UAH v6.1 Global Temperature Update for April, 2026: +0.39 deg. C

“Seasonality can introduce spurious trends”

I asked what seasonality are you talking about, not what effect seasonality can have. I know it can introduce spurious trends – if you remember I tried to explain that to Monckton when he used CET monthly temperatures.

But the point is we are talking about anomalies, not temperatures. There is no noticeable seasonality.

“Trends reflect a change in variance rather than an actual increase.”

How do you think that works? How does a change in variance change a trend?

“It is why ag science was the group to show that nighttime temperatures were increasing rather than climate science.”

You’re just making stuff up now aren’t you? Regardless, what has that got to do with seasonality?

“A linear regression is used to develop a functional relationship between an independent variable (x) and a dependent variable (y).”

Linear regression does not give you a functional relationship. There is always an epsilon term that is not predicted by the independent variables.

And you are again avoiding the question. I asked you explain what analysis you would do on the data.

“One, it does not predict when step changes will occur, nor why nor does it predict when pauses will occur.”

Why would you expect it to? If you have change points, you don’t have a linear regression over the entire data set. You need to use other techniques to estimate where such a change has happened.

“Two, extending the linear regression into the future results in temperatures that are unrealistic.”

Which is why you should not extend a linear trend into the future. It’s linear regression 101, that you should not extend the regression outside the data range.

“Remember, CO2 is not the independent variable, time is.”

CO2 can easily be an independent variable. I’ve shown this to you many times.

“Why do you think nowhere in climate science does anyone map CO2 vs temperature and do a linear regression?”

I keep showing you my graphs doing just that. E.g.

“Two, extending the linear regression into the future results in temperatures that are unrealistic.”

I think your problem is you only see the role of linear regression as predicting what will happen in the future, which is not something you should really be doing.

The main point of linear regression is to identify if correlations exist between different variables, and in the case of a time series, to identify if something has been changing over time, and if so how quickly.

You might be able to use a regression to make a rough estimate of what will happen in the future – but that’s only valid if you can assume that the trend will continue, and that depends on what the reasons are for the change. If you want to estimate how the climate will change over the next century, you have to look at climate models, not just assume a linear trend will continue indefinitely.

“A primary use of the estimated regression equation is to predict the value of the dependent variable when values for the independent variables are given. ”

You still don’t get that prediction does not mean predicting the future. It’s always dangerous to predict outside the data range. Look at the example in your source

For instance, given a patient with a stress test score of 60, the predicted blood pressure is 0.49(60) + 42.3 = 71.7.

That’s in relation to a graph giving a stress test range of 50 – 100, i.e. within the range of the data.

I also think you misunderstanding the word “prediction” in this context. The predicted value is not the actual value you will get. It’s what you would expect to get on average. Using this you can compare the actual result against the predicted result. You can use the prediction to see if someones blood pressure is unusually high or low.

“In physical science, experiments are run to gather data that occurs in the dependent variable when changes in the independent variable are made.”

But in this case we are using time as an independent variable, simply to see if temperatures are increasing or decreasing significantly, and if so by how much. Once again, you are hung up on one use of a regression and dismiss any other use as “not physical science”. You have a very blinkered view of science.

“This isn’t a statistical analysis, it is determining the physical functional relationship between the two variables.”

I’ve no idea how you think you can do that without a statistical analysis. And again, there is not a functional relationship between CO2 and temperature.

“If the relationship is a viable one, then predictions can be made of what the anomaly will be at various CO2 concentrations.”

How? You keep demanding the impossible then complaining when nobody does it for you? There are any number of factors that will determine the global temperature in a given year. And the relationships between them are not likely to be linear. If you think it’s possible to predict the exact global temperature for a given year, then why don’t you demonstrate how?

“The whole process is being done to attempt to convince folks that there are places on the globe warming to such an extent that cooler places do not offset the warming.”

What are you on now? Again, if you have a problem with the UAH data set, take your complaints to Spencer and Christie, before they retire.

“If you want to do something worthwhile, show us WHERE this warming is occurring on a constant basis.”

Did you notice my global anomaly maps, or the trend maps?

I don’t ignore what you “point out”, I explain why it’s wrong or irrelevant.

First. we are talking about seasonality, not variance.

Second, you need to state what variance you are talking about. If you mean the variance in monthly values across the year, then anomalies definitly have less variance than temperatutes. That’s because you are not transforming by a constant. The value you subtract in January will be different to the value you subtract in July. The variance you see in temperatures across the year is caused by seasonality. Using anomalies removes that seasonality.

If you mean the variance for a specific time of year across the years, then yes, there will be the same variance for all Decembers whether you use anomalies or temperatutes. This variance may be different for different months, although the difference isn’t large on a global scale. But the question is, so what? What specific problem do you think that causes, and how could it result in a spurious trend?

Please give a specific example, rather than your usual hand waving.

“The variance of each monthly value *should* inherit the added variance of the component daily values.. Var_total = Var1 + Var2 +…. VarN”

OK, so you don’t understand what a variance is. You’ve demonstrated this enough times, you don’t have to keep repeating it.

What you are describing is what happens when you add multiple random variables. The average of multiple random variables is not a sum. The Var_average will be Var_total / N².

“Anomalies obtained from the monthly values and their inherited variances will have the exact same variance.”

Did you read my comment? That’s what I said, if you are talking about the variance of values for a specific month across the years. But that’s not the same as the variance of all monthly values across the years.

“For the umpteenth time, variance is the uncertainty metric.”

It isn’t really, it’s standard deviation that’s the metric for uncertainty. But this has nothing to do with the discussion, which was about accounting for seasonality in a linear regression.

“random, Gaussian, and cancels”

You’ve lost the argument, and the plot, again.

“You *are* transforming by a constant.”

You think you subtract the same value for January as you do for July?

“You *have* to add the values of the random variables in order to calculate the average!”

And thrn you divide by N, and tgat neans dividing the variance by N². Your inability to remember or understand this basic fact is your problem. All I can do is keep pointing it out.

“Each month is linearly transformed by a constant. That constant does not have to be the same for each different month.”

Yes, that’s what I keep telling you. As I keep saying, these conversations woukd be far les painful if you just explained what variance you are talking about.

“The standard deviation remains the same no matter how much you scale the absolute value with a constant value.”

Again, what standard deviation? We were talking about removing seasonality by taking anomalies. That implies that the variance of the monthly anomalies is less than that gor temperatures because you’ve removed the variance caused by seasonality.

That’s complety different from the variance you see when looking at a specific calandar month and how much it varies year to year.

You can cherry pick parts of the GUM, and sometimes they suggest variance as a measure of uncertainty. But the primary unit is the standard uncertainty. which is a standard deviation. IMHO, variance is a poor value to use for incertainty giving it’s expressed in physically meaningless units and gives no real indication of the size of the uncertainty.

“The variance of a Gaussian distribution is related to the peakedness index. pi = max-value/sqrt(variance).
…
This has been explained to you multiple tomes. Yet you just continue to ignore it. Why?”

This is the first time I can remember you talking about a peakedness index. Your equation makes no sense. Could you privide a reference? As far as I can see the index was only proposed last year.

In this paper, we propose a new measure for quantifying peakedness, named the “peakedness index”. The proposed index is defined as the ratio of the maximum density (or peak density) of the distribution to its continuous informity, where “continuous informity” is a concept from the newly developed theory of informity.

https://www.preprints.org/manuscript/202509.2604

Then you are not talking about seasonality. That’s a change in the mean not in variance. You are talking about heteroscedasticity. You can fix this by doing a weighted regression, but it makes no significant difference.

When I tried it in a back of the envelope way, it just knocked about 0.001°C / decade from the trend, down to 0.155°C / decade compared to the unweighted 0.156°C / decade.

“FIRST you find the variance. THEN you find the standard deviation!”

Why do you think you “then find the standard deviation”? You claim, standard deviation is not the measure of uncertainty, so why go to the trouble of taking a square root for something you are never going to use?

“YOU CAN’T KNOW THE SD WITHOUT FIRST KNOWING THE VARIANCE!”

This is such a childish argument. You saidvthat cariance was the measure of uncertainty. I said standard deviation is the prefered measure. And now you realise you were wrong you rant and twist the argumrnt as being about how standard deviation is calculated.

Of course standard deviation is the root of variance. Variance is an intermediate step, it exists because you square to get rid of negative differencies. But in itself it isn’t a useful measurvof deviation because it’s the average of the square difference and has square units. That is why you take the square root, to get a value that is a useful metric of deviation, or uncertainty.

“Variance, however, IS *THE* metric for uncertainty.”

Nothing you quote says that.

“where you calculate the sum of u^2(y), not the sum of u(y).”

Why do you think it’s written u² and not varience? Because standard uncertainty is a standard deviation. Yes the convinience if varience is that when adding random variables you have to add the squares of the standard deviations and take the square root. which can easily be written as adding variances, but that doesn’t make the variance a useful value. It’s exactly the same as using the Pythagorean theorem. You are adding the square areas of the sides of a triangle to get the area
of the side of the hypotenuse, but the practical use is to take the square root to get the length if the hypotenuse.

“One of the main reasons for using standard deviation in expressing uncertainty is that it shows a plus/minus interval.”

Huh. Any number can be turned into a ± interval. It’s just that such an interval is meaningful for a standard deviation as it reflects the actual dispersion of values.

“Using a plus/minus interval allows the specification of a non-symmetric interval which variance doesn’t allow.’

Not this insanity again. Sorry. you just don’t understand how this works. I’m not rehashing your delusions about negative standard deviations again.

Much like an average. You usually calculate the sum and then divide by n. It doesn’t mean the sum or the variance is a meaningful or useful quantity, it’s the end result that has meaning.

So you don’t know what “peakedness” means.

What you say about sd is just wrong. As usual you are assuming that all distributions a Gaussian. Try applying your logic to a rectangular distribution. Does peakedness increase as the standard deviation decreases?

“I do *NOT* assume all distributions are Gaussian!”

\sarc You claim that, but you kerp making that assumption all the time.

“Variance does *NOT* require a Gaussian distribution to be valid.”

I never said it did. But your assumption that you can tell something about “the hump” from variance does. Deviation tells you nothing about the shape of the distribution.

“A rectangular distribution with a constant value has a variance of 0.”

That’s just a point. What about a distribution with a greater than zero variance?

“Since you obviously won’t take my word for it.”

Nullius in verba.

You need to explain what you mean and preferably demonstrate it. I’m not even saying you are wrong, but unless you can show your workings as far as the UAH trends Spencer states, then how can you say there is a serious problem with them?

But all you do is quote more stuff that has nothing to do with the claim. Your slide show says nothing about seasonality, let alone how different variances over the year can effect liner regression.

If I have time I’ll try to do some analysis on this, but it’s really up to you to demonstrate what you think the correct trend should be. You keep claiming to be an expert on this, yet never do anything than say that Dr Spencer doesn’t understand what he’s doing.

“Now you are talking statistics instead of physical science.”

Of course we are talking about statistics. What do you think linear regression is? I take it you think you should have a deterministic rather than a stochastic model. In which case I can only echo the charge leveled at me, you don’t live in the real world.

“Your graph is a mess.”

Sorry. I produced it in a hurry, to counter your lies. I’s sooner have a messy graph than your non-existent ones.

“The graph is useless as a forecasting tool.”

That’s not it’s purpose.

“Show us the regression equation you came up with and show what the predicted anomaly will be at 660 ppm, a doubling of CO2.”

And again, you should not use a regression outside the data range.

For the record the regression is 2.2 ± 0.47 °C / log2(CO2). With a 2σ uncertainty interval. Though note this is not corrected for auto-regression so it should probably be a bit larger.

The prediction for 660ppm of CO2 would be 1.8 ± 0.5 °C. That’s a prediction interval, not a confidence interval. But, as I said, it’s a mistake to take this as an actual prediction.

“I gave you resources to read.”

Typical deflection. Your resource is a slideshow from a lecture that makes no mention of seasonality, or anything else you claimed. And I keep telling you, if you want to be taken seriously, you need to be able to explain this in your own words, and give us your analysis. How are you interpreting the trend for UAH? How does it differ from the value Spencer gives in this article?

“Benice has made it plain to you that most of the increase in UAH is due to ENSO. It does exist.”

If you mean bnice2000, why do you think that troll has demonstrated anything? You are the one claiming linear regression is wrong for UAH, yet now you want to rely on arbitrary short term linear regression to claim that ENSO is causing multi-decade warming. This has not been demonstrated statistically, and is physically implausible.

And this is yet more deflection. The discussion was about seasonality, not ENSO.

“If you wish to know more, I suggest you delve into the UAH processing.”

Or maybe we should just stop using UAH.

“So your graph is useless in determining what the future holds.”

Not completely useless, but that’s not the purpose of a linear regression. Best you can say about future projections is that, if the linear trend is valid, and if UAH is an accurate measure of global temperature, and if it continues to be linear as CO2 increases, and if there are no confounding factors, then it might be a reasonable estimate.

“Cherry picking early 20th century temperatures…”

Huh. The data goes back to 1979. That is not early 20th century.

“Sorry you are so adverse to learning new things.”

You couldn’t imagine how many new things I’ve learned during the course of these arguments. It’s the only reason it’s worth continuing.

“The resource discusses spurious trends.”

But not seasonality, which is what you were claiming.

“Remove the annual cycle to avoid aliasing.”

Done that. Anomalies, remember.

“Account for autocorrelation because ENSO introduces persistence”

Ideally yes. but this generally increases uncertainty, not the trend. Remember all the times I had to point out the uncertainty in your pauses? Factoring in auto correlation is why the uncertainties are so large, but it doesn’t stop the trend being flat.

But it’s a complicated procedure and there is no one correct method. In the past I used the figures given from the trend calculator that results in UAH uncertainty being roughly 4 times larger than the default value. But I suspect this might be too large.

Most of the time I prefer to use annual averages that remove some but not allauto correlation. It also of course removes any seasonality.

“ENSO years can create apparent “steps” in tropospheric datasets due to shocks not decaying”

That’s your assetion and I see no reason to it. You have done nothing to determine these step changes statistically. but even if you did it wouldn’t counter the real world physical reasons why this is implausible.