From Dr. Roy Spencer’s Global Warming Blog

by Roy W. Spencer, Ph. D.

The Version 6 global average lower tropospheric temperature (LT) anomaly for January 2023 was -0.04 deg. C departure from the 1991-2020 mean. This is down from the December 2022 anomaly of +0.05 deg. C.

The linear warming trend since January, 1979 now stands at +0.13 C/decade (+0.11 C/decade over the global-averaged oceans, and +0.18 C/decade over global-averaged land).

Various regional LT departures from the 30-year (1991-2020) average for the last 13 months are:

YEAR | MO | GLOBE | NHEM. | SHEM. | TROPIC | USA48 | ARCTIC | AUST |

2022 | Jan | +0.03 | +0.06 | -0.00 | -0.23 | -0.13 | +0.68 | +0.10 |

2022 | Feb | -0.00 | +0.01 | -0.01 | -0.24 | -0.04 | -0.30 | -0.50 |

2022 | Mar | +0.15 | +0.27 | +0.03 | -0.07 | +0.22 | +0.74 | +0.02 |

2022 | Apr | +0.26 | +0.35 | +0.18 | -0.04 | -0.26 | +0.45 | +0.61 |

2022 | May | +0.17 | +0.25 | +0.10 | +0.01 | +0.59 | +0.23 | +0.20 |

2022 | Jun | +0.06 | +0.08 | +0.05 | -0.36 | +0.46 | +0.33 | +0.11 |

2022 | Jul | +0.36 | +0.37 | +0.35 | +0.13 | +0.84 | +0.55 | +0.65 |

2022 | Aug | +0.28 | +0.31 | +0.24 | -0.03 | +0.60 | +0.50 | -0.00 |

2022 | Sep | +0.24 | +0.43 | +0.06 | +0.03 | +0.88 | +0.69 | -0.28 |

2022 | Oct | +0.32 | +0.43 | +0.21 | +0.04 | +0.16 | +0.93 | +0.04 |

2022 | Nov | +0.17 | +0.21 | +0.13 | -0.16 | -0.51 | +0.51 | -0.56 |

2022 | Dec | +0.05 | +0.13 | -0.03 | -0.35 | -0.21 | +0.80 | -0.38 |

2023 | Jan | -0.04 | +0.05 | -0.14 | -0.38 | +0.12 | -0.12 | -0.50 |

The full UAH Global Temperature Report, along with the LT global gridpoint anomaly image for January, 2023 should be available within the next several days here.

The global and regional monthly anomalies for the various atmospheric layers we monitor should be available in the next few days at the following locations:

Lower Troposphere:

http://vortex.nsstc.uah.edu/data/msu/v6.0/tlt/uahncdc_lt_6.0.txt

Mid-Troposphere:

http://vortex.nsstc.uah.edu/data/msu/v6.0/tmt/uahncdc_mt_6.0.txt

Tropopause:

http://vortex.nsstc.uah.edu/data/msu/v6.0/ttp/uahncdc_tp_6.0.txt

Lower Stratosphere:

http://vortex.nsstc.uah.edu/data/msu/v6.0/tls/uahncdc_ls_6.0.txt

Ja. Past few years I am battling to get my pool up to temperature. It is getting cooler here. In South Africa.

https://breadonthewater.co.za/2022/08/02/global-warming-how-and-where/

Don’t tell the BBC…

“Why have there been no named winter storms this year?”

https://www.bbc.co.uk/news/uk-64454569

That will likely change in a week or so.

Then again it might not

Have you checked the models. What we’re getting here is set to visit Europe in 8-9 days.

I checked my model Avro Lancaster – no change there

Guess it didn’t belong to 617 Squadron.

626 – RAF Wickenby

This is what we are getting here:

https://earth.nullschool.net/#current/wind/isobaric/500hPa/overlay=temp/orthographic=-55.64,48.92,264/loc=-80.524,62.634

The coldest air in the arctic is marked, and is currently affecting the northern and northeastern parts of the U.S., along with large areas of Canada, and is working its way east.

The UK is south of the jet stream at the moment, keeping the weather mild there, but that cold air over the U.S. and Canada is headed the UK’s way.

Not according to any of the reputable medium range models. Which is disappointing because I was hoping for a cold winter and to rubbing some warmist noses in the snow

I’ve checked and they don’t forecast any untoward weather for Europe. For western Europe they’re forecasting that a weak anticycline will dominate for most of the next 10 days. Therefore there won’t be any strong winds and no named storms

Have you ever witness such a belch of BaffleGab, WeaselWords and Coulds&Maybes in your life?

They haven’t a fugging clue and are grasping at straws, even ones that are on The Other Side of the Earth in Latitude, Longitude

and(effectively) AltitudeWhen is any serious number of people gonna get off their backsides and call out this shyte for what it is..

And don’t tell the Australian leftists governments, Federal and. State.

By the Monckton method, with UAH monthly data updated to include January 2023, the “pause” in warming over Australia’s lower troposphere is now 10 years and 9 months.

There has been slight cooling from May 2012.

Hypothetical. If this pause lasts 5 more years, there will be no Australian school children who have been exposed to global warming in their home country Australia.

Why are they taught that global warming is an existential threat?

Geoff S

http://www.geoffstuff.com/uahfeb2023.jpg

I’m sure they will start naming the various polar vortexes that come down from the artic soon enough

There were no named winter storms because they didn’t feel like naming any. It’s not like hurricanes that have a set standard.

Well, that isn’t what was heard. What was heard was that January was one of the warmest on record for the US.

But February sure has started out with the deep freeze door wide open here. And it looks like all the models are showing Europe is in for their own blast of Arctic air starting late next week.

I’m not sure where you get that about Europe from. There is actually zero sign of any untoward cold weather in Western Europe in the next fortnight according to all of the medium range forecasts, or at least the reputable ones. A shame because I enjoy a bit of snow and ice.

I suggest that you follow Ventusky

See 12 Feb 23

https://wobleibtdieglobaleerwaermung.wordpress.com/2023/01/31/modelle-mit-eisigem-februar-in-mitteleuropa/

It’s German but you may have a look at the model output.

https://pbs.twimg.com/media/Fn73vHwWAAAHXrA?format=png&name=small

They are forecasting snow in the U.K. by the middle of this month, maybe.

Today’s BoM (Bureau of Meteorology) forecast for Thredbo, NSW, is “Cloudy. High (70%) chance of snow showers.”. And it’s mid-summer in Australia. On 31 Jan, a place I visited in Robertson, NSW (between Canberra and Sydney) had a log fire burning mid-afternoon – and they needed it. Hey, weather isn’t climate, and the Snowies do get summer snow, but an awful lot of places seem to be getting a bit of cold right now.

G’Day Mike,

A spot of history. Late April, 1970, we were in Canberra. The snow was down to 4,000 feet. We hightailed it to Brisbane.

https://www.leicestermercury.co.uk/news/local-news/weather-expert-says-still-chance-8102311 depends on which model you prefer.

I prefer the one that is right. In Ohio, the 5-day forecasts vary daily, and are often wrong 12-hours before. This is fairly flat country, unlike when I lived in Vermont in the late-60s and expected turbulence in the air masses passing over the Green Mountains to produce low predictability. Quite frankly, with the advent of Doppler Radar, geosynchronous weather satellites, and computer models, I would expect much better precipitation predictions. It is my subjective impression that about the only thing that can be depended on are the temperature forecasts. However, just using the historical averages would probably be nearly as good.

In my part of the Midwest, it was the ninth warmest January ever. But my tiny corner of the world is a mere speck in the larger climate. Looks like the southern hemisphere was quite cool — which some people tend to appreciate in the (southern) summertime. I know I like cooler summers myself.

Berlin minus four overnight Saturday week. Note that our gradually warming planet first reached this anomaly in 1983. So that’s 40 years of no warming.

That’s not quite how trends are calculated.

Linear warming trend since that first -0.04C anomaly (April 1983) is +0.14C per decade, according to UAH.

“That’s not how trends are calculated.” How do you calculate that the January global temperature (Dr. Roy Spencer) is 0.04 deg C under the 1991 to 2009 average, any way other than: in 32 years it has gotten a little colder/less warm?

By linear regression. The exact same method used by Roy Spencer to arrive at his +0.13C per decade warming value.

Explain why linear regression is appropriate from a statisical point of view. Does the series exhibit well behaved residuals, in accordance with the underlying assumptions behind OLS estimation? – i.e. normally distributed, with no substantive evidence of autocorrelation, homoscedastic? Is a linear model really appropriate? The Fourier analysis strongly suggests not.

Because it’s the method used by UAH and Roy Spencer and it’s their data set we are discussing here. Perhaps you should direct your comments to Dr spencer on his blog?

*YOU* were asked the question and you bailed. Meaning you have no idea if the method of analysis is proper or not.

So you just fall back on the argumentative fallacy of Appeal to Authority.

If you can’t support *your* assertions then don’t make them.

Let me get this straight. UAH posts its monthly update and uses linear regression to estimate the rate of warming in its global LT data set, +0.13C per decade. I now have to justify and explain UAH’s method of trend calculation? As I said before, if you don’t agree with it, take it up with UAH rather than me.

By the way, what do you make of Coeur de Lion’s approach of selecting a monthly anomaly from 40 years ago that happens to be the same as Jan 2023 and concluding from that that there has been no warming? You didn’t comment on it.

Is that a better statistical method than linear regression? Maybe you should pass that method on to Dr Spencer?

Look at this graph again.

Do temps below the baseline indicate warming to you.

This is a time series and the way it is forecasted is important!

What would you say if Dr. Christy used this graph and simply said there has been no CONSISTENT trend to warming?

What special significance do you attach to the base line? It’s just the 1991 – 2020 average. Would there be more warming if you stuck to using the 1981 – 2010 baseline?

Don;t you think the fact that there is more red in recent years and a lot more blue last century is some indication of warming?

No there would not be more warming. The temperatures would still revert to the mean. You just don’t get that natural variation is in control. You can trend what you want, but your trends NEVER show a reversion to the mean! Maybe you can rethink your analysis.

“

The temperatures would still revert to the mean.”What mean? The old or the new base line, or an earlier one?

“

You just don’t get that natural variation is in control.”If that’s correct we should expect at some point to see temperatures averaging around the same as they were in the past. So far this has not happened. One month that is below a baseline centered on the temperatures 15 years ago does not suggest that anything has reverted to the mean yet.

“

Maybe you can rethink your analysis.”I will do, when there is some evidence to suggest a change in the trend.

Attached is a graph of the 5min data from my Vantage Vue weather station for August, 2019.

Which would you use as part of the baseline to calculate anomalies from? The median? The average? The mid-range?

No matter which one you pick you are going to introduce an uncertainty into the anomaly calculation, it could be as much as 3.0F.

forgot the graph

Hmmm,,,, no answer. Didn’t really expect one I guess. It just really shows the folly in trying to come up with an accurate baseline from which to work that allows accurate anomalies in the hundredths digit! But that doesn’t stop the climate warmers!

Dr Spencer presents a centred 13 month moving average as a simple way of deseasonalising the data. He does not attempt to display a linear trend line. You did that.

“

He does not attempt to display a linear trend line.”And if you want to see an example of actually drawing a trend line with no challenge, here’s Monckton from last month.

https://wattsupwiththat.com/2023/01/04/the-new-pause-lengthens-100-months-with-no-warming-at-all

Monckton is not Spencer. Monckton majors on back-casting to find the longest period from the present where the estimated slope is zero. Now at 100 months…

As he notes:

The least-squares method was recommended by Professor Jones of the University of East Anglia as a reasonable method of showing the trend on stochastic temperature data.However, that is plainly false, as any consideration of the historic climate should tell you. The climate does not follow a linear temperature trend. Monckton is in effect jibbing Prof Jones for his lack of knowledge of statistics.

After all, a hockey stick is not a straight line.

Less than 50% of the variance is explained/predicted by the regression line. Would you use similar statistics to buy stocks and expect to make money?

I wouldn’t have a clue how to predict stock markets, but the fact that up to half of the monthly variation can be explained by a simple linear trend is a good indication to me that the trend is real.

“Less than 50% of the variance is explained/predicted by the regression line.”

The R^2 means nada here. If you detrended the data to zero, the R^2 would go away, but the standard error of the (flat) trend would be identical to that found from the current one.

Dr Spencer declares the linear trend in every update. His data set contains a linear trend for every single region covered by the data. It’s at the bottom of every column.

Why he doesn’t add a linear trend line to his charts is an interesting question. Perhaps he doesn’t like the look of it?

He always used to add a high order polynomial to his charts “for entertainment purposes only”.

https://www.drroyspencer.com/2012/07/uah-global-temperature-update-for-june-2012-0-37-deg-c/

The data is already deseasonalized (at least to some extent). Remember, there are actually 12 distinct baselines from the which the UAH TLT anomalies are constructed; one for each month.

They use it only because it compares to all the other joker climate alarmists.

Yep. What does a linear regression of sinusoidal data tell you?

A good rule of thumb is that if a linear curve fit provides no predictability over the graph’s x-axis, you shouldn’t draw it on the graph. Unfortunately, climateers love this particular transgression which allows them to extrapolate normal fluctuations into crises, thereby seemingly increasing their worth to society, and securing continued paychecks.

DMacKenzie said: “A good rule of thumb is that if a linear curve fit provides no predictability over the graph’s x-axis, you shouldn’t draw it on the graph.”The model Tx = slope[X:1=>(N-1)] * (N-1) + intercept[X:1=>(N-1)] has an RMSE of 0.176 C. That’s not too bad considering Christy et al. 2003 report the uncertainty of the observations as ±0.1 C (1σ). For comparison the model Tx = -0.24 + [1.3*log2(CO2)] + [0.14*ONIlag4] + [0.32*AMOlag2] + [-2.7*AODvolcanic] has an RMSE of 0.121 C. We can actually get a hair more skill by incorporating auto-correlation into both. Anyway, as you can see OLR has predictive power and it is actually reasonably skillful.

Read this site about linear regresson.

2.1 – What is Simple Linear Regression? | STAT 462 (psu.edu)

In regards to linear regression this document has some good information.

In general, to be absolutely predictive there must be a functional relationship (gosh, there is that term again) between the independent and dependent variables.

In a statistical relationship, there still must be a relationship between the predictor variable and the response variable although it may not be perfect as with a functional relationship.

In essence, when plotting temperature versus time, it is difficult to prove that time is a good predictor variable. Pauses immediately bring into question whether time has any direct relationship to temperature.

If you want to prove that GHG’s and more specifically CO2 are good predictors of temperature by using linear regression, then you should use those as the variable that is the predictor of a response.

I can tell you have never been responsible for large budgets of people, revenue and expenses. I can’t tell you how many times someone has come to me with a linear regression encompassing several past years and exclaimed that it would predict the upcoming year. When you start to ask about the underlying factors like wage growth, productivity changes, rate increases, etc., they had no answers. Time IS NOT a good predictor variable when something doesn’t directly depend it.

The linear regressions being touted are really trying to replace time series analysis. This data really needs to be looked at using tools that have been developed for time series analysis if that is what you are really looking for. You will still find out that time is not a factor in predicting temperature even after doing all the transformations to remove seasonality, make the trend stationary, etc.

You are going to end up with something like the attached graph which plainly shows that CO2 and temperature are not very well correlated.

Forgot the image.

“Does the series exhibit well behaved residuals, in accordance with the underlying assumptions behind OLS estimation?”

It seems to. The correlation between their residuals and their best fit normally distributed equivalents is ~0.992. And they look like they fit as well. Please provide your Fourier Analysis.

Here:

https://www.woodfortrees.org/plot/uah6/plot/uah6/fourier/low-pass:5/inverse-fourier

The residuals from linear regression of the UAH6 data show a very high degree of positive serial autocorrelation. The Durbin-Watson statistic is ~0.752, which is highly significant – way beyond a 1% criterion for a sample of over 500 readings. So OLS is NOT valid for the data.

Your WFT does not show the calculation of your DW statistic. Since this is

yourvalue, would you please show us from whence it came?And FYI, we certainly know that there are cyclical events, which would tend autocorrelate. But we also know that the underlying trend of the repeated cycles is undeniably,

up.Check it yourself. Take the sum of the squares of the residuals as the denominator, and the sum of the product of the residuals e(t) with those one period lagged e(t-1) as the numerator. Divide, and bob’s your answer… You can verify the formula here:

https://www.statology.org/durbin-watson-test/

For MY information there are cyclical events? LOL. That’s exactly why I conducted Fourier analysis, which is designed to elucidate the amplitudes of different frequencies and relative phases of cycles in the data.

We do not know anything about the future trend. See Sir Alan Cairncross.

From your link:

“When this assumption is violated, the standard errors of the coefficients in a regression model

are likely to beunderestimated which means predictor variables are more likely to be deemed statistically significant when they’re actually not.”Italics mine.

likelyto be found in an upward trend with cyclicity. Both the cyclicity and the positivity of the trend itself would tend to present those indications, without necessarily degrading the underlying statistical durability of that upward trend.Except that when we actually use the previous period reading as a variable, we find that it effectively eliminates a linear trend as an explanatory variable. The linear trend is not a good model. The autocorrelation model is much better (though still leaving a lot of holes).

As I pointed out, the DW statistic was strongly diagnostic of a high degree of positive serial autocorrelation. So the first step is to estimate an AR1 model.

“Except that when we actually use the previous period reading as a variable, we find that it effectively eliminates a linear trend as an explanatory variable.”I don’t think you know how to do Ar(1) regression. You regress against both the previous value and time. The trend is virtually unchanged.

Here is how to do it in R:

Without OLS, trendology is totally bankrupt.

See. bellman’s post above of Dr. Christy’s sinusoid curve. Which has a better fit, a linear regression or the polynomial one?

Are either one better than this one?

I don’t know. But his OLS fit of the post Jan 1983 UAH6 data is not as good as the fit to the cyclical fourier data of that same data by it doesn’t add up.

Data – 1.40 degC/century with a standard error of 0.07degC/century

Fourier data – 1.32 degC/century with a standard error of 0.04 degC/century

If you do this a few times you will notice that these are

terrificfits. If you consider the ramifications of the plot I posted separately of how unlikely the trend is to be much different than it’s expected value, the scalesshouldfall from your eyes.It was Roy Spencer’s graph.

A polynomial will always have a better fit the higher the order, simply because there are more degrees of freedom. That doesn’t mean it’s a better indicator of an underlying trend. How good would that polynomial have been at predicting the next 10 years?

Here, by the way, is what the 4th order polynomial fit looks like now.

“A polynomial will always have a better fit the higher the order, simply because there are more degrees of freedom.”

A key point. It is how the deniersphere tries to widgit its way into believing that CC is “natural”.

The purpose of statistical tests of model parameters is to establish whether they do offer a valid model. Adding more polynomial terms to a regression offers no such guarantee.

And nor does adding multiple sine waves.

I didn’t. I subtracted them, only showing the lower harmonics.

A Fourier Transform is not a regression.

An FT is a mapping from one domain to another. It is not a regression. How many times do you have to be told that before you actually go learn something about FT’s?

The residuals are also not homoscedastic. Another reason not to trust an OLS linear model.

I agree. The residuals go up and down, but exhibit a quite normal distribution. That, not how uniform they are, is the name of the game.

NOPE. All the criteria have to be met to justify the use of OLS.

NOPE. Please read up on both autocorrelation and heteroscedasticity.

When there are signs of autocorrelation, that in itself does not disqualify the trend identification. Both cyclical trends within the larger positive trend, and the positivity of the trend itself would tend towards a DW test of autocorrelation, even with the upward trend still statistically durable.

Please find any link to the use of the phrase “have to” or a synonymous one, w.r.t. autocorrelation of an OLS trend….

W.r.t. heteroscedasticity, in this case it is caused by normal cyclicity from ENSO, volcanism, etc. There is

noreason in and of itself that merely becuase there is variability in the variance of the residuals, that the underlying trend is invalid.Please read up on autocorrelation and heteroscedasticity.

I studed this at degree level, so I don’t need you trying to act as grandma.

Now look at the results of an AR1 model and tell me what is left by way of a trend.

“I studed this at degree level, so I don’t need you trying to act as grandma.”

I gave you

reasonsto catch up on these topics, complete with links. I should have guessed that all I would get in return would be a fact free appeal to authority.As for your cartoon, no accompanying data, as is the custom here. But I’m guessing that if you

didprovide it, the trend would be as durable as what I provided.My chart shows the UAH6 data, and the predicted values from an AR1 model. I have explained that entails using the previous period value as the variable to regress. Do you need more spoon feeding? I have quoted the regression results already.

Nullis in verba – you have the tools to verify for yourself. Assuming you know how to use them.

Ah, the usual deflection when substituting a cartoon for actual data. No, it’s not a request to spoon feed, by aksing you to do the minimum amount of man up.

Folks, Idau would rather **** a **** (maybe not a problem for him) than provide data that he claims to have, but that might actually

use. It channels a bit salesman from my past. It used to be the custom to get a bottle of Crown Royal for using certain brand name drill bits. But one pusher never got any. When I aksed why, the bit peddler looked at me with a grin and said “Why, he’ddrinkit!”.YOU have the data. If you’ve not downloaded them they are available from UAH. I have reported my results and methods. You can verify them. Do you want a post with 530 lines of data showing the variables, predicted values and residuals so you can check your spreadsheet works?

If it is merely the UAH data, already evaluated.

I’ve not explored AR models yet so I’m interested in learning more. One thing that interest me specifically is predicting the next value Xn using only the set {X1, …, Xn-1}. So I’m curious…what is the RMSE of your AR1 model in predicting value Xn using only X1 to Xn-1 as inputs for the training?

For example, Xn = average(X1:Xn-1) has an RMSE of 0.20 C. Xn = slope(X1:Xn-1) * (n-1) + intercept(X1:Xn-1) has an RMSE of 0.18 C. Xn = Xn-1 has an RMSE of 0.13 C. What is the RMSE of Xn = ar1next(X1:Xn-1) when applied to the UAH TLT values?

The data are all there on the UAH website, so why don’t you show us what the trend should look like?

Seems like no more than a couple of hours work for one so wise.

Please forgive my snarky tone (I’ve had the Canada Revenue Agency on the phone and feel the need to lash out at someone), but this is a serious ask. You’re not the first to deplore least-squares trends as inappropriate, but I can’t recall seeing the “proper” statistics applied to a temperature-time trend.

You could also respond to his lordship, who is going to post another verbose chapter of “the New Pause Lengthens” within the next few days, and tell him what he did wrong, because it looks as though he uses least squares to establish his trends. That might provoke an entertaining discussion. I always look forward to learning new words!

I already posted a Fourier filtered analysis which is much more appropriate than the linear trend.

the fourier trend itself is increasing at essentially the same rate as the original.

fourier transforms don’t have trends.

see the attached picture. A cosine wave in the time domain on the left and its representation in the frequency domain in the middle. How do you trend the frequency components in the frequency domain?

“fourier transforms don’t have trends.”

This one sure did. But I’m happy to revert to the original data evaluation, which had a

highertrend, and a still, relatively miniscule, standard error.Your cosine waves are flat. They don’t have to be, and in the case of temp seasonality (one of many examples) they never are.

To answer your question, you trend them the same way you trend

anydata, while trying to match cycles as best you can, and by losing the cyclicity component, if possible. The trend gets judged on its statistical durability, no matter what.No it did not have a trend. Try reading and understanding more about Fourier transforms. They can be used to model e.g. a sawtooth fuction. If you narrow your view to an ascending section of the graph you will con yourself into thinking it is modelling a rising trend. Yet the full curve has no trend at all. It is a sawtooth.

So, “sawtooth” and other cyclical functions can not have trends? Whoa! In what world….?

And

again,I have trended the actual data, and it’s even more pronounced than the fourier.How’z that provision of you Big Foot ARIMA data coming? To be fair, I can understand why you wish to withhold it….

They can have *short* term trends based on how the sinusoids combine.

What you get out of a FT is *NOT* statistical data, it is frequency components. You map the time domain data into the frequency domain. There is no trending in the frequency domain!

The FT data has a y component of degC and an x component of time. But for some Big Foot reason we can’t trend ddegC/dT.

But no problem in any case. I already trended the actual data. It trends slightly higher than the FT, with a relatively tiny standard error of that trend. Upon request I’ll happily provide the plot of probability of that trend being less than a table of values, with those values ranging from expected to zero.

trend this one. It has El Nino’s, La Nina’s, heating, cooling, etc.

“and by losing the cyclicity component,”

In other words, just ignore that which makes the temperatures what they are.

There are enough cycles to trend it with or without “losing it’s cyclicity component”. Eyeballing seems to indicate that the cycles are regular and repeating, and that the overall trend is flat, unlike the 01/83 to present UAH6 data. So, is there a pony under there?

Separately, Watts Up with the WUWT poster penchant for providing cartoons instead of actual data.? Could it be that you and the rest are

afraidof it? Nah! They’d be talkin’ about that!And I’ve now added an AR1 model.

How do you trend cyclical data?

Monckton only looks a small portion of the data. Like the very top or bottom of a cycle the derivative is 0, i.e. horizontal. He is basically trying to identify an inflection point and show that a linear trend will not work to do that. Along with that goes the forecasting truism that you must weight current data more heavily than past data if you want to know where things are actually going.

How does an OLS do that? An OLS is truly only good for the interval over which it is calculated. Extending it is a fools mission. Yet that is what the climate models basically do. Take a close look at them. After a few years into the future they all become linear trend lines, y = mx + b. “m” varies among them but they all have an “m” value. I might believe such a forecast for postal rates, not for climate however.

“

Monckton only looks a small portion of the data.”He’s looking at the entire 44 years of UAH to say the rate of warming is 0.134°C / decade. He’s drawn linear trends on the entire HadCRUT data set. He keeps going on about the trend over 40 years of CET, whilst ignoring the fact it really is cyclic.

“

Along with that goes the forecasting truism that you must weight current data more heavily than past data if you want to know where things are actually going.”Something he never does. Something you’ve never done. Show us what the forecast is when you weigh current data more than past data. Then explain how you determined the weighting and demonstrate how good your method was using past data.

“

An OLS is truly only good for the interval over which it is calculated.”All this pointless discussion has been about what has been happening over the given interval. It’s been about the claim that there has been no warming the past 40 years – past tense, not about predicting the future.

“

Extending it is a fools mission. Yet that is what the climate models basically do.”If that was all climate models did, they would all agree and there would be no talk about how the actual trend was less than predicted.

“He’s looking at the entire 44 years of UAH to say the rate of warming is 0.134°C / decade”

Not when he is calculating the length of the pause!

“Something he never does”

That’s the whole point of calculating the length of the pause. It is based on the most recent data!

“Something you’ve never done. Show us what the forecast is when you weigh current data more than past data.”

Look at his pause calculation! He gives everything earlier than that a weight of ZERO!

“Then explain how you determined the weighting and demonstrate how good your method was using past data.”

I did this already in another thread. I provided links to two different web sites on how to do it and started the calculations for you. As usual, you just blew it all off.

“All this pointless discussion has been about what has been happening over the given interval.”

Meaning you have absolutely no understanding what a Fourier Transform analysis actually is. Why am I not surprised?

“If that was all climate models did, they would all agree and there would be no talk about how the actual trend was less than predicted.”

They don’t agree because they all come up with a different value of “m” for their y = mx+b projections. And none of their values of “m” match the actual reality we live in! Do the words “they are all running too hot” mean anything to you?

“

Not when he is calculating the length of the pause!”Which is why I was not talking about the length of the so called pause, but all the times he’s used a linear trend over the entire data, whether it’s appropriate or not.

“

That’s the whole point of calculating the length of the pause. It is based on the most recent data!”You were talking about weighing recent data more than older data. That is not the same as ignoring all data before a certain data and giving equal weight to all data after that date.

“

Look at his pause calculation! He gives everything earlier than that a weight of ZERO!”And everything after that a weight of ONE. This is a very silly thing to do, if you are claiming you want to produce a weighted trend. Especially when you only choose the start date to get the trend you want. Another way of saying this, is you are ignoring all data you don;t want, and only looking at the data you do want.

“

I did this already in another thread. I provided links to two different web sites on how to do it and started the calculations for you. As usual, you just blew it all off.”And the lies keep coming. You showed me a method for a weighted regression, I showed what happens when you used it. I did not blow it off. I’m still waiting for you to do the work and demonstrate what happens when you apply your preferred method.

“

Meaning you have absolutely no understanding what a Fourier Transform analysis actually is. Why am I not surprised?”We were talking about linear regression, not a Fourier Transform. But why am I not surprised you throw another red herring along the path. Does your Fourier Transform allow you to answer the question, has there been warming over the last 40 years?

“

They don’t agree because they all come up with a different value of “m” for their y = mx+b projections.”Your claim was all they are doing is projecting the current trend into the future. Why would there be any disagreement. We know what

mis for any given data set.“

And none of their values of “m” match the actual reality we live in!”Make your mind up. First yopu complain they just use the current warming trend, now you complain the models don’t agree with the current warming trend.

“Which is why I was not talking about the length of the so called pause,”

In other words you are deflecting because you don’t have an answer. You never do.

“You were talking about weighing recent data more than older data.”

Again, using the most recent data while setting past data to a weight of zero *IS* weighting current data more than older data!

“That is not the same as ignoring all data before a certain data and giving equal weight to all data after that date.”

Did you actually read this before posting it? It’s not ignoring it, it is giving it a weight of zero!

“And the lies keep coming. You showed me a method for a weighted regression, I showed what happens when you used it. I did not blow it off. I’m still waiting for you to do the work and demonstrate what happens when you apply your preferred method.”

Malarky! You showed NOTHNING. You just did as you usually do and just said it was wrong!

Monckton has already done the work. And you won’t accept it. You just continue to say its wrong!

“We were talking about linear regression, not a Fourier Transform. But why am I not surprised you throw another red herring along the path. Does your Fourier Transform allow you to answer the question, has there been warming over the last 40 years?”

In other words you aren’t keeping up. Surprise, surprise! “It does not add up” posted a FT. It’s not a red herring. It shows the frequency components. It is *NOT* a linear trend line.

There has been warming and cooling since the Earth was formed. Yet you want to ignore everything except your lifeline that CO2 is going to turn the Earth into a cinder!

“Your claim was all they are doing is projecting the current trend into the future. Why would there be any disagreement. We know what

mis for any given data set.”Again, did you read this before you posted it? The climate models CREATE the future data set. And the equation they wind up with is a linear trend line, y = mx +b. And they all come up with different values for “m” which is different that “m” for actual observations! Again, that is why people are beginning to recognize the models are all “running too hot” – except for you I guess!

” First yopu complain they just use the current warming trend, now you complain the models don’t agree with the current warming trend.”

Shut it down troll! You can’t even recognize the difference between extending a linear regression of temperature observations and creating a future prediction based on models. You are just embarrassing yourself!

“In other words you are deflecting because you don’t have an answer. You never do.”

No, I was trying to keep on topic. You claimed he only ever looked at a small portion of the time series, and I pointed out he does show the trend over the whole series. This was in relation to the fact that people are now insisting that it’s meaningless to look at the trend over the entire series.

“

Did you actually read this before posting it? It’s not ignoring it, it is giving it a weight of zero!”Did you? Giving something a weight of zero is to ignore it.

“

Malarky! You showed NOTHNING. You just did as you usually do and just said it was wrong!”then provide a reference. I can’t keep up with your stream of nonsense. Which site did you ask me to look at, how do you want me to weight the values, what result do you get?

“

Monckton has already done the work. And you won’t accept it. You just continue to say its wrong!”Because I think it’s wrong, or at least misleading. You talked about weighing more recent data higher than older data, but all Monckton does is weigh the data he wants as 1 and the data he doesn’t want as zero. Claiming this is some sophisticated statistical technique when it’s just cherry picking hte start you want is a distraction.

“

Yet you want to ignore everything except your lifeline that CO2 is going to turn the Earth into a cinder!”More strawman fallacies.

“

The climate models CREATE the future data set. And the equation they wind up with is a linear trend line, y = mx +b. And they all come up with different values for “m” which is different that “m” for actual observations!”And you keep moving the goalposts. The statement I was disagreeing with, was you saying

You claim the models basically extend the trend into the future, and when I call you out on it you come up with a different claim.

“Because I think it’s wrong, or at least misleading.”

You’ve never once run a business where maintaining inventory was a requirement for a profitable business.

————————————

You claim the models basically extend the trend into the future, and when I call you out on it you come up with a different claim.

————————————————-

No moving of goal posts. Only your inability to understand a simple truism. Depending on an extended linear trend line, especially in a changing environment, simple doesn’t work. It might work in geology where you have a fixed, unchanging medium over a long period of time but weather and climate isn’t geology!

“

You’ve never once run a business where maintaining inventory was a requirement for a profitable business.”How many different jobs do I need to have had before I’m allowed to point out the flaws in Monckton’s pause analysis?

You need to show that you have been accountable for making decisions that affect your employment and the profitability of a business you are involved with. In other words some financial accountability.

Linear trends ONLY SHOW what has happened between the end points. Using them to forecast either the past or the future is fruitless unless you know what factors are going to change in the future.

If you don’t believe me, tell us what your linear trend says occurred in the past. If it is accurate to the future, in damned well better be accurate to the past beyond the beginning of the trend also.

What an utterly bizarre piece of ad hominem logic. Only people who have handled the company financiers are allowed to explain some basic statistics?

“Linear trends ONLY SHOW what has happened between the end points.”

Which is all I’ve been using them for. But I don’t think that’s ALL you can use them for.

You didn’t answer my question!

Does your trend accurately reflect the past beyond what you have shown?

If it doesn’t then you have cherry-picked your starting point haven’t you?

This one reason OLS is truly questionable on non-stationary time series!

“

Does your trend accurately reflect the past beyond what you have shown?”No, and I’ve never claimed it did. As always you keep inventing arguments you think I’m making and then shooting them down. A straw man.

“

If it doesn’t then you have cherry-picked your starting point haven’t you?”In this case the starting point is the first point of the data, December 1978. Difficult to see how that can be a cherry-pick. I could have easily picked later points that showed faster rates of warming.

If you were looking at a longer data set, e.g. HadCRUT, then a linear trend would not be appropriate. You need to try to find a model that fits the data better, and be honest about it. Not for example choosing the start point that will maximize the rate or warming, preferably using some analysis to identify a change point.

“

This one reason OLS is truly questionable on non-stationary time series!”You still don;t get stationary data do you. If data has a trend it is not stationary. There is no rule that says you can’t find a trend in non stationary data, it would be a pointless exercise to find a trend in stationary data.

And the ECS numbers they get out of the models are not much more than the CO2 concentrations versus time the operators assume will happen.

Exactly!

“The data are all there on the UAH website, so why don’t you show us what the trend should look like?

Seems like no more than a couple of hours work for one so wise.”

It’s 5 minutes worth of “work”, trend statistics and odds of the trend being qualitatively incorrect included. And we

knowwhy he won’t provide it…A warming rate of all of +0.13C per decade. Wow, should I panic?

You can panic if you like, or not. I was just pointing out that this is the linear warming trend in UAH, as opposed to Coeur de Lion, who believed that because there was a previous anomaly value of -0.04C 40-years ago that meant there had been no warming in between.

A trend is a trend is a trend. But the question is, will it bend? Will it alter its course through some unforeseen force and come to a premature end?Sir Alec Cairncross, Economist

Like I said above, linear regression is the method used by Roy Spencer to arrive at UAH’s overal warming trend of +0.13C per decade. Not sure what you’ve used in the above chart.

The steps are written out: Fourier transform, low pass filter, inverse Fourier transform.

It removes the high frequency oscillations to reveal the underlying low frequency oscillations of the trend, which ends up where we started, and heading down…

Perhaps best to stick to the method used by Spencer and UAH?

Perhaps best to take a course in statistics.

I’ll leave it to you to pass that on to Dr Spencer. It seems UAH have been getting their trend calculation method wrong for decades. You can now enlighten them.

*YOU* are the one advocating for the linear trend analysis. *YOU* should be able to support your advocacy.

All you are doing is throwing out the argumentative fallacy of Appeal to Authority. If you can’t support *YOUR* assertion then don’t make the assertion.

I’m not advocationg anything. I’m just following the trend calculation method used by UAH, since it’s their data set under discussion. If you disagree with their method then it seems to me it should be Dr Spencer and UAH you should be objecting to, rather than me.

Thefinalnail, my initial question was a very simple one “how do YOU calculate…”, because I like to view data as simply as possible, at least initially, to see if there is some common sense element, which in my question one is exposed.

I use the LINEST function on Excel, as I imagine Dr Spencer does.

No you aren’t. Dr Spencer clearly thinks a 13 monthe centred moving average, as presented on his charts, is much more informative. It picks out aperiodic anomalies like major El Niños, while removing the noise from seasonal factors.

There’s nothing wrong with a centred moving average. And there’s nothing wrong with a linear trend. The two aren’t mutually exclusive.

The linear trend is trying to impose a preconception on the data – that the linear trend exists, and will persist. There isn’t good evidence for that – either in the history or in the lack of skill of climate modelling. The moving average allows the underlying noise to be smoothed out, and leaves a lot of room for interpretation of what is happening. That is a much better approach.

Go back to Feynman.

In general, we look for a new law by the following process: First we guess it; then we compute the consequences of the guess to see what would be implied if this law that we guessed is right; then we compare the result of the computation to nature, with experiment or experience, compare it directly with observation, to see if it works. If it disagrees with experiment, it is wrong.We’re still looking for new laws of climate science. Linear temperature trends are failed guesses. They are wrong. Moving average data is a much better place to start understanding climate drivers.

What is the linear trend line for sin(x+a) + sin(y+b) + sin(z+c) + …..?

Does he think it is more informative? I ask because the linear trend is included in the data file, but the 13m centered average is not.

All that the slopes reveal is a crude estimate of the relative changes in the different series over the period of the data. So we can easily pick out that the Arctic has been warming, while Antarctic has not.

The data files are provided with the intent that anyone who wants to can analyse the data. Unlike UEA. He presents the moving average deseasonalisation for discussion in his blog. It is not controversial, and displays no other modelling: it follows the data wither it wanders.

I’m not saying a 13m centered is controversial. It’s not. But neither is a linear regression or many of the other statistical techniques.

I have explained that linear trends are imposed as a subliminal attempt to pretend that the trend is inexorable, even though it wis quite clear to anyone who is statistically competent they do not model the data. That is why they are controversial: they are propaganda. Even when used by Monckton.

OLR is no more or less a subliminal message than a 13m centered average or the countless other statistical techniques used ubiquitously in nearly all disciplines of science. And it does model data. That does not mean it is the best model but it is a model and can be used as an estimator for the data nonetheless. It can even be used to predict the next data point. I showed above that a simple OLR model had an RMSE of 0.18 C in predicting monthly UAH TLT anomalies. Does it model the data perfectly? Nope. Is it the best model? Nope. But it does model the data. That is indisputable.

How anyone can look at the UAH graph (I have attached and modified the graph to show how pulses occur) and get the idea that a linear trend will capture what is happening is beyond me.

The purpose of a linear trend is not to capture every up and down. The point is to try to identify a possible trend that is happening amid the variations.

And how anyone can look at that graph and not realise that the fact that nearly all the left hand side is blue and nearly all the red is on the right, and not realise that suggests a warming trend, is beyond me.

It only suggests a warming trend if, like you accuse Monckton of doing, you PICK a date that has only warming after it!

You can pick any start date up to August 2014 and it shows warming. December 1978 is the best value to pick as it covers the whole range with no bias in it’s selection. Warming of 0.13°C / decade.

I could easily pick start dates that show faster rates of warming, and I could “find” the start date that gives me the longest period where warming is twice as fast as the overall warming rate – i.e. “Since July 2007 the warming rate has been running at double the claimed overall warming rate. That means that for the past 15 years and 7 months, that’s 187 months, the warming rate has been equivalent to 0.27°C / decade.”

But I’d be sure to point out this means nothing, and is based on cherry-picking, I mean finding, the best start point to make that claim.

“

*YOU* are the one advocating for the linear trend analysis. *YOU* should be able to support your advocacy.”Will you ask Monckton to support his use of OLS trends next time he talks about the pause or uses the trend to claim the warming is less than predicted?

No. You can ask him again and save everyone else the trouble.

I’m not the one saying linear trends are meaningless.

I do question why he reports the trend with no confidence interval, especially when talking about his pause, and I challenge him when he talks about a liner trend over the last 150 years, when the trend clearly isn’t linear.

doonman said: “No. You can ask him again and save everyone else the trouble.”Is it safe for use to conclude then that you are okay with linear regression when it outputs < 0 C/decade, but are critical of it when it outputs > 0 C/decade?

Dude, linear regression on a periodic function is not worth the paper it is drawn on regardless of what it shows. You are asking an I’ll posed question. Try to ask a question that is appropriate to the subject.

“Dude, linear regression on a periodic function is not worth the paper it is drawn on regardless of what it shows.”

Not just wrong, but unsupportable. I outed you in a different post on this, Since this is

your convenient claim, please provide any linked support to it.Be so kind as to explain which trend line is the correct one! Or, any other trend line if you so wish.

The flat one I suppose. Using the same evaluative process that gives us the statisticall durable increasing trend for the UAH6 1/83 to present data.

trend this:

And this is a simple sinusoid.

I agree that it is not the cyclical, increasing UAH6 01/83 to present data.

Monckton’s justification is published every time: Dr Phil Jones claims it is OK.

The least-squares method was recommended by Professor Jones of the University of East Anglia as a reasonable method of showing the trend on stochastic temperature data.However, that is plainly false, as any consideration of the historic climate should tell you. The climate does not follow a linear temperature trend. Monckton is in effect jibbing Prof Jones for his lack of knowledge of statistics.

After all, a hockey stick is not a straight line.

What an odd justification. Why would you care if one person said it was OK?

It is done in mockery of a supposedly highly respected climate scientist – or one whose reputation never quite recovered from Climategate.

Because Dr Phil Johns is the only person to have ever used linear regression?

If you think Monckton is just using OLS in jest, do you also agree that all his claims that the rate of warming is much less than models said is also just a joke?

No, they appear to be based on fact. Moreover, fact that is accepted by many climate scientists who fear their work is undermined by their models running too hot.

Some of us Aussies like Warwick Hughes were asking Phil Jones pointed questions about his bad handling of data from about 1990. The Climategate publicity popularised his weaknesses in 2008/9, nearly 20 years later.

In a nutshell, it is fair game to tease Phil Jones because of his horrible contributions to public mistrust of Science in general.

No matter what Phil opined, it is not good science to use ordinary least squares regressions for data that diverge much from linearity. By using OLS on UAH data, you imply belief in a linear mechanism over time that affects air temperature. I do not think that many scientists have assumed that temperatures change with time in a linear manner. That would mean that a warming trend would never end.

I use OLS graphs now and then, but usually try to state their main limitations. They have become widespread in climate work. If I did not add the straight line, some readers would. That is not good, confusing science with eye candy.

Geoff S

“That would mean that a warming trend would never end.”

Which is what the models imply. Let alone AOC and Greta who thinks the Earth will become a burnt out cinder by 2100.

Like it or not but a piece wise analysis of a waveform does give a valid answer for the piece being analyzed. If it didn’t, calculus would be a waste of time and effort. We would be using statistics to do all the math in the world!

Then do it. You keep on saying there are better methods, but never say what they show. I’ve done piecewise evaluations on the UAH data and it shows the best place for a change is 2012 with a sharp uptick in the rate of warming, but I doubt a case could be made that this is significantly better than a single linear trend.

Monckton is using OLS regression to demonstrate that there is no statistically significant linear trend over the stated time interval.

No he isn’t. Where has he ever said that the trend over the last 44 years is not significant? I don’t think he’s ever done any significance test or even quoted a confidence interval.

Monckton is *not* using the trend line to predict the future, only to track the past over a limited period of time.

You *can* draw a linear trend line for sin(x) where x is from 0 to π/4 for instance. It’s not going to be a perfect match, especially at the ends, but if you limit the segment of the sine wave you are looking at you will at least be close.

But you can’t do the same thing from -π/2 to +π/2 or even from 0 to π.

Nobody should be using trend lines to predict the future, certainly not the long term future. This whole argument, I repeat, is not about predicting the future, but answering the question, has there been warming over the last 40 years.

There has been both warming and cooling over the life of the planet. And you are worried about just the past 40 years?

History didn’t start when you were born, you know, right? Far too many of the younger generation today don’t seem to understand that.

“

And you are worried about just the past 40 years?”Not particularly, no. I’m just trying to establish an answer to the question, has there or has there not been warming over the last 40 years?

“

History didn’t start when you were born, you know, right? Far too many of the younger generation today don’t seem to understand that.”It’s been a long time since anyone suggested I was part of the younger generation.

If there is dispute about the degree of warming it centers on poor measurement methodologies and the constant reinvention of the data to cool the past and warm the present. The satellite record is more secure – though not perfect – in that respect.

However, the desire to show a significant degree of warming in the recent past has nothing to do with an innocent enquiry into history and a lot to do with framing of climate derived policies. The use of inappropriate techniques, and the careful choice of starting point are all part of that picture.

“

The use of inappropriate techniques, and the careful choice of starting point are all part of that picture.”This entire thread starts because someone claims that on the basis of two carefully selected months of UAH data there has been no warming over 40 years.

It’s now resulted in people defending Monckton’s careful choice of a starting date to claim there has been a pause in warming.

“This entire thread starts because someone claims that on the basis of two carefully selected months of UAH data there has been no warming over 40 years.”

No one is claiming that. Your paranoia is showing again.

“It’s now resulted in people defending Monckton’s careful choice of a starting date to claim there has been a pause in warming.”

And, for the upteenth time, Monckton didn’t *PICK* a start date. He *found* a start date. You are one obsessed stalker! Like a stalker of a woman you’ve built an edifice in your mind that Monckton *picks* a date and you just can’t let it go.

“

No one is claiming that. Your paranoia is showing again.”Literally the first comment in the thread

https://wattsupwiththat.com/2023/02/01/uah-global-temperature-update-for-january-2023-0-04-deg-c/#comment-3674481

“

And, for the upteenth time, Monckton didn’t *PICK* a start date. He *found* a start date.”I don’t care how umpteen times you say that. It’s just your weird mental block that means you have to distinguish between “finding” and “picking”. It makes no difference. The objection is that Monckton “finds” the date that will give him the longest possible “pause” and chooses that date to be the start of his trend line. It is a bad statistical technique.

“

Like a stalker of a woman you’ve built an edifice in your mind that Monckton *picks* a date and you just can’t let it go.”Really offensive.

“The objection is that Monckton “finds” the date that will give him the longest possible “pause” and chooses that date to be the start of his trend line. It is a bad statistical technique.”

Simply unfreakingbelievable!

He is LOOKING for the length of the pause. *YOU* want to claim there is no pause so you keep accusing him of doing something that he isn’t doing.

It’s a PERFECTLY LEGITIMATE STATISTICAL TECHNIQUE!

“Really offensive.”

Sometimes the truth hurts. You can’t distinguish between finding something and picking something. You’ve already admitted that you think someone backtracking from a dead deer to FIND where he was shot is PICKING the spot where the deer was shot. It’s like you can’t distinguish between the present and the past!

“

It’s a PERFECTLY LEGITIMATE STATISTICAL TECHNIQUE!”Stop shouting, and provide some reference. Where does any text claim that looking back at every possible start point until you find the result you want is a legitimate statistical technique?

To claim you know the length of a pause requires you to first establish there is a pause. That requires you provide statistical evidence for the existence of a pause, not simply look for periods when the trend is flat.

Monckton’s “choice” of starting date is no such thing. It is derived from a pure statistical criterion. If we get another major El Nino his technique will rapidly show that there is no current “pause” until some time after it has subsided. That is of course what happened in 2016. Fourier analysis is more robust in not being side tracked by an El Nino spike.

“

It is derived from a pure statistical criterion”the criterion being to find the start date that will give you the longest possible non-positive linear trend. I’m not sure I would regard that as pure statistics.

“

Fourier analysis is more robust in not being side tracked by an El Nino spike.”Or any other form of curve fitting – high level polynomials, splines, Loess etc. They can all show the ups and downs, but that doesn’t mean they are actually describing what is happening. They are all just giving the best fit to the existing data.

“Or any other form of curve fitting”

AGAIN – FOURIER TRANSFORMS ARE

*NOT*CURVE FITTING.The frequency domain and the time domain are different domains! See the attached graph. There is *no* curve fitting.

You are still embarrassing yourself.

It seems that climastrology has it own esoteric definition of the term “transform”.

Beyond incredible.

It’s all got to be statistics all the time. There is no such thing as a frequency domain that you can map a time domain function into!

What do you think a frequency is if it doesn’t involve time? The only difference between a frequency and a time domain is the figures you use. A frequency is still something that maps to the time domain, and there’s no point in doing this analysis if you don’t think it describe the shape of the time series.

here is the graph showing a cosine function in the time domain and in the frequency domain.

By performing a low pass filter you are removing data.

Imagine if you set the low frequency cut off to 1 cycle per century, (since the data is well less than this length), you would effectively eliminate ALL cyclic data and be left with a straight line.

Similarly, if you used a HIGH pass filter, set for one month then you would have no linear data at all, it would all be sine waves from end to end.

When you exclude data, you exclude details that are most probably worthwhile. Would you listen to music with a low pass cut off of say 5kHz?

I am not throwing away data: the high frequency harmonics are the difference between the actual series and the low frequency elements by construction, and I show both in the chart. Linear trend estimates exclude almost all the data. The Fourier analysis is designed to use frequency analysis to clarify how the very noisy data is influenced on different timescales. High frequency components are usually associated with discontinuities: think of the Fourier analysis of a square wave. So when we look at the full spectral analysis we find strong aliasing high frequencies that help describe the El Nino spikes. Those clearly have a different, and reasonably well understood basis. So what are we left with? It’s not a linear trend. More medium/high frequency fuzziness and oscillation, and perhaps some slower moving elements that may be easier to understand if we have an idea of what we arae looking for.

“may be easier to understand if we have an idea of what we arae looking for.”

Are the CAGW advocates actually looking for anything?

Catastrophe.

Do you think the top is in?

The reliability of trend estimates is always flakiest at the ends of the data. Clearly the 2016 El Niño is going to be a local peak in the long run. In the very long run the earth will eventually get very hot as the sun goes through its red giant stage, so it is not a global peak.

I have your post bookmarked. What will your response be to challenges of your prediction if the local peak in 2016 is eclipsed?

It’s already a local peak. Not eclipsed for at least 6 years. I am not making predictions that I can’t justify. We do know that the sun will become a red giant, eventually engulfing the earth. Climate projections over the next century? I see no evidence that we have good models, so unlike Al Gore or David Wadhams I’m not going to make a stupid guess.

Oh, got it. You’re just saying it is a local peak on yearly time scales, but not necessarily on decadal. I get that it will almost certainly be warmer as the Sun (like all main sequency stars) continues to brighten. But the current brightening rate is like 1% every 120 million years and far beyond the decadal and centennial scales we typically discuss here.

The trend from your fourier analysis is not significantly different from FinalNail’s. His was ~1.40 degC/century, with a standard error of ~0.07degC/century. Yours is ~1.32 degC/century, with a standard error of ~0.04 degC/century. Yes, I can see the sinus rhythm, and also how it trends, per Mr. Gorman’s question. I’ll post it.

Since the f anal improves the statistical durability of that trend, let’s see how hard it would be for that trend to be down instead of up. Not lookin’ that promising for you…

Here’s the fourier output

It is quite inappropriate to draw a trend through the Fourier transform. If you look at the fundamental harmonic, which has the biggest amplitude, it is headed down. The phases of some other harmonics are now also in sympathy with the downward movement. But the analysis tells us nothing about what happens outside the data period.

It is important to understand that Fourier analysis says very little about the future. By decomposing to the frequency domain it allows us to consider whether there are factors that we can identify that account for the observed frequencies. If we cannot find such factors, then all it is telling us is that the mathematical technique deconstructs the data analysed into the given sum of sinusoids.

Far too many of the people supporting CAGW are statisticians only. Trend lines are their bread and butter. They don’t understand that FT gives you *frequency components*, not linear data points. It goes hand in hand with not understanding that trending cyclical processes can’t be done using trend lines, especially trend lines extending into the future.

What is the trend line for a sine wave?

“What is the trend line for a sine wave?”

Anycyclical wave can have an upward, a flat, or a declining underlying trend. Just the seasonality of upward trending temp data shows us that.Folks, the selectivity of trends some here like v those they find inconvenient, is all telling. The best example is the pimping of the current GAT “pause”, while deflecting from the much more statistically/physically significant rise, many times longer.

Who are these alleged “folks”, blob?

So define the trend of a sine wave, as you were asked.

Look at it over -π/4 to π/4 and you will conclude it has a positive slope. Look at it over 3π/4 to 5π/4 and you will conclude it has a negative slope. Or not.

The phasing of your fourier data appeared to have ended about when it began. FYI, it is cyclical, but not regular or repetitive. It’s biggest characteristic is that it is

increasing, with time. And no, I won’t cherry pick it…Of course you can have a function y(t)=αt + sin(βt+φ)

Which you can decompose into a linear trend αt and a cycle sin(βt+φ). But the cycle has no trend, and the linear trend has no cycle. The point about the AR1 analysis is that it confirms that the data show no sign or a trend, and the point of the Fourier analysis is that we find the important frequencies are either low or high. High frequencies are associated with discontinuities and spikes. The low frequencies therefore display the behaviour once those are accounted for.

You just love being hoist on your own petard don’t you?

Attached is the *long term* data you should be looking at as posted by Dr. Vinos.

What so many CAGW advocates *always* conveniently forget is that in its earliest formation periods there was *lots* of CO2 available in the atmosphere. A *lot* of it became oil and coal deposits. A *lot* of it because sedimentary rock. If CO2 actually “traps heat”, none of this would have ever happened. The earth would have remained a cinder throughout its entire history.

Let’s continue to run trend lines against time even when time is NOT a variable that predicts anything. Moving into the frequency domain will allow a closer look at factors that are truly part of the climate.

It is refreshing to have your to the point analysis of the limited data available.

The fact that the fourier series is last headed down tells us nada.

The trend of

anydata series tells us nada about what happens after. The name of the game is to identify those trends and use them to guide further inquiry. This is what the deniersphere attempts to avoid by statistically invalid whining about these strong trends….“deniersphere” — HAHAHAHAHAHAH

blob lets his true colors show, just another Klimate Change Kook.

A complete inversion of the truth. The statistically invalid trends are linear trends concocted from data that does not conform to the requirements for making linear trend estimates. In the course of this thread, I have shown that the UAH6 data do not conform to the requirements for making linear trend estimates. I have shown that if you construct an AR1 model of the data there is no trend left. I have shown that Fourier analysis reveals far more about the nature of the data, and helps to isolate the effects of the well known El Nino phenomenon. That process also suggests that the data are for now headed down. It says nothing about what is likely to happen more than a few months hence.

It is the catastrophists who wish to rely on linear trends where there are none, and who ignore what the data are revealing. If Newton had tried to covert everything to linear trends he would never have discovered the laws of gravitation.

Maybe you don’t know what conditions were like at the start of the record.

When are people going to learn that linear trends on high variance data aren’t useful for trending, especially linear trends.

Look at the graph at the link below and tell folks why temps continue to return to a base line. At the next 30 year baseline change what do you think this graph will show?

I’ll bet it continues to show up/down and down/up excursions.

What if we started our graph in March, 1998, instead of when all the doomsayers start it, near the end of the coldest period in the last century? So it would essentially show cooling of some sort in the last 25 years out of billions rather than a warming trend in the last 44 years.

Hey, but 0.14C per decade over a billion years is 14 million degrees of warming! Which would make our planet literally burn. Greta was right! OMG! Science!

“

Note that our gradually warming planet first reached this anomaly in 1983. So that’s 40 years of no warming.”And in 1984 it was -0.67°C, whereas three months ago the anomaly was +0.32°C, so that’s almost 1 degree of warming in 40 years.

Maybe best not to rely on picking single months to make a claim.

But today it’s -.04 deg and you haven’t explained what caused the cooling. It must be increased CO2 in the atmosphere, right?

Why do I have to explain anything?

There’s a clear upward trend, but with a lot of variation to each monthly value. The variation can be for a number of reasons, most noticeably ENSO conditions, but I don’t have to explain every single monthly value to see the underlying trend, and that clearly temperatures at present are not the same as they where in the 80s. The fact that people are getting exited over a single month which would have been one of the warmest in the 80s is a clear sign that temperatures now are on the whole warmer.

Is there a clear upward trend still?

From December 1978 to January 2023? Yes. Rate of 0.13°C / decade with a 2 sigma confidence of ± 0.05.

Has anything happened in the last few years to indicate the trend may still be upwards? Not that I can see. There was a big jump in temperatures since 2015 which increased the overall rate of warming a bit, temperatures since then seem to be following the trend, sometimes above it, currently below it, but nothing to indicate a significant change in the rate of warming.

Will this continue indefinitely? Couldn’t say, but I prefer to see some actual evidence for a a change before assuming it must be happening.

I have already explained why your confidence limit is nonsense: it is based on assumptions that do not hold. The Fourier analysis shows there is a significant chance that we are now in a cooling phase. It also clearly illustrates the “pause”. Analysis based on assuming linear trends is clearly flawed. Now, I am not claiming that I magically have the perfect climate model to explain it all. But it really is not difficult to show that what we have at present is junk. “If it disagrees with experiment, it’s wrong.”

“

I have already explained why your confidence limit is nonsense”Then say what you think the confidence interval should be.

“

it is based on assumptions that do not hold.”What assumptions do you think I’m making? My estimated interval was based on the correction for autocorrelation used by the Skeptical Science Trend Calculator. If you have a method that will increase the interval further let me know. But the problem is the larger the interval the less likely you going to be able to show a meaningful change in the rate of warming.

“

The Fourier analysis shows there is a significant chance that we are now in a cooling phase. It also clearly illustrates the “pause”.”What are the confidence intervals on your Fourier analysis? My problem with all the talk of Fourier analysis is that statistically all you are doing is an exercise in curve fitting. The danger is you are over-fitting. It’s not good enough to say that you can fit a curve to the existing data that shows a pause. You need to show that the pause could have been predicted with data prior to the pause.

“

Analysis based on assuming linear trends is clearly flawed.”Standard adage, all linear models are wrong, but they can be useful. As yet, I’ve yet to see any convincing evidence that a linear rate of warming is seriously flawed. It may not be correct, it may change in the future, but to date there’s no clear indication that there is anything over than a linear trend with noise.

“What are the confidence intervals on your Fourier analysis”

A Fourier Transform is *NOT* a statistical analysis with a confidence limit. Didn’t you even bother to go look up what a FT is?

From wikipedia: “The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that frequency, and the argument of the complex value represents that complex sinusoid’s phase offset. If a frequency is not present, the transform has a value of 0 for that frequency. ”

“My problem with all the talk of Fourier analysis is that statistically all you are doing is an exercise in curve fitting.”

Again, the FT is *NOT* a statistical tool. There is no curve fitting.

“As yet, I’ve yet to see any convincing evidence that a linear rate of warming is seriously flawed.”

Willfully blind. Go look at the recent thread started by Andy May. I’ve attached a graph from the talk by

Dr. Javier Vinós.If you can’t see the cyclical nature of both the temperature and CO2 then you *are* willfully blind.“

Willfully blind. Go look at the recent thread started by Andy May. I’ve attached a graph from the talk by Dr. Javier Vinós. If you can’t see the cyclical nature of both the temperature and CO2 then you *are* willfully blind.”We are not talking about changes over millions of years, just the last 40. And, no I’m not sure what cycles you are seeing in the graph. A cycle would imply that at some point you return to an original value. Both your lines are dropping on the whole throughout the last 50 million years. there are ups and downs along the way, and that may in part due to natural cycles, but there is no obvious repeating, predictable cycle that appears to be controlling either over that time period.

In other words “don’t confuse me with the facts”!

Good come back. I will try to follow your request.

“

A Fourier Transform is *NOT* a statistical analysis with a confidence limit.”Which is the problem. Even if temperature changes are caused by multiple sine waves, you still have to show that what you’ve got from your analysis is not just noise.

“

There is no curve fitting.”But that’s exactly what you are trying to do.

What do you think the “original function” is? You are trying to identify it by looking at the actual temperatures, and that means finding the composition of multiple sine waves that best fit the data.

“Which is the problem. Even if temperature changes are caused by multiple sine waves, you still have to show that what you’ve got from your analysis is not just noise.”

Noise, especially white noise, shows up as a flat line in a fourier transform. White noise is basically a combination of an infinite number of frequencies of the same magnitude. Other types of noise with different magnitudes and bandwidth still show up across the spectrum involved. If the noise magnitude and signal magnitude are very close together it can be almost impossible to separate them out. That doesn’t seem to be the case with the analysis of temperature and CO2.

“What do you think the “original function” is? You are trying to identify it by looking at the actual temperatures, and that means finding the composition of multiple sine waves that best fit the data.”

The original function is a periodic function made up of sinusoids – which is what the true historical temperature record is. Again, there is NO CURVE FITTING.

The FT is basically defined as F{g(t)] ∫ g(t) e^(-2πft) dt

It is a MAPPING, not a curve fitting.

These guys should give up anything that has “oscillation” or “cycle” in the description. ENSO, AMO, SUNSPOT CYCLE, PDO, SEASONS, and on and on. These periodic functions apparently have nothing to do with climate. The mapping from the time domain to the frequency domain appears to be a nonstarter amongst them! No wonder why CO2 is the easy choice to dwell upon.

Fourier analysis is not a problem. It is a way to help look for features that may be important in determining the behaviour we observe. If they chime, we have a winner. If not, at least we looked.

Having identified serial correlation, if we include the previous period reading as an explanatory variable we find that it dominates the regression with a coefficient of 0.754. The linear time trend falls to being 0.0333 C per decade as a central estimate, and borders on being statistically not different from zero.

I’m not sure you understand how autocorrelation works. It doesn’t cause a trend, unless the coefficient is 1.

Precisely. Since the coefficient of the lagged variable is significantly different from 1 (Dickey Fuller unit root test) the analysis finds NO trend. It is mean reverting.

I’m not sure you understand that.

Which is why the fact that temperatures have not reverted to the mean is a good indication that there is a trend.

No. It just means that we are still part way through a cycle.

Which is a completely different claim to the one about most the rise being caused by autocorrelation.

No. Autocorrelation just means that you cannot get reliable estimates of a trend using OLS. Simple example: Real data is a parabola – say the trajectory of a golf ball drive on the moon. A linear trend calculated through the data will chop through it, with sections where the residuals are of the same sign at each end, and the opposite sign in the middle. That is, the residuals are highly autocorrelated. That tells us that the linear model is wrong. We should be looking for some sort of curve function. We get further clues if we slide our data window to find that the linear slope changes accordingly. The linear trend has no reliable estimate, because there isn’t one.

A linear trend crossing a parabola is clearly wrong. That’s not because of autocorrelation, it’s just that the parabola is not linear.

“

We get further clues if we slide our data window to find that the linear slope changes accordingly.”That will happen with no autocorrelation as well, it’s just that autocorrelation increases the uncertainty of the trend so you will get more of a change.

Let’s see, I believe the IPCC said something along the lines of “long-term prediction of future climate states is not possible because the climate system is a coupled non-linear chaotic system.”

And, what did you say about a linear trend? “it’s just that the parabola is not linear.”

How do you reconcile these two disparate statements and use of linear trends?

Why do you think there is anything that needs reconciling those two statements? A linear trend is not a good fit for something that isn’t linear. You’d have to give me some context for the IPCC paraphrase, but it doesn’t in any way contradict the idea that a linear trend is not a good fit for a parabola. I’m really not sure what point you think you are trying to make.

Geez, you said that a linear trend IS NOT a good fit for something that is not linear.

The IPCC has said climate is non-linear. Why do you then insist that your linear regressions mean anything.

I’ll give you something from my business experience. If your linear trend depends on the starting and ending points, then you need to make it stationary before proceeding.

I’ve not claimed the linear trend means anything other than there appears to be a linear trend over the last 40+ years, and that this is a useful way to show there has been warming over that period.

We know what caused the cooling. ΔE < 0 in the TLT layer. Remember, the 1LOT says that ΔE = Σ[Ein_x, 1, N] – Σ[Eout_y, 1, N]. CO2 is but one among many of the Ein_x and Eout_y components. It is possible for Enet_CO2 > 0 simultaneously with Enet_others < 0 and ΔE < 0. Remember, the 1LOT is the law of conservation of energy. It says in no uncertain terms that it is a violation of the law to ignore the energy flows of the non-CO2 components.

We’re still in a La Niña so this isn’t surprising. I think it will still be cooler for a couple of more months, but then it will get interesting. ESNO conditions are expected soon and we’ll finally able to get a true sense of where the global temperature is without the influence of neither La Niña or El Niño. I’m hoping for a return to the old pause. There needs to not be global warming for this whole agenda to end.

Yea, but this La Nina has been weak, not far from neutral, for months now. Any way one cuts it, it is clear that natural variability rules over the magic molecule.

Not according to NOAA.

The index has been at or around -1.0 for most of the past year. Latest value (Oct-Nov-Dec 2022) is -0.9. The NOAA La Niña threshold value is -0.5.

This one is not even in the top 8 since 1950 according to NOAA.

A couple of posts back you were claiming that the current ENSO value was “not far from neutral”. Now you seem to be saying that it’s the 9th coolest La Niña since 1950. That’s quite a switch.

It has not been far from neutral relatively.

Well, it sort of

has. Declaring El Niño or La Niña conditions is, by definition, a relative departure from neutral.Keep in mind that NOAA changes the baseline every 5 years. As a result this La Nina is based on a higher baseline than previous ones. This has increased the index by several tenths of a degree. On a flat baseline it’s even weaker.

Yes Richard, but if it didn’t do that then the value would become meaningless, because the sea surface temperature in the region is rising over the long term.

If were based on a flat baseline then it would no longer be an oscillation. Remember, it is detrended specifically so that it can represent the El Nino Southern

Oscillation.TheFinalNail

In any case, the reason why it’s been so elevated lately despite La Niña is due to extra tropical warmth in the Northern Hemisphere. If you really think that that is being caused by greenhouse gases, I don’t know what tell you. I think it’s just easy to blame it on GHGs. I’m convinced at this point that the rise in global temperature has been mostly dominated by the oceans.

Well, GHGs block more of the Eout than the Ein. And the 1LOT says that ΔE = Ein – Eout. So if ΔEout < ΔEin then ΔE > 0. And because ΔT = ΔE/c*m then ΔT > 0 as well. Of course, if you don’t accept the 1LOT or that polyatomic gas species impede the transmission of terrestrial radiation more than solar radiation then you likely won’t accept that GHGs have an influence.

BTW…how do you think the oceans got warmer?

I’m convinced that the culprit responsible for the oceans warming are underwater volcanoes and the AMO. When looking at the graph, you see a slight cooling take place through the early 21st century but then the El Niño comes and ever since then we’ve been stuck on a new baseline, but maybe just maybe we’re going back down to the old pause. A good hypothesis for the El Niño are underwater volcano eruptions. I don’t think GHGs have no effect, but I’m not very convinced that it’s been the main culprit. All of what you’re saying is probably true. It’s just a question whether it’s the main culprit or not.

Here is a video explaining more of that and it’s effects around the world by Wyss Yim frong Hong Kong.

https://youtu.be/OlTlMXR_tSw

Which underwater volcanoes are responsible for the warming?

Where is the AMO getting the energy to warm the planet?

Walter,

We are still in a La Nina so this (cooling) isn’t surprising.

OR:

We are still cooling so it is not surprising to have a La Nina.

(Some definitions of La Nina involve cooling temperatures near Equatorial Pacific Ocean).

…………..

Temporal cause and effect is often confused in climate talk.

So many more mechanisms remain to be understood, while pop climate relies on CO2 control knob gossip.

Geoff S

Yesterday morning at 06:40 I started the big truck for a run up to Grand Rapids, MI and back. It was 6 deg. F. It was the kind of cold that is more bitter and bites harder than the temperature indicated though there was little wind.

Took 20 minutes idling before the truck got warm enough inside so that my Samsara tablet would work. The driver can’t move the truck until the logs can be accessed and the log and dispatch information is on that tab.

I’m sure that you are anxiously awaiting the day that all trucks are battery powered. 🙂

I am retiring this year!

I mentioned this data on the Facebook page of a certain group here in the U.K. and the response was, what does tropospheric temperature have to do with temperatures lower down, or words to that effect, clearly thinking there’s impenetrable barriers between the different layers of the atmosphere.

We live in the lower troposphere.

That is true, but you must remember the Alarmists are mostly an underground movement. It is pretty near impossible to get through their impenetrable brains. 🙂

Ask them if they think the lapse rate is changing. It scientifically links all the temperatures in the troposphere.

Good to see the spreadsheet in the text. One line could be added: the trend per region. People should be remembered the large regional differences resulting from natural variation.

The absence of warming in the Antarctic and the opposite, large warming of the Arctic, show that there cannot be a general cause for ‘average warming’. And also show there is no global warming. Natural variation and natural causes are in play.

You can check the trend per region in the UAH data. It’s the bottom value in each column.

The global value is shown as +0.13C per decade warming; so it’s hard to see how you reach the conclusion that there is no global warming.

The Final Nail:”You can check the trend per region in the UAH data. It’s the bottom value in each column.”

WR: Of course I know. The trend is 0.01 degrees per decade (!) for Antarctica and 0.25 degrees per decade for the Arctic. And there are still people who think that those numbers reflect a warming that is global.

It should be noted that there is an increase in the seasonal range of CO2 from the South Pole to the North Pole. Despite the claim of CO2 being “well-mixed,” the range is quite asymmetrical.

WR: If you refer to some maps or videos that suggest by using intense colors there is “quite an asymmetry”, you probably forgot to study the map legend. For example in the video below the legend shows a minimum and maximum value of resp. 390 and 408 ppm. Not “quite an asymmetry”.

https://www.google.com/search?sxsrf=AJOqlzVvUquRAOFzmnMuYpmAwu4FFxgXpg%3A1675380118013&lei=lkXcY_8xtI327w_s-aTgDw&q=nasa%20co2%20time%20lapse&ved=2ahUKEwj_1LCm_ff8AhW0hv0HHew8CfwQsKwBKAB6BAhaEAE&biw=1356&bih=705&dpr=2.5#fpstate=ive&vld=cid:ca2eb288,vid:TrQzbXc6LVE

I wonder if the alarmists are getting nervous yet?

El Nino is their only hope now.

El Ninos occurred during the cooling that took place from the 1940’s to the 1980’s. The El Ninos didn’t prevent the temperatures from cooling at that time.

Not much to hang your hat on.