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 resolution	Statistics of differences	Histogram of differences	Global	Europe
0.1x0.1	Maximum difference = 1.693253 Minimum difference = -1.505966

Average difference = 0.000041

Mean absolute difference = 0.

000041

022411
Median absolute difference =

-

0.

000107

009872
Standard deviation = 0.047950

Variance = 0.002299

RMS of differences = 0.047950

-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%

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.

338651

5:

0.000000 -

3432007 ( 52.933663%)

0.

000000 : 0.338651

5 -

3033555

6478007 (

46

99.

788127%

913736%)
0.

338651 : 0.677301 -       7733 ( 0.119270%)
0.677301 : 1.015952 -        771 ( 0.011892%)
1.015952 : 1.354602 -        140

5 : 1.5 - 2603 ( 0.

002159%

040147%)
1.

354602

5 :

1

2.

693253

5 -

50

27 ( 0.

000771%

000416%)

Image Removed

Image Added

Image Modified

0.125x0.125

Maximum difference = 2.510147
Minimum difference = -2.505478

Average difference = 0.000059

Mean absolute difference = 0.

000059

033943
Median absolute difference = 0.

000381

015244
Standard deviation = 0.072670

Variance

RMS of differences = 0.

005281

072670

RMS of differences = 0.072670-2.510147 : -2.008118 -         22 ( 0.000530%)
-2.008118 : -1.506088 -        115 ( 0.002771%)
-1.506088 : -1.004059 -        621 ( 0.014964%

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.

004059

5 : -0.

502029

5 -

5551

6237 ( 0.

133756%

150286%)
-0.

502029

5 : 0.

000000

5 -

2018900

4137753 (

48

99.

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%)

Image Removed

	Image Added	Image Modified
0.25x0.25	Maximum difference = 8.004074 Minimum difference = -7.327957

Average difference = -0.000261
Mean

Mean absolute difference =

-

0.

000261

114489
Median absolute difference = 0.

000168

050949
Standard deviation = 0.244372

Variance

RMS of differences = 0.

059717

244372

RMS of differences = 0.244372-8.004074

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.

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.

201630

5 - 87 ( 0.008380%)
-3.5 : -2.5 -

169

339 ( 0.

016278%

032651%)
-

3

2.

201630

5: -1.

600815

5 -

1595

1667 ( 0.

153625%

160560%)
-1.

600815 : 0.000000 - 514518 ( 49.556750%

5 : -0.5 - 17696 ( 1.704423%)
-0.5 : 0.5 - 998656 ( 96.187394%)
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%)

Image Removed

Image Added	Image Modified
0.5x0.5	Maximum difference = 13.379105 Minimum difference = -9.935349

Average difference = -0.002242
Mean

Mean absolute difference =

-

0.

002242

206355
Median absolute difference =

-

0.

001755

101761
Standard deviation = 0.414993

Variance

RMS of differences = 0.

172219

414999

RMS of differences = 0.414999-13.379105 : -10.703284 -

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

.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%)

Image Removed

.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%)

Image Added

Image Modified

1.0x1.0

Maximum difference = 9.762299
Minimum difference = -10.036530

Average difference = -0.006566
Mean

Mean absolute difference =

-

0.

006566

340498
Median absolute difference =

-

0.

002350

180267
Standard deviation = 0.635313

Variance

RMS of differences = 0.

403623

635347

RMS of differences = 0.635347-10.036530

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.

029224

5 -

14

10 ( 0.

021486%

015347%)
-8

.029224 : -6.021918 - 20

.5 : -7.5 -         11 ( 0.016882%)
-7.5 : -6.5 -          5 ( 0.007673%)
-6.5 : -5.5 -         15 ( 0.

030694%

023020%)
-

6

5.

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 (

49

81.

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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