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Comment: Confirmed: Information provided here refers to the introduction of MIR and is currently up to date.

Interpolation of temperature at 1000 hPa affected by:

  • MIR using

HRES T1279

  • Differences between EMOSLIB and MIR are due toUse by MIR of 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 uses using a more accurate truncation of the spectral series corresponding to correspond 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 +/-3K
    • differences are smaller than +/-1K 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 +/-2K for more than 99% 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 where target grid compared to the theoretical  ideal used by MIR is of truncation=T719
      • EMOSLIB uses truncation=T319 for a 0.5x0.5 where target grid compared to the theoretical  ideal used by MIR is of truncation=T359
      • EMOSLIB uses truncation=T213 for a 1.0x1.0 where target grid compared to the theoretical  ideal used by MIR is of truncation=T179
      Consequently, fields produced by EMOSLIB are more affected by 'aliasing'
    The
    • than those produced by MIR.
    • Generally, the use of the intermediate grid with MIR
    generally
    • produces smoother fields.

The plots show the differences with the contours chosen on a logarithmic scale to enhance the smaller differences.  Differences smaller than 0.1% of the field range are not shown.  Grid points where the absolute difference is greater than 50% of the maximum absolute difference are indicated with red (EMOSLIB greater than MIR) and blue (EMOSLIB less than MIR) filled circles.


Target resolutionStatistics of differencesHistogram of differencesGlobalEurope
0.1x0.1

Maximum difference = 1.693253
Minimum difference = -1.505966
Average difference = 0.000041
Mean absolute difference = 0.000041022411
Median absolute difference = - 0.000107009872
Standard deviation = 0.047950
Variance = 0.002299
RMS of differences = 0.047950

Percentage of points with absolute difference

        < 0.5 = 99.914%
        < 1.0 = 99.994%
        < 2.0 = 100.000%

-2.5 : -1.5 -          4 (  0.000062%)
-1.5 : -0.5 -       2959 (  0.045638%-1.693253 : -1.354602 -         28 (  0.000432%)
-1.354602 : -1.015952 -        127 (  0.001959%)
-1.015952 : -0.677301 -        905 (  0.013958%)
-0.677301 : -0.338651 -       8284 (  0.127769%)
-0.338651 5: 0.000000 -    3432007 ( 52.933663%)
  0.000000 : 0.338651 5 -    3033555 6478007 ( 4699.788127%913736%)
  0.338651 : 0.677301 -       7733 (  0.119270%)
  0.677301 : 1.015952 -        771 5 :  1.5 -       2603 (  0.011892%040147%)
  1.015952 5 : 1.354602 -        140 (  0.002159%)
  1.354602 : 1.693253 -         50    2.5 -         27 (  0.000771%000416%)



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0.125x0.125

Maximum difference = 2.510147
Minimum difference = -2.505478
Average difference = 0.000059
Mean absolute difference = 0.000059033943
Median absolute difference = 0.000381015244
Standard deviation = 0.072670
Variance RMS of differences = 0.005281072670RMS of differences = 0.072670

Percentage of points with absolute difference

        < 0.5 = 99.703%
        < 1.0 = 99.965%
        < 2.0 = 99.999%

-3.5 : -2.5 -          2 (  0.000048%)
-2.5 : -1.5 -        138 (  0.003325%-2.510147 : -2.008118 -         22 (  0.000530%)
-2.008118 : -1.506088 -        115 (  0.002771%)
-1.506088 : -1.004059 -        621 (  0.014964%)
-1.004059 5 : -0.502029 5 -       5551 6237 (  0.133756%150286%)
-0.502029 5 :   0.000000 5 -    2018900 4137753 ( 4899.647255%702970%)
  0.000000 : 0.502029 -    2118984 ( 51.058871%)
  0.502029 : 1.004059 -       5228 5 :  1.5 -       5805 (  0.125973%139877%)
  1.004059 : 1.506088 -        515 (  0.012409%)
  1.506088 : 2.008118 -        122 5 :  2.5 -        144 (  0.002940%003470%)
  2.008118 5 : 2  3.510147 5 -         22           1 (  0.000530%000024%)


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0.25x0.25

Maximum difference = 8.004074
Minimum difference = -7.327957
Average difference = -0.000261
Mean Mean absolute difference = - 0.000261114489
Median absolute difference = 0.000168050949
Standard deviation = 0.244372
Variance RMS of differences = 0.059717244372RMS of differences = 0.244372

Percentage of points with absolute difference

        < 0.5 = 96.187%
        < 1.0 = 98.910%
        < 2.0 = 99.820%

-8.5 : -7.5 -          0 (  0.000000%)
-7.5 -8.004074 : -6.403259 5 -          1 (  0.000096%)
-6.403259 5 : -5.5 -         11 (  0.001059%)
-5.5: -4.802444 5 -         18 19 (  0.001734%001830%)
-4.802444 : 5 : -3.5 -         87 (  0.008380%)
-3.201630 5 : -2.5 -        169 339 (  0.016278%032651%)
-32.201630 5: -1.600815 5 -       1595 1667 (  0.153625%160560%)
-1.5 : -0.5 -      17696 (  1.600815 : .704423%)
-0.5 :  0.000000 5 -     514518 998656 ( 4996.556750%187394%)
  0.000000 5 :  1.600815 5 -     520200 ( 50.104022%      17694 (  1.704230%)
  1.600815 : 3.201630 -       1527 5 :  2.5 -       1590 (  0.153144%)
  2.5 :  3.5 -        325 (  0.147076%031303%)
  3.201630 5 :  4.802444 5 -        168          91 (  0.016181%008765%)
  4.802444 : 6.403259 -         35 .5 :  5.5 -         40 (  0.003853%)
  5.5 :  6.5 -         16 (  0.003371%001541%)
  6.403259 : 8.004074 -          9 5 :  7.5 -          5 (  0.000482%)
  7.5 :  8.5 -          3 (  0.000867%000289%)

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0.5x0.5

Maximum difference = 13.379105
Minimum difference = -9.935349
Average difference = -0.002242
Mean absolute difference = - 0.002242206355
Median absolute difference = - 0.001755101761
Standard deviation = 0.414993
Variance RMS of differences = 0.172219414999RMS of differences = 0.414999

 Percentage of points with absolute difference

        < 0.5 = 90.877%
        < 1.0 = 97.080%
        < 2.0 = 99.299%

-13.5 : -12.5 -              0 (  0.000000%)             0 (  0.000000%)
-12.5 : -11.5 -              0 (  0.000000%)             0 (  0.000000%)
-11.5 : -10.5 -              0 (  0.000000%)   -13.379105 : -10.703284 -           0 (  0.000000%)
-10.703284 : -8.027463 -          5 (  0.001924%)
  -8.027463 : -5.351642 -         49 (  0.018852%)
  -5.351642 : -2.675821 -        412 (  0.158510%)
  -2.675821 : 0.000000 -     130551 ( 50.227378%)
    0.000000 : 2.675821 -     128490 ( 49.434441%)
    2.675821 : 5.351642 -        366 (  0.140813%)
    5.351642 : 8.027463 -         38 (  0.014620%)
    8.027463 : 10.703284 -          6 (  0.002308%)
  10.703284 : 13.379105 -          3 (  0.001154%).5 : -9.5 -              2 (  0.000769%)             2 (  0.000769%)
  -9.5 : -8.5 -              2 (  0.000769%)             2 (  0.000769%)
  -8.5 : -7.5 -              4 (  0.001539%)             4 (  0.001539%)
  -7.5 : -6.5 -             11 (  0.004232%)            11 (  0.004232%)
  -6.5 : -5.5 -             30 (  0.011542%)            30 (  0.011542%)
  -5.5 : -4.5 -             51 (  0.019621%)            51 (  0.019621%)
  -4.5 : -3.5 -            114 (  0.043860%)           114 (  0.043860%)
  -3.5 : -2.5 -            319 (  0.122730%)           319 (  0.122730%)
  -2.5 : -1.5 -           1212 (  0.466297%)          1212 (  0.466297%)
  -1.5 : -0.5 -          10435 (  4.014697%)         10435 (  4.014697%)
  -0.5 : 0.5 -         236207 ( 90.876808%)        232907 ( 89.607187%)
   0.5 : 1.5 -           9823 (  3.779240%)          9823 (  3.779240%)
   1.5 : 2.5 -           1218 (  0.468606%)          1218 (  0.468606%)
   2.5 : 3.5 -            300 (  0.115420%)           300 (  0.115420%)
   3.5 : 4.5 -            110 (  0.042321%)           110 (  0.042321%)
   4.5 : 5.5 -             39 (  0.015005%)            39 (  0.015005%)
   5.5 : 6.5 -             18 (  0.006925%)            18 (  0.006925%)
   6.5 : 7.5 -             11 (  0.004232%)            11 (  0.004232%)
   7.5 : 8.5 -              7 (  0.002693%)             7 (  0.002693%)
   8.5 : 9.5 -              2 (  0.000769%)             2 (  0.000769%)
   9.5 : 10.5 -              2 (  0.000769%)             2 (  0.000769%)
 10.5 : 11.5 -              2 (  0.000769%)             2 (  0.000769%)
 11.5 : 12.5 -              0 (  0.000000%)             0 (  0.000000%)
 12.5 : 13.5 -              1 (  0.000385%)             1 (  0.000385%)



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1.0x1.0

Maximum difference = 9.762299
Minimum difference = -10.036530
Average difference = -0.006566
Mean Mean absolute difference = - 0.006566340498
Median absolute difference = - 0.002350180267
Standard deviation = 0.635313
Variance RMS of differences = 0.403623635347RMS of differences = 0.635347

Percentage of points with absolute difference

        < 0.5 = 81.599%
        < 1.0 = 93.099%
        < 2.0 = 98.275%

-10.5 : -9.5 -          2 (  0.003069%)
  -9.5 -10.036530 : -8.029224 5 -         14 10 (  0.021486%015347%)
  -8.029224 5 : -7.5 -         11 (  0.016882%)
  -7.5 : -6.021918 5 -          5 (  0.007673%)
  -6.5 : -5.5 -         20 15 (  0.030694%023020%)
  -65.021918 5 : -4.014612 5 -         81 31 (  0.124309%047575%)
  -4.014612 5 : -3.5 -         95 (  0.145795%)
  -3.5 : -2.007306 5 -        462 190 (  0.709024%291590%)
  -2.007306 .5 : -1.5 -        696 (  1.068140%)
  -1.5 : -0.5 -       5038 (  7.731737%)
  -0.5 : 0.000000 5 -      32208 53170 ( 4981.429098%599141%)
    0.000000 .5 : 1.5 -       4915 (  7.542971%)
    1.5 : 2.007306 5 -      31834 ( 48.855126%        670 (  1.028238%)
    2.007306 .5 : 3.5 -        167 (  0.256292%)
    3.5 : 4.014612 5 -        438          65 (  0.672192%099754%)
    4.014612 .5 : 5.5 -         39 (  0.059853%)
    5.5 : 6.021918 5 -         68 17 (  0.104359%026090%)
    6.021918 .5 : 7.5 -         10 (  0.015347%)
    7.5 : 8.029224 5 -         24 11 (  0.036832%016882%)
    8.029224 5 : 9.5 -          2 (  0.003069%)
    9.5 : 10.036530 5 -         11           1 (  0.016882%001535%)  

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