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Akima Tests
The following graphs illustrate comparisons between an Akima Interpolation and Linear Interpolation for single missing points. The title gives the time of the missing value, which is located at Hours=3 on each graph. The linear interpolation is the square on the straight line segment. The real data are displayed as blue squares. The curve is the Akima Spline and the corrected value that would be provided by the Akima Interpolation is indicated by the triangle.
StationID = 59800; Start Time=20080706-06
Investigation with some longer time intervals.
- Point selected at Hour=33, Actual Original Value = 15.9 degrees Celsius.
- Neighbours: (32,15.2) (36,17.1) ⇒ Linear Interpolation = 16.2 (16.15)
- The point is treated as a missing point for the following Akima interpolations.
Key:
| Blue Squares: | Original data |
|---|---|
| Red circles: | Points used in the interpolation |
| Triangle: | The Akima Point |
| Curve: | The Akima Fit |
StationID = 18700; Start Time=20080706-06; Example 1
- Actual original = 10.1 Degrees Celsius
- Square below is the linear interpolation:
StationID = 18700; Start Time=20080706-06; Example 2
Using Akima in the DipTest Algorithm
stationid | obstime | original | paramid | tbtime | typeid | sensor | level | corrected | controlinfo | useinfo | cfailed
-----------+---------------------+----------+---------+---------------------+--------+--------+-------+-----------+------------------+------------------+------------------------------------
99990 | 2027-07-08 12:00:00 | -30.8 | 211 | 2007-07-08 12:03:18 | 1 | 0 | 0 | -30.8 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-08 13:00:00 | -28.1 | 211 | 2007-07-08 13:03:26 | 1 | 0 | 0 | -28.1 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-08 14:00:00 | -27.8 | 211 | 2007-07-08 14:03:27 | 1 | 0 | 0 | -27.8 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-08 15:00:00 | -32 | 211 | 2007-07-08 15:03:35 | 1 | 0 | 0 | -32 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-08 16:00:00 | -31.8 | 211 | 2007-07-08 16:03:39 | 1 | 0 | 0 | -31.8 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-08 17:00:00 | -24.1 | 211 | 2007-07-08 17:03:20 | 1 | 0 | 0 | -31 | 1119000000100010 | 5033300000000001 | QC1-3a-211:1,QC2d-1-A,Linear=-30.8
99990 | 2027-07-08 18:00:00 | -29.8 | 211 | 2007-07-08 18:03:25 | 1 | 0 | 0 | -29.8 | 1114000000100010 | 5010300000000001 | QC2d-1
99990 | 2027-07-08 19:00:00 | -26.8 | 211 | 2007-07-08 19:03:31 | 1 | 0 | 0 | -26.8 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-08 20:00:00 | -25.6 | 211 | 2007-07-08 20:03:12 | 1 | 0 | 0 | -25.6 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-08 21:00:00 | -26.8 | 211 | 2007-07-08 21:03:18 | 1 | 0 | 0 | -26.8 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-08 22:00:00 | -26.6 | 211 | 2007-07-08 22:02:43 | 1 | 0 | 0 | -26.6 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-08 23:00:00 | -25.5 | 211 | 2007-07-08 23:03:28 | 1 | 0 | 0 | -25.5 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-09 17:00:00 | -31.3 | 211 | 2007-07-09 17:02:50 | 1 | 0 | 0 | -31.3 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-09 18:00:00 | -29.3 | 211 | 2007-07-09 18:02:55 | 1 | 0 | 0 | -29.3 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-09 19:00:00 | -30.6 | 211 | 2007-07-09 19:03:01 | 1 | 0 | 0 | -30.6 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-09 20:00:00 | -28.8 | 211 | 2007-07-09 20:03:20 | 1 | 0 | 0 | -28.8 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-09 21:00:00 | -25.1 | 211 | 2007-07-09 21:02:25 | 1 | 0 | 0 | -25.1 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-09 22:00:00 | -32.7 | 211 | 2007-07-09 22:03:39 | 1 | 0 | 0 | -28 | 1119000000100010 | 5033300000000001 | QC1-3a-211:1,QC2d-1-A,Linear=-28.5
99990 | 2027-07-09 23:00:00 | -32 | 211 | 2007-07-09 23:04:18 | 1 | 0 | 0 | -32 | 1114000000100010 | 5010300000000001 | QC2d-1
99990 | 2027-07-10 00:00:00 | -32 | 211 | 2007-07-10 00:03:19 | 1 | 0 | 0 | -32 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-10 01:00:00 | -34.7 | 211 | 2007-07-10 01:03:28 | 1 | 0 | 0 | -34.7 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-10 02:00:00 | -34.7 | 211 | 2007-07-10 02:03:53 | 1 | 0 | 0 | -34.7 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-10 03:00:00 | -31.3 | 211 | 2007-07-10 03:03:55 | 1 | 0 | 0 | -31.3 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-10 04:00:00 | -30.3 | 211 | 2007-07-10 04:04:01 | 1 | 0 | 0 | -30.3 | 1111000000100010 | 7000000000000000 |
99990 | 2027-07-10 05:00:00 | -31 | 211 | 2007-07-10 05:04:32 | 1 | 0 | 0 | -31 | 1111000000100010 | 7000000000000000 |
paule@pc3029:~/TESTDATA$
Some results from dev-vm101
stationid | obstime | original | paramid | tbtime | typeid | sensor | level | corrected | controlinfo | useinfo | cfailed
-----------+---------------------+----------+---------+---------------------------+--------+--------+-------+-----------+------------------+------------------+--------------------
90800 | 2011-03-23 12:00:00 | 29.4 | 90 | 2011-03-23 11:56:04.26427 | 330 | 0 | 0 | 29.4 | 0101000000000000 | 7000000000000000 |
90800 | 2011-03-23 13:00:00 | 16.1 | 90 | 2011-03-23 12:56:07 | 330 | 0 | 0 | 31.4 | 0119000000000000 | 5033300000000001 | QC1-3a-90,QC2d-1-L
90800 | 2011-03-23 14:00:00 | 33.4 | 90 | 2011-03-23 13:56:05 | 330 | 0 | 0 | 33.4 | 0114000000000000 | 5010300000000001 | QC1-3a-90,QC2d-1
(3 rows)
stationid | obstime | original | paramid | tbtime | typeid | sensor | level | corrected | controlinfo | useinfo | cfailed
-----------+---------------------+----------+---------+----------------------------+--------+--------+-------+-----------+------------------+------------------+---------------------------------------
79600 | 2011-03-23 15:00:00 | 19.3 | 90 | 2011-03-23 14:53:09.732768 | 311 | 0 | 0 | 19.3 | 0101000000000000 | 7000000000000000 |
79600 | 2011-03-23 16:00:00 | 36.4 | 90 | 2011-03-23 15:53:15 | 311 | 0 | 0 | 15.2 | 0409000000000000 | 5033300000000002 | QC1-1-90,QC1-3a-90,QC2d-1-A,Linear=15
79600 | 2011-03-23 17:00:00 | 10.8 | 90 | 2011-03-23 16:53:10 | 311 | 0 | 0 | 10.8 | 0404000000000000 | 5020300000000002 | QC1-3a-90,QC2d-1
(3 rows)
The following example is incorrect implementation. The Akima interpolkation gives a -ve value for Vindhastighet that is always positive!
stationid | obstime | original | paramid | tbtime | typeid | sensor | level | corrected | controlinfo | useinfo | cfailed
-----------+---------------------+----------+---------+----------------------------+--------+--------+-------+-----------+------------------+------------------+----------------------------------------------
25830 | 2011-03-23 16:00:00 | 0.6 | 81 | 2011-03-23 15:50:54.548297 | 330 | 0 | 0 | 0.6 | 0111500000000000 | 7000000000000001 | QC1-4-81,QC1-4-81
25830 | 2011-03-23 17:00:00 | 11.8 | 81 | 2011-03-23 16:50:51 | 330 | 0 | 0 | -1.5 | 0119100000000000 | 5033300000000001 | QC1-3a-81,QC1-3a-81,QC2d-1-A,Linear=1.1
25830 | 2011-03-23 18:00:00 | 1.6 | 81 | 2011-03-23 17:50:50 | 330 | 0 | 0 | 1.6 | 0114100000000000 | 5010300000000001 | QC1-3a-81,QC1-4-81,QC1-3a-81,QC1-4-81,QC2d-1
(3 rows)
stationid | obstime | original | paramid | tbtime | typeid | sensor | level | corrected | controlinfo | useinfo | cfailed
-----------+---------------------+----------+---------+----------------------------+--------+--------+-------+-----------+------------------+------------------+-----------------------------------------
39100 | 2011-03-24 00:00:00 | 12.4 | 90 | 2011-03-23 23:52:01.558744 | 330 | 0 | 0 | 12.4 | 0111000000000000 | 7000000000000000 |
39100 | 2011-03-24 01:00:00 | 25 | 90 | 2011-03-24 00:52:03 | 330 | 0 | 0 | 11.4 | 0219000000000000 | 5033300000000002 | QC1-1-90,QC1-3a-90,QC2d-1-A,Linear=11.4
39100 | 2011-03-24 02:00:00 | 10.4 | 90 | 2011-03-24 01:52:02 | 330 | 0 | 0 | 10.4 | 0214000000000000 | 5010300000000002 | QC1-3a-90,QC2d-1
(3 rows)
stationid | obstime | original | paramid | tbtime | typeid | sensor | level | corrected | controlinfo | useinfo | cfailed
-----------+---------------------+----------+---------+---------------------------+--------+--------+-------+-----------+------------------+------------------+-----------------------------------------
94500 | 2011-03-24 01:00:00 | 24.5 | 90 | 2011-03-24 00:52:38.94146 | 330 | 0 | 0 | 24.5 | 0111000000000000 | 7000000000000000 |
94500 | 2011-03-24 02:00:00 | 41.9 | 90 | 2011-03-24 01:52:38 | 330 | 0 | 0 | 23.7 | 0419000000000000 | 5033300000000002 | QC1-1-90,QC1-3a-90,QC2d-1-A,Linear=23.5
94500 | 2011-03-24 03:00:00 | 22.5 | 90 | 2011-03-24 02:52:38 | 330 | 0 | 0 | 22.5 | 0414000000000000 | 5020300000000002 | QC1-3a-90,QC2d-1
(3 rows)
stationid | obstime | original | paramid | tbtime | typeid | sensor | level | corrected | controlinfo | useinfo | cfailed
-----------+---------------------+----------+---------+----------------------------+--------+--------+-------+-----------+------------------+------------------+-------------------------------
85040 | 2011-03-24 04:00:00 | 8.3 | 90 | 2011-03-24 03:51:40.216838 | 330 | 0 | 0 | 8.3 | 0111000000000000 | 7000000000000000 |
85040 | 2011-03-24 05:00:00 | 24.5 | 90 | 2011-03-24 04:51:37 | 330 | 0 | 0 | 8.1 | 0119000000000000 | 5033300000000001 | QC1-3a-90,QC2d-1-A,Linear=8.8
85040 | 2011-03-24 06:00:00 | 9.2 | 90 | 2011-03-24 05:51:40 | 330 | 0 | 0 | 9.2 | 0114000000000000 | 5010300000000001 | QC1-3a-90,QC2d-1
(3 rows)
stationid | obstime | original | paramid | tbtime | typeid | sensor | level | corrected | controlinfo | useinfo | cfailed
-----------+---------------------+----------+---------+----------------------------+--------+--------+-------+-----------+------------------+------------------+---------------------------------------
85450 | 2011-03-25 02:00:00 | 5.2 | 90 | 2011-03-25 01:54:18.460609 | 311 | 0 | 0 | 5.2 | 0101000000000000 | 7000000000000000 |
85450 | 2011-03-25 03:00:00 | 32.5 | 90 | 2011-03-25 02:54:06 | 311 | 0 | 0 | 10.9 | 0409000000000000 | 5033300000000002 | QC1-1-90,QC1-3a-90,QC2d-1-A,Linear=11
85450 | 2011-03-25 04:00:00 | 16.8 | 90 | 2011-03-25 03:54:15 | 311 | 0 | 0 | 16.8 | 0404000000000000 | 5020300000000002 | QC1-3a-90,QC2d-1
(3 rows)
stationid | obstime | original | paramid | tbtime | typeid | sensor | level | corrected | controlinfo | useinfo | cfailed
-----------+---------------------+----------+---------+----------------------------+--------+--------+-------+-----------+------------------+------------------+--------------------
94500 | 2011-03-25 13:00:00 | 16.6 | 90 | 2011-03-25 12:52:42.714296 | 330 | 0 | 0 | 16.6 | 0111000000000000 | 7000000000000000 |
94500 | 2011-03-25 14:00:00 | 36 | 90 | 2011-03-25 13:52:39 | 330 | 0 | 0 | 16.7 | 0119000000000000 | 5033300000000001 | QC1-3a-90,QC2d-1-L
94500 | 2011-03-25 15:00:00 | 16.8 | 90 | 2011-03-25 14:52:38 | 330 | 0 | 0 | 16.8 | 0114000000000000 | 5010300000000001 | QC1-3a-90,QC2d-1
(3 rows)
stationid | obstime | original | paramid | tbtime | typeid | sensor | level | corrected | controlinfo | useinfo | cfailed
-----------+---------------------+----------+---------+----------------------------+--------+--------+-------+-----------+------------------+------------------+----------------------------------------
79600 | 2011-03-25 21:00:00 | 3.2 | 90 | 2011-03-25 20:53:22.679937 | 311 | 0 | 0 | 3.2 | 0101000000000000 | 7000000000000000 |
79600 | 2011-03-25 22:00:00 | 28.6 | 90 | 2011-03-25 21:53:10 | 311 | 0 | 0 | 3.9 | 0409000000000000 | 5033300000000002 | QC1-1-90,QC1-3a-90,QC2d-1-A,Linear=3.9
79600 | 2011-03-25 23:00:00 | 4.6 | 90 | 2011-03-25 22:53:21 | 311 | 0 | 0 | 4.6 | 0404000000000000 | 5020300000000002 | QC1-3a-90,QC2d-1
(3 rows)