Interpolation of temperature 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 +/-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 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 0.1% 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
Mean absolute difference = 0.022411
Median absolute difference = 0.009872
Standard deviation = 0.047950
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%)
-0.5:    0.5 -    6478007 ( 99.913736%)
  0.5 :  1.5 -       2603 (  0.040147%)
  1.5 :   2.5 -         27 (  0.000416%)



0.125x0.125

Maximum difference = 2.510147
Minimum difference = -2.505478
Mean absolute difference = 0.033943
Median absolute difference = 0.015244
Standard deviation = 0.072670
RMS 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%)
-1.5 : -0.5 -       6237 (  0.150286%)
-0.5 :   0.5 -    4137753 ( 99.702970%)
  0.5 :  1.5 -       5805 (  0.139877%)
  1.5 :  2.5 -        144 (  0.003470%)
  2.5 :  3.5 -          1 (  0.000024%)


0.25x0.25

Maximum difference = 8.004074
Minimum difference = -7.327957
Mean absolute difference = 0.114489
Median absolute difference = 0.050949
Standard deviation = 0.244372
RMS 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 : -6.5 -          1 (  0.000096%)
-6.5 : -5.5 -         11 (  0.001059%)
-5.5: -4.5 -         19 (  0.001830%)
-4.5 : -3.5 -         87 (  0.008380%)
-3.5 : -2.5 -        339 (  0.032651%)
-2.5: -1.5 -       1667 (  0.160560%)
-1.5 : -0.5 -      17696 (  1.704423%)
-0.5 :  0.5 -     998656 ( 96.187394%)
  0.5 :  1.5 -      17694 (  1.704230%)
  1.5 :  2.5 -       1590 (  0.153144%)
  2.5 :  3.5 -        325 (  0.031303%)
  3.5 :  4.5 -         91 (  0.008765%)
  4.5 :  5.5 -         40 (  0.003853%)
  5.5 :  6.5 -         16 (  0.001541%)
  6.5 :  7.5 -          5 (  0.000482%)
  7.5 :  8.5 -          3 (  0.000289%)

0.5x0.5

Maximum difference = 13.379105
Minimum difference = -9.935349
Mean absolute difference = 0.206355
Median absolute difference = 0.101761
Standard deviation = 0.414993
RMS 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%)             0 (  0.000000%)
-10.5 : -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%)



1.0x1.0

Maximum difference = 9.762299
Minimum difference = -10.036530
Mean absolute difference = 0.340498
Median absolute difference = 0.180267
Standard deviation = 0.635313
RMS 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 : -8.5 -         10 (  0.015347%)
  -8.5 : -7.5 -         11 (  0.016882%)
  -7.5 : -6.5 -          5 (  0.007673%)
  -6.5 : -5.5 -         15 (  0.023020%)
  -5.5 : -4.5 -         31 (  0.047575%)
  -4.5 : -3.5 -         95 (  0.145795%)
  -3.5 : -2.5 -        190 (  0.291590%)
  -2.5 : -1.5 -        696 (  1.068140%)
  -1.5 : -0.5 -       5038 (  7.731737%)
  -0.5 : 0.5 -      53170 ( 81.599141%)
    0.5 : 1.5 -       4915 (  7.542971%)
    1.5 : 2.5 -        670 (  1.028238%)
    2.5 : 3.5 -        167 (  0.256292%)
    3.5 : 4.5 -         65 (  0.099754%)
    4.5 : 5.5 -         39 (  0.059853%)
    5.5 : 6.5 -         17 (  0.026090%)
    6.5 : 7.5 -         10 (  0.015347%)
    7.5 : 8.5 -         11 (  0.016882%)
    8.5 : 9.5 -          2 (  0.003069%)
    9.5 : 10.5 -          1 (  0.001535%)