.388, 1990.903, 2376.855, 2797.944, 3249.913, 3727.662,
> > 4225.386,
> >     4736.739 ;
> >
> >  zw_edges_ocean = 5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105, 115,
> > 125, 135,
> >     145, 155, 165, 175, 185, 195, 205, 215, 225, 238.4779, 262.2945,
> >     303.0287, 366.7978, 459.091, 584.6193, 747.187, 949.5881, 1193.53,
> >     1479.588, 1807.187, 2174.619, 2579.091, 3016.798, 3483.029,
> > 3972.294,
> >     4478.478, 4736.739 ;
> > }



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