Guest Post by Willis Eschenbach
I have the world’s best science gig. I can research whatever I want, whenever I want, for as long as I want, and I don’t get paid a dime no matter how hard I work. What’s not to like?
In any case, I got to wondering about how many temperature stations we’d need to get an accurate idea of the average temperature of the earth. Being a data guy rather than a theory guy, I figured I could use the CERES dataset to take a first cut at the question.
Let me preface this by explaining the temperature dataset I use in my analyses. The CERES radiation datasets don’t contain a surface temperature dataset. However, they have an upwelling surface upwelling longwave (thermal) radiation dataset. Because many of my analyses use the CERES dataset, I used the CERES surface radiation dataset to create a surface temperature dataset. I did the calculation using the Stefan-Boltzmann equation and utilizing the gridded surface emissivity from here.
How good is the resulting CERES calculated temperature dataset? Here’s a comparison with the Berkeley Earth, HadCRUT, and Japanese Meteorological Agency datasets. Seasonal variations have been removed from all datasets.
As you can see, the calculated CERES surface temperature agrees with the other three as well as they agree with each other. Turns out it also agrees better than either the HadCRUT or the JMA dataset with the Berkeley Earth dataset… so I use the CERES data in this and my other analyses. However, as indicated by the graph above, it makes no practical difference which dataset is used. Doing the following analysis on the Berkeley Earth gridded temperature dataset gives essentially the same results as using the CERES dataset.
With that as prologue, my scheme was to randomly pick a subset of the 64,800 1° latitude by 1° longitude gridcells that make up the earth’s surface, and see what that subset gave me as an average temperature.
The most interesting results were when I used just one percent of the gridcells (n = 648). Here’s an example of one of the random selections of 1% of the gridcells.
As you might imagine, running the random example many times gave very different average temperatures from different random subsets of 1% of the gridcells. Here’s a histogram of the average temperatures of a typical run of 100 trials using only 1% of the gridcells.
The average temperatures range from 13.5 to 16.5 degrees, so there is little agreement between subsets. No surprise, as I said.
But my next graph was a surprise. I decided to plot the monthly data for some of the individual runs. Here’s an example of ten runs, including the linear trend lines. I’ve removed the seasonal variations from each dataset.
Two things were surprising about this. One was that the trends were all pretty much identical. I expected much greater differences using only 1% of the data.
The other was that the actual monthly results were all so similar, having the same overall shape with just a different average temperature.
To investigate further, I plotted up the anomalies for each of the runs. I created the anomalies by subtracting the average of each run from the values of that run. Here are those results.
Fascinating. Although we can’t get much clarity on the absolute global average temperature from 1% of the data, we can use that same 1% of the data to get a pretty good idea regarding the overall trend and the monthly variations in the global average data. None of the individual 1% runs vary much at all from the global average, and their trends are tightly clustered. I didn’t expect that at all.
Next, I got to thinking about the oft-repeated claims that the Little Ice Age back in the 1600’s – 1700’s was just a Northern Hemisphere phenomenon, or that it’s only based on land records, or both. So, I thought I’d take a look at just the NH land data, to see how random subsets of just the northern hemisphere land matched up with the global data. Of course, since the NH land is much smaller than the globe and it’s land rather than ocean, the temperature swings in the average NH land temperature will be larger than the swings in the entire global average. So in order to compare them, I’ve adjusted for that in the following graph.
Again, most interesting. With knowledge of the temperature in around a hundred twenty randomly selected gridcells out of the 64,800 total gridcells, with the known gridcells located only on land and covering less than a quarter of one percent of the earth’s surface, we can closely approximate both the global temperature anomaly and the global temperature trend.
Any given run may or may not be all that exact a match to the entire globe, but none of them are much different, and their trends only vary slightly … which makes me misdoubt the idea that the Little Ice Age was a local phenomenon.
Seems like a validation of what I modestly call “Willis’s First Rule Of Climate“, which states:
“In climate, everything is related to everything else, which in turn is related to everything else … except when it isn’t.”
Best of life to everyone,
w.
As Always: I ask that when you comment you quote the exact words you are referring to. I can defend my words. I can’t defend your idea of what my words say.
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Interesting approach. Berkeley Earth appears to have been stepped on.
The top chart seems to show reasonable agreement among the various approaches, but I don’t think any of them ‘track’ very well with CO2 over the period in question.
Willis,
Yes, you don’t need that many cells. A decade or so ago Eric Steig wondered what could be done with just 60 stations. Much later I tried, using surface thermometers (land+SST), the following method. I tried successively culling by the assigned weights of my spatial method (those of least weight). But I included some randomness in the successive culling, so there was a range of different trajectories. I started with 4759 stations (GHCN V3 days). And indeed it was good up to around 648 locations, and diverged after that. Here is the plot:
I think if you want to take this further, you’ll need an area weighting scheme. Not by area of cell, but by the area around the cell – ie taking account of the empty cells. The need is small while you can rely on the iinitial regularity, but that gets more as you cull randomly.
I think too that you should use cell anomalies – ie subtract cell average before spatial averaging, rather than after, as I think you are doing. Again it doesn’t matter so much with a regular grid, but will as you subselect.
Oops, bad link there. It should be
https://moyhu.blogspot.com/2017/04/global-60-stations-and-coverage.html
Nick – If I’m reading Willis and you correctly, you are not addressing Willis’ point, which was that 1% of stations are enough for overall trend and monthly variations in the global average data, but not the global average temperature at a point in time (which is what you appear to be addressing).
Mike,
Well, he said
“In any case, I got to wondering about how many temperature stations we’d need to get an accurate idea of the average temperature of the earth.”
But yes, I did not go on to look at time variation. Still, if you get the monthly right, the rest should follow.
Again, as I read it – Willis’ very interesting point is that with the 1% you get the rest without the monthly.
Nick, Nick, Nick… Puhleeze!
Eric Steig has proven himself to be a climate alarmist with ZERO credibility.
Remember this?
https://www.nature.com/articles/nature07669
https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2Ftse1.mm.bing.net%2Fth%3Fid%3DOIP.k6OimBGzMtKN2ktdBCBIIwAAAA%26pid%3DApi&f=1&ipt=afb775898460df27476cf9bfc8bbc70f2e46c3b04f4f2d38a904348468cb2baf&ipo=images
Willis,
For years, I continue to be amazed by your clarity, brevity of reasoning.
For all our sake, we need to somehow completely undress the IPCC, to show its emptiness beneath all the lies.
It wouldn’t matter what station temperatures you use and from where gathered, unless there are adjustments made for surface pressure, wind direction and speed, the surface the wind has travelled over, relative humidity and the elevation of each station, the data derived is untrue and as useless as the concept of a global average.
There is no average weather around the globe nor can there be any average components of the weather. The most that can be said is that such measurements lie between high and low limits and how long should the time interval be over what is being measured? One year, ten years or the thousand? Unless you have experienced first hand the weather at many altitudes at all times of the day and night and the year and over a wide area, you really can’t appreciate the large variations occurring all the time.
This apparent evidence that climate trends are worldwide lends further credence to the below “proof’ that our climate is perfectly normal since it is within historical norms. it does this by removing the counter clam that previous warm periods were local to the European region:
The argument that our climate is normal:
5000 years ago, there was the Egyptian 1st Unified Kingdom warm period
4400 years ago, there was the Egyptian old kingdom warm period.
3000 years ago, there was the Minoan Warm period. It was warmer than now WITHOUT fossil fuels.
Then 1000 years later, there was the Roman warm period. It was warmer than now WITHOUT fossil fuels.
Then 1000 years later, there was the Medieval warm period. It was warmer than now WITHOUT fossil fuels.
1000 years later, came our current warm period.
Climate alarmists are claiming that whatever caused those earlier warm periods suddenly quit causing warm periods, only to be replaced by man’s CO2, perfectly in time for the cycle of warmth every 1000 years to stay on schedule. Not very believable.
The entire climate scam crumbles on this one observation because it shows that there is nothing unusual about today’s temperature and thus CO2 is not causing warming or any unusual climate effects that are frequently blamed on warming.
Evidence that those warm periods actually occurred:
http://www.debunkingclimate.com/climatehistory.html
Evidence that the Roman & Medieval warm periods were global:
http://www.debunkingclimate.com/warm_periods.html
http://www.debunkingclimate.com/page216.html
Jim Karlock:
The earlier warm periods were due to a near absence of volcanic eruptions, so that their atmospheres were essentially free of volcanic SO2 aerosol pollution, As a result, the intensity of the solar radiation striking the Earth’s surface was undimmed, resulting in higher temperatures, and causing them to be global events.
They ended when volcanic eruptions became more frequent, polluting the air, and after the MWP resulted in the LIA, which was also a world-wide event,
The point of this is simply that cleansing the air WILL cause temperatures to increase, and that is exactly what we have been doing through our Clean Air and Net Zero efforts.
People are trying to explain away our rising temperatures because they have happened before. Yes, they have, but now WE are causing them to rise.
We are approaching a catastrophe of our own making! And we may already be at a tipping point.
Burl wrote “The earlier warm periods were due to a near absence of volcanic eruptions,”
Really ALL FIVE, right on schedule with today’s warming every 1000 years!
Burl wrote: “Yes, they have, but now WE are causing them to rise.”
So you are claiming that five were due to volcanoes but they quit so now man’s CO2 takes over RIGHT ON SCHEDULE!
WOW – What logic!!
Jim Karlock:
The Minonan Warm period, the Roman Warm period, and the MWP were all due to low volcanic activity, I haven’t researched the others, but to claim that they occur every 1000 years is nonsense.
And it is NOT man’s CO2. It is our cleansing of the air.
So, you advocate having dirty air to prevent beneficial warming?
Tom in Florida
You are wrong on both counts.
I am NOT advocating dirty air, just pointing out that the cleaner the air, the hotter it will get. A scientific fact.
And warming is beneficial only up to a certain point. If it reaches the level of an El Nino, there will be many weather disasters
Actually that crazy idea is one that the eco-nazis toss around. Ocean fertilization with a little bit of iron powder is VERBOTEN! But take a known pollutant, that every one agrees is a pollutant, design a ridiculous scheme to spread it out high in the skies over everyone’s home, and suddenly you have government grant funding.
Vesuvius obviously never happened, Thera never happened, none of the other historic and pre-historic volcanoes we have proof of never happened? There is enough proof in the landscape that our present level of vulcanism is about the same as it has been for millennia. Just because you didn’t see it happen on CNN doesn’t mean it didn’t happen.
Richard Page;
My data source is “Volcanoes of the World, Third Edition (2010).”
Far from just looking at the landscape!
That’s a shame because if you looked at the landscape you’d see a world of wonders, a world littered with evidence of our volcanic past. A book like that will just mention a limited few of the interesting ones, the ones that were witnessed (hence CNN), not the ones that we have abundant geological evidence for but no eyewitness statements.
Richard Page:
You obviously have not seen the book, 550 large pages.
It lists dated (with uncertainty estimates) eruptions from 9,950 BC through 2006, 110 pages with ~200 volcanoes per page, with VEI’s of 0 through 7+, and durations (both also with uncertainty estimates), locations, and how identified.. A very detailed volume
If “you own the science”, you can spout any “logic” you want, and spread that “logic” using the big tuba of the subsidized, lapdog Media
Please quantify how much cleaner the air is today than in say, 1970, with double the population and double the manufacturing and consumption. (at the very least)
Mike:
Industrial SO2 aerosol emissions into the troposphere peaked at 136 million tons in 1979, then began falling in 1980 due to global “Clean Air” efforts, dropping to 72 million tons by 2019 (latest data available, but less than that now).
Since 1980, satellites have been used to measure the amount of SO2 injected into the stratosphere by VEI4 and larger volcanic eruptions.
For a VEI4 eruption, the average amount is 0.2 million tons, and it cools the Earth by about 0.2 deg. C. (and warms it by approx. the same amount, when the SO2 aerosols eventually settle out).
The increase in average anomalous global temperatures due to the 64 million ton reduction in SO2 aerosol pollution easily accounts for all of the warming that has occurred since 1980. Jan-Dec land-ocean avg temp was 0.196 Deg. C in 1980, and 0.801 Deg. C in 2022, per HadCrut5.
Bear in mind that temperatures ALWAYS rise when there is less pollution in the atmosphere
The amount of SO2 aerosol pollution in Earth’s atmosphere in 1980 versus today can be visualized by examining NASA/GMAO images of global SO2 aerosol pollution. This image is for 1980
This image is for 2023
Looks like Atlantis’ sister mythical city of Pacifica was polluting with abandon in 1980, but then the green gods looked upon them with disfavour and they disppeared by 2019.
Seriously, though, what was causing that huge plume in the Pacific? Is there a huge volcano there?
PCman999
Yes, the blob in the Pacific was from the VEI4 eruption of Sierra Negra, in the Galapagos islands, 1979, Nov 30. .
BurlHenry October 22, 2023 9:56 am
So, according to your theory that SO2 is the Earth’s secret temperature control knob, the Earth’s temperature dropped until 1979 due to increasing SO2, and has warmed since then from decreasing SO2?
Funny how that doesn’t show up in the temperature records …
w.
Just about every global temperature chart shows slightly decreasing temperature from about 1940 to 1979, then increasing temperature. eg: https://www.metoffice.gov.uk/hadobs/hadcrut5/
That’s why the narrative switched from global cooling to global warming.
Willis:
?? That is exactly what the temperature records show, if you eliminate temporary events, such as volcanic eruptions, La Ninas and El Ninos.
According to the Wikipedia article, the 1991 eruption of Mt. Pinatubo in the Philippines injected 17 million tons of SO2 into the atmosphere, “causing global cooling by 0.5 °C (0.9 °F) between 1991–1993.”
I don’t know how accurate any of that is, but I do remember Pinatubo. It made the sunsets in Southern California quite spectacular for months. So there was, at least, an effect on atmospheric optics that was plainly visible, and of global reach. I would think that would show up in the temperature records.
In a way you’re both right – if you google the world so2 emissions you will see that at about 1975 we reached a peak and due to NA and European drops in emissions the total global numbers fell, then thete was a drop in the firmer Soviet states in the 90s. However after the 2000s China and the rest of Asia have come on strong, so revels have rebounded but not to 1975 levels, though none of the graphs I saw were up to 2023 so it’s possible that we’ve surpassed 1975 – actually I wouldn’t be surprised considering the huge switch to coal since the invasion of Ukraine.
For example: https://ourworldindata.org/grapher/so-emissions-by-world-region-in-million-tonnes?facet=none
It displays the idea nicely but it hides the 1975 peak because it goes decade by decade. I’m sure there’s better examples out there, or to come out in the future.
The atmosphere is cleaner in Europe and the US, but not in the rest of the world, with a lot more people, burning more and more coal, about 8.3 BILLION METRIC TONS PER YEAR AND INCREASING, almost all of it by high-particulate-emission power plants, and open-pit cooking, as in India, etc.
“The point of this is simply that cleansing the air WILL cause temperatures to increase, and that is exactly what we have been doing through our Clean Air and Net Zero efforts.”
There was no Clean Air Act or Net Zero efforts during the period from the 1910’s to the 1940’s, yet the temperatures during that time period rose as high or higher than today. Something other than the Clean Air Act or Net Zero was the cause.
“People are trying to explain away our rising temperatures because they have happened before. Yes, they have, but now WE are causing them to rise.”
Rising temperatures have happened before, without human intervention, but now you are saying that is all changed and SO2 is the control knob of the Earth’s temperatues.
We need more evidence, Burl.
Granted SO2 can change temperatures temporarily. The Mount Pinatubo eruption of 1991 proves it, but I haven’t seen any correlation of SO2 with the ups and downs of the temperature record.
What about the SO2 in the atmosphere after the Little Ice Age ended? Can you show a correlation between SO2 and the temperature trends from that period of time to the present?
Remember now: The official global temperature record (Hockey Stick) is a bastardization of the real temperature profile, so if you correlate with that, then you’ve lost me.
Correlate SO2 with the unmodified Tmax temperature record. That’s the real temperature profile of the Earth, and although the coverage is spotty, it does cover the whole world, and the time period does go back to the end of the Little Ice Age around 1850.
Tom Abbott:
No, nothing has changed. Changing levels of SO2 aerosols have always been the Control Knob of Earth.s climate.
There is strong correlation between changing industrial SO2 aerosol levels and our climate In 1850, they totaled 2.4 million tons, and by 1979 they had risen to 136 million tons, and there were fears of a return to an ice age. Then in 1980, they began decreasing because of Clean Air efforts, and temperatures began rising because of the cleaner air. There have been are a lot of bumps along the way (El Ninos, La Ninas, etc.), but that is the trend.
On a previous thread I had explained to you the cause of the temperature rise between 1910 and 1940, and it was also caused by decreased SO2 aerosol levels, but for other reasons.
(You have a habit of asking a question, but leaving the site and never coming back to check for a possible answer)
You need to look at the global maps that I posted, decreased SO2 levels always cause increased temperatures, and the fewer there the hotter it gets This observation is independent of any measured temperatures, whatever they may be..
Google: “A Graphical Explanation of Climate Change”. It shows that global temperatures are so sensitive to temporarily decreases in SO2 aerosol levels that they rise whenever there are fewer aerosols due to an American business recession, due to idled factories, etc.
(Springer disabled the DOI, but it is still on Google),
Thanks, Burl. Here’s the history of SO2 emissions. Please explain how this resembles earth’s temperature history.
I ask because according to your theory, the world should have been cooling up until around 1980, then turned around and started warming again … and by now, again according to your theory, after forty years of warming we should finally be as warm again as we were back in 1960.
???
What am I missing?
w.
Willis:
It is not my theory. YOUR chart shows increased SO2 levels up to 1980 (which cause cooling), and decreased levels thereafter, due to “Clean Air” activities, which causes warming.
You say that after 40 years of warming, we should finally be as warm as we were back in 1960.
?? We are WELL beyond the temp. of 1960 (-)0.115 Deg. C, and (+)0.881 for 2022 (HadCrut5). And going even higher in 2023!
Dang, Burl, miss the story much? Re-read my post, LOOK AT THE GRAPH, and start over.
w.
Willis:
You lost me.
The graph shows increasing SO2 aerosol levels up to 1980, then decreasing levels thereafter, as I have pointed out.
What do you see?
BurlHenry October 23, 2023 7:00 am
It’s what I don’t see. As you point out, the graph shows increasing SO2 levels from 1850 to 1980. By your theory, the world should have COOLED from 1850 to 1980 due to increasing SO2.
What I don’t see is 130 years of cooling from SO2.
w.
Willis:
It was not a monotonic increase in SO2 aerosol emissions. There were also significant periods of decreased emissions during volcanic-induced El Ninos, volcanic droughts (3 or more years between eruptions), and American business recessions (due to idled foundries, factories, etc.), prior to the decreases after 1980.due to “Clean Air” reductions.
Burl, here is a U.S. regional chart, Hansen 1999:
As you can see. the coolest period on the chart is in the 1910’s, and then from the 1910’s until the 1930’s, the temperatue increased by about 2.0C. Then, from the 1940’s to the 1980’s, the tempertures cooled by about 2.0C, then from the 1980’s to 1998, the temperatures again increased by about 2.0C from the coldest to the warmest.
So if SO2 is the control knob, then SO2 amounts must have changed drastically, decreasing when the temperatures warmed for 30 years, from 1910’s to 1930’s, and then increasing (causing cooling)from the 1940’s to the 1980’s, and then decreasing again (causing warming) from the 1980’s to 1998.
Do SO2 amounts correlate with these warming and cooling cycles?
I’ll stick around for your answer.
Tom Abbott;
Looking at your graph, the 1910 cooling period was due to SO2 aerosols from the VEI5 volcanic eruption of Ksudach, in March, 1907, which typically take a year or more to reach their maximum cooling effect, as they circulate around the globe.
According to Bob Tisdale’s chart “Long Term Index of El Nino (red) and La Nina (blue) events, there was a strong La Nina between Sep 1908 and Jul 1911, due to Ksudach’s aerosols.
This was followed by a volcanic-induced El Nino Oct 1911 – May 1912, as Ksudach’s SO2 aerosols settled out of the atmosphere.
There was a business recession Jan 1913-Dec 14, which caused temps to increase because of fewer industrial SO2 aerosol emissions due to idled foundries, factories, etc,
This was followed the eruptions of 5 volcanoes between 1911-1914 causing the La Nina of Jun 1916-Apr 1917
The warming spike after 1920 was due to another business recession Jan 1920-Jul 1921, as well as the settling out of volcanic SO2 aerosols from the 5 earlier eruptions, resulting in the El Nino of Aug 1918-Sep 1919.
The warming of the early 1930’s was due to a massive 13 million ton decrease in industrial SO2 aerosol emissions between 1929 and 1932, because of the the depression, resulting in the strong El Nino of Jun 1930-Jul 1931. The later Dust Bowl years, 1932-1936, were due to a stalled High Pressure weather system over the Mid-west, where industrial SO2 aerosols within the stalled system settle out of the atmosphere without being replaced, and temperatures rise. They are characterized by high temperatures, clear, cloudless skies, a lack of precipitation, and high winds at their peripheries. The hottest temperature of the 1930’s (111 Deg. F) occurred on July 14, 1936.
The post war peak in temperatures was due to a 7 million ton decrease in industrial SO2 aerosol emissions, and the following temperature decrease was caused by a rise in industrial SO2 aerosols that peaked at 136 million tons in 1979. Beginning in 1980, temperatures began to rise because of Clean Air reductions of Industrial SO2 aerosol emissions.
So to answer your question, I find that cooling and warming events always correlate with changing levels of SO2 aerosols in the atmosphere
I should have said “the postwar peak in temperatures SHOWN ON YOUR GRAPH”
“Looking at your graph, the 1910 cooling period was due to SO2 aerosols from the VEI5 volcanic eruption of Ksudach, in March, 1907, which typically take a year or more to reach their maximum cooling effect, as they circulate around the globe.”
But the temperatures cooled from the 1880’s to the 1910’s, so a volcanic eruption in 1907 would not have been the influence for a temperature decrease of about 2.0C from the 1880’s to the 1910’s.
Tom Abbott:
There were other eruptions responsible for the cooling between the 1880’s and 1910:
Fuego 1880 Jun 28 VEI4?
Krakatau 1883 Aug 27 VEI6
Augustine 1883 Oct 6 VEI4
Tungurahra 1886 Jun 11 VEI4
Nafo’ou’ 1886 Mar 31 VEI5
Tarawera 1886 Jun 10 VEI4?
Banda 1888 Jul 15 VEI4
and 14 others, to Vesuvius 1906 Apr 8 VEI4?
I think I have made my point.
I bet you have NO solar panels on your house and that you use FF every day, and that would be hypocrisy.
J Boles
How so??
Nothing Burl Henry said advocated so-called renewables – everyone is just arguing about natural ~1000yr warm cycles or volcanism being the cause of warm/cold cycles.
It’s probably both, and a bunch of other things in the climate stew.
PCman999:
A correction. There are no 1000yr warm cycles or volcanism.
Minoan Warm Period, 3500-1000 BC, avg. 5 volcanic eruptions/century
Roman Warm Period, 250 BC-450 AD, avg 8 eruptions/century
Medieval Warm Period, 950-1250 AD, avg 10 eruptions /century
VEI4 and higher eruptions
To save time, every WUWT post should come with a BH version. BH should be banned from the primary. Anyone wanting to engage with BH could do so on his.
Bigoilbob:
I have the data to back up my comments.
What do you want, hand waving garbage?
Nice work, Willis. Maybe I missed it, but are the surface temperatures calculated from the CERES data based on the wavelengths corresponding to the so-called atmospheric window?
Thanks, Frank. The window has nothing to do with the calculated temperatures. The temperatures are calculated based on surface emissions, not atmospheric absorption.
w.
But the surface emissions are calculated from the CERES sensor data, which are the wavelengths and strengths escaping the TOA. The sensor data is run through a sort of reverse Modtran calculation to see what the surface emission must have been. This is complicated by cloud cover and cloud equivalent optical depth which CERES algorithms have capability of estimating from various IR filters. Willis’ statement that the window has nothing to do with the calculated temp, is only so far as HIS calcs are concerned.
Willis,
If WUWT accept them, I have a couple of articles in prep where the trend of temperature over time is the main chosen metric for large amounts of historic Australian data. Units of deg C per century.
There are trend differences between the hundreds of Australian weather stations I have analysed, all long term of 50 to 150 years. Daily data and annual data inputs. Gathered for UHI research.
Trends range from about 3 deg C per century equivalent to about minus 1.5. I am trying to imagine what factors affect these trends so I can collect data for those factors.
If you and readers have thoughts to share about trend causation factors, I’d be delighted to hear them. Geoff S
Sherr001;
You will find that all temperature trends are due to changing levels of SO2 aerosols in our atmosphere, from volcanic eruptions, and industrial activity.
Good luck in trying to predict them.
Hi Willis,
“Fascinating. Although we can’t get much clarity on the absolute global average temperature from 1% of the data, we can use that same 1% of the data to get a pretty good idea regarding the overall trend and the monthly variations in the global average data. “
I think this is just part of the old story that you should never average absolute temperatures over space. They are too inhomogeneous. The scatter you get comes from sometimes having a lot of hot places in your sample, sometimes cold. If you subtracted the mean of each location (anomaly) before averaging, I think you would get a much better anomaly average.
Averaging trends works, because the trend of the absolute temperature for a location is the same as the trend of the anomaly.
Nick – “absolute global average temperature” is the “average absolute temperature*. You can’t get it from anomalies.
But then he derives anomalies by subtracting the mean, after spatial averaging. That is the wrong order. You must form the anomalies first.
The error of averaging absolute temperatures is well shown by Willis’ histogram. You can’t get anything useful that way. But you can get useful results, as W found, for trends. You just have to do it properly.
‘Properly’ according to whom? Sometimes doing things that aren’t on the ‘approved’ list will generate surprising and very informative results. Like here – the details are unimportant but the overall pattern is very significant.
If you form the anomalies first, then you hide information. It’s like rounding in maths – always calculate unrounded and only ever round final results.
“I think this is just part of the old story that you should never average absolute temperatures over space.”
How about you should never average temperature across different physical media ?!
Am I misreading this?
How does your last chart tell us anything about the 1650s? Or anything before the year 2000?
M, the claim has been that the Little Ice Age, a time of extreme low temperatures, was limited only to the northern hemisphere and the rest of the world didn’t cool. The claim has also been that it’s only NH land temperatures used to establish the LIA, so the LIA may have been just an NH land-only phenomenon.
The graph shows that as goes the northern hemisphere land, so goes the world. This makes it far less likely that the NH could radically cool and the rest of the world be unchanged.
Regards,
w.
Willis:
It’s not so much that as the NH land goes, so goes the world.
All decreased LIA temps in the Central England Instrumental Temperatures Data Set are coincident with a known VEI4 or larger volcanic eruption, resulting in a world-wide event.
So your graph is correct.
Willis,
A good rule of thumb is that the sample size be the sqrt of the sample. The sqrt in this case is about 250, so 650 is more than adequate.
Sampling like you are doing is more accurate statistically than the accepted grinding because it relies on the central limit theorem to create a normal distribution which is an assumption in lots of analysis.
“A good rule of thumb is that the sample size be the sqrt of the sample.”
But the original set of 64800 cells is already a sample. There is nothing in nature to suggest 1° gridding has any special status.
In fact the sampling is of a continuum. The sampling, for surface measure, is the set of stations and ARGOs etc. Gridding is just a way of matching them to a continuum.
Although we can’t get much clarity on the absolute global average temperature from 1% of the data
=======
I have posted multiple times on this site over the years that this approach is going to give a much more statistically reliable result than the normal climate science grinding approach, so it is good to see a test in action. A sample of sqrt(n) random gridcells repeated will tend to give a much more accurate normal or standard distribution to analysis, even if the underlying data is not normally distributed.
Because of the holder inequality, there are limits to using S-B to get temperature from average radiation.
S-B(Radiation) is fine, it gives temperature.
but S-B(average radiation) yields upper bound temperature, not average temperature.
ferd, while that’s true, in general for earth-range temperatures, the error is very small.
Note that in my analysis we’re talking about anomalies of ~ ± 0.8°C around a mean of ~ 14.8°C. So here are the numbers for the error in that calculation. We have to go out to three decimal places to see the effect of the error.
Regards,
w.
Hi Willis,
Agree to a point. Do the same test using S-B of ceres average global radiation and you get an average global temperature of 17C. A 2C error.
The point is that the error is small if your surface area being converted all has the same temp. The more the temp varies, the greater the error.
Thanks, ferd. All true.
w.
Again, most interesting. With knowledge of the temperature in around a hundred twenty randomly selected gridcells out of the 64,800 total gridcells,
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It has been 20+ years since I used this. I recall that the representative sample is from n(n-1) which gives sqrt(land measurement) as a sample size so 120 is likely more than enough for land Temps. And because of heat capacity land Temps contribute almost nothing to average surface Temps.
Looking forward to more articles from you using random sampling in place of archaic climate science approach. I think it will open eyes how little data is required to get great results due to sqrt(n) and large n.
We can probably improve the accuracy of climate forecasts by removing land temperatures from any analysis and using only ocean temperatures.
Air has almost no heat capacity as compared to water, so it is unlikely that land Temps will stray too far from ocean Temps over time.
The problem is human bias as a land creature. We think the land is large and the ocean a small strip along the coast.
Still, land is where most humans lives and where we raise most of our food. Therefore, it is important to know what is happening both over land and in the oceans. I have long advocated not averaging temperatures from areas with very different reflectivities and specific heats. Put both of them on a graph to compare and contrast.
The oceans probably best reflect long-term trends, while the land air-temperatures inform us if the trend tells us anything about existential threats.
Which is Willis and which is NASA:
Because that is what we have here – the data and the results are Just Too Perfect.
1/ We are pointed to a place that supposedly measures Earth’s emissivity. Fantastic.
Except that they do at at a shortest wavelength (maximum temperature) of 89GHz
If one has an object wit its spectral peak at that wavelength, Wien tells you that it is at a temperature of 1.5Kelvin
(No typo, that is 2.5 Celsius less than the Cosmic Background)
Arising; How does that in any way relate to anything or anywhere on Planet Earth?
2/ As best I recall, the emissivity of a dry Oxygen/Nitrogen is anywhere between 0.01 and 0.03
For gases, those numbers are immensely dependant on pressure and temperature.
(This was the work of Hottel in the 1950’s)
IOW: To know the emissivity you need to know the temperature – so relying on one to find the other is a perfectly circular fool’s errand
3/ Enter centre stage: Water. In all its manifestations.
Adding even tiny amounts of water to the atmospheric gases causes their apparent emissivity to skyrocket – you wanna see a hockey stick fall of a cliff propelled by one of Shuttle’s solid-rocket boosters – there you have it.
4/ See the attached – figures for some common Earthy Substances
Straight away, anyone can see that assuming everything has an emissity of unity is utter madness.
Look at the implications of that. especially of Sand and Snow
Isn’t that just sooo delicious that significant amounts of either/both would have a huuuuge effect of Earth’s temperature.
Esp snow – snow has a heating effect. ha ha ha – while Climate Science says that its disappearance via Arctic Amplification would have a heating effect
(How did those people get to be soooo stupid, lazy and ignorant. just how)
5/ Nobody did did they = built a simple spreadsheet to work out an Earth comprised all water and no atmosphere.
In the process did some Sines, Cosines and Stefans to get an area weighted average temperature for such a thing.
I did.
On mine, running the ‘model’ with an emissivity of 0.95 (that of water) yields a Global Average Temp of 11.31°C
Changing *just* the emissivity to ‘just’ 0.90 yields a global average of 15.18°C
Make assumptions about emissivity at your very grave peril –
Especially see the difference between wet soil and dry soil – there alone in that tiny change from .95 to .92 is temperature change from 11.3°C to 13.6°C and is all your observed global warming plus a whole lot more
Use the emissivity figure for sand and you get a globe running at an average of 23.8°C
Makes you wonder doesn’t it – what would a planet composed of 100% water and 100% sand look like.
What if it was composed 50/50 sand and snow = as exactly what happens inside Ice Ages.
See that low emissivity figure?
That is how Earth escapes The Ice.
Nothing al all to do with carbon dioxide.
PS Hottel tried to measure the emissivity of CO2 – that was after all his primary task researching the efficiency of engines, heaters and boilers.
At the temps they work at, he got a figure of around 0.20
So he tried to measure CO2’s emissivity at ‘Room Temperature and Pressure’ with a CO₂ concentration of what existed then of 340ppm
(It stinks to High Heaven that all CO₂ graphs show a much lower level at that time – go check.)
Hottel couldn’t see anything and in his experiment CO₂ only started emitting at a temp of 33°C with a figure of 0.001
(A guy name-of Leckner came along a few years later and got an even lower figure)
haha – so much for “The energy is re-emitted in all directions‘
Oh yeah?
By a substance that doesn’t emit and THAT is going to Waste The World – who are you kidding?
The old adage of if it’s dry you fry came about for a reason. In the summer, if an area is in drought the average temperature is hotter than if it has rained a lot. You have emissivity in play but also energy from incoming sunlight will be spent evaporating the water in the soil along with vegetation differences. I think this is a great example of Willis’s First Rule of Climate.
Willis writes
While you have your procedure set up, how does it go if you use just, say a dozen points like a proxy study might use?
Tim, it would depend on the proxies. Some proxies reflect conditions in a much larger area than other proxies.
w.
Yes but often the claim is that just a few proxy locations can be enough data to represent global temperatures.
Keep in mind that 650 cells is not 1% of the surface. It is a representative sample. You still need to sample repeatedly.
The main point is that a sample is more representative than an average. Sampling should deliver better results than climate science averaging.
Also, cells should be 1 km by 1 km. Not 1 degree by 1 degree. Km is a unit of distance. Degree is a unit of time when applied to the earths surface.
Because ofvthe holder inequality, the smaller the grid area the sample is drawn from the more accurate the SB temperature conversion
Convert to temp before averaging radiation
Using an equal-angle grid means that the area of the grids varies by latitude a lot—about an order of magnitude from the equator to the poles.
NASA must have a mountain of computers to process 1km x 1km 10min data:
https://ceres.larc.nasa.gov/instruments/
The area (circumferential length) of the grids is reduced by the cosine of the latitude.
That is, by a factor of π/2=1.57.
The average, that is.
A while back I calculated the area of the UAH 2.5 x 2.5 degree grid as a function of latitude; as Dan P wrote, it is a cosine curve:
No disagreement. I merely quantified the total or average difference.
I mean the difference between treating all grids of equal area and treating their true areas.
No problem here!
I read through a couple of times and can’t seem to find the base line for the anomalies. Perhaps somone can point that out. Thanks.
For each of the runs he performed, he subtracted the average of the values from the values themselves, creating the anomalies.
Probably better called “residuals.”
I’m not a statistician, I’m just relaying what Willis wrote.
I really appreciate everything you write. The problem with past data sets is they’re not random at all. They’re biased toward areas that had both educated populations and thermometers to use. Simply random sampling the NH won’t get you an analogy to what we see in the little ice age or the end of it.
Too bad we don’t have CERES data from the Little Ice Age forward.
How exactly are seasonal variations calculated and removed?
If if cold periods (aka winter) become milder, which I understand to be the case, and are largely responsible for the general warming, then doesn’t the seasonal variation change too?
Monthly average values are determined, and subtracted from the original data.
w,
Willis, you’ve done enough of the leg work already that you could expand into other kinds of interesting data denial experiments. One idea is to use jackknife resampling to quantify the uncertainty of the warming trend. Another idea is to use kriging to fill in grid cells and compare the results to the observed value to see how well kriging performs.
Willis says: “As you can see…”
Well actually I can’t see that much with that line thickness, noise level and everything over-lapped.
It seems that BEST isn’t , and CERES starts cooler and ends up warmer. Not stunning differences but hard to make much of that graph. Some low pass filtering , thinner lines or separate graphs may make it more legible.
As always, I dispute the scientific legitimacy of “averaging” land and sea temps. It is physically meaningless and typical of the “basic physics” climatologists claim to use but do not even understand. It’s politics, not science. They need to stop lying.
So your claim is that we can’t tell if the various datasets are very similar because the graph lines overlap so much … ???
w.
Wouldn’t the Betas and alphas and their standard errors help? Is sample A regression statistically different from sample B?
I am curious how the temperatures you calculate from CERES for the US match up with the temperature data from the CRN? Would you post a graphic or actual data for monthly temperature data calculated from CERES for a US-centric grid cell?
The BEST data makes little sense to me. It tells me that 1921 was cooler than 1971. 1921 was an extremely warm year in the US, Europe, China, the Artic, etc. The early 70s were cold.
Not to beat a dead horse, but the whole idea of an average temperature for Earth makes little sense. Suppose you had 2 temperature measures, one from the north pole and one from the equator. Calculate an average. A 1 degree temperature increase in either would raise the average by .5 degree. However, the actual energy involved is 70X greater to get a 1 degree increase at the equator relative to the north pole.
Nelson October 22, 2023 7:25 am
Interesting question, never looked at that. However, we’re a full-service website, so hang on …
… OK, here you go.
Because the USCRN is an average of a small number of point temperature measurements and the CERE data is from area measurements from satelllites, we’d expect the variations in USCRN to be larger … and they are.
But the trends and overall shape are very similar, and their correlation is high. Overall, I’d say my calculated CERES temperature record is spot on.
w.
“a subset of the 64,800 1° latitude by 1° longitude gridcells”
When using Lat-Lon gridding, the cells are packed tightly together in polar regions. I don’t see it in the graphs. How does Willis “randomly” select gridcells?
Also, a polar cell represents a much smaller area than an equatorial cell. For an average temperature of the Earth, the weight of individual data points should be adjusted according to corresponding areas.
George, I selected gridcells totally at random. Then I simply area-weighted the results.
w.