Guest Post by Willis Eschenbach
There is a new paper out by Xu and Powell, “Uncertainty of the stratospheric/tropospheric temperature trends in 1979–2008: multiple satellite MSU, radiosonde, and reanalysis datasets” (PDF, hereinafter XP2011). It shows the large differences between the satellite, balloon (radiosonde), and reanalysis temperatures for the troposphere and the stratosphere. The paper is well worth a read, and is not paywalled. Figure 1, from their paper, shows their tropospheric temperature trends by latitudinal band from each of the sources.
Figure 1. From XP2011 Fig. 3a. Original caption says: Inter-comparison of tropospheric temperature (TCH2) trends (K decade−1) for the MSU (RSS, UAH, STAR), Radiosonde (RATPAC, HADAT2, UK, RAOBCORE, RICH) and Reanalysis (JRA25, MERRA, NCEP- CFSR, NCEP-NCAR, NCEP-DOE) products for the period of 1979–2008. (a) Trend changes with latitude for each individual dataset;
In Figure 1, the three groups are divided by color. The satellite observations are in blue. The balloon-borne observations are in green. And the climate reanalysis model results are in orange. Now, bear in mind that these various results are all purporting to be measuring the same thing—which way and how much the temperature of the lower troposphere is trending. The paper closes with the following statement (emphasis mine):
In general, greater consistency is needed between the various data sets before a climate trend can be established in any region that would provide the reliability expected of a trusted authoritative source.
I can only heartily agree with that. However, there are a few conclusions that we can draw in the interim.
First, despite the fact that these are all plotted together as though they were equals, in fact only two of the groups represent observational data. The results shown in orange are all computer model outputs. Unfortunately, these model outputs are usually referred to as “reanalysis data”. They are not data. They are the output of a special kind of computer climate model. This kind of climate model attempts to match its output to the known datapoints at a given instant (temperatures, pressures, winds, etc.). It is fed a stream of historical data, including satellite MSU and other data as well as station reports from around the world. It then gives its best estimate of what is happening where we have no data, in between the stations and the observation times.
Given that the five different reanalysis products were all fed on a very similar diet of temperatures and pressures and the like, I had expected them to be much, much closer together. Instead, they are all over the map. So my first conclusion is that not only are the outputs of reanalysis models not data. As a group they are also not accurate. They don’t even agree with each other. To see what the rest of the data shows, I have removed the reanalysis model outputs in Figure 2.
Figure 2. Same as in Figure 1, but with the computer reanalysis model results removed, leaving satellite (blue) and balloon-borne (green) observations.
The agreement between the balloon datasets is not as good as that of the satellite data, as might be expected from the difference in coverage between the satellite data (basically global) and balloon data (in certain scattered locations).
Once the computer model results are removed, we find much better agreement between the actual observations. Figure 3 shows the correlation between the various datasets:
Figure 3. Correlations between the various observations (Satellite and Balloon) and computer model (Reanalysis) data. Red indicates the lowest correlation, blue shows the highest correlation. Bottom row shows the correlation of each dataset with the average of all datasets. HadAT is somewhat affected due to incomplete coverage (only to -50°S see Fig. 2), as is RAOBCORE to a lesser degree (coverage to -70°S).
Numerically, this supports the overall conclusion of Figure 1, which is that as a group the reanalysis model results do not agree well with each other. This certainly does not give confidence in the idea of blindly treating such model output as “data”.
Finally, Figure 4 shows the three satellite records, along with the MERRA reanalysis model output.
Figure 4. Same as in Figure 1, but with the balloon and computer reanalysis model results removed, leaving satellite (blue) and one reanalysis model (violet).
In general the three satellite records are in good agreement. The STAR and RSS datasets are extremely similar, somewhat disturbingly so, in fact. Their correlation is 1.00. It make me wonder if they are not sharing large portions of their underlying analysis mathematics. If so, one might hope that they would resolve whatever small differences remain between them.
I have read, but cannot now lay my hands upon, a document which said that the RSS team use climate model output as input to a part of their calculation of the temperature. In contrast, the UAH team do not use climate model for that aspect of their analysis, but do a more direct calculation. (I’m sure someone will be able to verify or falsify that.) [UPDATE: Stephen Singer points to the document here, which supports my memory. The RSS team uses the output of the CCSM3 climate model as input to their analysis.] If so, that could explain the similarity between MERRA and the RSS/STAR pair. On the other hand, the causation may be going the other way—the reanalysis model may be overweighting the RSS/STAR input … because remember, some dataset from among the satellite data, perhaps the RSS data, is used as input for the reanalysis models.
This leads to the interesting situation where the output of the CCSM3 is used as input to the RSS temperature estimate. Then the RSS temperature estimate is used as input to a reanalysis climate model … recursion, anyone?
Finally, this points to the difficulty in resolving the question of tropical tropospheric amplification. I have written about this question here. The various datasets give various answers regarding how much amplification exists in the tropics.
CONCLUSIONS? No strong ones. Reanalysis models are not ready for prime time. There is still a lot of variation in the different measurements of the global tropospheric temperature. This is sadly typical of the problems with the a number of the other observational datasets. In this case, this affects the measurement of tropical tropospheric amplification. Further funding is required …
Regards to all,
w.
DATA:
The data from Figure 1 is given below, in comma-separated format
Latitude, STAR , UAH , RSS , RATPAC , HADAT , IUK , RAOBCORE , RICH , JRA25 , MERRA , NCEP-CFSR , NCEP-DOE , NCEP-NCAR -80, -0.104, -0.244, -0.134, 0.085, , 0.023, , 0.023, -0.243, -0.154, 0.028, 0.294, 0.304 -70, -0.074, -0.086, -0.094, 0.09, , -0.035, 0.071, -0.034, -0.218, -0.115, -0.045, 0.147, 0.148 -60, -0.055, -0.142, -0.074, 0.09, , -0.088, 0.1, -0.148, -0.285, -0.051, -0.094, 0.059, 0.104 -50, 0.005, -0.069, -0.043, -0.006, 0.138, 0.022, 0.081, 0.01, -0.232, 0.032, 0.029, 0.03, 0.114 -40, 0.07, -0.076, 0.026, -0.01, 0.118, -0.107, 0.08, 0.074, -0.081, 0.115, 0.116, -0.005, 0.077 -30, 0.143, 0.082, 0.087, 0.114, 0.123, 0.122, 0.127, 0.126, 0.047, 0.178, 0.22, 0.047, 0.108 -20, 0.182, 0.08, 0.13, 0.12, 0.085, 0.087, 0.143, 0.125, 0.116, 0.213, 0.289, 0.071, 0.097 -10, 0.199, 0.056, 0.153, 0.114, -0.02, 0.082, 0.116, 0.098, 0.069, 0.226, 0.313, -0.003, 0.053 0, 0.195, 0.038, 0.154, 0.089, 0.038, 0.028, 0.136, 0.089, 0.063, 0.284, 0.324, -0.007, 0.061 10, 0.179, 0.034, 0.144, 0.09, 0.064, 0.192, 0.162, 0.137, 0.087, 0.273, 0.328, 0.027, 0.065 20, 0.21, 0.093, 0.166, 0.09, 0.18, 0.16, 0.194, 0.207, 0.115, 0.245, 0.307, 0.115, 0.114 30, 0.23, 0.133, 0.162, 0.247, 0.239, 0.137, 0.238, 0.291, 0.152, 0.257, 0.307, 0.154, 0.153 40, 0.238, 0.164, 0.161, 0.237, 0.213, 0.189, 0.246, 0.3, 0.153, 0.244, 0.268, 0.161, 0.194 50, 0.241, 0.125, 0.161, 0.24, 0.314, 0.213, 0.247, 0.283, 0.166, 0.236, 0.238, 0.161, 0.201 60, 0.299, 0.167, 0.222, 0.283, 0.289, 0.207, 0.335, 0.324, 0.224, 0.288, 0.266, 0.202, 0.239 70, 0.317, 0.177, 0.245, 0.288, 0.289, 0.237, 0.427, 0.393, 0.254, 0.304, 0.269, 0.232, 0.254 80, 0.357, 0.276, 0.301, 0.278, 0.438, 0.384, 0.501, 0.323, 0.226, 0.328, 0.326, 0.235, 0.26
What is the point of ‘reanalysis data’ when you have empirical observational data?
Why not and would it not be better to work from the empirical observational data?
I agree that the model creations (ie., the ‘reanalysis data’) appear way off target (although if they were to be averaged they may well provide a better fit with reality) and are another example as to how poor the models are. I guess nothing new there.
Hi Willis,
thanks for sharing this with us. I have not worked with the satellite or reanalysis data, but having just completed a step change analysis of nearly all complete and long term records in the GHCN (except North-America and Australia) I find strong support for the likely existence of real step changes in temperature records (hopefully I can post this later). If that is the case, the basic assumption of linearity underlying the widespread use of linear trend analysis (as also used in the XP2011) is violated and the resulting trend misleading. Given your insight and experience with the temperature records and analyses, would you have any thoughts on this fundamental issue, eg. should we discourage the use of linear regression as a method to identify “the pattern” in temperature records ?
Thanks … jens
I suspect that error bars on the reanalysis data would be wider than any anomaly.
Data are readings taken from instruments. Period.
Missing data are forever missing.
Nothing produced by a model is “data”.
Rumplestiltskin is not a climate modeler.
Gee. That’s funny.
Last time I heard of temperature “data” for the Arctic, NASA-GISS’s Hansen was claiming +4 degrees across the whole Arctic landmass…… (Seems like he is plotting a huge “red” mass of hot air based on some 1200 km “averaging” and extrapolation scheme he came up with in some 1988 paper with a r^2 of 0.42 ….)
Now, is it +4.0 degrees? Or +0.4 degrees?
Ha! “Further funding is required …”
Here’s a simple Idea, Just scrap the Idea of ‘average global temperature’ problem solved!! And people like yourself can get on with real science.
All this averaging out of large amounts of data seems to show irrelevant results anyway, it does not relate very well to temperature nor can the result be used for any study related to causality which AGW enthusiasts do all the time, an environment with a variable range of temperature of between 0°C and 20°C can have any average temperature anywhere in-between at any giving time and it isn’t too hard to get the result you want just by mixing up and using different methods or by adding/subtracting favorable data.
Here’s an 8 day average temperature
1°C + 19°C + 3°C + 20°C + 2°C + 18°C + 0°C + 20°C :=83 /8 :=10.3 °C
Here’s another 8 day average temperature
1°C + 1°C + 1°C + 20°C + 1°C + 1°C + 0°C + 20°C :=44 /8 :=5.5 °C
Here’s a 16 day day average temperature from the above data calculated in two different ways
First 8 days + second 8 days 10.3 °C + 5.5 °C / 2 := 15.8°C
Complete 16 day
1°C + 19°C + 3°C + 20°C + 2°C + 18°C + 0°C + 20°C+1°C + 1°C + 1°C + 20°C + 1°C + 1°C + 0°C + 20°C :=128/16 :=8°C
Not a very scientific result to use or to show an accurate representation of the temperature of an environment over time, the margin of error on any variable temperature average is 50-100% Why? because it produces variable average results. if we model variable averages to trends such as Co2 the results become unusable as the rising trend of Co2 takes over and the the margin of error becomes 100% and all the data becomes unusable. Try to relate Solar effects to average global temperatures with a Co2 trend, It cant be done but reliable individual temperature readings fit very well.
Here’s my processors average temperature which is less variable over 8 days between 48°C and 50°C
49°C + 50°C + 48°C + 50°C + 49°C + 50°C + 49°C + 50°C :=395/8 := 49.3 °C
average temperature over 16 days
49°C + 50°C + 48°C + 50°C + 49°C + 50°C + 49°C + 50°C + 49°C + 50°C + 49°C + 50°C + 50°C + 48°C + 50°C + 49°C :=790/16 :=49.3°C
First 8 days + second 8 days 49.3 °C + 49.3°C:= 98.6/ 2 := 49.3°C
very accurate result!
Further funding is required …
Willis have you contacted the “TEAM” to see if they could steer you towards some “Obama Money” to continue your research. They would be my first choice because they have really deep pockets. (Oh wait, their hands are in my pants pockets). Good luck.
If you get the chance tell Mann I want my data I paid for.
Sparks says:
November 7, 2011 at 5:45 am
“Here’s a 16 day day average temperature from the above data calculated in two different ways
First 8 days + second 8 days 10.3 °C + 5.5 °C / 2 := 15.8°C
”
10.3 + 5.5 = 15.8
15.8 / 2 = 7.9
Forgot a bracket?
DirkH says:
November 7, 2011 at 6:21 am
Sparks says:
November 7, 2011 at 5:45 am
//////////////////////////////////////////////////////////
Yes and isn;t 83 (first period) + 44 (second period) = 127 and not 128, so that the average of these periods should be 127/16 and not 128/16.
I have not checked the addition of the individual series.
Interesting post Willis, wise analysis.
It would be interesting to see the horizontal line recalculated for your stripped down versions. I presume this is the all latitudes average for all the data. It appears to be 0.14 K/decade
This is exactly what I just got from a totally different method looking at d2T/dt2 in HadCrut3
It needs writing up and checking but the bottom line was 1900 dT/dt trend of 0.2 K/century and second diff of 1.2 K/century^2 .
That would give a current value of 1.4 K / c as shown in that paper, and an average around 0.7 K/c for the last century, which seems to be a generally accepted value.
This sort of value is firmly in the DON’T PANIC zone.
If our degree of “agreement” were broadened, would not the correlation be near perfect? As in let’s round to the nearest whole degree and call anything less noise. That would solve a lot of problems with a noisy data set. Of course it would also cause a great deal of funding to simply dry up and blow away. Can anybody guess why?
Isn’t the real question why the norther hemisphere is getting warmer and the southern hemisphere is getting colder if CO2 is well mixed?
How is it even possible that the southern hemisphere is getting colder? AGW certainly doesn’t explain that. Aerosols certainly don’t explain that unless China and India have suddenly shifted to the southern hemisphere.
This is a huge mystery completely unaccounted for in current theories of climate change. There is no way the southern hemisphere should be cooling while the northern hemisphere is warming over a 30 year timespan.
Why isn’t climate science all over this? It is a huge unexplained mystery in an area in which the science was supposed to be settled.
jens raunsø jensen says:
>>
would you have any thoughts on this fundamental issue, eg. should we discourage the use of linear regression as a method to identify “the pattern” in temperature records ?
Thanks … jens
>>
The post war drop is significant oddity in the 20c record. The problem seems to arise when pretend scientists decide to use this trough as point of reference when calculating temperature “trends”.
GH warming is a log function of gas concentration. CO2 concentration is reckoned to be rising in a roughly exponential way. That gives a linear increase in the “forcing”. A radiative forcing will produce a rate of change of temperature not a simple change of temp. Anyone trying to fit a linear model to temperature has not understood the first thing about the physics. They are trying to fit a straight line to a parabola.
Fitting a century long linear regression to dT/dt using HadCrut3 temps gives credible figures. It would appear that that sort of timescale may be sufficient to even out the steps.
richard verney,
All temperature data has problems. All. We just don’t have God-like observational tools. Which is why data has to be tested and adjusted where appropriate, and why reanalyses are done, combining many different data streams. The goal is always to improve the fidelity of the data.
Willis gives the impression that the satellite data are better than the rest. But this is not necessarily the case. There are 5 global temperature satellite data sets that I know of, and the decadal trend for each ranges from 0.14 to 2.0C/decade degrees over the last 30 years or so.
Problems abound with satellite data. From the study Willis is citing:
Choices must be made. This paper builds on others (written by, for example, Kevin Trenberth), that try to point out problems with the data so that they can be better dealt with.
Seriously, anyone have an “evidence based” explanation of why there is almost perfect agreement between all the datasets that the NH has been warming for 30 years while the SH has been cooling?
What feature of the the earth has been changing that could account for this? I’m not buying CFC’s and Ozone as a cause. The ozone hole “appeared” at the south pole when almost all the CFC use was in the northern hemisphere. Looking further at the graphs above, there really hasn’t been very much net heating once you add the SH (negative) data from the NH (positive) data.
It makes one wonder if GW is more a product of land versus sea temperature? Most of the land is in the NH, while most of the oceans are in the SH. Is this what we are seeing in this data? Evidence that GW is mostly connected to portions of the globe where there is land. In which case, AGW would be more likely due to land use, which cannot be well mixed, because the land doesn’t move very fast.
The reanalysis datasets do have their issues including that they include the likely flawed RSS and UAH data. A discussion is at the following URL:
http://www.skepticalscience.com/Eschenbach_satellite_part.html
Willis, don’t know if you saw this…………..
Envirocensors Hide Explosive Japanese Satellite Data
Scorching new evidence of the environmental left’s scientific obstruction has surfaced in the squelching of reports of Japanese satellite data, which suggest that the underdeveloped world emits far more carbon dioxide than previously imagined, even more than many Western nations! If the claim is substantiated, it could turn the entire meme that industrialized civilization is endangering the planet on its head.
http://rogueoperator.wordpress.com/2011/11/07/envirocensors-hide-explosive-japanese-satellite-data/
How is it possible that the SH has been cooling for 30 years and CO2 is well mixed?
DirkH says:
November 7, 2011 at 6:21 am
Thanks, I had it right the first time before someone came in and interrupted me, I’ve been rushing about all day, probably should have waited until later and put a bit more time into my comment. but I hope you still understand where I was going with it despite the error. It’s a travesty. 🙂
jens raunsø jensen says:
>>
would you have any thoughts on this fundamental issue, eg. should we discourage the use of linear regression as a method to identify “the pattern” in temperature records ?
Thanks … jens
>>
Most would agree that today’s temperature is not independent of yesterdays (autocorrelation).
Here is what wikipedia has to say:
Autocorrelation violates the ordinary least squares (OLS) assumption that the error terms are uncorrelated. While it does not bias the OLS coefficient estimates, the standard errors tend to be underestimated (and the t-scores overestimated) when the autocorrelations of the errors at low lags are positive.
In other words, linear regression can under-estimate data errors and natural variability.
Latitude says:
November 7, 2011 at 7:22 am
Envirocensors Hide Explosive Japanese Satellite Data
http://rogueoperator.wordpress.com/2011/11/07/envirocensors-hide-explosive-japanese-satellite-data/
I’d read about the Japanese findings and wondered why they were not being widely reported. This is huge because it shows that land use, not industrialization is driving CO2 emissions. Definitely not a message that the IPCC, WWF, and REDD wants anyone to hear.
I think it would be a fairer presentation of the analysis for the x-Axis to be plotted
Not as 90S to 90 N as equidistant increments.
rather the increments should be cos(of latitude) so that
0 to 10N is the widest increment and 80N to 90N is quite narrow.
This would visually reflect their contribution to their areas on the earth.
It is harder to label Latitude in the chart Excel with X = cos(latitude) than incrementing by latitude. But it might be effective to do it at least once.
Robert:
I generally don’t bother with Sks but followed it since you linked it. I agree with Tom Curtis’ critique of the SkS post you linked.
“Likely flawed” just shows your (IMO) confirmation bias.
Another excellent article by Willis. As always, I gave it 5 stars.☺
Pamela Gray says:
“If our degree of ‘agreement’ were broadened, would not the correlation be near perfect? As in let’s round to the nearest whole degree and call anything less noise.”
Pamela rightly points out the elephant in the room: click
Error bands are wider than the tenths of a degree puportedly being measured. When a normal y-axis is used, the obvious conclusion is that there’s nothing to panic about. The small changes over the past fifteen decades are down in the noise.
Actually, it isn’t much of a mystery. The ratio of land to ocean in the NH is about 1:1.5 whereas in the SH it is 1:4. The ocean is much more efficient at storing heat than the land is.
http://www.physicalgeography.net/fundamentals/8o.html
Sparks (November 7, 2011 at 5:45 am )
You make a good attempt to prove something which is mathematically impossible.
Here’s your 8 day average temperature series as you present it –
1°C + 19°C + 3°C + 20°C + 2°C + 18°C + 0°C + 20°C :=83 /8 :=10.3 °C
Actually, the average is not 10.3, it is 10.375, and if you want to prove your point that you can get different answers by ‘mixing up’ the data, then you have to the sums accurately -then you’ll find you can’t.
For the next 8 day average temperature you say “1°C + 1°C + 1°C + 20°C + 1°C + 1°C + 0°C + 20°C :=44 / 8 :=5.5 °C”, but this is wrong. The temperatures total 45, not 44, so the correct average for the second set is 45/8 = 5.625
So, correcting for this and ignoring the obvious slip which DirkH pointed out…
First 8 days + second 8 days (10.375 + 5.625) / 2 := 16 / 2 = 8.0 °C
….and the complete 16 day average is (45+ 83)/2 = 128/16 := 8.0 °C…
…which is exactly the same – so dividing up the numbers differently makes no difference.
“Carrick says:
November 7, 2011 at 7:53 am
I generally don’t bother with Sks but followed it since you linked it. I agree with Tom Curtis’ critique of the SkS post you linked.
“Likely flawed” just shows your (IMO) confirmation bias.”
Likely flawed is maybe too strong, likely biased low is the appropriate description. It isn’t about confirmation bias it is about science and there is strong evidence that RSS and UAH have underestimated trends in the atmosphere. UAH in particular has a LONG history of making mistakes in their analysis (and allowing their analysis to subsequently be used to substantiate false claims vis-a-vis global temperature). I’m not familiar with Tom Curtis’ critique of the SKS post linked to, could you point me to the exact comment?
I think the point of this whole discussion is that the reanalysis products will always have inherent biases when the input datasets have them. I very much condemn the argument seen here and elsewhere quite frequently that the satellite records are the definitive “gatekeeper” of global temperature trends. As has been demonstrated throughout the history of their development, the satellite record has had substantial errors pointed out on numerous occasions (Zou et al 2010 have corrected some ones still embedded in the UAH and RSS analysis) and yet it is used as a gold standard against the surface temperature measurements. That’s the “confirmation bias”.
Reanalysis models are not ready for prime time but it has been on stage and in the limelight of the congress for enough time to be the dominate factor in their decision making. Why, because someone has presented models as undeniable proof of global warming to an all too receptive congress.
The problem is not the models but the unprofessionalism of those who present them for what they are not, those who willingly accept them without question and those who fund research with strings attached to the desired results.
Willis is right further funding is needed. It is the general purpose of the funding that has become the problem.
jens raunsø jensen says:
November 7, 2011 at 4:51 am
Linear trends are not my tool of choice by a long ways. I use them because their use is so widespread, but I don’t like them. Nature moves in steps and chunks, not in straight lines.
In addition any attempt to mechanically determine the “breakpoints” in climate data needs to be very carefully researched and tested. Far too often it seems like someone had a bright idea for an algorithm and applied it to 1,500 datasets without checking them all, individually, to see what the algorithm has done.
Thanks,
w.
barry says:
November 7, 2011 at 7:02 am
richard verney,
What is the point of ‘reanalysis data’ when you have empirical observational data?
All temperature data has problems. All. We just don’t have God-like observational tools. Which is why data has to be tested and adjusted where appropriate, and why reanalyses are done, combining many different data streams. The goal is always to improve the fidelity of the data.
Right, barry, we don’t have God-like observational tools, so we must “test” and “adjust” the data, which means we must act like God anyway, you know, to make the data fit the hypothesis we also simply confabulated right out of our “just so” imagination, and producing a perfect record of failure as to its predictions compared to empirical data, data which must therefore be wrong, now even including the satellite data to boot! We not being “God” and all.
Your God, Mammon, says, “Thou shalt always repeat memes, repeat, repeat, repeat.” Making them come true!
Well, barry, enc.: ~
But it’s just your imagination
Running away with you
It’s just your imagination
Running away again….. [Oh, the Temptations!]
“Imagine” that!
Reanalysis products are useful if you know what the limitations are – for example, anyone trying to do trend analysis with reanalysis should be extremely cautious. There are issues with data assimilation – eg, data sources change – and the resolution of the model can have a profound impact on many variables. Further, when people use tropopause products directly from these groups I cringe. It’s much better to calculate things like that yourself, so you know how the diagnostic was obtained, because a lot of these groups have no documentation.
The reason they’re useful is that they combine many different data sources through an assimilation process similar to the initialization of a weather model. The drawbacks are a lack of data in the SH, so you have varying degrees of data density, spurious trends, etc.
Again, these have their uses, you just need to be careful and understand the limitations. For us dynamics folk, they are often the best source to understanding mean states of the atmosphere – just not trends!
A pretty good description of reanalysis from RC:
http://www.realclimate.org/index.php/archives/2011/07/reanalyses-r-us/
Makes many of the same caveats as Willis does here, but provides more detail.
Robert says:
November 7, 2011 at 8:32 am
UAH was the first team to attempt calculating the temperature from the MSU sensors. Of course they made errors, that is inevitable. And unlike the folks at RC and at RSS, when the UAH errors were pointed out, they were acknowledged and fixed.
However, from there you part company with science, because this history of corrected errors should improve rather than decrease our confidence in their results. This kind of rooting out of error is what science does best, and what gives us confidence in the results.
For example, the measurements of the speed of light have become more and more accurate over the years … should this “LONG history” of errors in the calculation of the speed of light decrease or increase our confidence in the final result? Or take Milliken’s oil drop experiment, which famously has been shown to be flawed … should we believe less in the charge of the electron because of his error?
Finally, the UAH team did not “allow their analysis to subsequently be used to substantiate false claims”, any more than Robert Milliken did. There is no way to stop anyone’s analysis from being used by others in whatever way they might use it. All that sentence does is reveals you’ve left the scientific reservation entirely, and are now just feeding us your dislike of the UAH results …
w.
Robert says:
November 7, 2011 at 8:32 am
I very much condemn your argument seen here that I have said somewhere above that the satellite records are the definitive “gatekeeper” of global temperature trends, or of anything else. Recall that I said that I agreed strongly with the following from the paper:
and I closed by saying that:
So I said nothing about “gatekeepers” in any shape or form. In other words, Robert, you’re just pulling stuff out of your fundamental orifice in order to attack me. That loses you points and can get your vote cancelled, because very quickly people start to point and laugh and no one listens to you any more.
w.
ndcodeblue says:
November 7, 2011 at 9:56 am
Unfortunately, your logic is circular. You say that “Reanalysis products are useful if you know what the limitations are” … but if we know what the limitations are then we can fix them. The problem is, we don’t know what the limitations of any given model output might be, if we knew that we’d fix them and they wouldn’t be limitations.
So it’s not at all clear to me, ndcodeblue, just how you would verify whether some given result from some given reanalysis model was “limited” or not. I mean, the only way we could determine that the model gives bad answers would be to compare the model to the observations … but we only need the model because we don’t have the desired observations.
That’s what I mean by circular. If the reanalysis model tells us the temperature at point X was 17°C, we cannot check that temperature because we don’t have an observation at point X … if we did, we wouldn’t need the reanalysis model …
Finally, the existence of the five widely separated answers from the five different reanalysis models should make it clear that some of the models have very real problems … but that tells us nothing about the “limitations” of those models in any given instance.
w.
Bomber_the_Cat says:
November 7, 2011 at 8:29 am
Yes thanks Bomber_the_Cat, we established it was wrong, a good point that you raised tho is why I used 10.3 and not 10.375, these are just quick figures off the top of my head done on the fly to use as an example so I rounded it off, like I said, I was a little bit rushed. apologies.
“Dividing up the numbers differently makes no difference” correct, I wasn’t trying to say this.
it’s good thing you and dirk came along to put me right, it does show that readers here are sharp and don’t miss much.
“You make a good attempt to prove something which is mathematically impossible.”
I try, need more funding to be able to spend more time on it.
Either way despite the error the averages still do Not relate temperature to cause on a time line.
Robert: I very much condemn the argument seen here and elsewhere quite frequently that the satellite records are the definitive “gatekeeper” of global temperature trends. As has been demonstrated throughout the history of their development, the satellite record has had substantial errors pointed out on numerous occasions
FWIW, I agree with Willis’ response on this post of yours. That’s if you care how the audience responds.
Willis, this was a good post. Thanks.
Has anyone produced an explanation of why the far SH is cooling, the periequtorial region near unchanged, and the far NH is warming?
Sounds more accurate and precise… to me, climatically speaking! GK
Smokey has the good call.
If you are going to plot observational data, please provide reasonable (or ANY) error bars for that data.
We see less than 1 degree C total variance both within and between much of these various series so it would seem even minor sources of errors would make the observations (I assume they are simple arithmetic averages) meaningless.
Straining at gnats.
Aerosols certainly don’t explain that unless China and India have suddenly shifted to the southern hemisphere.
Aerosols do explain it.
This is satellite and radiosonde data measuring troposphere temps.
Aerosols block and scatter solar radiation directly warming the troposphere. And this is the mechanism by which they exert a cooling influence on the climate. This energy gets radiated out to space faster than solar radiation that reaches the land/ocean surface.
Which means troposphere temps don’t measure climate warming/cooling.
Long but interesting paper on aerosols.
http://medias.obs-mip.fr/igac/html/book/chap4/chap4.html#aerosols
Willis, I have one small input;
UAH data; I remember reading somewhere that Roy Spencer said that there is very good match between balloon data and satelite data. And that he therefore is confident the UAH data is correct.
Therefore I think you miss an important plot up there; UAH data versus balloon data.
Alone, together. Not tarnished by model outputs.
commieBob says November 7, 2011 at 8:22 am:
“——————Actually, it isn’t much of a mystery. The ratio of land to ocean in the NH is about 1:1.5 whereas in the SH it is 1:4. The ocean is much more efficient at storing heat than the land is.”
And therein, whether you realize it or not, you have explained “The Natural Greenhouse Effect” in a couple of sentences. – All you have got to do is to add the fact that the Earth spins on its axis fast enough for most of the surface (70.9%) to face the Sun every morning at a temperature that is by far much higher than -18 °C.
Next time, just before you start doing the ironing, suspend the iron by the handle (use a piece of string to tie the iron in place as the electrical cable is not meant for this particular purpose) a couple of feet or so above the floor upon which you must put a thermometer. (Make sure the thermometer is directly in line with the iron’s “hot-plate” and do use another “check thermometer” close by, but not too close, just in case the under-floor heating comes on) – Now turn the iron on and leave this set-up for an hour or two while doing regular temperature checks. – Note down the time-span between when the iron is turned on and back-radiation from the iron starts to warm the thermometer and by how much the rise of T is.
And by the way John Tyndall (1861) never used a thermometer in his experiment to prove that CO2 was a greenhouse gas.
All he proved was that CO2 and some other gases blocked the electro magnetic signal – or signals – from either the thermo-pile – or from the heat source – or more unlikely both, but as he never used a thermometer in the brass tube into which he introduced CO2, he never proved that “Black heat radiation from a “heat-source” can heat anything.
I’d go as far as saying that we are seeing 2 different signals in the SH and NH data.
In the SH, there are limited amounts of anthropogenic aerosols and the troposphere cooling is IMO largely natural. IE, the SH troposphere temps are showing a genuine climate cooling signal.
In the NH and tropics we seeing a anthropogenic aerosol signal and the tropospheric warming is in fact evidence the NH is cooling, for the reason I explained above.
Smokey says:
>>
Error bands are wider than the tenths of a degree puportedly being measured. When a normal y-axis is used, the obvious conclusion is that there’s nothing to panic about. The small changes over the past fifteen decades are down in the noise.
>>
The signal to noise ration does make finding out what is happening and proving or disproving why a whole lot harder.
However, it has no bearing on whether there is anything to worry about.
Remember the ostrich? Not being able to see the danger does not mean it does (or does not) exist.
Getting more serious about error estimation is part of what BEST claim to be about. Thoug I think they have some work to do before they publish.
Why does their algorithm take out the 1998 El Nino. ?
http://tinypic.com/r/11brrqe/5
I’m a little confused here. I agree the water is a superior heat retainer compared to land…..but if the NH land-to-ocean ratio is 1:1.5 and the SH is 1:4…..shouldn’t the exact opposite be happening.Or am I looking at the wrong temp sets(SST’S)?
“In general the three satellite records are in good agreement. The STAR and RSS datasets are extremely similar, somewhat disturbingly so, in fact”.
Willis, all the satellite datasets use the same satellite data. Why is it a surprise to you if they arrive at similar results? The real intriguing question is – why don’t they all come to exactly the same result?
Here’s a link to the RSS document that describes how they use radiative transfer models and GCM(CCSM3?) in their processing of the raw satellite AMSU data.
Perhaps you’ve seen this before, if not enjoy.
http://www.ssmi.com/data/msu/support/Mears_and_Wentz_TMT_TTS_TLS_submitted.pdf
fred berple,
You may have got the impression from the article that you are looking at lower tropospheric temperature trends, but channel 2 covers a broad band of the mid troposphere. 80% of the measurement is troposphere, and the rest is land surface and stratosphere. The comparison is with radiosonde and and renanalyses of mid-tropospheric temps. While the mean temperature trend is positive, most data sets show slight cooling south of 40S.
RSS discuss CH2 issues in this 2003 paper, similarly showing mid-tropospheric cooling trends over the Southern oceans and Antarctica.
http://www.remss.com/papers/msu/A_Reanalysis_of_the_MSU_Channel_2_Tropospheric_Temperature_Record.pdf
Just to stress, ‘mid-tropospheric’ is a bit of a misnomer, and despite Willis’ suggestion that the various data sets are “all purporting to be measuring the same thing,” they do not measure the same thing. MSU measures radiance, radiosondes measure temperature, and the reanalyses try to combine datasets. In the case of the satellite data, the radiance measurements come from a deep section of the atmosphere which includes the lower stratosphere (which is cooling). There are bound to be discrepancies.
As to why there are negative trends South of 40S in the mid-troposphere – beats me. I wonder if it might have something to do with ozone depletion, or it may simply be the natural thermal characteristics of the planet in that region of the sky, even with warming at the surface.
A few quotes from the study Willis has shared with us;
You’re not confused at all. More water coverage should mean less extremes. But it may also mean more clouds leading to a cooling.
I personaly don’t think it’s a mystery at all. The two hemispheres do mirror each other in some aspects of climate (i.e. less ice in Arctic, more ice in Antarctic) so if one is warming for whatever reason, the other may well cool.
The atmosphere is a gas afterall and will behave as such. Think about high pressure and low pressure and air movements.
I had to lol at the ‘fundamental orifice’ comment. Too funny. Ok, continue.
I think correlation isn’t a good measure to compare these trends. RSS and Star are almost perfectly correlated though they differ by an offset (or factor, they could even differ by any positve factor and would still be perfectly correlated).
Perhaps, a rms difference is a better measure.
Manfred says:
November 7, 2011 at 4:36 pm
There’s always more to learn from a dataset. That’s why I included their data at the bottom of the post, so you and others could do those alternative kinds of analyses that might reveal more.
w.
Where does the difference between RSS and UAH of perhaps 0.05 deg/decade come from ?
Is this a mistake ? RSS and UAH should be much closer:
http://www.woodfortrees.org/plot/uah/plot/rss
http://www.woodfortrees.org/plot/uah/trend/offset:0.23/plot/rss/trend/offset:0.14
barry says:
November 7, 2011 at 4:19 pm
First, barry, thank you for a very interesting post.
Second, clearly my words have not been clear.
When I said that they were “all purporting to be measuring the same thing,” I meant they were purporting to measure the mid-tropospheric temperature trend (Channel 2, actually a weighted average). It might have been clearer to say that they were all “purporting to be estimating the same thing”.
Usually, however, when we say we are “measuring the temperature” with a thermometer … would you protest and say that actually we were measuring the volumetric expansion of mercury and using that to estimate the temperature?
So you are assuredly correct sensu stricto … and I think most people understood my meaning, that in a perfect world those measurements should all agree, because they are all measuring (estimating) the same variable. So any departures from that ideal would point to flaws/weaknesses in either the observations or the method or both.
w.
Manfred says:
November 7, 2011 at 5:52 pm
It’s been the subject of much discussion. IIRC it’s to do with using different methods in the processing of the raw data to produce the temperature estimates.. I alluded to that in the head post.
w.
Stephen Singer says:
November 7, 2011 at 2:13 pm
Many thanks, stephen, that’s the document I asked for in the head post. I’ve added it up top, along with the following comment:
Gotta love the power of crowdsourcing, guys like you make it work.
w.
Septic Matthew says:
Has anyone produced an explanation of why the far SH is cooling, the periequtorial region near unchanged, and the far NH is warming?
—
Matt, go see icecap.us. There is a link about high warm bias in measure arctic and antarctic temperatures. More anecdotal evidence that there was a real decline to hide.
Manfred, likewise a simple offset of +0.085 to the UAHs’ raw data seems to show that UAH is clearly higher in recent months (or RSS low): Most data points closely match in the body viewed that way.
http://www.woodfortrees.org/plot/uah/offset:+0.085/plot/rss
Willis,
I completely agree. That there are flaws and weaknesses (and strengths) in the various data sets and methods is well-known, and discussed at length in the literature, here, the IPCC and all over the semi-popular climate blogosphere.. The point of your article seems to be that reanalyses should not be treated ‘blindly’ as data, because they diverge most from the ensemble and each other. But I’m not sure that the point doesn’t rest on a straw man. Who is ‘blindly’ treating reanalyses as empirical data?
The same authors find good agreement amongst data sets for the global mid-troposhpere. The discrepancies are mainly to do with trends at latitude, but the global results are not far off each other. The ensemble mean (for want of a better term) seems to be pretty robust – with the caveat that there is some cross-fertilisation of data! Less confidence is attached to stratospheric trends – the most one could say about them is that the global trend is all the same sign (negative), but the rate globally and zonally tend to diverge. Least well-constrained of all is stratospheric trends over the Antarctic.
Of course, putting the skeptic cap on firmly, one must consider that the paper itself may be flawed. I’ve not the skill to assess that. But I certainly appreciate learning about the trend differences between data sets depending on latitude – something I didn’t know about before today.
W says ‘… model outputs are usually referred to as “reanalysis data”. They are not data.’
Words that should be hung in any science class. Thany you Willis!
Interesting that STAR and UAH have the tropics trending in opposite directions. That looks like a fundamental disagreement about the planet’s heat engine, to me.
Bomber_the_Cat says:
November 7, 2011 at 1:54 pm
“In general the three satellite records are in good agreement. The STAR and RSS datasets are extremely similar, somewhat disturbingly so, in fact”.
Willis, all the satellite datasets use the same satellite data.
=========
I’ve heard that claim also, but I think it is not quite true and that at times UAH and RSS use different instruments. Here’s an excerpt from a Roy Spencer article http://www.drroyspencer.com/2011/07/on-the-divergence-between-the-uah-and-rss-global-temperature-records/ :
“Anyway, my UAH cohort and boss John Christy, who does the detailed matching between satellites, is pretty convinced that the RSS data is undergoing spurious cooling because RSS is still using the old NOAA-15 satellite which has a decaying orbit, to which they are then applying a diurnal cycle drift correction based upon a climate model, which does not quite match reality. …”
I read that as RSS is using NOAA-15 and (by implication) UAH is using a different satellite as well as different processing.
Willis Eschenbach says:
November 7, 2011 at 6:09 pm
Manfred says:
November 7, 2011 at 5:52 pm
Where does the difference between RSS and UAH of perhaps 0.05 deg/decade come from ?
Is this a mistake ? RSS and UAH should be much closer:
It’s been the subject of much discussion. IIRC it’s to do with using different methods in the processing of the raw data to produce the temperature estimates.. I alluded to that in the head post.
w.
————————————————
My point was that RSS and UAH TRENDS differ a lot in THIS study while they are now, after all these discussions, almost identical in reality (less 0.1 deg/decade difference). (http://www.woodfortrees.org/plot/uah/trend/offset:0.23/plot/rss/trend/offset:0.14).
What are you referring to, specifically? Cite?
barry says:
November 7, 2011 at 9:47 pm
Where does the difference between RSS and UAH of perhaps 0.05 deg/decade come from ?
What are you referring to, specifically? Cite?
====================
Eyeballing at figure 4 above, RSS and UAH trends differ approx. up to approx 0.12 K/decade, averaged over all latitudes perhaps 0.05 K/decade, probably even a bit more, because area at 0 deg latitude is largest.
Manfred says:
November 7, 2011 at 9:17 pm
My point was that RSS and UAH TRENDS differ a lot in THIS study while they are now, after all these discussions, almost identical in reality (less 0.1 deg/decade difference). (http://www.woodfortrees.org/plot/uah/trend/offset:0.23/plot/rss/trend/offset:0.14).
=========================
Sorry, should be “less 0.01 deg/decade difference”
Manfred, the woodfortrees graph is a plot of TLT trends for the UAH/RSS – lower troposphere. The graph from the study is of mid-troposphere temperatures. One of the results the authors arrive at is that there is less disagreement between trends the lower in the atmosphere you go. However, as they do not deal with TLT trends, I don’t know if that necessarily follows for lower tropospheric trends. Any case, the trends in your graph and the ones in the study are for different altitudes of the atmosphere.
@barry, that probably explains the differences. Cheers.
It seems to me that much of the excitement in climate science is generated by the scale of the X/Y axes. Looking at the graphs, we are talking about something around 0.2degC range between sets. Pamela Gray, November 7, 2011 at 6:43 am has said it best:
“…let’s round to the nearest whole degree and call anything less noise. That would solve a lot of problems with a noisy data set. Of course it would also cause a great deal of funding to simply dry up and blow away. Can anybody guess why?”
I didn’t see one other posting that took this on.
Septic Matthew says:
November 7, 2011 at 10:39 am
Has anyone produced an explanation of why the far SH is cooling, the periequtorial region near unchanged, and the far NH is warming?
Anything that is atmospheric related should have the same sign in both the NH and SH due to mixing. There might be a lag due to relative ocean areas, but there cannot be a difference in sign between hemispheres related to the atmosphere due to mixing. Atmospheric heat transport alone should prevent this.
What we are left with is the difference in ocean/land/ice surface areas between the hemispheres. This is the most logical cause and effect explanation for differential heating.
What has changed about the land? 100 years ago 4% of the land was used by humans. Today it is 40%, made possible largely through the introduction of widespread mechanization. Most of that change has been in the NH.
Atmospheric changes can’t be the cause because of the effects of mixing. A similar argument holds for the oceans, over a longer time scale. Only the land doesn’t mix, which does allow for differential heating.
In any case, measuring atmospheric temperatures without measuring humidity is nonsense science. Temperature on it own tells you almost nothing about the heat content of the atmosphere. It points to a huge failing in the IPCC and climate science to focus on temperature.
For example, in much of S and SE Asia, the summer monsoon is much hotter than the winter monsoon. Yet it is the summer monsoon that brings life to S and SE Asia.
It isn’t the temperature of the air that is important, it is its moisture content in relation to its temperature that determines feast or famine.
If scientists have a such hard time using all of today’s technology to measure “What is,” I wonder how good the “What was” data is that we are comparing against?
@ commieBob
Oceans being a more efficient heat sink would only account for moderating the rate of warming in the Southern hemisphere, not for a cooling trend.
Gary Pearse @ here
Precision to tenths of a degree is strengthened by having many measurements. The power of large groups of numbers makes this possible. Averaging large groups of numbers statistically, gives a more precise value than having just one or averaging several values. Tamino had a post on it once…
Ah, here it is, from web archives.
http://web.archive.org/web/20080402030712/tamino.wordpress.com/2007/07/05/the-power-of-large-numbers/
Check it out, it’s a pretty interesting post. Or read the wiki entry on the Law of Large Numbers
[Formatting fixed -w.]
barry says:
November 8, 2011 at 2:52 pm
Gary Pearse @ here
Precision to tenths of a degree is strengthened by having many measurements. The power of large groups of numbers makes this possible. Averaging large groups of numbers statistically, gives a more precise value than having just one or averaging several values. Tamino had a post on it once…
barry, as is not uncommon, Grant Foster (who masquerades as “tamino”) left out some of the story.
First, note that despite having thousands and thousands of observations, the average only improved on the accuracy of individual measurements by an order of magnitude. Grant didn’t discuss that at all.
Second, this is a record of one man repeatedly measuring the same thing. Compare and contrast that with a number of men measuring different things … Grant also left that part out.
Third, it assumes a symmetrical distribution, that is to say, it assume the chance of missing high is the same as the chance of missing low. Humans, on the other hand, tend to round maximum temperatures up and minimum temperatures down … I didn’t see Grant mention that.
Fourth (and Grant did mention this one) this is only applicable to relative measurements. Relative to what? Relative to itself. It cannot be used to compare to any other dataset.
So while in theory a number of temperature could be averaged to give us an answer accurate to the nearest 0.000000001, in practice (as tamino has amply demonstrated) about the best we can expect is an order of magnitude improvement over the original measurements. Since thermometers are generally read to the nearest whole degree, I generally don’t believe much past the first decimal point.
And that’s not even touching the problem that temperature is an intensive rather than an extensive variable …
w.
ferd berple says:
November 7, 2011 at 6:50 am
Isn’t the real question why the norther hemisphere is getting warmer and the southern hemisphere is getting colder if CO2 is well mixed? …This is a huge mystery completely unaccounted for in current theories of climate change… Why isn’t climate science all over this?
I’m surprised nobody else has answered you with this:
Svensmark.
With generally increasing solar radiation batting away cosmic-ray-inducing clouds, for the time period of the study 1979-2008, the landmasses warm a lot, and the sea temp rises less and falls less owing to larger thermal inertia. But the icecaps COOL because ice has an even higher albedo than clouds.
BTW I’m sure I’ve seen a damn good piece of analysis of 90S – 90N profiles, by Erl Happ, that reminds me of the clearly asymmetric profile here. Fascinating material about the Roaring Forties IIRC.
Thanks for fixing the formatting Willis.
Trends are even more robust than data points, yes? I was responding to the doubt that trends to a tenth of a degree could be validated mathematically. Isn’t this the order of magnitude you are just now saying we have improved accuracy to? I see no disagreement here, if so.
Thousands of instruments (thermometers) measuring one thing (air temperature)? And several sensors on satellites reading the same thing (spectral radiance)? I do not know what you mean by ‘a number of men’ measuring different things. If reanalysis, then the base data is the thousands/millions of measurements of one thing by many instruments.
Tamino’s example is also of many people measuring the same thing with their imperfect instruments (eyes). With enough data, the noise is reduced and precise estimates can be gleaned. But in the end this isn’t based on anecdote.The Law of Large Numbers is a statistical phenomenon used in many fields. Error bars come from doubts about measurement bias, coverage etc, not from doubts about the power of averaging.
Philip Bradley says: November 7, 2011 at 11:59 am
Aerosols do explain it… Long but interesting paper on aerosols, http://…
I think the neatest answer to aerosols was provided by Warren Meyer. You can find it in the comments around slide 62 in my Climate Science presentation
Lucy,
Temperature trends in all data sets show warming in the Southern Hemisphere at the surface/lower troposphere.
Svensmark’s cloud/cosmic ray theory predicts that climate shifts should be opposite in sign between the North and South poles, not the Southern hemisphere. The jury is out on whether the South Pole is cooling, flat or warming for the last 30 years or so (UAH decadal trend is -0.05C/decade). But it is clear from satellite measurements and land-based sun spot counts that the sun, and therefore GCR trends, have not changed much over that period, and therefore GCR/cloud theory is unlikely to be substantiated by reference to the study above.
Solar output shows little trend for the last 60 years. Svensmark’s theory does not seem to be corroborated by the surface temperature records, which has a significant (statistically/magnitude) positive sign for that period.
barry says:
November 8, 2011 at 5:41 pm
Trends are like averages, in that the more data points you have, the narrower your statistical error bars are.
Tamino’s example is of one man measuring one thing over and over again—the repeated cycle of a single variable star. Read the link again, they give the man’s name. One man measuring one thing, many times.
Weather observations are many men at different locations around the planet. Each one is measuring, one time only, something which is constantly varying without repeating—the local temperature. This is many men measuring many things, once.
Of course it is. But measurement bias is not the issue I’m pointing to. I’m discussing a different problem.
Suppose you take a tape measure and you have ten thousand people measure the length of a steel bar. Each one measures it to the nearest millimetre.
How accurate is the final average of the measurements? Yes, we can be sure of the statistical standard error of the mean of those measurements. It’s the standard deviation (call it half a mm) divided by the square root of the number of measurements. That’s 0.5 / 100 = 0.005 mm, or five microns …
But does that mean that we have actually measured the bar to the nearest five microns with a tape measure?
No way. We can gain about an order of magnitude, and that’s it. We could have ten million people measure the bar with a tape measure, we won’t get any more accurate than that.
w.
Not according to statistical probability. The larger the sample, the more the mean of the sample converges on the ‘true’ value. There is no ceiling where adding more samples makes no difference to the convergence. I find this to not only be a mathematical result, but also quite intuitive. It just makes sense.
it turns out to be a fundamental property of statistics that the average of a large number of estimates is more precise than any single estimate. The more data go into the average, the more precise is the average — even though the source data are all imprecise.
Large numbers do indeed improve precision, but they have no effect on accuracy.
Unfortunately Tamino and others fail to understand this distinction.
from wikipedia
The accuracy[1] of a measurement system is the degree of closeness of measurements of a quantity to that quantity’s actual (true) value. The precision[1] of a measurement system, also called reproducibility or repeatability, is the degree to which repeated measurements under unchanged conditions show the same results.
Thanks Lucy for the link.
That’s a bit of a red herring, Philip. The accuracy of individual measurements is a different metric and doesn’t apply to large sample averaging per se. In temperature measurement systems, the metric you’re introducing here come from systemic biases, not averaging. I was careful to distinguish these in a previous post. Accuracy, in the context you mean, doesn’t impact on the query I was responding to.
Studies like the one Willis has brought here try to quantify systemic biases by comparing data packages. This is quite different to the concept of convergence from averaging. Let’s keep them distinct lest we muddy the waters.
barry says:
November 8, 2011 at 8:24 pm
No, it doesn’t make sense. If you were right, by increasing the number of people measuring a steel bar with a tape measure, we could measure it to the nearest tenth of a micron … and clearly that is not true.
Increasing the number of people measuring the bar gives us more information about what the true average of people’s measurements actually is. But the true average of people’s measurements is not the length of the bar. It’s just the average of their measurements. Beyond a certain point, increasing the numbers of measurements does not increase the accuracy of the measurement of the actual bar.
In other words, we can’t measure a bar’s actual length to ± one micron with a tape measure, no matter how many times we might measure it.
w.
Willis,
The mathematical point is that the larger the sample size the greater convergence to the true value. Individual measurements will vary, but the mean will converge on the true value, and this convergence increases with increasing measurements to infinity. There are numerous formulae, simple and more complex establishing this statistical fact. Some are shown here:
http://en.wikipedia.org/wiki/Law_of_large_numbers
You have stated that there is a limit to convergence, but offered no mathematical proof. Can you defend this mathematically? I would be intrigued to see how you do it.
barry says:
November 8, 2011 at 10:12 pm
Willis,
You are right that the larger the sample size, the greater the convergence to the true value. So let us examine the question, “convergence to the true value of what?”
What it is converging on is the true value of the mean. You are right, you can get that as accurate as you want, and adding measurements increases the convergence.
But the true value of the mean is different from the true value of the length of the steel bar being measured with a tape measure. You are not converging on the length of the bar, only on the true value of the mean of the measurements.
I already showed it above, using logic rather than math. If we assume your claim is correct, then we should be able to measure a steel bar to an accuracy of ±1 micron using just a tape measure and a whole lot of measurements. Since this is obviously impossible, your claim can’t be correct.
(There’s actually a name for that kind of logical proof. You assume the other guy is correct, and show that if he’s right it leads to something impossible. Someone will know the name of that kind of proof.)
w.
It would be nice to see an image of the “anomaly” where the mean value used to calculate the “anomaly” is the arithmetic mean of only the balloon and satellite data.
At first glance, it appears the mean used to calculate the so-called “anomaly” in Figure 1 may be polluting the results in Figure 2.
The mathematical point is that the larger the sample size the greater convergence to the true value. Individual measurements will vary, but the mean will converge on the true value
It doesn’t converge on the true value. It converges on the measured value.
The deeper point here is the unstated assumption that measurement errors are random. Some are, some aren’t. Large sample size does nothing to correct non-random errors.
Willis,
the argument you are making is known as reductio ad absurdum. I concede to the logic. But it in the context of my reply to Gary, it comes with a false premise. My response to the original statement.
was to explain why averaging makes 10ths of a degree a valid value. Which you have agreed with.
Philip,
No one is making this assumption. Non-random errors are tangential to Gary’s query.
Just occurred to me that the power of averaging the changes in data can be seen WRT the trends from the paper. Global surface trends are comprised of many more measurements than zonal (latitudinal) and than higher in the atmosphere. We spend so much time picking at the disagreement between data sets that perhaps we overlook the quite amazing agreement between them. In the case of satellite TLT and surface trends, the differences are less than tenths of a degree C. For statistically significant periods, say 30 years, the differences amount to no more than 5 hundredths of a degree C. That’s a pretty remarkable result when two completely different phenomena are being measured and different methods for all the data sets are employed.
barry says:
November 9, 2011 at 2:35 pm (Edit)
Thanks, barry. I hear this all the time. Here’s the thing. During the 20th century, the warming that everyone is screaming about was on the order of 0.6°C per century.
The difference between the trends of the various datasets is, as you say, a tenth of a degree per decade … which is a whole degree per century. And if you’re using the BEST data, its even more than that.
So while “a tenth of a degree” sounds impressive, it’s a degree per century. The difference between datasets is still way too large to settle important questions relating to recent warming.
w.
I did not say that the difference in trends was a tenth of a degree per decade. I said, as you quoted me “the differences amount to no more than 5 hundredths of a degree C,” which is half a degree C per century.
But I was conservative in my rounding – I know that the difference between the means is actually smaller. The decadal linear trend for 4 temperature sets (2 satellite and 2 surface) between Jan 1979 and Dec 2010 is less than 3 hundredths of a degree C different from each other (source).
That amounts to a difference of less than 0.3C a century. And UAH is not calibrated to surface temperature, as Roy Spencer consistently points out. That is remarkable, agreement considering the many different issues troubling both surface and satellite data sets and the relative shortness of the time period (less than a third of a century).
And the deeper you look the more you can qualify the results. Satellite temperature records are influenced more strongly by el Nino/la Nina patterns than surface records. UAH has steadily converged with the other records, having been an outlier. While it is de rigeur in some parts to diss the official records, time keeps validating their robustness. Even Fall et al corroborated mean trends for the US – and this was a regional study, where you would expect greater variance with different methods if the average temp record was very flawed. BEST is just another example of corroborating evidence. The evidence against tends to be anecdotal, highly selective (handful of stations, or non-random selections), but when the numbers are crunched for large, random samples, people always seem surprised – outraged even – that the results tend to confirm the official records. Not perfectly, of course, but within the error bounds. Eventually one has to recognize this. Doesn’t mean there isn’t plenty of uncertainty to discuss or work to be done, but I think avoiding or downplaying the convergence of these results while critiquing the temp records takes the discussion beyond skepticism, which should balance evidence neutrally rather than directing doubt all in one direction.