Guest essay by Clyde Spencer 2017
Introduction
I recently had a guest editorial published here on the topic of data error and precision. If you missed it, I suggest that you read it before continuing with this article. This will then make more sense. And, I won’t feel the need to go back over the fundamentals. What follows is, in part, prompted by some of the comments to the original article. This is a discussion of how the reported, average global temperatures should be interpreted.
Averages
Averages can serve several purposes. A common one is to increase accuracy and precision of the determination of some fixed property, such as a physical dimension. This is accomplished by confining all the random error to the process of measurement. Under appropriate circumstances, such as determining the diameter of a ball bearing with a micrometer, multiple readings can provide a more precise average diameter. This is because the random errors in reading the micrometer will cancel out and the precision is provided by the Standard Error of the Mean, which is inversely related to the square root of the number of measurements.
Another common purpose is to characterize a variable property by making multiple representative measurements and describing the frequency distribution of the measurements. This can be done graphically, or summarized with statistical parameters such as the mean, standard deviation (SD) and skewness/kurtosis (if appropriate). However, since the measured property is varying, it becomes problematic to separate measurement error from the property variability. Thus, we learn more about how the property varies than we do about the central value of the distribution. Yet, climatologists focus on the arithmetic means, and the anomalies calculated from them. Averages can obscure information, both unintentionally and intentionally.
With the above in mind, we need to examine whether taking numerous measurements of the temperatures of land, sea, and air can provide us with a precise value for the ‘temperature’ of Earth.
Earth’s ‘Temperature’
By convention, climate is usually defined as the average of meteorological parameters over a period of 30 years. How can we use the available temperature data, intended for weather monitoring and forecasting, to characterize climate? The approach currently used is to calculate the arithmetic mean for an arbitrary base period, and subtract modern temperatures (either individual temperatures or averages) to determine what is called an anomaly. However, just what does it mean to collect all the temperature data and calculate the mean?
If Earth were in thermodynamic equilibrium, it would have one temperature, which would be relatively easy to measure. Earth does not have one temperature, it has an infinitude of temperatures. In fact, temperatures vary continuously laterally, vertically, and with time, giving rise to an indefinite number of temperatures. The apparent record low temperature is -135.8° F and the highest recorded temperature is 159.3° F, for a maximum range of 295.1° F, giving an estimated standard deviation of about 74° F, using the Empirical Rule. Changes of less than a year are both random and seasonal; longer time series contain periodic changes. The question is whether sampling a few thousand locations, over a period of years, can provide us with an average that has defensible value in demonstrating a small rate of change?
One of the problems is that water temperatures tend to be stratified. Water surface-temperatures tend to be warmest, with temperatures declining with depth. Often, there is an abrupt change in temperature called a thermocline; alternatively, upwelling can bring cold water to the surface, particularly along coasts. Therefore, the location and depth of sampling is critical in determining so-called Sea Surface Temperatures (SST). Something else to consider is that because water has a specific heat that is 2 to 5 times higher than common solids, and more than 4 times that of air, it warms more slowly than land! It isn’t appropriate to average SSTs with air temperatures over land. It is a classic case of comparing apples and oranges! If one wants to detect trends in changing temperatures, they may be more obvious over land than in the oceans, although water-temperature changes will tend to suppress random fluctuations. It is probably best to plot SSTs with a scale 4-times that of land air-temperatures, and graphically display both at the same time for comparison.
Land air-temperatures have a similar problem in that there are often temperature inversions. What that means is that it is colder near the surface than it is higher up. This is the opposite of what the lapse rate predicts, namely that temperatures decline with elevation in the troposphere. But, that provides us with another problem. Temperatures are recorded over an elevation range from below sea level (Death Valley) to over 10,000 feet in elevation. Unlike the Universal Gas Law that defines the properties of a gas at a standard temperature and pressure, all the weather temperature-measurements are averaged together to define an arithmetic mean global-temperature without concern for standard pressures. This is important because the Universal Gas Law predicts that the temperature of a parcel of air will decrease with decreasing pressure, and this gives rise to the lapse rate.
Historical records (pre-20th Century) are particularly problematic because temperatures typically were only read to the nearest 1 degree Fahrenheit, by volunteers who were not professional meteorologists. In addition, the state of the technology of temperature measurements was not mature, particularly with respect to standardizing thermometers.
Climatologists have attempted to circumscribe the above confounding factors by rationalizing that accuracy, and therefore precision, can be improved by averaging. Basically, they take 30-year averages of annual averages of monthly averages, thus smoothing the data and losing information! Indeed, the Law of Large Numbers predicts that the accuracy of sampled measurements can be improved (If systematic biases are not present!) particularly for probabilistic events such as the outcomes of coin tosses. However, if the annual averages are derived from the monthly averages, instead of the daily averages, then the months should be weighted according to the number of days in the month. It isn’t clear that this is being done. However, even daily averages will suppress (smooth) extreme high and low temperatures and reduce the apparent standard deviation.
However, even temporarily ignoring the problems that I have raised above, there is a fundamental problem with attempting to increase the precision and accuracy of air-temperatures over the surface of the Earth. Unlike the ball bearing with essentially a single diameter (with minimal eccentricity), the temperature at any point on the surface of the Earth is changing all the time. There is no unique temperature for any place or any time. And, one only has one opportunity to measure that ephemeral temperature. One cannot make multiple measurements to increase the precision of a particular surface air-temperature measurement!
Temperature Measurements
Caves are well known for having stable temperatures. Many vary by less than ±0.5° F annually. It is generally assumed that the cave temperatures reflect an average annual surface temperature for their locality. While the situation is a little more complex than that, it is a good first-order approximation. [Incidentally, there is an interesting article by Perrier et al. (2005) about some very early work done in France on underground temperatures.] For the sake of illustration, let’s assume that a researcher has a need to determine the temperature of a cave during a particular season, say at a time that bats are hibernating. The researcher wants to determine it with greater precision than the thermometer they have carried through the passages is capable of. Let’s stipulate that the thermometer has been calibrated in the lab and is capable of being read to the nearest 0.1° F. This situation is a reasonably good candidate for using multiple readings to increase precision because over a period of two or three months there should be little change in the temperature and there is high likelihood that the readings will have a normal distribution. The known annual range suggests that the standard deviation should be less than (50.5 – 49.5)/4, or about 0.3° F. Therefore, the expected standard deviation for the annual temperature change is of the same order of magnitude as the resolution of the thermometer. Let’s further assume that, every day when the site is visited, the first and last thing the researcher does is to take the temperature. After accumulating 100 temperature readings, the mean, standard deviation, and standard error of the mean are calculated. Assuming no outlier readings and that all the readings are within a few tenths of the mean, the researcher is confident that they are justified in reporting the mean with one more significant figure than the thermometer was capable of capturing directly.
Now, let’s contrast this with what the common practice in climatology is. Climatologists use meteorological temperatures that may have been read by individuals with less invested in diligent observations than the bat researcher probably has. Or temperatures, such as those from the automated ASOS, may be rounded to the nearest degree Fahrenheit, and conflated with temperatures actually read to the nearest 0.1° F. (At the very least, the samples should be weighted inversely to their precision.) Additionally, because the data suffer averaging (smoothing) before the 30-year baseline-average is calculated, the data distribution appears less skewed and more normal, and the calculated standard deviation is smaller than what would be obtained if the raw data were used. It isn’t just the mean temperature that changes annually. The standard deviation and skewness (kurtosis) is certainly changing also, but this isn’t being reported. Are the changes in SD and skewness random, or is there a trend? If there is a trend, what is causing it? What, is anything, does it mean? There is information that isn’t being examined and reported that might provide insight on the system dynamics.
Immediately, the known high and low temperature records (see above) suggest that the annual collection of data might have a range as high as 300° F, although something closer to 250° F is more likely. Using the Empirical Rule to estimate the standard deviation, a value of over 70° F would be predicted for the SD. Being more conservative, and appealing to Tschbycheff’s Theorem and dividing by 8 instead of 4, still gives an estimate of over 31° F. Additionally, there is good reason to believe that the frequency distribution of the temperatures is skewed, with a long tail on the cold side. The core of this argument is that it is obvious that temperatures colder than 50° F below zero are more common than temperatures over 150° F, while the reported mean is near 50° F for global land temperatures.
The following shows what I think the typical annual raw data should look like plotted as a frequency distribution, taking into account the known range, the estimated SD, and the published mean:
The thick, red line represents a typical year’s temperatures, and the little stubby green line (approximately to scale) represents the cave temperature scenario above. I’m confident that the cave-temperature mean is precise to about 1/100th of a degree Fahrenheit, but despite the huge number of measurements of Earth temperatures, the shape and spread of the global data does not instill the same confidence in me for global temperatures! It is obvious that the distribution has a much larger standard deviation than the cave-temperature scenario and the rationalization of dividing by the square-root of the number of samples cannot be justified to remove random-error when the parameter being measured is never twice the same value. The multiple averaging steps in handling the data reduces extreme values and the standard deviation. The question is, “Is the claimed precision an artifact of smoothing, or does the process of smoothing provide a more precise value?” I don’t know the answer to that. However, it is certainly something that those who maintain the temperature databases should be prepared to answer and justify!
Summary
The theory of Anthropogenic Global Warming predicts that the strongest effects should be observed during nighttime and wintertime lows. That is, the cold-tail on the frequency distribution curve should become truncated and the distribution should become more symmetrical. That will increase the calculated global mean temperature even if the high or mid-range temperatures don’t change. The forecasts of future catastrophic heat waves are based on the unstated assumption that as the global mean increases, the entire frequency distribution curve will shift to higher temperatures. That is not a warranted assumption because the difference between the diurnal highs and lows has not been constant during the 20th Century. They are not moving in step, probably because there are different factors influencing the high and low temperatures. In fact, some of the lowest low-temperatures have been recorded in modern times! In any event, a global mean temperature is not a good metric for what is happening to global temperatures. We should be looking at the trends in diurnal highs and lows for all the climatic zones defined by physical geographers. We should also be analyzing the shape of the frequency distribution curves for different time periods. Trying to characterize the behavior of Earth’s ‘climate’ with a single number is not good science, whether one believes in science or not!
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Thank you Clyde Spencer for this important post.
Temperature and its measurement is fundamental to science and deserves far more attention than it gets.
I disagree with Nick Stokes and assert that average temperature is almost always wrong. I will explain in part what is right.
If I open the door of my wood stove, and a hot coal with temperature roughly 1000F falls on the floor, does that mean the average temperature of my room is now (68 + 1000)/2 = 534 F ? How ridiculous, you say. However, I can calculate the temperature that might result if the coal looses its heat to the room from (total heat)/(total heat capacity) Since the mass of air is many times that of the coal, the temperature will change only by fractions of a degree.
A property that can be averaged and converted to an effective temperature for air is the moist enthalpy. When properly weighted by density it can usefully be averaged then converted back to a temperature.
More relevant for analysis of CO2 impact is to use the total energy which includes kinetic and potential energies, converted to an equivalent temperature This latter measure is the one which might demonstrate some impact of CO2 induced change in temperature gradients , and should be immune to effects of inter conversion of energies to internal, convection, and moisture content.
With all the billions of dollars spent on computers and measurements it is ridiculous to assert that we cannot
calculate global average energy content equivalent temperature.
A discussion which contains other references to Pielke and Massen is:
https://aea26.wordpress.com/2017/02/23/atmospheric-energy/
That would inevitably lead to the end of this scam, however.
You make a good argument against using average temperatures, or average anomalies, as a stand-in for global average energy content. However, we’re currently dealing with a shell game and not Texas hold’em, so we first have to concentrate on showing how this game is fixed.
“We should be looking at the trends in diurnal highs and lows for all the climatic zones defined by physical geographers.”
There is research that follows this direction, using the generally accepted Köppen zones as a basis to measure whether zonal boundaries are changing due to shifts in temperature and precipitation patterns.
The researchers concluded:
“The table and images show that most places have had at least one entire year with temperatures and/or precipitation atypical for that climate. It is much more unusual for abnormal weather to persist for ten years running. At 30-years and more the zones are quite stable, such that is there is little movement at the boundaries with neighboring zones.”
https://rclutz.wordpress.com/2016/05/17/data-vs-models-4-climates-changing/
I think is thread amply demonstrates how poorly people, some people at least, understand statistics, measurements, and how they both relate to science. In their defense, it’s not a simple subject.
Statistics are a way to analyze large amounts of data. What’s being demonstrated here is not how poorly some people understand the subject, but how differences of opinion in the appropriate application of statistical tools will result in vastly different results.
Thomas,
Would you care to clarify your cryptic statement? Are you criticizing me, or some of the posters, or both?
The other point is that CO2 is a constant for any short period of time. CO2 is 400 ppm no matter the latitude, longitude and/or altitude. The temperature isn’t what needs to be measured, the impact of CO2 on temperature. Gathering mountainous amounts of corrupted data doesn’t answer that question. We shouldn’t be gathering more data, we should be gathering the right data. Gathering data that requires “adjustments” is a complete waste of time and money, and greatly reduces the validity of the conclusion. If we want to explore the impact of CO2 on Temperature collect data from areas that measure that relationship and don’t need “adjustments.” Antarctica and the oceans don’t suffer from the urban heat island effect. Antarctica and the oceans cover every latitude on earth. CO2 is 400 ppm over the oceans and Antarctica. Collecting all this corrupted data opens the door for corrupt bureaucrats to adjust the data in a manner that favors their desired position. Collecting more data isn’t beneficial is the data isn’t applicable to the hypothesis. The urban heat island isn’t applicable to CO2 caused warming. Don’t collect that data.
the difference between the diurnal highs and lows has not been constant during the 20th Century.
B I N G O !
The average of 49 and 51 is 50 and the average of 1 and 99 is 50.
And if you pay attention to the Max and Min temperatures some interesting things drop out of the data.
I’ve spammed this blog too many times with this US Map but it illustrates the point.
This is a really cool map, and contains some clues as to to how to duplicate this result – but could you give a few more clues? This is great information, and combined with the info in the main article regarding how minimums have been going up, it really closes the link about how temperatures have been rising without having been exposed to higher daytime temperatures. This was a great response!
Haven’t been able to replicate that map. Can someone help me?
I read your referenced article, and I have to disagree with your logic on the point of location uncertainty. You say “You measured in sampled locations – what if the sample changed?” However, in your example, you are not “changing the sample” — you are changing a sample of the sample. Your example compares that subset of data with the results from the full set of data, to “prove” your argument. In the real world you don’t have the “full set” of data of the Earth’s temperature; the data you have IS the full set, and I think applying any more statistical analyses to that data is unwarranted, and the results unprovable — without having a much larger data set with which to compare them.
In a response to another post, you stated that the author provided no authority for his argument. I see no authority for your argument, other than your own assertion it is so. In point of fact, it seems that most of the argument for using these particular adjustments in climate science is that the practitioners want to use them because they like the results they get. You like using anomalies because the SD is smaller. But where’s your evidence that this matches reality?
The Law of Large Numbers (which I presume is the authority under which this anomaly averaging scheme is justified) is completely about multiple measurements and multiple samples. But the point of the exercise is to decrease the variance — it does nothing to increase the accuracy. One can use 1000 samples to reduce the variance to +/- 0.005 C, but the statement of the mean itself does not get more accurate. One can’t take 999 samples (I hate using factors of ten because the decimal point just ends up getting moved around; nines make for more interesting significant digits) of temperatures measured to 0.1 C and say the mean is 14.56 +/- 0.005C. The statement of the mean has to keep the significant digits of its measurement — in this case, 14.6 — with zeros added to pad out to the variance: 14.60 +/- 0.005. That is why expressing anomalies to three decimal points is invalid.
Measuring Jello® cubes multiple times with multiple rubber yard sticks won’t get you 3 place accuracy.
No, but the cleanup might be tasty and nutritious.
“However, in your example, you are not “changing the sample” — you are changing a sample of the sample.”
Yes. We have to work with the record we have. From that you can get an estimate of the pattern of spatial variability, and make inferences about what would happen elsewhere. It’s somewhat analogous to bootstrapping. You can use part of he sample to make that inference, and test it on the remainder.
None of this is peculiar to climate science. In all of science, you have to infer from finite samples; it’s usually all we have. You make inferences about what you can’t see.
Two problems that I can see with that approach. First, bootstrapping works where a set of observations can be assumed to be from an independent and identically distributed population. I don’t think this can be said about global temperature data.
Secondly, the method works by treating inference of the true probability distribution, given the original data, as being analogous to inference of the empirical distribution of the sample.
However, if you don’t know how your original sample set represents your actual population, no amount of bootstrapping is going to improve the skewed sample to look more like the true population.
If the sample is from temperate regions, heavy on US and Europe, all bootstrapping is going to give one is a heavy dose of temperate regions/US/Europe. It seems pretty obvious that the presumption of bootstrapping is that the sample at least has the same distribution as the population — something that certainly can NOT be presumed about the global temperature record.
Clyde, I like your ball bearing analogy. Perhaps you could expand on later in the series.
1) Yes we know that when one micrometer is used to measure one ball bearing (293 mm in diameter), multiple measurements help reduce micrometer measurement errors.
2) Yes we know that when we measure many near identical ball bearings (293 mm in diameter) with one micrometer, the more ball bearings we measure the more accurate the average reading will be.
3) Climate: we measure random ball bearings, whose diameter varies between 250 mm up to 343 mm, and we use 100 micrometers.
4) If we measure 100 of the ball bearings chosen at random twice per day, how does averaging the measured random ball bearing measurement increase the measurements accuracy?
5) Replace mm with K and you get the global average temperature problem.
6) Stats gives us many ways to judge a sample size but if the total population for this temperature measurement is 510,000,000 square kilometers, and each temperature sample represented the temperature of one square kilometer, how many thermometers do we need?
My concern is that average temperatures are then averaged again, sometimes many times before a global average is obtained.
First you have min and max then you average them. Then you have daily figures and you average them then there is the area weighting (Kriging) etc etc.
OK you can do the math(s) but when you average an average you do not necessarily end up with a meaningful average.
Consider two (cricket) batsmen. A batting average is number of runs divided by number of times bowled out. In the first match, batsman A gets more runs than batsman B and both are bowled out. “A” has the higher average. A maintains that higher average all season and in the final match both batsmen are bowled out but A gets more runs than B. Who has the higher average over the season?
The answer is, You can’t tell.
For instance. A gets 51 runs in match 1 and B gets 50 runs. A was injured and only plays again in the last match. B gets 50 runs and is out in every one of the other 19 matches apart from the last one. So A’s average all year was 51 while B’s was 50. In the last match A gets 2 runs and B gets 1.
Average of averages for A gives (51 + 2)/2 = 26.5
Average of averages for B gives (50 + 1)/2 = 25.5
True average for A is 26.5
True average for B is (20*50 + 1)/21 = 47.666..
i>”True average for A is 26.5
True average for B… ”
Obviously, you can tell. You just have to weight it properly. This is elementary.
Thanks Nick, I know how to do it. My concern is that with all the processing that the temperature data is subjected to, I would find it hard to believe that they apply all the necessary weightings – even if they calculate them.
For instance, taking the average of min and max temperatures by summing and dividing by two is already not the best system. An electrical engineer would not quote an average voltage that way.
Shouldn’t you also weight the readings by the local specific heat value? For example by taking into account local humidity? Basically, you need to perform an energy calculation not a temperature one.
Is it known how much area a temperature value represents? If not, where do the weightings come from?
It would be interesting to know just how much the global average surface temperature could be varied just by changing the averaging procedures.
“Is it known how much area a temperature value represents? If not, where do the weightings come from?
It would be interesting to know just how much the global average surface temperature could be varied just by changing the averaging procedures.”
The first is a matter of numerical integration – geometry. I spend a lot of time trying to work it out. But yes, it can be worked out. On the second, here is a post doing that comparison for four different methods. Good ones agree well.
It is change in the earth’s energy content that is important — energy flow into and out of the earth system. This seems like a job for satellites rather than a randomly distributed network of thermometers in white boxes and floats bobbing in the oceans.
You have no future as a government paid political hac…I mean climate scientist.
That much is clear.
What is global average temperature anyway? How is it defined and how is it measured? As a metrologist and statistician, if you asked me to propose a process of measuring the average global temperature, my first reaction would be I need a lot more definition of what you mean. When dealing with the quite well defined discipline of Measurement Uncertainty analysis, the very first concern that leads to high uncertainty is “Incomplete definition of the measurand”. Here’s the list of factors that lead to uncertainty identified in the “ISO Guide to the Expression of Uncertainty in Measurement” (GUM).
• Incomplete definition of measurand.
• Imperfect realization of the definition of the measurand.
• Non-representative sampling – the sample measured may not represent the defined measurand.
• Inadequate knowledge of the effects of environmental conditions on the measurement or imperfect measurement of the environmental conditions.
• Personal bias in reading analogue instruments.
• Finite instrument resolution or discrimination threshold.
• Inexact values of measurement standards and reference materials.
• Approximations and assumptions incorporated into the measurement method and procedure.
• Variations in repeated observations of the measurand under apparently identical conditions.
• Inexact values of constants and other parameters obtained from external sources and used in the data-reduction algorithm.
As far as I can tell there is no such thing as a complete “definition of the measurand” (global average temperature). It seems that every researcher in this area defines it as the mean of the data that is selected for their analysis. Then most avoid the issue of properly analyzing and clearly stating the measurement uncertainty of their results.
This is, IMHO, bad measurement practice and poor science. One should start with a clear definition of the measurand and the design a system – including instrumentation, adequate sampling, measurement frequency, data collection, data reduction, etc. – such that the resulting MU will be below the level needed to produce a useful result. Trying to use data from observations not adequate for the purpose is trying to make a silk purse out of a sow’s ear.
Here, Here! I have said the same thing, just not as detailed as you. What is global temperature? Does comparing annual figures, as computed now, say more about weather phenomena in a particular region than the actual temperature of the earth as a whole? I bet almost none of the authors of climate papers can adequately address the issues brought up here. Precision to 0.001 or even 0.01 when using averages of averages of averages is a joke.
Having spent an entire 40 yr career in the laboratory measuring temperatures of all kinds of things in many different situations, I can say that over a range of – 40 to + 40 C, it is extremely difficult to achieve uncertainties of less than +/- 0.2 C. I can’t buy the claim that global average temperature can be determined within anything close to even +/- 1 C.
Rick C PE and Jim Gorman. It’s a pleasure to read your opinions on this topic.
Rick,
I agree completely with your advice. However, the problem is that in order for the alarmists to make the claim that it is warming, and doing so anomalously, they have to reference today’s temperatures to what is historically available. There is no way that the historical measurements can be transmogrified to agree with your recommended definition. We are captives of our past. Again, all I’m asking for is that climatologists recognize the limitations of their data and be honest in the presentation of what can be concluded.
Clyde: Yes, obviously we are stuck with historical records not fit for the purpose. I’m not opposed to trying to use this information to try to determine what trend may exist. I just don’t think it should be presented without acknowledgement of the substantial uncertainties that make reliance on this data to support a hypothesis highly questionable.
Rick,
You said, “I just don’t think it should be presented without acknowledgement of the substantial uncertainties that make reliance on this data to support a hypothesis highly questionable.”
And that is the point of this and the previous article!
IPCC AR5 glossary defines “surface” as 1.5 m above the ground, not the ground itself.
If the earth/atmosphere are NOT in thermodynamic equilibrium then S-B BB, Kirchhoff, upwelling/downwelling/”back” radiation go straight in the dumpster.
Nicholas,
We obviously can’t treat the entire globe as being in equilibrium. However, we might be able to treat patches of the surface as being in equilibrium for specified periods of time and integrate all the patches over time and area. Whether that is computationally feasible or not, I don’t know. However, I suspect it is beyond our capabilities.
Exactly agree with all (most, will confess I’ve not read every little bit) of the above.
There are soooo many holes in this thing, not least
1. Temperature is not climate
2. Temperature per-se does not cause weather (averaged to make Climate somehow – I ain’t holding any breath) Temperature difference causes weather
This entire climate thing is just crazy.
This artical completely focuses on data problems with current temperature measurements. It never ties back to CO2s impact on temperature. 1) the urban heat island is an exogenous factor that requires “abjustments,” and that is just one exogenous factor. 2) CO2 is a constant 400 ppm, constants can’t explain variations 3) CO2 doesn’t warm water 4) CO2’s only way to affect climate change is through absorbing 13 to 18 microns, and its impact is largely saturated 5) CO2 can’t cause record high daytime temperatures, CO2 only traps outgoing non-visible light. Climate science is a science, only data collected that helps isolate the impact of CO2 on temperature is relevant. The law of large numbers doesn’t apply when applied to corrupt data. Only data that isolates the impact of CO2 on temperature should be used. All this other stuff is academic. Focus on the science, and how a good experiment would be run. If I was doing an experiment I wouldn’t be collecting data that needs to be adjusted. The issue isn’t if we are warming, the issue is does CO2 cause warming. Global temperatures won’t prove that, it doesn’t isolate the cause of CO2.
Often, taking things to an extreme helps illustrate a point. If we had a temperature measuring device near Moscow, and another near Rio de Janeiro, both with zero measurement errors, and without urban heat effects, with readings taken hourly for 100 years, we could then average all these numbers and come up with a number. Exactly what would that average mean? Absolutely nothing, it is simply a number with no actual meaning. Throwing more such stations into the mix doesn’t change that. It is still a meaningless number.
Oh, did I forget to mention that the measurement stations are at different altitudes? And different hemispheres?
We could fix that with sea level thermometers, one on the US west coast, and another on the east coast. Same as above, average the readings, and what do you have? Let’s see, one is measuring the temperature of air from over thousands of miles of ocean, and the other thousands of miles of land. Exactly what would this average mean, then? The point is that these averages are meaningless to start with, and throwing more stations in does not add value, regardless of measurement errors. You do not get a ‘better’ average.
If climate science was applied to your automobile, and an average temperature of it was contrived, what would knowing that average temp be worth?
Andrew
Cannot read article because of page moving to share this.
I am a pit bull latching to political fake news about global warming and delighted to have found your site, However my I am neither a scientist or mathematician. Is it reasonable to ask you to “translate” important points to lay language? I would like to pass some of your points on to others in language they will understand, as will I if challenged. Thanks for sanity.
[Of course, pull in and ask away. There are many individuals here who know a great deal about a great deal and are always happy to pass their knowledge along to a genuine questioner. Just be polite and clear about what you are looking for, nobody likes ambiguity. . . . mod]
John there is much stuff you can use, written for laymen, in my ebook Blowing Smoke. All illustrated. Nothing as technical as this guest post.
John,
You will note that there are no mathematical formulas, much to the chagrin of some regulars such as Windchasers. Some WUWT articles range from just whining about alarmists, to others, say by Monckton, that have mathematical formulas and are fairly rigorous. It seems that there are a lot of retired engineers and scientists that frequent this blog. Therefore, I tried to strike a balance between trying to have my ideas accepted by those with technical backgrounds without losing intelligent layman. Sort of a Scientific American for bloggers. 🙂 If you have any specific questions, I’ll try to respond over the next couple of days.
Displaying temperature distributions should be graphic. Once upon a time, such as when I was in college, that was involved and expensive to print. Graphing software is cheap and available, and a graph will show any skewness of the distribution, and if trying to use Gaussian statistical tests is reasonable.
I think trying to use as much of the data as possible is a good thing,
What is the standard deviation of the absorption of IR by CO2? Temperatures have a huge variation, the physics of CO2’s absorption doesn’t. CO2 at best can explain a parallel shift in temperatures, it can’t explain the huge variation.once again, tie everything back to how can CO2 explain the observation. CO2 doesn’t cause the urban heat island effect, CO2 doesn’t cause record daytime temperatures, CO2 doesn’t warm water, etc etc. Stay focused on the hypothesis. Evidence of warming isn’t evidence CO2 is causing it.
Forget about how to represent “…reported. average temperatures.” There is no average. Forget about data error and precision, they don’t belong. Global temperature is not a random quantity and cannot be understood by statistics meant for analyzing random data. Now plot the entire temperature curve from 1850 to 2017 on a graph. Use a data set that has not been edited to make it conform to global warming doctrine. HadCRUT3 would fit the bill. On the same graph, also plot the Keeling curve of global carbon dioxide and its ice core extension. Now sit back and contemplate all this. What do you see? The first thing you should notice is that the two curves are very different. The Keeling curve is smooth, no ups or downs. But the temperature curve is irregular, It has its ups and downs and is jagged. Two peaks on the temperature curve especially stand out. The first one is at year 1879, the second one at year 1940. Warmists keep telling us that global temperature keeps going up because of the greenhouse effect of carbon dioxide. Take a close look at the part of the Keeling curve directly opposite these two temperature peaks. Where is that greenhouse effect? There is no sign that the Keeling curve had anything to do with these two global warm peaks. Problem is that from 1879 to 1910 temperature actually goes down, not up, completely contrary to global warming doctrine. That distance is just over 30 years, the magic number that turns weather into climate. There is a corresponding warm spell from 1910 to 1940 that also qualifies as climate, warm climate in fact. But this is not the end. 1940 is a high temperature point and another cooling spell begins with it. That coolth is from the cold spell that ushered in World War II. It stayed cool until 1950, at which point a new warming set in. Global temperature by then was so low that it took it until 1980 to reach the same temperature level that existed in 1940. f And in 1980 a hiatus began that lasted for 18 years. The powers that control temperature at IPCC decided, however, to change that stretch into global warming instead. That is a scientific fraud but they apparently don’t care because they control what is published. By my calculation this act adds 0.06 degrees Celsius to every ten year stretch of temperature from that point on to the present. I cannot see how statistics can have any use for interpreting such data. I have laid out the data. What we need is for someone to throw out the temperature pirates who spread misinformation about the real state of global temperature.
Do you have a reference for this?
Knowing that the multi-decadal oscillations (e.g. the PDO) are on the order of 65-80 years, anyone with a modicum of signal processing experience would understand how stupid it is to look at something over a mere 30 years. You need at least double the cycle length, or about 140 years, and with the amount of error in the measurements and the number of overlapping cycles you need hundreds of years of data to make a call on anything.
The widest confidence interval metric (i.e. least confidence) one could come up with for any time series data is the trend of the data. It just doesn’t get worse than that. That’s not signal processing 101, but it’s definitely 501 (early grad school). There’s just very little useful information for the lowest frequency portion of a time series.
reference: http://paos.colorado.edu/research/wavelets/bams_79_01_0061.pdf
Peter
Peter,
NOAA, NASA, and other organizations use 30-year averages for their baselines, although they use different 30-year intervals. Go to their websites.
Jim Gorman
April 23, 2017 at 6:44 am
NS: “None of this means much unless you come to terms with the fact that they are averaging anomalies. Fluctuations about a mean are much more likely to be approx normal than the quantities themselves.”
”If that is the case, why all the adjustments to past temperature readings? The absolute values of the anomalies shouldn’t change if you are right.”
According to a February 9, 2015 Climate Etc. blog titled Berkeley Earth: raw versus adjusted temperature data, “The impact of adjustments on the global record are scientifically inconsequential.”
Adjustments to the data are one of the most frequent criticisms. Is there anything in the above post or comments that justifies data adjustments?
“Is there anything in the above post or comments that justifies data adjustments?”
No, nor should there be. It is a separate issue. You average temperature anomalies that are representative of regions. Sometimes the readings that you would like to use have some characteristic that makes you doubt that they are representative. So other data for that region is used. Arithmetically, that is most simply done as an adjustment.
The adjustments done makes very little difference to the global average.
Clyde Spencer ==> Well done on this…..the whole idea of LOTI temps (Land and Ocean) is absurd — I have been calling it The Fruit Salad Metric. (apples and oranges and bananas) .
Any number created by averaging averages, of spatially and temporally diverse measurements, creates an informational abomination – not a “more precise or accurate figure”. This is High School science and does not require any fancy statistical knowledge at all — my High School science teacher was able explain this clearly to a class of 16-year-olds suffering from hormone-induced insanity in twenty minutes with a couple of everyday examples. How today’s Climate Scientists can fool themselves into believing otherwise is a source of mystery and concern to me.
Clyde Spencer ==> My piece on Alaska is a good example of averages obscuring information.
Kip,
When I was in the army, I was assigned to the Cold Regions Research and Engineering Laboratory in 1966. It didn’t snow in Vermont, where I was living, until Christmas Eve. We got 18″ overnight! The next year, we got snow in mid-October during deer hunting season.
Clyde Spencer ==> And the same sort of variability exists at all scales, within the envelope of the boundaries of the weather/climate system. I have an essay in progress on the averaging issue — mathematically. (Been in progress for more than a year…:-)
Kip,
I look forward to reading your essay.
Clyde Spencer ==> Somewhere above you mention Occam’s razor….”Occam’s Razor dictates that we should adopt the simplest explanation possible for the apparent increase in world temperatures. ”
I’m pretty sure that you know that although that is the “popular science” version of Occam’s, it is not actually what he said nor what the concept really is.
Newton phrased it “”We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.””
The misapplication of Occam’s results in such things as the false belief that increasing CO2 concentrations alone explain changing climate justified by Occam’s as “simplest explanation”.
Kip,
Yes, I’m aware that the original statement in archaic English was a lot more convoluted. But, I think that the “popular” form captures the essence of the advice. What we are dealing with is a failure to define “simplest.” I would say that if Earth were experiencing warming after the last glaciation, and then started to cool, we should look for an explanation. However, continued warming is most easily explained by ‘business as usual.’
However, the real crux of the problem is not knowing what typical climate variation is like, and averaging averages further hides that information. We don’t know what was changing climate before humans, so we aren’t in a strong position to state to what degree we are impacting it today.
Plus many!
Clyde ==> Occam’s calls for the fewest unsupported (not in evidence) prior assumptions.
Postulating that wind is caused by “Pegasus horses chasing Leprechauns who are in rebellion against the Fairy Queen” has too many unsupported priors.
The CO2 hypothesis fails Occam’s test because it relies on the unsupported, not in evidence (in fact, there is a great deal of contrary evidence) assumption that nothing else causes (or caused) the warming and cooling of the past and that the present is unique and that CO2 is the primary mover of climate. The number of assumptions — assumptions of absence of effect, past causes not present cause, etc — necessary to make the CO2 hypothesis “sufficient” is nearly uncountable. While it seems “simple”, it requires a huge number of unstated assumptions — and it is the necessity of those assumptions that result in the CO2 hypothesis’ failure to meet the requirements of Occam’s.
CO2 may yet be found to be one of the true causes of recent warming, none the less, but not in such a simplistic formulation as is currently promoted by the Consensus.
I think we are both in the same general page on this topic.
Yes, I think we are. I will go where the believable evidence leads me.
A discussion of random error vs. systematic error would be good too. Any measure prior to the advent of digital thermometers is sure to have random error.
Andrew,
Did you go to this link: https://wattsupwiththat.com/2017/04/12/are-claimed-global-record-temperatures-valid/