Guest Post by Willis Eschenbach
I have long suspected a theoretical error in the way that some climate scientists estimate the uncertainty in anomaly data. I think that I’ve found clear evidence of the error in the Berkeley Earth Surface Temperature data. I say “I think”, because as always, there certainly may be something I’ve overlooked.
Figure 1 shows their graph of the Berkeley Earth data in question. The underlying data, including error estimates, can be downloaded from here.
Figure 1. Monthly temperature anomaly data graph from Berkeley Earth. It shows their results (black) and other datasets. ORIGINAL CAPTION: Land temperature with 1- and 10-year running averages. The shaded regions are the one- and two-standard deviation uncertainties calculated including both statistical and spatial sampling errors. Prior land results from the other groups are also plotted. The NASA GISS record had a land mask applied; the HadCRU curve is the simple land average, not the hemispheric-weighted one. SOURCE
So let me see if I can explain the error I suspected. I think that the error involved in taking the anomalies is not included in their reported total errors. Here’s how the process of calculating an anomaly works.
First, you take the actual readings, month by month. Then you take the average for each month. Here’s an example, using the temperatures in Anchorage, Alaska from 1950 to 1980.
Figure 2. Anchorage temperatures, along with monthly averages.
To calculate the anomalies, from each monthly data point you subtract that month’s average. These monthly averages, called the “climatology”, are shown in the top row of Figure 2. After the month’s averages are subtracted from the actual data, whatever is left over is the “anomaly”, the difference between the actual data and the monthly average. For example, in January 1951 (top left in Figure 2) the Anchorage temperature is minus 14.9 degrees. The average for the month of January is minus 10.2 degrees. Thus the anomaly for January 1951 is -4.7 degrees—that month is 4.7 degrees colder than the average January.
What I have suspected for a while is that the error in the climatology itself is erroneously not taken into account when calculating the total error for a given month’s anomaly. Each of the numbers in the top row of Figure 2, the monthly averages that make up the climatology, has an associated error. That error has to be carried forwards when you subtract the monthly averages from the observational data. The final result, the anomaly of minus 4.5 degrees, contains two distinct sources of error.
One is error associated with that individual January 1951 average, -14.7°C. For example, the person taking the measurements may have consistently misread the thermometer, or the electronics might have drifted during that month.
The other source of error is the error in the monthly averages (the “climatology”) which are being subtracted from each value. Assuming the errors are independent, which of course may not be the case but is usually assumed, these two errors add “in quadrature”. This means that the final error is the square root of the sum of the squares of the errors.
One important corollary of this is that the final error estimate for a given month’s anomaly cannot be smaller than the error in the climatology for that month.
Now let me show you the Berkeley Earth results. To their credit, they have been very transparent and reported various details. Among the details in the data cited above are their estimate of the total, all-inclusive error for each month. And fortunately, their reported results also include the following information for each month:
Figure 3. Berkeley Earth estimated monthly land temperatures, along with their associated errors.
Since they are subtracting those values from each of the monthly temperatures to get the anomalies, the total Berkeley Earth monthly errors can never be smaller than those error values.
Here’s the problem. Figure 4 compares those monthly error values shown in Figure 3 to the actual reported total monthly errors for the 2012 monthly anomaly data from the dataset cited above:
Figure 4. Error associated with the monthly average (light and dark blue) compared to the 2012 reported total error. All data from the Berkeley Earth dataset linked above.
The light blue months are months where the reported error associated with the monthly average is larger than the reported 2012 monthly error … I don’t see how that’s possible.
Where I first suspected the error (but have never been able to show it) is in the ocean data. The reported accuracy is far too great given the number of available observations, as I showed here. I suspect that the reason is that they have not carried forwards the error in the climatology, although that’s just a guess to try to explain the unbelievable reported errors in the ocean data.
Statistics gurus, what am I missing here? Has the Berkeley Earth analysis method somehow gotten around this roadblock? Am I misunderstanding their numbers? I’m self-taught in all this stuff and I’ve been wrong before, am I off the rails here? Always more to learn.
My best to all,
w.
@richardscourtney says:
August 19, 2013 at 12:30 am
YES! Nobody is” doing the calibrations” because no calibration is possible.
No Richard what you mean to say is you don’t know how to calibrate it because climate scientist seem to understand statistics and that technique is useless here you can’t filter your way to a result it doesn’t work in any other science either. There are ways to do it and other sciences do it often and on much more complicated and more technically challenging systems than climate.
@richardscourtney says:
August 19, 2013 at 12:30 am
This thread is equivalent to discussion of the possible errors in claimed measurements of the length of Santa’s sleigh.
That is true so if climate scientists stop trying to claim a measurement of Santa’s sleight to some unrealistic accuracy no one would have a problem. If what you claim is true the signal will grow to an obviously measurable problem in time … see there is an easy answer if you don’t want to do the work …. oh wait there is a political agenda here I forgot.
So back to the drawing board if you want to claim the length of Santa’s sleigh to some incredible accuracy (AKA the climate signal) then do your homework on the background signals and noise and eliminate them like every other non political science does and stop whining about it.
LdB:
Thankyou for your reply at August 19, 2013 at 1:04 am
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394337
to my post at August 19, 2013 at 12:30 am
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394322
Unfortunately, you miss the point and (offensively) ‘put words in my mouth’ to state what you would have preferred me to have said. Then you discuss your ‘red herring’.
I stated my point as being
You say you want to determine the number of ‘angels on a a pin’, and I am saying there is no ‘pin’.
To prove me wrong you only need to state an agreed definition of ‘global temperature’ which does not alter from month-to-month (i.e. show me that the ‘pin’ exists).
A rational discussion of the error in the estimated value (i.e. the number of ‘angels’) is not possible until that agreed definition is stated.
Please comment on what I said and NOT what you wish I had said.
Richard
@richardscourtney says:
August 19, 2013 at 1:19 am
I see so your argument above there is no global temperature because such a thing does not exist or are you trying to say we are saying that such a thing does not exist?
I certainly think such a thing exists and it is no different to “rest mass” in science, we don’t know exactly what causes gravity but we can and certainly do parameterize rest mass to other well known and well understood variables.
So that argument itself is total rubbish just do the same trick parameterize the term “global temperature” to the other well understood variables rather than insisting on a specific absolute value.
Again do you think climate science is special and these sorts of things haven’t been seen before most of the world of particle physics is reparametrisations.
LdB:
I concluded my post addressed to you at August 19, 2013 at 1:19 am
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394340
saying
Your reply at August 19, 2013 at 1:58 am
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394353
DOES IT AGAIN!
It begins saying
NO!
I am saying – and have repeatedly explained – that
1.
there is no agreed definition of global temperature
2.
each team that provides global temperature data uses a different definition
3.
each team that provides global temperature data often changes the definition it uses.
So, there is no DEFINED metric of global temperature.
Therefore, the metric(s) said to be global temperature are meaningless: they may be different next month and – history shows – they probably will be.
There can be NO meaningful determination of the error in a datum, and there cannot be a calibration standard, for a metric which does not have an agreed definition.
This is true whether or not ‘global temperature’ exists in the real world.
I am reaching the conclusion that your repeated misrepresentations and refusal to address the issue I am presenting are examples of you being deliberately obtuse.
Richard
@LdB Why don’t you answer Richard’s challenge and provide a reference to the standard definition of Earth’s temperature? It’s not enough to merely assert that there is one, or that one might be possible. You have made some interesting comments in this thread, but I’m with Richard on this until the angels and the pinhead are defined. As I understand this, there have been many statements of what Earth’s temperature is over the years with no two experts stating the same number. It’s also notable that the magnitude of this stated temperature has declined, rather than increased.
Averaging a time series is bad statistical practice. What the anomaly is the average of an average of a time series. A double whammy.
It is impossible to get the true temperature of any object until that object is at thermodynamic equilibrium. The earth never is at this impossible state.
The Pompous Git:
My post at August 19, 2013 at 1:19 am said to LdB
And your post at August 19, 2013 at 3:24 am asked LdB
It is not possible for him to provide such a reference because as UCAR says
https://www2.ucar.edu/climate/faq/what-average-global-temperature-now
{emphasis added: RSC}
Were LdB to state what he thinks is a “universally accepted definition for Earth’s average temperature” his statement would be wrong because at most his definition would only be accepted by one of NCAR, NASA and NOAA. And that definition would be transient because NCAR, NASA and NOAA each often changes the definition it uses.
My repeatedly state point is that
There can be NO meaningful determination of the error in a datum, and there cannot be a calibration standard, for a metric which does not have an agreed definition.
My point is true for every metric including global temperature.
Richard
richardscourtney says:
August 19, 2013 at 4:55 am
No wonder climate science is in a mess if they think like you and I may sound like a Pompous Git but perhaps just stop and listen.
You are talking about ENERGY not some nebulous concept … ENERGY is invariant it can not be created and destroyed and the particular question you are asking is the energy on the earth increasing or decreasing because of the addition of CO2 into the atmosphere.
I don’t care how you define your point to measure ENERGY the datum exists because ENERGY is defined clearly and precisely.
Your problem in climate science is people want to choose a different condition you are calling the metric of global temperature.
The answer is simple make them define that particular definition (we call it a frame of reference) to that of the global energy balance after all that is the question you are seeking.
Look at invariant mass and guess how we make them define it
http://en.wikipedia.org/wiki/Invariant_mass
See what we make scientists do:
The invariant mass, rest mass, intrinsic mass, proper mass, or (in the case of bound systems or objects observed in their center of momentum frame) simply mass, is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations.
Pick whatever frame of reference you like make up your own definitions, make up your own units do what you like because you MUST tie it to the total energy balance of the earth there by definition has to be a transform between any two frames of reference.
If you make every climate science group as part of there choosing whatever reference point they like to measure tie it to global energy balance you can create a translation of results GUARANTEED because energy can not be created or destroyed.
If the scientists in climate science haven’t worked that out by now they have serious issues and need to get some real physicists involved ENERGY is not a toy you can redefine.
The Pompous Git says:
August 19, 2013 at 3:24 am
@LdB Why don’t you answer Richard’s challenge and provide a reference to the standard definition of Earth’s temperature?
Pick whatever definition you like I don’t care provide me the relationship to global energy balance and I can convert any two definitions between each other … problem solved it’s not hard.
LdB:
Your post addressed to me at August 19, 2013 at 5:15 am is yet another in your series of evasions and ‘red herrings’.
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394432
It makes no reference – and has no relation – to anything I have written in this thread (but adds another of your ad homs).
It makes no mention of temperature, global temperature, measurement theory or error estimation.
It says
BOLLOCKS!
We are talking about temperature and NOT energy.
To be specific, we are talking about the possibility of error estimation in global temperature determinations. And that is what I have been discussing: I have made no mention of “energy” (it is an irrelevance) and your assertion that I have is a falsehood.
Temperature is NOT energy.
Your post seems to be an indication of desperation because I refuse to accept that you are so ignorant that you don’t know temperature is not energy.
Are you involved in compiling a global temperature data set and, if so, are you obtaining income from it?
Richard
LdB:
Your post at August 19, 2013 at 5:19 am
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394434
addressed to The Pompous Git is yet another of your ‘red herrings’ and misrepresentations.
It says
The required definition was of “global temperature”.
It was NOT about “global energy balance”.
And nobody can “convert” between “global temperature” and “global energy balance” because they can vary independently (e.g. because of ocean currents, spatial variation in surface temperatures, variations in ice formation or melting, etc.).
Richard
richardscourtney says:
August 19, 2013 at 5:34 am
BOLLOCKS!
We are talking about temperature and NOT energy.
Temperature is NOT energy
OMG Richard please don’t say another word
Here is google for you:
http://en.wikipedia.org/wiki/Temperature
Please read it before you make any more statements I am not trying to pick on you simply explaining and you obviously need some things explained.
Richard I found a reasonable link for you I am not being smart just making sure you follow how it works.
http://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/Chapter3a.html
Chapter 3: The First Law of Thermodynamics for Closed Systems
LdB said:
“ENERGY is invariant it can not be created and destroyed and the particular question you are asking is the energy on the earth increasing or decreasing because of the addition of CO2 into the atmosphere.”
More energy need not affect temperature.
Potential Energy is not registered as heat by thermometers.
If a gas molecule rises more of its energy converts from KE to PE and it cools.
Any molecule that absorbs energy so as to become warmer than its surroundings then becomes part of an expanded, less dense and lighter air parcel which rises against gravity until it cools once more so the net effect on temperature of radiative characteristics is zero but PE increases instead.
No need for a rise in surface temperature to push the atmosphere higher. One only needs the presence above the surface of molecules capable of carrying more energy in PE form.
LdB:
It seems I owe you an apology. In my post to you at August 19, 2013 at 5:34 am
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394449
I wrote
Clearly, I was wrong to imply that you are being disingenuous because your posts at August 19, 2013 at 6:08 am and August 19, 2013 at 6:43 am
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394467
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394488
proclaim that you ARE so ignorant that you don’t know temperature is not energy.
I apologise for suggesting you were being disingenuous when you were merely demonstrating your ignorance of elementary physics.
Please read the comment of Stephen Wilde at August 19, 2013 at 6:47 am
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394490
It may initiate your education in elementary physics.
And, concerning your mention of thermodynamics, I cannot help you to understand thermodynamics until you gain sufficient knowledge of elementary physics for you to understand why temperature is not energy.
Richard
Stephen Wilde says:
August 19, 2013 at 6:47 am
Potential Energy is not registered as heat by thermometers.
If a gas molecule rises more of its energy converts from KE to PE and it cools.
You are dealing with earths energy balance Stephen cycling energy like that is irrelevant as you already worked out the energy is the same so it doesn’t matter.
PE or KE is irrelevant energy is energy if earth is retaining it is a problem because it can easily become temperature as you have already shown above.
The energy can’t hide that is why you make every group reconcile the full energy balance.
What happens at the moment yes like you are trying to do here you can slide the energy into somewhere you aren’t measuring your system is open … you have to close the system and everyone must close there system you enforce it .. no closure = no publish.
What then usual happens is several groups will pick certain frames of reference and others will do just small bits an tie back to these group positions rather than having to do a full balance themselves.
So yes you can change the energy from KE to PE but it matters not it will get accounted.
No more playing hide the heat or energy anymore 🙂
LdB says:
August 19, 2013 at 6:43 am
Richard I found a reasonable link for you I am not being smart just making sure you follow how it works.
http://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/Chapter3a.html
Chapter 3: The First Law of Thermodynamics for Closed Systems
>>>>>>>>>>>>>>>>>>>>
I need to learn how to quote. But anyways, energy = temp – work, if I am not mistaken so no energy and temp are not the same thing. Honest question, why would we consider the earth a closed system?
@LdB: You wrote,
But you are missing the point you are assuming a controlled enviroment and this is real world data you may be only getting consistancy based on a fallacy.
I think you’re misunderstanding the purpose of the experiment. I am not trying to use a linear model to predict trends in monthly anomalies. That would be futile: the r^2 value is 3%, which is ludicrous.
All I’m doing is to try to answer the question that Willis posed: Does an error in the monthly averages have an effect on secular trends?
The answer is, No.
Then you wrote, Lets extend the problem initially the shooters only shot on fine days because windy days makes there sights wobble so they avoid shooting on windy days. Later sights are improved and they shoot on windy days and sunny days suddenly your neat assumption goes to pieces.
Anthony’s own urban heat island argument is a classic in this sort of problem you need to understand the problem properly you can’t just assume you can average it away.
In other words, you suggest that improvements in thermometers and UHI are two potentially confounding variables that affect trends? I agree. And if I were trying to predict trends, your objection would need to be fully accounted for.
However, I cannot think of a reason for either of those variables to alter the answer to Willis’ question. Can you? If you can, then construct a multivariate experiment with all three variables, and show the effect when you control for each.
It will significantly advance the discussion if you can quantify your objections rather than arguing by analogy. As it stands, your shooter analogy does not match the state of the data very well. Instead of a marksman (tight variance on shots) we have a novice (only hits the target — anywhere! — about 68% of the time, corresponding to a temp variance of 2.86 deg C). Instead of a wind (random large variance), we have a kind of “target-gremlin” (small variance with a pattern repeating every twelve shots, corresponding to an error in monthly averages of 0.1 deg C). Arguments by analogy are potentially misleading or confusing; straight math would be better.
So for example, if you think my estimate of 0.1C is too small, tell me why.
(Sorry if this is a duplicate — WordPress is acting weirdly)
@LdB: You wrote,
But you are missing the point you are assuming a controlled enviroment and this is real world data you may be only getting consistancy based on a fallacy.
I think you’re misunderstanding the purpose of the experiment. I am not trying to use a linear model to predict trends in monthly anomalies. That would be futile: the r^2 value is 3%, which is ludicrous.
All I’m doing is to try to answer the question that Willis posed: Does an error in the monthly averages have an effect on secular trends?
The answer is, No.
Then you wrote, Lets extend the problem initially the shooters only shot on fine days because windy days makes there sights wobble so they avoid shooting on windy days. Later sights are improved and they shoot on windy days and sunny days suddenly your neat assumption goes to pieces.
Anthony’s own urban heat island argument is a classic in this sort of problem you need to understand the problem properly you can’t just assume you can average it away.
In other words, you suggest that improvements in thermometers and UHI are two potentially confounding variables that affect trends? I agree. And if I were trying to predict trends, your objection would need to be fully accounted for.
However, I cannot think of a reason for either of those variables to alter the answer to Willis’ question. Can you? If you can, then construct a multivariate experiment with all three variables, and show the effect when you control for each.
It will significantly advance the discussion if you can quantify your objections rather than arguing by analogy. As it stands, your shooter analogy does not match the state of the data very well. Instead of a marksman (tight variance on shots) we have a novice (only hits the target — anywhere! — about 68% of the time, corresponding to a temp variance of 2.86 deg C). Instead of a wind (random large variance), we have a kind of “target-gremlin” (small variance with a pattern repeating every twelve shots, corresponding to an error in monthly averages of 0.1 deg C). Arguments by analogy are potentially misleading or confusing; straight math would be better.
So for example, if you think my estimate of 0.1C is too small, tell me why.
You are wrong Man Berarpig, because you mix two notions, one is “Standard deviation” and the other is “Standard error of the mean”. The first one will not be smaller for the central state statistics than for the school. However, the standard error of the mean will decrease toward zero as the sample size increases. Standard deviation is a measure of the spread and Standard error of the mean is a measure of the accuracy of the mean in I finite sample size.
LdB:
At August 19, 2013 at 7:16
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394500
you write
NO! Not by a temperature measurement it won’t.
Since you failed to understand the point made by Stephen Wilde, I offer you another example.
Consider ice cubes melting in a glass of water. The temperature in the glass is 0 deg.C. Add heat and the temperature stays at 0 deg.C bust some of the ice melts. The heat in the glass has changed but the temperature has not.
Ice melts and freezes at places over the surface of the Earth, too.
This thread is about assessment of errors in determinations of global temperature.
It is NOT about heat.
And I now understand why you could not comprehend my statement
Your subsequent posts demonstrate that you don’t comprehend my statement because you need to buy a clue concerning the subject under discussion.
I offer you some kindly and sincere advice: remember the First Rule Of Holes and stop digging.
Richard
Joseph Murphy says:
August 19, 2013 at 7:17 am
I need to learn how to quote. But anyways, energy = temp – work, if I am not mistaken so no energy and temp are not the same thing. Honest question, why would we consider the earth a closed system
Sure so you just subtracting two things that are not the same and you got something else so an apple – orange = banana 🙂 They are all the same thing or you couldn’t do what you just did.
Put “change of” in front of energy in your equation and you are right and yes work is also energy 🙂
Earth isn’t closed however earths energy balance IS CLOSED BY DEFINITION
Earth’s Energy Balance extended definition:
Earth’s Energy balance describes how the incoming energy from the sun is used and returned to space. If incoming and outgoing energy are in balance, the earth’s temperature remains constant.
LdB:
I saee you have rejected my advice and have continued to ‘dig’ by posting your comment at August 19, 2013 at 7:49 am
http://wattsupwiththat.com/2013/08/17/monthly-averages-anomalies-and-uncertainties/#comment-1394521
which says
NO!
If incoming and outgoing energy are in balance, the earth’s EFFECTIVE RADIATIVE TEMPERATURE remains constant.
Unless, of course, you want to claim that either
(a) global temperature is the same in glacial and interglacial periods
or
(b) the Sun is a unique g-type star because it is variable.
LdB, you have added another meter to the depth of your hole.
Richard
@Richardscourtney says:
August 19, 2013 at 7:45 am
NO! Not by a temperature measurement it won’t.
Since you failed to understand the point made by Stephen Wilde, I offer you another example.
No you failed to understand my answer .. I understand what you think you are doing.
Temperature = energy … it is actually roughly the Kinetic energy of the molecules its a slight approximation but we can ignore for now.
PE = energy … as Stephen says.
You can argue whether PE is climate change or not that’s up to each groups view. So in Stephens example the excess energy is going into PE but at least we know that and account for it because he has to balance the full budget.
The likelyhood of that energy coming back out to haunt you the groups can argue about that but you aren’t arguing with “hiding energy” everything is out on the table.
You also get large amounts of energy disappear into chemical processes predominately photosynthesis by plants and that can come back to haunt you in the same way.
Now some groups may add those different energies into climate change some may not at least everyone has the same total energy and there is no missing energy.
Wherever you want to put the energy is up to each groups framework but anyone can easily follow what energy is where and that is how you start to build reference frames.
There is no way to separate out a natural climate signal from and anthropogenic signal because the two signals act exactly like each other. Natural climate is based on a statistical calculation from weather data, and so is an anthropogenic climate. They have the same up and down character and trends. You cannot filter one from the other and then say “this one” is anthropogenic and “that one” is natural. In human brains you cannot detect the auditory brainstem brainwave signal just by filtering through all the brainwave signals. You have to tickle the auditory nerve to fire on and off at regular intervals in order to then filter it out of background brainwaves. Same is true of weather pattern variations. You cannot simply take a stream of weather data and filter out such a tiny component unless you can cause some component of weather to fire at regular intervals. We would have to set up a large CO2 pump that we fire up at regular intervals into the background noise of weather (and do it thousands of times), and then remove the pumped in CO2 just as rapidly, to see if there is a tiny regular signal buried in the background.
But who cares. We haven’t thoroughly studied the weather signal and its weather pattern variations yet. HUGE assumptions are still made about weather pattern variations (erroneously referred to as “noise”). Which is why I propose several different ways of averaging, combining, and graphing the temperature data, aka weather pattern variations. A global number is such a low hanging fruit statistic for such a complicated thing. The data and graphs we have for ocean and atmospheric oscillations are WAY ahead in that department.