Update: This post has changed to correct a mistake I made with the ERA-5 data.
I keep hearing about such-and-such month being the “hottest such-and-such month on record.” October of this year, for example. For data sources like NASA and NOAA in the U.S. and HadCRU in the U.K., the time needed to do the computations (mainly waiting for all the observing stations to report) delayed such announcements until mid-month, but lately I’ve been hearing it early in such-and-such month, often based on announcements from the Copernicus Climate Change group in Europe. I think they base their announcments on the ERA-5 data, a re-analysis data set, which incorporates both observed data and computer simulation.
I looked at the ERA-5 data, which starts in 1979 (probably because that’s when the satellites really kick in). The interesting thing is that it doesn’t just show increase, it shows (statistically significant) acceleration.
I decided to apply my method of removing the influence of el Niño, volcanic eruptions, and solar variations. It still shows acceleration when adjusted for those factors:
I decided to look again for acceleration/deceleration in global temperature data sets, five for surface temperature (NASA, NOAA, HadCRUT4, Cowtan & Way, and Berkeley Earth) and two for lower-troposphere temperature (RSS and UAH), by fitting a quadratic polynomial to each for the data from 1979 to the present. Here are the quadratic coefficients with 2-sigma error bars (roughly the 95% confidence interval):
Except for the ERA-5 data, none of the confidence intervals excludes zero, so we don’t have significant evidence of acceleration (yet). NASA and NOAA data are close.
To make the test more sensitive, I also adjusted these data sets for el Niño, volcanic eruptions, and solar variations. All these factors are significant for all data sets (except ERA-5). Here are the quadratic coefficients for the adjusted data:
We now have statistical significance at 95% confidence for NOAA data, and almost so for NASA data. Their error bars are smaller, but their estimated quadratic coefficients are smaller too. Both HadCRUT4 and UAH data show signs of deceleration, but not even close to statistical significance.
I’m not ready to declare “acceleration” yet. But if the “hottest such-and-such month on record” reports keep piling up, that may change. I’ll keep you posted.
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Open Mind 
Does the ERA-5 already remove those effects, so that’s why the adjusted version doesn’t seem any different?
Nope, ERA5 tries to calculate the best estimate of almost all weather properties at the same time.
Whereas the other records give you estimates of temperature anomaly, ERA5 calculates absolute temperature (in Kelvin), and not just at the surface but at loads of different levels in the atmosphere. And at the same time it calculates consistent cloud coverage, precipitation, wind speed & direction etc. I say “calculates”, but it basically does a calculation which provides the best match to the available data where we have it, including things like satellite measurements of outgoing radiation.
Its sea surface temperatures are basically set to match an observation-based dataset though. It’s possible there’s some weirdness going on there if there are changes with time in ERA5 SST versus e.g. HadSST4.
Tamino, did you have a chance to look at land versus ocean in each of these?
AIUI from their papers, the ERA5 global average uses the air temperature at 2 meters everywhere, unlike the purely instrumental reconstructions that typically use SST over the oceans. Over land the ERA5 2m analysis closely tracks the instrumental record, but over the oceans there is more model dependence in extracting a 2 m field from the various inputs and some systematic differences from the SST analysis. It’s at least plausible that some of Tamino’s adjustments (esp el Niño) are dominated by SST effects, and that effect gets smeared out some in the 2m field.
wrt the original question, what Tamino said is that the differences from the adjustments weren’t all statistically significant for ERA5, which isn’t the same as saying there’s no difference. There’s a subtle but sometimes significant difference.
We have not crossed the scientific threshold where a scientist can say, yes, temperature rise is accelerating, but we will and I expect you will announce when the data shows acceleration in a convincing scientific fashion. One question I have is whether the temp rise is clearly occurring faster than scientists expected. I think I know the answer to that one.
Keep up the excellent work!
Warm regards
Mike
The warming clearly is getting faster, there used to be a slight cooling for thousands of years. The above conclusion was just for the chosen climatologically short period.
The significance of acceleration depends on the start point. If you start not in 1979 but in 1950 (for the surface temperature data sets) it should be significant.
You have adjusted these data sets for el Niño, volcanic eruptions, and solar variations.
Can you significantly detect solar variations in the temperature?
I tried but failed due to very strong correlation of solar variation with the influence of volcanic eruptions. The bad timing of the major eruption give a strong correlation with the solar variations over short time periods of the last view decades. The combined solar volcanic signal has a strong periodicity of about 9.7 years.
The ERA-5 project has announced to include the years from 1950 on soon.
But what’s puzzling is the lack of significance of volcano, ENSO and solar variation in their data set. This should not be the case, should it? Has anybody an explanation for it?
Your ERA5 plot is different from one I get at KNMI Climate Explorer, and looks strange to me. There’s no 1998 spike and 2018 looks about as warm as 2016.
[Response: I got it at KNMI too. Perhaps I made some mistake, I’ll take another look.]
Thanks to everybody who asked about problems with the ERA-5 data. I made some mistake, and now that I’ve corrected it the ERA-5 data show strong response to el Nino and volcanic eruptions just like the others, weak response to solar variations like the others. I’ve updated the post to use the correct ERA-5 data.
It’s good to have sharp people looking over your shoulder.
If the traditional observational datasets do not show acceleration and a new reanalysis dataset is the outlier, I will trust the observational datasets produced to be as homogeneous as possible. Changes in the way observations are made or used (inhomogeneities) especially affect the variability over long time scales and with that the acceleration. So for such a metric, the homogeneity of the datasets is the most important thing.
Reanalysis data is especially good if you need the best possible estimate of the weather on a certain day or globally data without gaps.
Worth keeping in mind a couple of things here. First as others have noted the 2-m air temperature for reanalysis versus 2-m air temperature + SST for obs.
Second there have been some studies recently suggesting we are missing some Arctic warming in the observational datasets for example Wang et al; Way et al but also this satellite one
https://iopscience.iop.org/article/10.1088/1748-9326/aafd4e/pdf
Third, The SST dataset choices matter a lot here and explain much of the discrepancy.
Great article! Thanks.
Robert Way
“Recent global warming as confirmed by AIRS”
Thanks for providing the link to this interesting paper.
Is there any AIRS monthly time series available in text form for comparison by interested laypersons?
I think it’d have to be collated together. Might be something to ask the authors of the study. Would certainly be interesting to add to the list.
Thanks for the reply.
Stuart: you speak of growing up 2 miles from Trump in Queens. I know it’s a matter of extreme horror, but is it possible that your parents were tenants of Trump pere or Trump vater rather? It is said that the Mustachioed German sleazeball owned almost all the apartments in New York and rented them at exhorbitant rates.
I’ll see you in Madrid on 12/13! I have flights and hotel booked, so I just need to know what to say, when and where,
Best wishes
Peter
The folksinger Woody Guthrie rented from the elder Trump and wrote a song about it.
Hi Tamino, good post..
I’ve always thought that a significant acceleration could be shown by a significant trend in the first differences vs time. However, when I do this with ERA5, the trend is positive but not even close to significant.
I have tried with annual average differences, monthly differences, and sliding 12 month differences.
How am I thinking/doing wrong?
I guess that In your case above significance is shown when the quadratic polynomial fit has a significantly lower residual variance than the linear fit.
[Response: Taking first differences magnifies the noise level. Hence even though the trend is there, it won’t reach statistical significance because the noise is so large.
For the quadratic fit, statistical significance comes from a t-test of the quadratic coefficient.]
@Olof R, @Tamino,
The general theory, from EE land, is convolving with, e.g., a Gaussian, and then taking differences or derivatives. Because the difference/derivative and the Gaussian convolution commute and associate, you can just as well apply it to the Gaussian, and then reduce it to one operation, convolving with the modified Gaussian. The Gaussian needs a characteristic scale, parameterized by its
. That’s the counterpart to choice-of-natural support which Tamino has done and explores.
Thanks, Tamino and Ecoquant
I think I understand now. The first differences of ERA5 (and others likely) have actually a significantly negative autocorrelation. A deviation of one data point will magnify the difference to next data point, and so on.
I have to get software that can do quadratic polynomial fitting. There seems to be a lot of acceleration going on in climate data now.
I guess that radiosonde and reanalysis data of troposphere temps show significant acceleration 1979-2019, considering the typical “boomerang” shape in the differentials vs satellite data.
You could try with Ratpac A 850-300 mbar for instance..
Tamino,
Could we interest you in investigating Southern Ocean wind speeds? Some claim satellite datasets demonstrate increased wind speed since ~1979, and others, not. E.g., see discussion on the Arctic Sea Ice Forum, e.g.: https://forum.arctic-sea-ice.net/index.php/topic,2205.msg236303.html#msg236303
The ERA5 data does have an acceleration-esque look about it which the temperature records don’t have.
So I did think to compare ERA5 with GISTEMP and while COPERNICUS-GISTEMP is as flat as a pancake 1985-2015, the two ends of the data 1979-84 and 2016-to-date are significantly warmer in COPERNICUS. I wonder if the re-analysis has struggled to cope with the El Chichón eruption and then again with the 2016 El Niño, thus resulting in an upward bendy bit at each end of the data.
ERA5 is unique in having 2018 as the third warmest year, a feature only shared by Gistemp dTs.
The latter is still produced “behind the curtain” (no mention or direkt link from the Gistemp web pages)
https://data.giss.nasa.gov/gistemp/tabledata_v4/GLB.Ts.txt
I found by land/ocean masking that “air temp over oceans” made 2018 warmer than 2015 in these both datasets
Olof R,
The GISTEMP Global Station Temperature Index data used to be linked on the GISTEMP website just below the LOTI links. I think those links disappeared when GHCN-v3 was replaced by GHCN-v4.
There is still a land-only/ocean-only data set on the GISTEMP site, the data available from the graph page. Mind this is only annual data, not monthly. And it does show 2018 in 4th place, not 3rd. I haven’t myself compared this data with GHCN-v4.
Just gotta say this is what we have to struggle with here in Australia…
My country is run by idiots….
This while we’re facing terrible bushfires… And the worst drought ever recorded…
In fact, as a result of people like the good senator claiming biased adjustments, the Abbot government set up a panel of statistical experts to review BOM’s data homogenisation methods. The panel found that the methods were sound.
[Response: Both BOM in Australia, and NOAA in the USA, have done an outstanding job correcting temperature data for its many quirks and flaws. They have pioneered the science and made it sound, and deserve all our thanks.]
Indeed!
And this chump was probably in that Government. That was 3 or 4 years ago and yet they still say this crap.
It does my head in… Why do people vote for these morons?
… and while Tamino discusses here about science, we see here the ‘open review’ [sic] of something I do not know how to name:
170 Years of Earth Surface Temperature Data Show No Evidence of Significant Warming
by
Thomas K. Bjorklund, University of Houston, Dept. of Earth and Atmospheric Sciences
HA HA HA HA HA HA HA!
That one sentence tells you all you need to know.
In her recent post on Climategate, Judith Curry repeated the usual false claims she’s made on a supposed hiatus. Anyone want to try rebutting them? I tried, but it seems she’s blocking rebuttals (again), so my comment doesn’t appear.