Interpolation of winds at 1000 hPa affected by::

  • MIR using an  intermediate full (regular) Gaussian grid at a resolution corresponding to the target lat-lon resolution for the spectral to grid transformation followed by grid-to-grid interpolation
  • MIR using a more accurate truncation of the spectral series corresponding to the target grid resolution to avoid ripples from aliasing effects

HRES T1279

  • For transformations to high resolution target grids (0.1x0.1 and 0.125x0.125) for which no spectral truncation occurs
    • differences are at most +/-3.5m/s
    • differences are smaller than +/-0.5m/s for more than 99% of grid points
    These differences are due to MIR making the spectral transformation to an intermediate Gaussian grid followed by grid-to-grid interpolation to the regular lat-lon grid whereas EMOSLIB transforms directly to the lat-lon target grid.
  • For transformations to lower resolution target grids:
    • the maximum and minimum differences are significantly larger.
    • differences are smaller than 1 m/s for more than 80% of grid points
    • larger differences are due to sub-optimal default truncation of the spectral series used by EMOSLIB:
      • EMOSLIB uses truncation=T799 for a 0.25x0.25 target grid compared to the theoretical  ideal used by MIR of truncation=T719
      • EMOSLIB uses truncation=T319 for a 0.5x0.5 target grid compared to the theoretical  ideal used by MIR of truncation=T359
      • EMOSLIB uses truncation=T213 for a 1.0x1.0 target grid compared to the theoretical  ideal used by MIR of truncation=T179
      Consequently, fields produced by EMOSLIB are more affected by 'aliasing' than those produced by MIR.
  • Generally, the use of the intermediate grid with MIR produces smoother fields.

The plots show the differences with the contours chosen on a logarithmic scale to enhance the smaller differences.  Differences smaller than 0.5% of the field range are not shown.  Grid points where the absolute difference is greater than 25% of the maximum absolute difference are indicated with red (EMOSLIB greater than MIR) and blue (EMOSLIB less than MIR) filled circles.


Target resolutionParameterStatistics of differencesHistogram of differencesGlobalEurope
0.1x0.1u

Maximum difference = 2.019257
Minimum difference = -1.974884
Mean absolute difference = 0.040151
Median absolute difference = 0.022186
Standard deviation = 0.070667
RMS of differences = 0.070667

Percentage of points with absolute difference

        < 0.10 = 91.262%
        < 0.25 = 98.637%
        < 0.50 = 99.817%
        < 1.00 = 99.991%

-2.5 : -2.0 -              0 (  0.000000%)             0 (  0.000000%)
-2.0 : -1.5 -             17 (  0.000262%)            17 (  0.000262%)
-1.5 : -1.0 -            226 (  0.003486%)           226 (  0.003486%)
-1.0 : -0.5 -           5381 (  0.082994%)          5381 (  0.082994%)
-0.5 : 0.0 -        3248347 ( 50.100978%)       3165179 ( 48.818234%)
  0.0 : 0.5 -        3223408 ( 49.716330%)       3132650 ( 48.316522%)
  0.5 : 1.0 -           5850 (  0.090228%)          5850 (  0.090228%)
  1.0 : 1.5 -            350 (  0.005398%)           350 (  0.005398%)
  1.5 : 2.0 -             20 (  0.000308%)            20 (  0.000308%)
   2.0 : 2.5 -              1 (  0.000015%)             1 (  0.000015%)

v

Maximum difference = 1.914169
Minimum difference = -1.721573
Mean absolute difference = 0.046585
Median absolute difference = 0.026260
Standard deviation = 0.078025
RMS of differences = 0.078025

Percentage of points with absolute difference

        < 0.10 = 88.455%
        < 0.25 = 98.182%
        < 0.50 = 99.827%
        < 1.00 = 99.996%

-2.0 : -1.5 -         10 (  0.000154%)
-1.5 : -1.0 -        125 (  0.001928%)
-1.0 : -0.5 -       5388 (  0.083102%)
-0.5 : 0.0 -    3203002 ( 49.401598%)
  0.0 : 0.5 -    3269394 ( 50.425597%)
  0.5 : 1.0 -       5532 (  0.085323%)
  1.0 : 1.5 -        134 (  0.002067%)
  1.5 : 2.0 -         15 (  0.000231%)


0.125x0.125u

Maximum difference = 2.638397
Minimum difference = -3.040314
Mean absolute difference = 0.059515
Median absolute difference = 0.031952
Standard deviation = 0.106560
RMS of differences = 0.106560

Percentage of points with absolute difference

        < 0.10 = 84.039%
        < 0.25 = 96.518%
        < 0.50 = 99.352%
        < 1.00 = 99.933%

-3.5 : -3.0 -              1 (  0.000024%)             1 (  0.000024%)
-3.0 : -2.5 -              1 (  0.000024%)             1 (  0.000024%)
-2.5 : -2.0 -             32 (  0.000771%)            32 (  0.000771%)
-2.0 : -1.5 -            118 (  0.002843%)           118 (  0.002843%)
-1.5 : -1.0 -           1033 (  0.024891%)          1033 (  0.024891%)
-1.0 : -0.5 -          12236 (  0.294838%)         12236 (  0.294838%)
-0.5 : 0.0 -        2066135 ( 49.785426%)       2027359 ( 48.851082%)
  0.0 : 0.5 -        2057047 ( 49.566442%)       2013191 ( 48.509691%)
  0.5 : 1.0 -          11895 (  0.286621%)         11895 (  0.286621%)
  1.0 : 1.5 -           1363 (  0.032843%)          1363 (  0.032843%)
  1.5 : 2.0 -            163 (  0.003928%)           163 (  0.003928%)
  2.0 : 2.5 -             48 (  0.001157%)            48 (  0.001157%)
  2.5 : 3.0 -              8 (  0.000193%)             8 (  0.000193%)
  3.0 : 3.5 -              0 (  0.000000%)             0 (  0.000000%)

v

Maximum difference = 2.837143
Minimum difference = -2.504654
Mean absolute difference = 0.069448
Median absolute difference = 0.038315
Standard deviation = 0.117622
RMS of differences = 0.117622

Percentage of points with absolute difference

        < 0.10 = 79.683%
        < 0.25 = 95.303%
        < 0.50 = 99.193%
        < 1.00 = 99.951%

-3.0 : -2.5 -          1 (  0.000024%)
-2.5 : -2.0 -         16 (  0.000386%)
-2.0 : -1.5 -         69 (  0.001663%)
-1.5 : -1.0 -        907 (  0.021855%)
-1.0 : -0.5 -      15802 (  0.380764%)
-0.5 : 0.0 -    2045563 ( 49.289725%)
  0.0 : 0.5 -    2071008 ( 49.902845%)
  0.5 : 1.0 -      15693 (  0.378137%)
  1.0 : 1.5 -        913 (  0.022000%)
  1.5 : 2.0 -         90 (  0.002169%)
  2.0 : 2.5 -         10 (  0.000241%)
  2.5 : 3.0 -          8 (  0.000193%)

0.25x0.25u

Maximum difference = 7.823715
Minimum difference = -6.886246
Mean absolute difference = 0.206354
Median absolute difference = 0.107925
Standard deviation = 0.368593
RMS of differences = 0.368593

Percentage of points with absolute difference

        < 0.10 = 47.241%
        < 0.25 = 76.027%
        < 0.50 = 90.373%
        < 1.00 = 97.323%

-8.0 : -7.0 -          0 (  0.000000%)
-7.0 : -6.0 -         12 (  0.001156%)
-6.0 : -5.0 -         13 (  0.001252%)
-5.0 : -4.0 -         76 (  0.007320%)
-4.0 : -3.0 -        370 (  0.035637%)
-3.0 : -2.0 -       1636 (  0.157574%)
-2.0 : -1.0 -      11706 (  1.127485%)
-1.0 : 0.0 -     503796 ( 48.524041%)
  0.0 : 1.0 -     506646 ( 48.798544%)
  1.0 : 2.0 -      11704 (  1.127292%)
  2.0 : 3.0 -       1689 (  0.162679%)
  3.0 : 4.0 -        408 (  0.039297%)
  4.0 : 5.0 -        135 (  0.013003%)
  5.0 : 6.0 -         33 (  0.003178%)
  6.0 : 7.0 -         12 (  0.001156%)
  7.0 : 8.0 -          4 (  0.000385%)

v

Maximum difference = 9.905029
Minimum difference = -7.118408
Mean absolute difference = 0.214605
Median absolute difference = 0.116943
Standard deviation = 0.366808
RMS of differences = 0.366808

Percentage of points with absolute difference

        < 0.10 = 44.908%
        < 0.25 = 74.036%
        < 0.50 = 89.647%
        < 1.00 = 97.294%

-10.0 : -9.0 -          0 (  0.000000%)
   -9.0 : -8.0 -          0 (  0.000000%)
   -8.0 : -7.0 -          1 (  0.000096%)
   -7.0 : -6.0 -          5 (  0.000482%)
   -6.0 : -5.0 -         14 (  0.001348%)
   -5.0 : -4.0 -         74 (  0.007127%)
   -4.0 : -3.0 -        268 (  0.025813%)
   -3.0 : -2.0 -       1461 (  0.140719%)
   -2.0 : -1.0 -      12227 (  1.177666%)
   -1.0 : 0.0 -     503768 ( 48.521344%)
     0.0 : 1.0 -     506380 ( 48.772923%)
     1.0 : 2.0 -      12235 (  1.178437%)
     2.0 : 3.0 -       1475 (  0.142067%)
     3.0 : 4.0 -        263 (  0.025331%)
     4.0 : 5.0 -         56 (  0.005394%)
     5.0 : 6.0 -          7 (  0.000674%)
     6.0 : 7.0 -          2 (  0.000193%)
     7.0 : 8.0 -          1 (  0.000096%)
     8.0 : 9.0 -          2 (  0.000193%)
     9.0 : 10.0 -          1 (  0.000096%)

0.5x0.5u

Maximum difference = 10.179855
Minimum difference = -9.166824
Mean absolute difference = 0.365231
Median absolute difference = 0.206863
Standard deviation = 0.622578
RMS of differences = 0.622578

Percentage of points with absolute difference

        < 0.10 = 28.037%
        < 0.25 = 56.549%
        < 0.50 = 78.538%
        < 1.00 = 92.510%

-11.0 : -10.0 -          0 (  0.000000%)
-10.0 : -9.0 -          1 (  0.000385%)
   -9.0 : -8.0 -          6 (  0.002308%)
   -8.0 : -7.0 -         12 (  0.004617%)
   -7.0 : -6.0 -         35 (  0.013466%)
   -6.0 : -5.0 -         57 (  0.021930%)
   -5.0 : -4.0 -        151 (  0.058095%)
   -4.0 : -3.0 -        425 (  0.163512%)
   -3.0 : -2.0 -       1506 (  0.579409%)
   -2.0 : -1.0 -       7510 (  2.889351%)
   -1.0 : 0.0 -     119503 ( 45.976839%)
     0.0 : 1.0 -     120948 ( 46.532779%)
     1.0 : 2.0 -       7476 (  2.876270%)
     2.0 : 3.0 -       1527 (  0.587488%)
     3.0 : 4.0 -        445 (  0.171207%)
     4.0 : 5.0 -        177 (  0.068098%)
     5.0 : 6.0 -         88 (  0.033857%)
     6.0 : 7.0 -         27 (  0.010388%)
     7.0 : 8.0 -         15 (  0.005771%)
     8.0 : 9.0 -          5 (  0.001924%)
     9.0 : 10.0 -          5 (  0.001924%)
  10.0 : 11.0 -          1 (  0.000385%)

v

Maximum difference = 11.994492
Minimum difference = -10.408829
Mean absolute difference = 0.368936
Median absolute difference = 0.218124
Standard deviation = 0.607771
RMS of differences = 0.607773

Percentage of points with absolute difference

        < 0.10 = 26.601%
        < 0.25 = 54.811%
        < 0.50 = 77.828%
        < 1.00 = 92.495%

-12.0 : -11.0 -          0 (  0.000000%) -11.0 : -10.0 -          1 (  0.000385%) -10.0 : -9.0 -          4 (  0.001539%)
   -9.0 : -8.0 -          2 (  0.000769%)
   -8.0 : -7.0 -         11 (  0.004232%)
   -7.0 : -6.0 -         25 (  0.009618%)
   -6.0 : -5.0 -         45 (  0.017313%)
   -5.0 : -4.0 -        119 (  0.045783%)
   -4.0 : -3.0 -        409 (  0.157356%)
   -3.0 : -2.0 -       1460 (  0.561711%)
   -2.0 : -1.0 -       7676 (  2.953216%)
   -1.0 : 0.0 -     120111 ( 46.210757%)
     0.0 : 1.0 -     120302 ( 46.284241%)
     1.0 : 2.0 -       7701 (  2.962835%)
     2.0 : 3.0 -       1473 (  0.566713%)
     3.0 : 4.0 -        357 (  0.137350%)
     4.0 : 5.0 -        137 (  0.052709%)
     5.0 : 6.0 -         52 (  0.020006%)
     6.0 : 7.0 -         24 (  0.009234%)
     7.0 : 8.0 -          7 (  0.002693%)
      8.0 : 9.0 -          2 (  0.000769%)
      9.0 : 10.0 -          0 (  0.000000%)
   10.0 : 11.0 -          1 (  0.000385%)
   11.0 : 12.0 -          1 (  0.000385%)

1.0x1.0u

Maximum difference = 12.553375
Minimum difference = -11.167328
Mean absolute difference = 0.576833
Median absolute difference = 0.346344
Standard deviation = 0.950006
RMS of differences = 0.950007

Percentage of points with absolute difference

        < 0.10 = 17.397%
        < 0.25 = 38.972%
        < 0.50 = 63.338%
        < 1.00 = 84.401%

-13.0 : -12.0 -          0 (  0.000000%)
-12.0 : -11.0 -          2 (  0.003069%)
-11.0 : -10.0 -          0 (  0.000000%) -10.0 : -9.0 -          4 (  0.006139%)
  -9.0 : -8.0 -          8 (  0.012277%)
   -8.0 : -7.0 -         18 (  0.027624%)
   -7.0 : -6.0 -         29 (  0.044506%)
   -6.0 : -5.0 -         57 (  0.087477%)
   -5.0 : -4.0 -        152 (  0.233272%)
   -4.0 : -3.0 -        300 (  0.460405%)
   -3.0 : -2.0 -        862 (  1.322897%)
   -2.0 : -1.0 -       3648 (  5.598527%)
   -1.0 : 0.0 -      27096 ( 41.583794%)
     0.0 : 1.0 -      27900 ( 42.817680%)
     1.0 : 2.0 -       3625 (  5.563229%)
     2.0 : 3.0 -        870 (  1.335175%)
     3.0 : 4.0 -        323 (  0.495703%)
     4.0 : 5.0 -        120 (  0.184162%)
     5.0 : 6.0 -         72 (  0.110497%)
     6.0 : 7.0 -         31 (  0.047575%)
     7.0 : 8.0 -         14 (  0.021486%)
     8.0 : 9.0 -         12 (  0.018416%)
     9.0 : 10.0 -          9 (  0.013812%)
  10.0 : 11.0 -          6 (  0.009208%)
  11.0 : 12.0 -          0 (  0.000000%)
  12.0 : 13.0 -          2 (  0.003069%)

v

Maximum difference = 11.211227
Minimum difference = -15.431351
Mean absolute difference = 0.569787
Median absolute difference = 0.359665
Standard deviation = 0.903314
RMS of differences = 0.903316

Percentage of points with absolute difference

        < 0.10 = 16.687%
        < 0.25 = 37.482%
        < 0.50 = 62.307%
        < 1.00 = 84.652%

-16.0 : -15.0 -          1 (  0.001535%)
-15.0 : -14.0 -          0 (  0.000000%)
-14.0 : -13.0 -          0 (  0.000000%)
-13.0 : -12.0 -          2 (  0.003069%)
-12.0 : -11.0 -          0 (  0.000000%)
-11.0 : -10.0 -          3 (  0.004604%)
-10.0 : -9.0 -          3 (  0.004604%)
  -9.0 : -8.0 -          5 (  0.007673%)
  -8.0 : -7.0 -          7 (  0.010743%)
  -7.0 : -6.0 -         22 (  0.033763%)
  -6.0 : -5.0 -         59 (  0.090546%)
  -5.0 : -4.0 -        114 (  0.174954%)
  -4.0 : -3.0 -        258 (  0.395948%)
  -3.0 : -2.0 -        822 (  1.261510%)
  -2.0 : -1.0 -       3659 (  5.615408%)
  -1.0 : 0.0 -      27178 ( 41.709638%)
    0.0 : 1.0 -      27981 ( 42.941989%)
    1.0 : 2.0 -       3719 (  5.707489%)
    2.0 : 3.0 -        824 (  1.264579%)
    3.0 : 4.0 -        309 (  0.474217%)
    4.0 : 5.0 -        108 (  0.165746%)
    5.0 : 6.0 -         47 (  0.072130%)
    6.0 : 7.0 -         21 (  0.032228%)
    7.0 : 8.0 -          9 (  0.013812%)
    8.0 : 9.0 -          4 (  0.006139%)
    9.0 : 10.0 -          2 (  0.003069%)
  10.0 : 11.0 -          2 (  0.003069%)
  11.0 : 12.0 -          1 (  0.001535%)
  12.0 : 13.0 -          0 (  0.000000%)
  13.0 : 14.0 -          0 (  0.000000%)
  14.0 : 15.0 -          0 (  0.000000%)
  15.0 : 16.0 -          0 (  0.000000%)