UAH Global Temperature Update for August 2020: +0.43 deg. C

Tim and Clyde,
What we are getting to with this discussion is the question, “ Is there such a thing as a global average temperature?”
The answer is “Yes,” but it is difficult to assess and its usefulness is not established.
Public discussions of ‘global average temperature’ or ‘global average sea level’ throw up averages that are difficult to assess and have no physical existence, but represent convenient statistics that are generated from many separate pieces of data gathered from disparate places.
Nevertheless a global average temperature can obviously be calculated using the results from many individual weather stations.
Some scientists argue that such a number is no more meaningful than is a global average telephone number.
The fact that you can calculate such numbers does not confer, per se, any deep meaning or usefulness on them.
More importantly, while changes in regional temperature contribute towards changes in global average temperature, a change in global average temperature tells us nothing about the regional patterns that have led to the changed average.
This is important in considering the potential impact of changing global average temperature on regional climate.

In order to claim 95% confidence intervals requires that the probability distributions be known. Simply multiplying sigma times two does not produce 95% confidence.

Your table reports temperatures (and uncertainties) to 1 milliCelsius for measurements made in the nineteenth century, total nonsense. It is hard to resolve even 1 Celsius with a mercury thermometer.

Calculating the standard deviations of various model outputs is nonsense, this is like calculating standard deviations of moth wings and orange peel ripples—they are not multiple measurements of the same quantity. They don’t even qualify as measurements.

Javier,

You are confusing error and uncertainty. Error can have a probability distribution from which a confidence interval can be calculated.

An uncertainty interval has no probability distribution, especially when you are taking multiple measurements of different things. Uncertainty is not a random variable.

Look at what you posted: “bias uncertainty” “error covariance matrices” “measurement and sampling and bias uncertainties.”

None of these are “uncertainties” and using the word uncertainty doesn’t make them so. These are *errors*, not uncertainty. You don’t mention anywhere what the uncertainty is for each individual measurement. If you can’t do that then you are lost. You can’t calculate an uncertainty interval by analyzing what you think is a normal random variable because uncertainty is not a normal random variable, it’s not *any* kind of distribution of a random variable.

Again, just for emphasis, everything you posted is an *error*, not an uncertainty.

Javier,

“Tim, what I copied in italics I did not write. It comes directly from the people that make the calculations:”

YOU posted them. I’m guessing you did so because you buy into what they are selling.

YOU are responsible for what you post. You can’t shuffle the blame off onto someone whose words you posted. It is *you* that are confused about error and uncertainty. The fact that someone may be also doesn’t justify *your* lack of knowledge about error and uncertainty.

Javier,

“In simple terms one could take 100 measurements of something and select the 95 closest to the mean. They will define the uncertainty interval as the true value is believed to be within that interval. In practical terms the uncertainty is taken as the 2σ variation of all the things known to affect the measurement.”

1. When you talk of a mean you are talking about a probability distribution. Uncertainty has no mean. It is not a probability distribution.
2. When you talk of 2sigma you are talking about standard deviation. Again, that is associated with a probability density. Uncertainty has no probability density.

I simply do not understand what has happened to teaching about error and uncertainty over the past couple of decades. Far too many people simply don’t understand the difference. With error you can use the law of large numbers to get a more accurate reading because there is supposedly a gaussian distribution of error. You can not use the law of large numbers with uncertainty because it has no probability density.

The met office is not calculating uncertatinty and neither are you. You are calculating error which is not the same as uncertainty. It really is just that simple. Uncertainty grows with size of the data set. As you add data points your uncertainty grows until it overwhelms the differences you are trying to measure.

Say you are trying to use 10 different, independent data points. The uncertainty associated with each is .25. The total uncertainty is sqrt[0.25**2 + …. 0.25**2] = sqrt[10 x .25]. That becomes sqrt[2.5] = 1.25. Your uncertainty has grown far beyond the uncertainty of each component. And at some point it will overwhelm the small differences your are trying to discern.

go here: https://www.isobudgets.com/combining-measurement-uncertainty/

Maybe it will help you understand abut uncertainty. It has nothing to do with probability densities, means, sampling. law of large numbers, or anything else.

Let’s say you have 1000 independent temperature readings each with an uncertainty of 0.1degF. The total uncertainty you will have when you combine them all is sqrt[0.01 x 1000] = sqrt[10] = 3.2degF. Now how can you say one set of 1000 measurements is 0.01degF hotter than another when you don’t know either within 3degF uncertainty?

Doug,

You are right. I was typing ahead of my brain. Most of the temperature values have an uncertainty of +/- 0.5degF. When you square this it becomes. 0.25.

Since it is root sum square the square is .25, the sum is 2.5, and the sqrt is 1.58. (I came up with 1.25 doing it in my head – Sorry.)

There is no “accuracy” of the mean when it comes to uncertainty. Uncertainty is not a probability density and therefore has no mean. It is just an interval in which the true value probably lies. No point in the interval has a probability assigned to it.

“If the satellite thermometers are accurate to 1 degree, the uncertainty of each measuremrnt is .5, the uncertainty of the mean of 100 measurements is .05., of the mean of 10,000 measurements is .005, etc.”

Nope. The uncertainty of each measurement is +/- .5. When you do the root sum square the square becomes 0.25. When you do the sum you get (100 x .25) or 25. The square root of 25 is 5. The uncertainty has expanded from .5 for each measurement to 5 for the combination of the 100 independent temperature measurements. That means any data set you compare this data set against must have a temperature differential of more than five degrees from the first data set to be able to tell whether one or the other is hotter or colder.

You are doing the same thing Javier is trying to do. Minimize error using the law of large numbers and then call it uncertainty. It *is* uncertainty but it is uncertainty of the mean. What you are doing is trying to say how accurate the mean of a probability density is. First that requires that you have a Gaussian probability density and second, that you *have* a probability density function.

Again, uncertainty is not error and it has no probability density. So it has no mean. And the law of large numbers don’t apply.

Doug,

You didn’t read the entire document you linked to.

The samples you speak of are of the DATA VALUES. When you do this you assume the data values are accurate, that there is no uncertainty and they make up a probability density. You calculate the mean and then use samples of the data set to get that mean more and more accurately. The uncertainty of each data point is totally ignored in this process.

The problem is that uncertainty doesn’t have a probability density. You can’t pull samples from a +/- 0.5 uncertainty interval for 1000 independent uncertainties. What would your sample values be? You would wind up with 1000 data points at +/- 0.5, all laid over the top of each other!

You are referring back to the example with 10 data points. 10 data points with an uncertainty of +/- 0.5 winds up with an overall uncertainty of 1.58. When you expand this to 100 data points you get an overall uncertainty of 5. When you expand it to a 1000 data points you get an overall uncertainty of 25. The overall uncertainty goes up, not as fast as the number of data points but it still goes up.

Look on Page 7 of the document (paraphrased)

————————————
However, statistics tells us that if the uncertainties are independent of one another, the uncertainty in a sum or difference of two numbers is obtained by quadrature.

delta d = sqrt[(delta x)**2 + (delta y)**2]
————————————–

Again, uncertainty of the mean is *NOT* the same thing as the uncertainty associated with the combination of all the data points. Uncertainty of the mean tells you absolutely nothing about the uncertainty of the data when it is combined. When you calculate the uncertainty of the mean you have to totally ignore the uncertainty of each individual measurement.

Doug,

You are not reading the document for meaning.

“The uncertainties in individual measurements tend to “average out” when taking the mean, something everyone is familiar with”

This is true when you are taking multiple measurements of the same thing using the same tool. In this situation it is *error* that is at the heart of the matter, not uncertainty. Error is a random variable with a probability density and you can find the mean of the probability distribution. This kind of situation is not the same as using multiple measurements of different things using different tools. You are not looking at measurement error, you are looking at the uncertainty in each totally independent measurement, different measurands and different tools.

“The best estimate for the combined uncertainty is the square root of the sum of the squares of each uncertainty caused by each uncertain quantity.”

This is talking about combining the uncertainties of two independent measurements, mass and diameter. You do so using root sum square. There is not a probability density for two unrelated measurements of different things using different tools. So you can’t calculate a mean nor can you use multiple samples to more accurately define the means.

Think about it. The tome says “Up until now we have been discussing only the uncertainty in a single measurement, even though we determined what it was by
making many measurements”. That “many measurements” is of the same thing using the same tool.

One more time – how do you take a sample of different things measured in different ways in order to calculate a mean more accurately? How many samples of D and m do you include in each attempt? You certainly can’t sample all D’s and then all m’s in order to define the mean. What would the mean of D’s and m’s mean anyway?

It’s the same thing with multiple measurements of temperatures in different locations taken with different tools. Each of these are INDEPENDENT. There is no overall probability density associated with them so there is no “mean”. But you can still combine their uncertainties using root sum square just as the article states at U5!