Yesterday's post about Eureka has led to some comments, regarding how important this issue is. Anthony Watts has made some very good points explaining why this is important. I would like to further expand on this.Maximum temperatures are very important, as mean temperatures result from the average between the maximum and minimum temperatures of a day. That can be seen for the July 2009 values, where the mean temperature for July 14th, was 14.1ºC. This results from adding the minimum temperature (7.3ºC) to the maximum temperature (20.9ºC), and dividing the result by 2, thus giving 14.1ºC. Now, as can be seen from the hourly temperatures of the day, 14.1ºC was only surpassed at 19:00, with 14.4ºC. Now, the mean monthly temperatures seem to be derived from the daily means, giving the 8.0ºC mean temperature for July 2009. This value is the same as given in GHCN data (note: very large file!) and they confer with the National Climate Data and Information Archive, with only a minor difference in April, in all of 2009. Please notice the data in the GISS file:
| 4037191700062009 -340 -386 -386 -273 -98 40 80 56 -56 -234 -233 -296 |
Now, readers following this might wonder how much big the impact is when maximum temperatures have sky-rocketed, as we have shown yesterday. More in a little moment. First I had to be sure about how the mean temperatures were calculated. Reverse engineering the values for 2009, I found that the monthly mean is the mean of the daily means. This can be seen by calculating other months mean values, namely March 2009 and November 2009. This has an interesting impact, as the value rounding observed in each day's value, is incorporated in the monthly value. Please see the following table for the details on the July average:
| Day | Max | Min | NCDIA mean | Math mean |
|---|---|---|---|---|
| July 1 | 10 | -0.1 | 5 | 4.95 |
| July 2 | 7.8 | 2.1 | 5 | 4.95 |
| July 3 | 7.6 | 1.9 | 4.8 | 4.75 |
| July 4 | 9.3 | 4.4 | 6.9 | 6.85 |
| July 5 | 6.2 | 2.6 | 4.4 | 4.4 |
| July 6 | 9.5 | 2.9 | 6.2 | 6.2 |
| July 7 | 8.6 | 2.7 | 5.7 | 5.65 |
| July 8 | 10.1 | 2.5 | 6.3 | 6.3 |
| July 9 | 10.4 | 3.9 | 7.2 | 7.15 |
| July 10 | 11.5 | 3.4 | 7.5 | 7.45 |
| July 11 | 9.3 | 2.9 | 6.1 | 6.1 |
| July 12 | 9.3 | 2.8 | 6.1 | 6.05 |
| July 13 | 19.8 | 2.8 | 11.3 | 11.3 |
| July 14 | 20.9 | 7.3 | 14.1 | 14.1 |
| July 15 | 15.7 | 4.5 | 10.1 | 10.1 |
| July 16 | 12.6 | 3.7 | 8.2 | 8.15 |
| July 17 | 14.4 | 3 | 8.7 | 8.7 |
| July 18 | 14.8 | 6.6 | 10.7 | 10.7 |
| July 19 | 13.4 | 6.7 | 10.1 | 10.05 |
| July 20 | 16.4 | 3.7 | 10.1 | 10.05 |
| July 21 | 15 | 2.6 | 8.8 | 8.8 |
| July 22 | 17.1 | 9.1 | 13.1 | 13.1 |
| July 23 | 13.8 | 6.8 | 10.3 | 10.3 |
| July 24 | 12 | 3.1 | 7.6 | 7.55 |
| July 25 | 14.4 | 7.3 | 10.9 | 10.85 |
| July 26 | 13.4 | 6.3 | 9.9 | 9.85 |
| July 27 | 9.5 | 4.1 | 6.8 | 6.8 |
| July 28 | 7.2 | 2.1 | 4.7 | 4.65 |
| July 29 | 9.4 | 1.2 | 5.3 | 5.3 |
| July 30 | 13.1 | 4.4 | 8.8 | 8.75 |
| July 31 | 10.3 | 4.7 | 7.5 | 7.5 |
| 8.006 | 7.981 |
Please notice that the math mean will always be lower than the NCDIA mean. How much depends on the specific values, but one would expect it to be 0.025ºC (15x0.05/30) on a 30 day month. This is in range with the difference observed for July 2009.
Now finally we can measure the impact of the strange temperatures in July 2009. If we admit that the July 13th maximum value of 19.6ºC is an absurd, we can use the second lowest value of that day, which is 13.7ºC. Some of you might argue that it is still a high value, as can be seen in the daily graph, but for simplicity, let's use it. And we'll use 14.4ºC as the maximum temperature for July 14, as this is the highest value for that day.
| Day | Max | Min | NCDIA mean | Math mean | delta for 13 and 14 |
|---|---|---|---|---|---|
| July 1 | 10 | -0.1 | 5 | 4.95 | 4.95 |
| July 2 | 7.8 | 2.1 | 5 | 4.95 | 4.95 |
| July 3 | 7.6 | 1.9 | 4.8 | 4.75 | 4.75 |
| July 4 | 9.3 | 4.4 | 6.9 | 6.85 | 6.85 |
| July 5 | 6.2 | 2.6 | 4.4 | 4.4 | 4.4 |
| July 6 | 9.5 | 2.9 | 6.2 | 6.2 | 6.2 |
| July 7 | 8.6 | 2.7 | 5.7 | 5.65 | 5.65 |
| July 8 | 10.1 | 2.5 | 6.3 | 6.3 | 6.3 |
| July 9 | 10.4 | 3.9 | 7.2 | 7.15 | 7.15 |
| July 10 | 11.5 | 3.4 | 7.5 | 7.45 | 7.45 |
| July 11 | 9.3 | 2.9 | 6.1 | 6.1 | 6.1 |
| July 12 | 9.3 | 2.8 | 6.1 | 6.05 | 6.05 |
| July 13 | 19.8 | 2.8 | 11.3 | 11.3 | 8.25 |
| July 14 | 20.9 | 7.3 | 14.1 | 14.1 | 10.85 |
| July 15 | 15.7 | 4.5 | 10.1 | 10.1 | 10.1 |
| July 16 | 12.6 | 3.7 | 8.2 | 8.15 | 8.15 |
| July 17 | 14.4 | 3 | 8.7 | 8.7 | 8.7 |
| July 18 | 14.8 | 6.6 | 10.7 | 10.7 | 10.7 |
| July 19 | 13.4 | 6.7 | 10.1 | 10.05 | 10.05 |
| July 20 | 16.4 | 3.7 | 10.1 | 10.05 | 10.05 |
| July 21 | 15 | 2.6 | 8.8 | 8.8 | 8.8 |
| July 22 | 17.1 | 9.1 | 13.1 | 13.1 | 13.1 |
| July 23 | 13.8 | 6.8 | 10.3 | 10.3 | 10.3 |
| July 24 | 12 | 3.1 | 7.6 | 7.55 | 7.55 |
| July 25 | 14.4 | 7.3 | 10.9 | 10.85 | 10.85 |
| July 26 | 13.4 | 6.3 | 9.9 | 9.85 | 9.85 |
| July 27 | 9.5 | 4.1 | 6.8 | 6.8 | 6.8 |
| July 28 | 7.2 | 2.1 | 4.7 | 4.65 | 4.65 |
| July 29 | 9.4 | 1.2 | 5.3 | 5.3 | 5.3 |
| July 30 | 13.1 | 4.4 | 8.8 | 8.75 | 8.75 |
| July 31 | 10.3 | 4.7 | 7.5 | 7.5 | 7.5 |
| 8.006 | 7.981 | 7.777 |
The value has come down from 8.0ºC to 7.8ºC. But one might argue that this max/min temperature simple calculations are really too simplistic. I moved on, gathering the hourly values for July 2009, in CSV format, and doing the necessary calculations. Another column emerges, and as can be seen below, another reality appears: mean monthly temperatures for July 2009 are at 7.6ºC!
| Day | Max | Min | NCDIA mean | Math mean | delta for 13 and 14 | hourly mean |
|---|---|---|---|---|---|---|
| July 1 | 10 | -0.1 | 5 | 4.95 | 4.95 | 3.895 |
| July 2 | 7.8 | 2.1 | 5 | 4.95 | 4.95 | 4.305 |
| July 3 | 7.6 | 1.9 | 4.8 | 4.75 | 4.75 | 3.691 |
| July 4 | 9.3 | 4.4 | 6.9 | 6.85 | 6.85 | 6.564 |
| July 5 | 6.2 | 2.6 | 4.4 | 4.4 | 4.4 | 4.255 |
| July 6 | 9.5 | 2.9 | 6.2 | 6.2 | 6.2 | 5.659 |
| July 7 | 8.6 | 2.7 | 5.7 | 5.65 | 5.65 | 4.773 |
| July 8 | 10.1 | 2.5 | 6.3 | 6.3 | 6.3 | 4.636 |
| July 9 | 10.4 | 3.9 | 7.2 | 7.15 | 7.15 | 7.241 |
| July 10 | 11.5 | 3.4 | 7.5 | 7.45 | 7.45 | 7.564 |
| July 11 | 9.3 | 2.9 | 6.1 | 6.1 | 6.1 | 5.027 |
| July 12 | 9.3 | 2.8 | 6.1 | 6.05 | 6.05 | 5.573 |
| July 13 | 19.8 | 2.8 | 11.3 | 11.3 | 8.25 | 8.527 |
| July 14 | 20.9 | 7.3 | 14.1 | 14.1 | 10.85 | 11.464 |
| July 15 | 15.7 | 4.5 | 10.1 | 10.1 | 10.1 | 9.65 |
| July 16 | 12.6 | 3.7 | 8.2 | 8.15 | 8.15 | 9.927 |
| July 17 | 14.4 | 3 | 8.7 | 8.7 | 8.7 | 7.95 |
| July 18 | 14.8 | 6.6 | 10.7 | 10.7 | 10.7 | 11.164 |
| July 19 | 13.4 | 6.7 | 10.1 | 10.05 | 10.05 | 10.823 |
| July 20 | 16.4 | 3.7 | 10.1 | 10.05 | 10.05 | 12.845 |
| July 21 | 15 | 2.6 | 8.8 | 8.8 | 8.8 | 7.809 |
| July 22 | 17.1 | 9.1 | 13.1 | 13.1 | 13.1 | 13.973 |
| July 23 | 13.8 | 6.8 | 10.3 | 10.3 | 10.3 | 10.15 |
| July 24 | 12 | 3.1 | 7.6 | 7.55 | 7.55 | 7.995 |
| July 25 | 14.4 | 7.3 | 10.9 | 10.85 | 10.85 | 10.809 |
| July 26 | 13.4 | 6.3 | 9.9 | 9.85 | 9.85 | 9.286 |
| July 27 | 9.5 | 4.1 | 6.8 | 6.8 | 6.8 | 7.118 |
| July 28 | 7.2 | 2.1 | 4.7 | 4.65 | 4.65 | 3.991 |
| July 29 | 9.4 | 1.2 | 5.3 | 5.3 | 5.3 | 4.686 |
| July 30 | 13.1 | 4.4 | 8.8 | 8.75 | 8.75 | 7.614 |
| July 31 | 10.3 | 4.7 | 7.5 | 7.5 | 7.5 | 6.482 |
| 8.006 | 7.981 | 7.777 | 7.595 |
For some strange reason, data for this station doesn't include the first two hours of the day. Seems like temperatures should be colder in that period, despite the fact that there is always a sun up there in July. Couldn't help testing this one too. So, with no surprise, temperatures went down again:
| Day | Max | Min | NCDIA mean | Math mean | delta for 13 and 14 | hourly mean | 24 hour mean |
|---|---|---|---|---|---|---|---|
| July 1 | 10 | -0.1 | 5 | 4.95 | 4.95 | 3.895 | 3.804 |
| July 2 | 7.8 | 2.1 | 5 | 4.95 | 4.95 | 4.305 | 4.217 |
| July 3 | 7.6 | 1.9 | 4.8 | 4.75 | 4.75 | 3.691 | 3.633 |
| July 4 | 9.3 | 4.4 | 6.9 | 6.85 | 6.85 | 6.564 | 6.471 |
| July 5 | 6.2 | 2.6 | 4.4 | 4.4 | 4.4 | 4.255 | 4.346 |
| July 6 | 9.5 | 2.9 | 6.2 | 6.2 | 6.2 | 5.659 | 5.492 |
| July 7 | 8.6 | 2.7 | 5.7 | 5.65 | 5.65 | 4.773 | 4.742 |
| July 8 | 10.1 | 2.5 | 6.3 | 6.3 | 6.3 | 4.636 | 4.504 |
| July 9 | 10.4 | 3.9 | 7.2 | 7.15 | 7.15 | 7.241 | 7.108 |
| July 10 | 11.5 | 3.4 | 7.5 | 7.45 | 7.45 | 7.564 | 7.592 |
| July 11 | 9.3 | 2.9 | 6.1 | 6.1 | 6.1 | 5.027 | 4.954 |
| July 12 | 9.3 | 2.8 | 6.1 | 6.05 | 6.05 | 5.573 | 5.717 |
| July 13 | 19.8 | 2.8 | 11.3 | 11.3 | 8.25 | 8.527 | 8.208 |
| July 14 | 20.9 | 7.3 | 14.1 | 14.1 | 10.85 | 11.464 | 11.004 |
| July 15 | 15.7 | 4.5 | 10.1 | 10.1 | 10.1 | 9.65 | 9.717 |
| July 16 | 12.6 | 3.7 | 8.2 | 8.15 | 8.15 | 9.927 | 10.138 |
| July 17 | 14.4 | 3 | 8.7 | 8.7 | 8.7 | 7.95 | 7.713 |
| July 18 | 14.8 | 6.6 | 10.7 | 10.7 | 10.7 | 11.164 | 10.921 |
| July 19 | 13.4 | 6.7 | 10.1 | 10.05 | 10.05 | 10.823 | 10.742 |
| July 20 | 16.4 | 3.7 | 10.1 | 10.05 | 10.05 | 12.845 | 12.638 |
| July 21 | 15 | 2.6 | 8.8 | 8.8 | 8.8 | 7.809 | 7.846 |
| July 22 | 17.1 | 9.1 | 13.1 | 13.1 | 13.1 | 13.973 | 13.95 |
| July 23 | 13.8 | 6.8 | 10.3 | 10.3 | 10.3 | 10.15 | 10.246 |
| July 24 | 12 | 3.1 | 7.6 | 7.55 | 7.55 | 7.995 | 8.083 |
| July 25 | 14.4 | 7.3 | 10.9 | 10.85 | 10.85 | 10.809 | 10.729 |
| July 26 | 13.4 | 6.3 | 9.9 | 9.85 | 9.85 | 9.286 | 9.608 |
| July 27 | 9.5 | 4.1 | 6.8 | 6.8 | 6.8 | 7.118 | 7.104 |
| July 28 | 7.2 | 2.1 | 4.7 | 4.65 | 4.65 | 3.991 | 4.1 |
| July 29 | 9.4 | 1.2 | 5.3 | 5.3 | 5.3 | 4.686 | 4.563 |
| July 30 | 13.1 | 4.4 | 8.8 | 8.75 | 8.75 | 7.614 | 7.429 |
| July 31 | 10.3 | 4.7 | 7.5 | 7.5 | 7.5 | 6.482 | 6.421 |
| 8.006 | 7.981 | 7.777 | 7.595 | 7.540 |
So, instead of 8.0ºC, we are down to 7.5ºC! Well, I'll stop for now. Before it gets too cold!
Note: The photo at the beginning of the post was given by Tim Clark, in the Watts Up With That post, and is available here.
Note2: Reference to GISS was replaced with the correct reference to GHCN, above.
