Guest Post By Werner Brozek, Edited By Just The Facts
(Note: If you read my report with the January data and just wish to know what is new with the February data, you will find the most important new things from lines 7 to the end of the table.)
In order to answer the question in the title, we need to know what time period is a reasonable period to take into consideration. As well, we need to know what the slope should be for the time period in question. For example, do we mean that the slope of the temperature-time graph must be 0 or do we mean that there has to be a lack of “significant” warming over a given period? With regards to what a suitable time period is, NOAA says the following:
”The simulations rule out (at the 95% level) zero trends for intervals of 15 yr or more, suggesting that an observed absence of warming of this duration is needed to create a discrepancy with the expected present-day warming rate.”
To verify this for yourself, see page 23 here.
Below, we will present you with just the facts and then you can decide whether or not the climate models are still valid. The information will be presented in three sections and an appendix. The first section will show for how long there has been no warming on several data sets. The second section will show for how long there has been no “significant” warming on several data sets. The third section will show how 2013 to date compares with 2012 and the warmest years and months on record so far. The appendix will illustrate sections 1 and 2 in a different way. Graphs and a table will be used to illustrate the data.
Section 1
This analysis uses the latest month for which data is available on WoodForTrees.com (WFT). However WFT is not updated for GISS, Hadcrut3 and WTI past November so I would like to thank Walter Dnes for the GISS and Hadcrut3 numbers. All of the data on WFT is also available at the specific sources as outlined below. We start with the present date and go to the furthest month in the past where the slope is a least slightly negative. So if the slope from September is 4 x 10^-4 but it is – 4 x 10^-4 from October, we give the time from October so no one can accuse us of being less than honest if we say the slope is flat from a certain month.
On all data sets below, the different times for a slope that is at least very slightly negative ranges from 4 years and 9 months to 16 years and 4 months.
1. For GISS, the slope is flat since January 2001 or 12 years, 2 months. (goes to February)
2. For Hadcrut3, the slope is flat since April 1997 or 15 years, 11 months. (goes to February)
3. For a combination of GISS, Hadcrut3, UAH and RSS, the slope is flat since December 2000 or an even 12 years. (goes to November)
4. For Hadcrut4, the slope is flat since November 2000 or 12 years, 4 months. (goes to February)
5. For Hadsst2, the slope is flat from March 1, 1997 to March 31, 2013, or 16 years, 1 month. Hadsst2 has not been updated since December. The slope from March 1997 to December 2012 is -0.00015 per year and the flat line is at 0.33. The average for January and February 2013 is 0.299, so at least two months can be added to the period with a slope of less than 0. Furthermore, Dr. Spencer said that “Later I will post the microwave sea surface temperature update, but it is also unchanged from February.“ So since we can rule out a huge upward spike in Hadsst2 for March, I believe I can conclude that if Hadsst2 were updated to March, then there would be no warming for 16 years and 1 month.
6. For UAH, the slope is flat since July 2008 or 4 years, 9 months. (goes to March)
7. For RSS, the slope is flat since December 1996 or 16 years and 4 months. (goes to March) RSS is 196/204 or 96% of the way to Ben Santer’s 17 years.
The next graph, also used at the head of this article, shows just the lines to illustrate the above. Think of it as a sideways bar graph where the lengths of the lines indicate the relative times where the slope is 0. In addition, the sloped wiggly line shows how CO2 has increased over this period.
When two items are plotted as I have done, the left only shows a temperature anomaly. It goes from 0.1 C to 0.6 C. A change of 0.5 C over 16 years is about 3.0 C over 100 years. And 3.0 C is about the average of what the IPCC says may be the temperature increase by 2100.
So for this to be the case, the slope for all of the data sets would have to be as steep as the CO2 slope. Hopefully the graph illustrates that this is untenable.
The next graph shows the above, but this time, the actual plotted points are shown along with the slope lines and the CO2 is omitted.
Section 2
For this analysis, data was retrieved from SkepticalScience.com. This analysis indicates for how long there has not been significant warming according to their criteria. The numbers below start from January of the year indicated. Data have now been updated either to the end of December 2012 or January 2013. In every case, note that the magnitude of the second number is larger than the first number so a slope of 0 cannot be ruled out. (To the best of my knowledge, SkS uses the same criteria that Phil Jones uses to determine significance.)
For RSS the warming is not significant for over 23 years.
For RSS: +0.127 +/-0.134 C/decade at the two sigma level from 1990
For UAH the warming is not significant for over 19 years.
For UAH: 0.146 +/- 0.170 C/decade at the two sigma level from 1994
For Hadcrut3 the warming is not significant for over 19 years.
For Hadcrut3: 0.095 +/- 0.115 C/decade at the two sigma level from 1994
For Hadcrut4 the warming is not significant for over 18 years.
For Hadcrut4: 0.095 +/- 0.110 C/decade at the two sigma level from 1995
For GISS the warming is not significant for over 17 years.
For GISS: 0.111 +/- 0.122 C/decade at the two sigma level from 1996
If you want to know the times to the nearest month that the warming is not significant for each set to their latest update, they are as follows:
RSS since September 1989;
UAH since June 1993;
Hadcrut3 since August 1993;
Hadcrut4 since July 1994;
GISS since August 1995 and
NOAA since June 1994.
Section 3
This section shows data about 2013 and other information in the form of a table. The table shows the six data sources along the top and bottom, namely UAH, RSS, Hadcrut4, Hadcrut3, Hadsst2, and GISS. Down the column, are the following:
1. 12ra: This is the final ranking for 2012 on each data set.
2. 12an: Here I give the average anomaly for 2012.
3. year: This indicates the warmest year on record so far for that particular data set. Note that two of the data sets have 2010 as the warmest year and four have 1998 as the warmest year.
4. anom: This is the average of the monthly anomalies of the warmest year just above.
5. month: This is the month where that particular data set showed the highest anomaly. The months are identified by the first two letters of the month and the last two numbers of the year.
6. anom: This is the anomaly of the month just above.
7. y/m: This is the longest period of time where the slope is not positive given in years/months. So 15/11 means that for 15 years and 11 months the slope is slightly negative.
8. Ja.an: This is the January, 2013, anomaly for that particular data set.
9. Fe.an: This is the February, 2013, anomaly for that particular data set.
10. M.an: This is the March, 2013, anomaly for that particular data set.
20. avg: This is the average anomaly of all months to date taken by adding all numbers and dividing by the number of months. Only the satellite data includes March.
21. rank: This is the rank that each particular data set would have if the anomaly above were to remain that way for the rest of the year. Of course it won’t, but think of it as an update 10 or 15 minutes into a game. Expect wild swings from month to month at the start of the year. As well, expect huge variations between data sets at the start.
| Source | UAH | RSS | Had4 | Had3 | Sst2 | GISS |
|---|---|---|---|---|---|---|
| 1. 12ra | 9th | 11th | 10th | 10th | 8th | 9th |
| 2. 12an | 0.161 | 0.192 | 0.433 | 0.406 | 0.342 | 0.56 |
| 3. year | 1998 | 1998 | 2010 | 1998 | 1998 | 2010 |
| 4. anom | 0.419 | 0.55 | 0.540 | 0.548 | 0.451 | 0.66 |
| 5. month | Ap98 | Ap98 | Ja07 | Fe98 | Au98 | Ja07 |
| 6. anom | 0.66 | 0.857 | 0.818 | 0.756 | 0.555 | 0.93 |
| 7. y/m | 4/9 | 16/4 | 12/4 | 15/11 | 16/1 | 12/2 |
| 8. Ja.an | 0.504 | 0.441 | 0.432 | 0.390 | 0.283 | 0.60 |
| 9. Fe.an | 0.175 | 0.194 | 0.482 | 0.431 | 0.314 | 0.49 |
| 10. M.an | 0.184 | 0.204 | ||||
| 20. avg | 0.288 | 0.280 | 0.457 | 0.411 | 0.299 | 0.55 |
| 21. rank | 3rd | 6th | 9th | 9th | 12th | 10th |
| Source | UAH | RSS | Had4 | Had3 | Sst2 | GISS |
If you wish to verify all 2012 rankings, go to the following:
For UAH, see here, for RSS see here and for Hadcrut4, see here. Note the number opposite the 2012 at the bottom. Then going up to 1998, you will find that there are 9 numbers above this number. That confirms that 2012 is in 10th place.
For Hadcrut3, see here. Here you have to do something similar to Hadcrut4, but look at the numbers at the far right. One has to back to the 1940s to find the previous time that a Hadcrut3 record was not beaten in 10 years or less.
For Hadsst2, see here. View as for Hadcrut3. It came in 8th place with an average anomaly of 0.342, narrowly beating 2006 by 2/1000 of a degree as that came in at 0.340. In my ranking, I did not consider error bars, however 2006 and 2012 would statistically be a tie for all intents and purposes.
For GISS, see here. Check the J-D (January to December) average and then check to see how often that number is exceeded back to 1998.
To see all points since January 2012 in the form of a graph, see the WFT graph below:
Appendix
In this part, we are summarizing data for each set separately.
RSS
The slope is flat since December 1996 or 16 years and 4 months. (goes to March) RSS is 196/204 or 96% of the way to Ben Santer’s 17 years.
For RSS the warming is not significant for over 23 years.
For RSS: +0.127 +/-0.134 C/decade at the two sigma level from 1990.
The RSS average anomaly so far for 2013 is 0.280. This would rank 6th if it stayed this way. 1998 was the warmest at 0.55. The highest ever monthly anomaly was in April of 1998 when it reached 0.857. The anomaly in 2012 was 0.192 and it came in 11th.
Following are two graphs via WFT. Both show all plotted points for RSS since 1990. Then two lines are shown on the first graph. The first upward sloping line is the line from where warming is not significant according to the SkS site criteria. The second straight line shows the point from where the slope is flat.
The second graph shows the above, but in addition, there are two extra lines. These show the upper and lower lines using the SkS site criteria. Note that the lower line is almost horizontal but slopes slightly downward. This indicates that there is a slight chance that cooling has occurred since 1990 according to RSS per graph 1 and graph 2.
UAH
The slope is flat since July 2008 or 4 years, 9 months. (goes to March)
For UAH, the warming is not significant for over 19 years.
For UAH: 0.146 +/- 0.170 C/decade at the two sigma level from 1994
The UAH average anomaly so far for 2013 is 0.288. This would rank 3rd if it stayed this way. 1998 was the warmest at 0.419. The highest ever monthly anomaly was in April of 1998 when it reached 0.66. The anomaly in 2012 was 0.161 and it came in 9th.
Following are two graphs via WFT. Everything is identical as with RSS except the lines apply to UAH.
Hadcrut4
The slope is flat since November 2000 or 12 years, 4 months. (goes to February.)
For Hadcrut4, the warming is not significant for over 18 years.
For Hadcrut4: 0.095 +/- 0.110 C/decade at the two sigma level from 1995
The Hadcrut4 average anomaly so far for 2013 is 0.457. This would rank 9th if it stayed this way. 2010 was the warmest at 0.540. The highest ever monthly anomaly was in January of 2007 when it reached 0.818. The anomaly in 2012 was 0.433 and it came in 10th.
Following are two graphs via WFT. Everything is identical as with RSS except the lines apply to Hadcrut4.Graph 1 and graph 2.
Hadcrut3
The slope is flat since April 1997 or 15 years, 11 months (goes to February)
For Hadcrut3, the warming is not significant for over 19 years.
For Hadcrut3: 0.095 +/- 0.115 C/decade at the two sigma level from 1994
The Hadcrut3 average anomaly so far for 2013 is 0.411. This would rank 9th if it stayed this way. 1998 was the warmest at 0.548. The highest ever monthly anomaly was in February of 1998 when it reached 0.756. One has to go back to the 1940s to find the previous time that a Hadcrut3 record was not beaten in 10 years or less. The anomaly in 2012 was 0.406 and it came in 10th.
Following are two graphs via WFT. Everything is identical as with RSS except the lines apply to Hadcrut3. Graph 1 and graph 2.
Hadsst2
For Hadsst2, the slope is flat since March 1, 1997 or 16 years, 1 month. (goes to March 31, 2013). Hadsst2 however has not been updated since December on WFT. The slope from March 1997 to December 2012 is -0.00015 per year and the flat line is at 0.33. The average for January and February 2013 is 0.299, so at least two months can be added to the period with a slope of 0. Furthermore, Dr. Spencer said that “Later I will post the microwave sea surface temperature update, but it is also unchanged from February.“ So since we can rule out a huge upward spike in Hadsst2 for March, I believe I can conclude that if Hadsst2 were updated to March, then there would be no warming for 16 years and 1 month.
As mentioned above, the Hadsst2 average anomaly for the first two months for 2013 is 0.299. This would rank 12th if it stayed this way. 1998 was the warmest at 0.451. The highest ever monthly anomaly was in August of 1998 when it reached 0.555. The anomaly in 2012 was 0.342 and it came in 8th.
Sorry! The only graph available for Hadsst2 is the following this.
GISS
The slope is flat since January 2001 or 12 years, 2 months. (goes to February)
For GISS, the warming is not significant for over 17 years.
For GISS: 0.111 +/- 0.122 C/decade at the two sigma level from 1996
The GISS average anomaly so far for 2013 is 0.55. This would rank 10th if it stayed this way. 2010 was the warmest at 0.66. The highest ever monthly anomaly was in January of 2007 when it reached 0.93. The anomaly in 2012 was 0.56 and it came in 9th.
The highest ever monthly anomaly was in January of 2007 when it reached 0.93. The anomaly in 2012 was 0.56 and it came in 9th.
Following are two graphs via WFT. Everything is identical as with RSS except the lines apply to GISS. Graph 1 and graph 2
Conclusion
Above, various facts have been presented along with sources from where all facts were obtained. Keep in mind that no one is entitled to their facts. It is only in the interpretation of the facts for which legitimate discussions can take place. After looking at the above facts, do you feel that we should spend billions to prevent catastrophic warming? Or do you feel we should take a “wait and see” attitude for a few years to be sure that future warming will be as catastrophic as some claim it will be? Keep in mind that even the MET office felt the need to revise its forecasts. Look at the following and keep in mind that the MET office believes that the 1998 mark will be beaten by 2017. Do you agree?
By the way, here is an earlier prediction by the MET office:
“(H)alf of the years after 2009 are predicted to be hotter than the current record hot year, 1998.”
When this prediction was made, they had Hadcrut3 and so far, the 1998 mark has not been broken on Hadcrut3. 2013 is not starting well if they want a new record in 2013.
Here are some relevant facts today: The sun is extremely quiet; ENSO has been between 0 and -0.5 since the start of the year; it takes at least 3 months for ENSO effects to kick in and the Hadcrut3 average anomaly after February was 0.411 which would rank it in 9th place. Granted, it is only 2 months, but you are not going to set any records starting the race in 9th place after two months. So even if a 1998 type El Nino started to set in tomorrow, it would be at least 4 or 5 months for the maximum ENSO reading to be reached. Then it would take at least 3 more months for the high ENSO to be reflected in Earth’s temperature. How hot would November and December then have to be to set a new record? In my opinion, the odds of setting a new record in 2013 are extremely remote.
jorgekafkazar says:
April 8, 2013 at 6:27 pm
Have you ever estimated the average distance that radiation travels to space from a spherical mass of gas at ground level?
Try the following:
http://wattsupwiththat.com/2011/03/29/visualizing-the-greenhouse-effect-molecules-and-photons/
“In this posting, we consider the interaction between air molecules, including Nitrogen (N2), Oxygen (O2), Water Vapor (H2O) and Carbon Dioxide (CO2), with Photons of various wavelengths. This may help us visualize how energy, in the form of Photons radiated by the Sun and the Surface of the Earth, is absorbed and re-emited by Atmospheric molecules.”
I don’t understand why the uncertainties are degrees per decade. In a hundred years, if the earth’s temps were 1.23 degrees C warmer than today (consistently), would one say “No warming has occurred?”
Ed Barbar says:
April 8, 2013 at 9:26 pm
I don’t understand why the uncertainties are degrees per decade. In a hundred years, if the earth’s temps were 1.23 degrees C warmer than today (consistently), would one say “No warming has occurred?”
As far as SkS is concerned, they just happen to give the numbers per decade and WFT uses per year. That is no big deal. If the warming is 1.0/decade or 0.10/year, it would amount to the same thing.
As for what an additional 1.23 C would mean, of course it would be a warming, however I seem to be missing the context that you are talking about. Are you talking about a slope of 0.00 with an uncertainty of +/- 0.123/decade? In that case, we would say there is a 50/50 chance that warming or cooling of up to 1.23 C can occur in 100 years. And furthermore, we are 95% certain that 1.23 would not be exceeded in either direction. But if it had actually happened, then there would no longer be a probability of it happening.
But so what if it went from the present 0.80 to 2.03; would it be catastrophic and should billions be spent to prevent that from happening? We have survived the added 0.80 C very well and I just do not see that an additional 1.23 C would be all that bad. However that is a different topic.
Susan says:
April 8, 2013 at 11:28 am
If the hypothesis is correct, Mauna Loa should have shown something significant
in 2008-2009.
Since it didn’t where did the CO2 come from and what are the characteristics of
that source?
+++++++
The world slowed down, but China and emerging growth countries are GROWING and putting out more CO2 than other countries have cut. Even Germany is building a dozen new Coal Burning plants now while they are not growing.
Ed Barbar:
re your question at April 8, 2013 at 9:26 pm.
Warming is an increase in temperature.
So, if in a hundred years the temperature had not risen for 50 years then there would have been no warming for 50 years, and this would be true whatever the temperature then was,
Richard
> Personally I don’t think the 1998 El Nino counts as part of the
> current flat trend, for instance. It sure helps keeping the past
> end of many of your trend lines up, but at the time it was a
> huge positive anomaly, definitely not “business as usual”.
Ever heard of “Cherry Picking”? BTW, at that time, the warm-mongers were screaming about how it was going to be “the new normal”.
> And don’t forget that most of GCMs involved in the
> mentioned statement can’t actually simulate ENSO so you
> should remove the ENSO influence first, and only then
> start looking for flat trends you want to compare with them.
Let me get this straight… because your all-knowing/singing/dancing GCMs can’t model some parts of the climate record, you want that record thrown out? What’s next? Does all indication of cooling, which is contrary to the models, get thrown out, because it’s “inconvenient” for the carbon-tax money-grab? The science I was taught in high school was that if a theoretical model failed to conform with the data, the model was either thrown out (e.g. 19th century “ether” theory) or fixed until it did conform with the data. The science I was taught did not consist of throwing out data that did not conform with a theoretical model.
jorgekafkazar says
If I read Werner Brozek’s graph at the top of this post correctly; the sawtooth line is the plot of CO2 concentration in ppm(v) over time. It has nothing to do with the temperature. It does not need to have a zero point. What I think is causing the confusion is that there is no concentration scale on the graph. It would have been better to have put a concentration scale on the right side of the graph and making note that the trend lines and the concentration are not related.
Re rogerknights says: April 8, 2013 at 3:16 pm
With respect to Mr Lean’s perspective in the Telegraph;
He concedes that the “pause” in warming has occurred but sees it as a chance to avoid worse, more dangerous, warming that will supposedly follow unless certain policies are undertaken.
It may be useful to think about how long the pause needs to be before the policies become redundant.
If, for example, infrastructure has a thirty year life-cycle and the pause lasts thirty years then no policy would needs to be implemented. Natural wear and tear would lead to society compensating at no extra cost. And anything less than thirty years is arguably weather, not climate.
If infrastructure had a fifteen year life-cycle and the pause also lasts 15 years then any policies implemented in 1998 would have been wasteful and so harmful.
So how long is infrastructure expected to last?
That varies from system to system. Power plants, transport systems and flood defences will all vary depending on location, use and obsolescence from new technology. It is open to discussion. Don’t take my word as a Holy Oracle.
But the current pause is getting near the lower end of infrastructure lifetimes. For example EUROPEAN STANDARD EN 61400-1 “The design lifetime for wind turbine classes I to III shall be at least 20 years.”
And so the current pause is getting near the point where climate change is not a justification for that infrastructure.
We are experiencing exactly such a peak as in mid-forties; 30-year warming (1910-1945) followed by 30 years of cooling. Climate easily changes without help of CO2.
http://www.woodfortrees.org/plot/hadcrut3vgl/from:1910/to:1945
To
justthefactswuwt,
richardscourtney,
Mario Lento, and anyone else who responded.
While I suspect that due to the clueless WordPress, non-discussion technology, you likely won’t see this. Sigh.
Thanks for responding with all the measurements and beliefs that have been evangelized.
Unfortunately, as you mention, apart from a few bits of real data, must of what was espoused was conjectures, calculation (based on a multiplicity of assumptions), and wishful thinking.
We have real data and a real world event:
the U.S., supposedly 30% of the CO2 production,
has been flat for 8 years.
Mauna Loa doesn’t even come close to showing this:
it just keeps on trucking with no changes.
So, just where is it coming from?
As far as I can tell,
we don’t know
and
we have no clue.
so, No, the Climate models are just plastic models for belly bucking little boys.
For RSS the warming is not significant for over 23 years.
For RSS: +0.127 +/-0.134 C/decade at the two sigma level from 1990
For UAH the warming is not significant for over 19 years.
For UAH: 0.146 +/- 0.170 C/decade at the two sigma level from 1994
For Hadcrut3 the warming is not significant for over 19 years.
For Hadcrut3: 0.095 +/- 0.115 C/decade at the two sigma level from 1994
For Hadcrut4 the warming is not significant for over 18 years.
For Hadcrut4: 0.095 +/- 0.110 C/decade at the two sigma level from 1995
For GISS the warming is not significant for over 17 years.
For GISS: 0.111 +/- 0.122 C/decade at the two sigma level from 1996
If you’re claiming that the warming is not significant, for it to be a meaningful statement you should state the level of the significance. In this case it’s at the 0.025 level, that is there’s somewhere between a 2.5% and 5% chance that it’s not warming, or there’s a greater than 95% chance that it’s actually warming! In horse race terms that’s 30 or 40 to one odds, looks like you’re backing an outsider!
greymouser70 says:
April 9, 2013 at 12:01 am
jorgekafkazar says
If I read Werner Brozek’s graph at the top of this post correctly; the sawtooth line is the plot of CO2 concentration in ppm(v) over time. It has nothing to do with the temperature. It does not need to have a zero point. What I think is causing the confusion is that there is no concentration scale on the graph. It would have been better to have put a concentration scale on the right side of the graph and making note that the trend lines and the concentration are not related.
The confusion is deliberate, only the CO2 data is normalized and the scale adjusted to fill the scale and plotted vs trends to give the impression that there’s a huge mismatch between CO2 and T. An honest way to present the data would be to normalize it all and plot the values (not the trends for T) on the same scale or plot ln(CO2) instead. If you realize that it’s the T trends that are plotted then what the graph is showing is that T is increasing linearly with a fairly constant trend (the CO2 is increasing with a fairly linear trend too, of ~0.5%/year).
Susan:
I am saddened by your reply at April 9, 2013 at 9:27 am .
It says
That is so wrong that it is risible.
Clearly, you did not read a word of the answer I took the trouble to provide.
OK. I have learned: you don’t ask questions wanting answers so I will not bother to provide an answer if you ask another question.
Richard
Phil.:
Your post at April 9, 2013 at 10:03 am displays complete ignorance of what confidence limits indicate.
To avoid others being misled by your post I copy a post I provided on another WUWT thread to here. Please note its part which concludes saying,
“And that is all the confidence limits say; nothing more.”
Richard
In the thread at
http://wattsupwiththat.com/2013/04/03/proxy-spikes-the-missed-message-in-marcott-et-al/
richardscourtney says:
April 6, 2013 at 6:44 am
Werner Brozek:
Thankyou for your post addressed to me at April 5, 2013 at 5:47 pm.
Following several attempts to answer your specific questions in different ways – and cognisant of the need to use language comprehensible to onlookers – I have decided to provide this general answer in hope that it adequately covers all the issues you raise.
A full and proper consideration of these issues requires reference to text books concerning the use of statistical procedures as part of the philosophy of science. This very brief answer is my attempt at an overall view of confidence limits.
Nothing is known with certainty, but some things can be inferred from a data set to determine probabilities of being ‘right’ and ‘wrong’. These probabilities are the ‘confidence’ which can be stated.
As illustration, consider a beach covered in pebbles.
There are millions of the pebbles. A random sample of, say, 100 pebbles is collected and each pebble is weighed. This provides 100 measurements each of the weight of an individual pebble. From this an average weight of a pebble can be calculated. One such average is the ‘mean’ and it is obtained by dividing the total weight of all the pebbles by the number of pebbles (in this case, dividing by 100).
The pebbles on the beach can then be said to have the deduced mean weight.
However, none of the pebbles in the sample may have a weight equal to the obtained average. In fact, none of the millions of pebbles on the beach may have a weight equal to that average. Any average – including a mean – is a statistical construct and is not reality.
(This difference of an average from reality is demonstrated by the average – i.e. mean – number of legs on people. On average people have less than two legs because nobody has more than two and a few people have less than two.)
In addition to considering the mean weight of pebbles in the sample, one can also determine the ‘distribution’ of weights in the sample. Every pebble may be within 1 gram of the mean weight. In this case, there is high probability that any pebble collected from the beach will have a weight within 1 gram of the obtained average. But that does NOT indicate there are no pebbles on the beach which are 10 grams heavier than the obtained average. (This leads to the wider discussions of sampling and randomness which I am ignoring.)
Importantly, there is likely to be a distribution of weights such that most pebbles in the sample each have a weight near the mean weight, and a few pebbles have weights much lower and much higher than that average. This may provide a uniform distribution of weights within the sample. However, the sample may not have a uniform distribution because no pebble can weigh less than nothing, but a few pebbles may be much, much heavier than the mean weight: in this case, the sample is said to be ‘skewed’.
Assuming the sample is uniform then it is equally likely that a pebble will be within a range of weights heavier or lighter than the mean weight. (If the sample is skewed in the suggested manner then the likely range of weights heavier than mean weight is greater than the likely range of weights lighter than that average.) These ranges are the + and – ‘errors’ of the average and have determined probabilities.
The probable error range of +/-X at 99% confidence says that 99 out of 100 pebbles will probably be within X of the mean.
The probable error range of +/-X at 95% confidence says that 95 out of 100 (i.e. 19 out of 20) pebbles will probably be within X of the mean.
The probable error range of +/-X at 90% confidence says that 90 out of 100 (i.e. 9 out of 10) pebbles will probably be within X of the mean.
etc.
And that is all the confidence limits say; nothing more.
Therefore, if the weights of two pebbles are within the probable error range then at the stated confidence they cannot be distinguished as being different from the sample mean. And if a ‘heavy’ pebble has a weight within the probable error then that pebble’s weight says nothing about the sample mean.
In the above example, the sample mean is a statistical construct obtained from individual measurements of pebbles. And it is meaningless in the absence of a probable error with stated confidence: such an absence removes any indication of what the weight of a pebble from the beach is likely to be. And every pebble has equal chance of being within the +/- range of the mean.
The linear trend of a time series is also a statistical construct obtained from individual measurements. It has confidence limits with stated probability and it, too, is meaningless without such confidence limits.
At stated confidence a trend is equally likely to have any value within its limits of probable error.
(This is the same as any pebble is equally likely to have any weight within its limits of probable error from the mean weight.)
Therefore, if the trend is 0.003 ±0.223 °C/decade at 95% confidence then there is a 19:1 probability that the trend is somewhere between
(0.003-0.223) = -0.220 °C/decade and (0.003+0.223) = 0.226 °C/decade.
And, in this example, -0.220 °C/decade is not discernibly different from 0.226 °C/decade or from any value between them. There is a range of values from -0.220 °C/decade to 0.226 °C/decade which are not discernibly different. And similar is true for all probable error ranges.
Importantly, this lack of discernible difference is not affected by whether or not the range straddles 0.000 °C/decade.
I hope this is adequately clear.
Richard
Phil. says:
April 9, 2013 at 10:03 am
In this case it’s at the 0.025 level, that is there’s somewhere between a 2.5% and 5% chance that it’s not warming, or there’s a greater than 95% chance that it’s actually warming!
In addition to what Richard has already said on this matter, I would like to add the following. As you can see from NOAA’s statement at the start of my article, the climate community regards 95% as the appropriate level by which to measure whether warming is “significant” or not.
Generally speaking, I agree with you. When it comes to the 2.5%, that would be more true when I give the nearest month for which there is no significant warming. So for RSS, there would be about a 2.5% chance that there is cooling from September 1989. However from 1990, the numbers are 0.127 +/- 0.134. So that gives a 0.007/0.268 = 0.026 or a 2.6% chance of being below 0 based on the 95%. Then when we add the other 2.5%, we get 5.1%. In other words, there is a 94.9% chance of warming since 1990 based on RSS since 1990. I agree this is a large number! But the more important number for me is that since December, 1996, or for 16 years and 4 months, there is a less than 50% chance of warming since the slope is very slightly negative at -2.3524e-05 per year.
Susan says:April 8, 2013 at 10:24 am
Steve Keohane says: April 8, 2013 at 10:08 am
Humans account for some 3-4% of the CO2 released into the
atmosphere annually, so changing a fraction of a percent
of that 3-4% doesn’t do much.
OK,
so where does the CO2 indicated by Mauna Loa actually come from on the cycle measured?
Do we have any empirical measurements showing the source?
Here is a video of the AIRS satellite showing where in the world it comes from.
http://airs.jpl.nasa.gov/news_archive/2010-03-30-CO2-Movie/
Under Images and then CO2 on the menu bar to the left of this video, there are many options to look at CO2 over time.
Phil. says:
April 9, 2013 at 10:22 am
The confusion is deliberate, only the CO2 data is normalized and the scale adjusted to fill the scale and plotted vs trends to give the impression that there’s a huge mismatch between CO2 and T.
See:
http://newsbusters.org/blogs/noel-sheppard/2012/12/04/climate-realist-marc-morano-debates-bill-nye-science-guy-global-warmi#ixzz2E8w1uK5F
Here is part of the exchange between Nye and Morano:
“MORANO: Sure. Carbon dioxide is rising. What’s your point?
NYE: OK.
MORANO: No.
NYE: So here’s the point, is it’s rising extraordinarily fast. That’s the difference between the bad old days and now is it’s –”
Note that it is Nye, one of “your” people, who says that CO2 is “ rising extraordinarily fast”. And you accuse me of misrepresenting things? Would Nye not fully endorse what I showed?
However if you wish, we could look at it another way. Let us compare the change with reference to 0 K and 0 CO2 since 1750. It is generally agreed that since 1750, temperatures have gone up by 0.8 C and that CO2 has gone up from 280 ppm to 395 ppm. If we convert temperatures to K, the percent increase is (287.8 – 287)287 x 100 = 0.28%. However the CO2 increase is (395 – 280)/280 x 100 = 41%!
richardscourtney @April 9, 2013 at 11:43 am
1. 30% risible..
2. didn’t read…
3. don’t want answers
a) according to one source, the U.S. in 2011 was 8,876 mt out of 33,992 world mt.
(everyone’s numbers can and do vary)
=> somewhere between 25 and 30% of anthropological CO2 is allegedly the U.S.
b) Yes, I read most of the diatribes.
While interesting, they repeat of what has been articulated
many times.
c) so, just how does Mauna Loa measurements tie to reality?
I’m still waiting for an “out of the box”, thinking answer
rather than a regurgitation of the mundane, party line,
which is known to be an over simplification of an ill-understood
set of phenomena.
So, any good ideas on just what Mauna Loa actually measures from a source perspective?
I am, however, very impressed by the crudeness and lack of utility embodied in the WordPress commenting function. Even with the commenting indenting like the Nova and Curry blogs, it is still a pontification device, not a collaborative dialogue facility.
RichardCourtney sez:
“Therefore, if the trend is 0.003 ±0.223 °C/decade at 95% confidence then there is a 19:1 probability that the trend is somewhere between (0.003-0.223) = -0.220 °C/decade and (0.003+0.223) = 0.226 °C/decade.”
Richard’s post is very good – all of them are. If you cannot hang with them, then start reading philosophy of science and statistics.
BUT
This statement above is not quite accurate. In terms of science and likelihood testing.
This is very esoteric. but a sample cannot ever say very much about a parameter. A sample is merely a sample. Gathering a sample is ALWAYS a compromise.
The point estimate gives a point estimate, based upon available data. And can be tortured to yield a confidence interval.
But the statistical methods can ONLY calculate this based upon available data.
gigo
R, SAS, and any other program – indeed, your pencil and paper – can only work with what they have.
If sampling is great, then the confidence interval will happen to be very coincident with reality.
If sampling is biased, then the confidence interval, a relatively straightforward maths operation, will be biased. If the sampling has little bias, the conf interval will eventually be shown to have captured reality in its estimate.
If sampliong is moderately or significantly biased, then the CI will be lousy.
Dewey beats Truman.
Con interval is generated based on internal evidence – the variability observed within the sample, plus some conjectures about the degree that a sample might be expected to diverge from a population parameter.
Essentially, there is no guarantee. just a very useful estimate. That is why CIs come in different denominations.
i hate to see models reified as reality. I also hate to see stat analyses reaified as reality.
statistic: parameter
sample: population
thelastdemocrat:
Thankyou for your comment at April 9, 2013 at 8:54 pm (and for its unjustifiable flattery) in response to my post at April 9, 2013 at 11:53 am.
I write to make clear to onlookers that I agree your post. It addresses the part of my post which said;
emphasis added: RSC
Richard
Werner Brozek says:
April 9, 2013 at 2:12 pm
Phil. says:
April 9, 2013 at 10:22 am
“The confusion is deliberate, only the CO2 data is normalized and the scale adjusted to fill the scale and plotted vs trends to give the impression that there’s a huge mismatch between CO2 and T.”
Note that it is Nye, one of “your” people, who says that CO2 is “ rising extraordinarily fast”. And you accuse me of misrepresenting things? Would Nye not fully endorse what I showed?
I don’t know anything about Nye, he’s certainly not one of ‘my’ people! I can’t understand why anyone would endorse plotting the trends of T over a period of time vs the normalized CO2 data on the same graph, it’s meaningless and makes no sense. Certainly when the scale of the CO2 plot isn’t shown it’s even more difficult to understand.
The data you plot show a range of trends in T between ~0.57 for GISTEMP and ~0.18 for UTI, in what units are those?
However if you wish, we could look at it another way. Let us compare the change with reference to 0 K and 0 CO2 since 1750. It is generally agreed that since 1750, temperatures have gone up by 0.8 C and that CO2 has gone up from 280 ppm to 395 ppm. If we convert temperatures to K, the percent increase is (287.8 – 287)287 x 100 = 0.28%. However the CO2 increase is (395 – 280)/280 x 100 = 41%!
It’s also ‘generally agreed’ that the forcing by CO2 depends on ln(CO2) so why would you exaggerate by plotting vs. CO2 rather than ln(CO2)?
Phil. says:
April 10, 2013 at 12:37 pm
I don’t know anything about Nye, he’s certainly not one of ‘my’ people!
Do you mean you have never heard of Bill Nye, the science guy? He has often been mentioned on TV as well as WUWT. For example, one article is
Al Gore and Bill Nye FAIL at doing a simple CO2 experiment
If you wish to read about it, see:
http://wattsupwiththat.com/climate-fail-files/gore-and-bill-nye-fail-at-doing-a-simple-co2-experiment/
I can’t understand why anyone would endorse plotting the trends of T over a period of time vs the normalized CO2 data on the same graph, it’s meaningless and makes no sense. Certainly when the scale of the CO2 plot isn’t shown it’s even more difficult to understand. It’s also ‘generally agreed’ that the forcing by CO2 depends on ln(CO2) so why would you exaggerate by plotting vs. CO2 rather than ln(CO2)?
I am not a computer expert and must rely on WFT. As far as I know, WFT does not allow any numbers to be given on both sides of the y-axis. Nor am I aware of how to plot ln(CO2) using WFT. If you can get WFT to change things so I can plot them, I will do that. One thing that I can do is have two separate plots, one with the lines and the other with just CO2. I was in the process of responding to a person who asked what the squiggly line was when I noticed someone has beat me to it with an excellent explanation. If you are able to plot RSS since December 1996 and ln(CO2) since December 1996 on the same graph, please do so and post it. I would be interested in seeing what it would look like.
The data you plot show a range of trends in T between ~0.57 for GISTEMP and ~0.18 for UTI, in what units are those?
This illustrates the problems we run into when every different source of temperature anomalies uses a different base line from which to express their anomalies. Everyone should use the most recent three decades such as 1980 to 2009 or something like that. But GISS uses a relatively cool base period of 1951-1980. So their anomalies are higher, but 2013 is not warmer because of it. It just looks that way. With GISS for example, 2013 is 10th warmest so far with an average of 0.55 and with RSS, it is 6th warmest even though its average so far is only 0.28.
Werner Brozek:
In your post at April 10, 2013 at 3:54 pm you make the important point
Indeed, this draws attention to the fact that all these data are statistical constructs which have no physical reality (as explained in my post at April 9, 2013 at 11:53 am).
More importantly, variations in temperature anomaly are trivially small .
The total variation in global temperature anomaly was only ~0.8 deg.C over the entire twentieth century; i.e. a rate of change of 0.08 deg.C per decade.
But global temperature varies by 3.8 deg.C during 6 months of each year; i.e. a rate of change of 38.00 deg.C per decade.
The variation in global temperature is hidden because anomalies are computed as differences from a 30 year mean; i.e. the anomaly for a month (e.g. April) is the difference in temperature from an average of 30 months (e.g. 30 Aprils).
This issue is discussed in an above post from you. To save others needing to find it, I copy it here.
Richard
————-
Werner Brozek says:
April 8, 2013 at 10:45 am
Tenuk says:
April 8, 2013 at 9:14 am
That is true. Another way of looking at this whole thing is how Richard Courtney stated on another post that the yearly temperature changes by 3.8 C over the course of the year anyway. And then some are concerned about the 0.8 C that we have gone up since 1750 and are worried that we may reach the dreaded 2 C mark soon. To read about the normal yearly variation, see:
http://theinconvenientskeptic.com/2013/03/misunderstanding-of-the-global-temperature-anomaly/
OOps! I typed too fast.
Clearly I intended to write
But global temperature varies by 3.8 deg.C during 6 months of each year; i.e. a rate of change of 76.00 deg.C per decade.
Sorry
Richard
richardscourtney says:
April 11, 2013 at 2:03 am
a rate of change of 76.00 deg.C per decade
This of course is 760.0 C per century. At that rate, the oceans will soon be boiling. : – )
However while no one would seriously extrapolate the 6 month change to a period of years and attach any meaning to it, the warmunists totally ignore the 60 year cycle as shown here:
http://wattsupwiththat.files.wordpress.com/2009/03/akasofu_ipcc.jpg
The IPCC took the upward portion of the sine wave from 1970 to 2000 and projected it to the year 2100. However now that we are in the downward cycle, they are scrambling to explain it.