Tag: NOAA data

How Unusual Is 1.1°C? Rare for the Holocene, Routine in Deeper Time

The heat dome was a natural weather pattern — correct. Some daily and annual records from the 1930s persist — also correct. But framing March 2026 as “nothing new” or purely alarmist ignores that it produced the largest monthly temperature anomaly in 132 years of U.S. records, set dozens of new March-specific benchmarks across the West, and occurred against a clear long-term warming background. Natural variability and human influence both play roles; the data show their interaction is pushing extremes further.

March 2026 delivered the warmest March on record for the contiguous United States (CONUS, or lower 48 states) in NOAA’s 132-year dataset (since 1895)—and by the largest temperature anomaly of any month in that entire record.

March 2026 was not just “warm”—it was historically, record-shatteringly hot for the U.S. by every major metric NOAA tracks. It underscores how a modestly warmer climate amplifies seasonal extremes, turning what would have been a notable heat wave into something unprecedented. Data are from the official NOAA National Centers for Environmental Information (NCEI) March 2026 National Climate Report, with supporting confirmation across independent analyses and media summaries of the same release.

Official NOAA NCEI numbers (released ~April 8–13, 2026)

National average temperature: 50.85°F (10.47°C).

Anomaly: +9.35°F (+5.19°C) above the 20th-century (1901–2000) March average. This beat the prior record anomaly of +8.9°F (set in March 2012) and marked the first time any U.S. month has exceeded +9°F above its long-term norm.

Daytime highs were even more extreme: +11.4°F above the March average (and ~0.9°F warmer than the typical April average).

  • Record setters:
    • 10 states set all-time warmest March records: Arizona, California, Colorado, Idaho, Nevada, New Mexico, Oklahoma, Texas, Utah, and Wyoming.
    • 1,432 counties (over half the CONUS area, affecting ~one-third of the population) recorded their single warmest March day on record (data from 1950 onward).
    • Thousands of daily high-temperature records fell, especially during the mid-to-late March heat dome (peaking ~March 16–27).

The heat was most intense across the western and southwestern U.S., where a persistent “heat dome” brought summer-like conditions (90–104°F in places) weeks ahead of schedule. Every one of the 48 contiguous states ran warmer than normal.

In the full 132-year instrumental record, March 2026 stands alone: it is both the warmest March and the month with the single largest departure from normal in U.S. history. Satellite data (UAH lower-troposphere) independently confirmed record warmth over the lower 48 for March in its 48-year record.

This warmth capped an even longer streak: the 12-month period from April 2025 through March 2026 is now the warmest 12-month span ever recorded for the CONUS.

A large-scale, persistent high-pressure pattern (the heat dome) dominated the West and much of the interior.

While weather patterns always play a role in any single month, the background warming trend—tied to human-caused greenhouse gas increases—has raised the baseline temperature, making extreme early-spring heat events more likely and more intense.

Attribution studies of similar recent Western North American heat waves have found such extremes are now virtually impossible without the ~1.3°C of global warming observed to date.

March 2026 was also extremely dry in many areas (January–March 2026 was the driest three-month start to any year on record), raising early wildfire concerns in the West.

What the expert gets right

Heat dome as the driver: Yes, a persistent high-pressure system (heat dome) over the western and southwestern U.S. caused the extreme March 2026 warmth. It trapped hot, dry air, leading to temperatures 20–35°F (11–19°C) above normal in many areas, with peaks over 100–112°F in places like Arizona and California—unusually early for March.

1934 and 1936 context: The 1930s Dust Bowl era featured some of the most intense U.S. heat waves on record, especially in summer (June–August). Many all-time high-temperature records for individual days or states (particularly in the Plains and Midwest) were set then and still stand today. The warmest year in Phoenix, for example, was 1934. Summers in 1934 and 1936 were exceptionally hot and dry due to natural factors like ocean temperature patterns (Atlantic and Pacific anomalies) combined with severe drought and poor land management.

Heat domes and blocking patterns have occurred historically; they are not new.

March 2026 vs. 1934/1936: The 1930s extremes were primarily summer events (peak heat in July 1936, for instance), not March. Comparing a record-warm early spring month in 2026 to peak-summer Dust Bowl years is apples-to-oranges. NOAA data confirm March 2026 as the warmest March in the 132-year contiguous U.S. record, with a national anomaly of +9.35°F (+5.19°C) above the 20th-century average—the largest anomaly for any month in that dataset. Ten western states set all-time warmest March records.

National vs. regional: While some individual stations or short-term records in the West may echo 1930s values, the contiguous U.S. average for recent periods (including the 12 months ending March 2026) shows modern warmth exceeding most 1930s benchmarks when adjusted for the full year or season. The 1930s heat was largely regional (central U.S.) and tied to exceptional drought; it was not a globally synchronized signal like recent decades.

Urban Heat Island (UHI) and station changes: UHI has increased since the 1930s (up to several °C in cities like Phoenix), which would tend to inflate modern readings. However, official NOAA/NCEI datasets apply adjustments for station moves, time-of-observation biases, and instrumentation changes. Raw unadjusted data can show different rankings, but homogenized records (the standard for climate trends) account for this. Many 1930s records persist because they were extreme daily highs under specific conditions—not because every modern event is cooler.

Overall trend: U.S. temperatures have risen ~2–3°F since the early 20th century due to human-caused greenhouse gases, superimposed on natural variability. This raises the baseline, making heat domes produce hotter outcomes today. Attribution studies for similar Western heat events find them “virtually impossible” at this intensity without the background warming.

The heat dome was the immediate weather driver, just as in past events. But the magnitude—shattering March records by such a wide margin (first time any U.S. month exceeded +9°F anomaly), combined with the ongoing long-term warming trend—makes it stand out. The 1930s provide important historical context for natural extremes, but they do not negate the measured acceleration in recent decades or the role of elevated greenhouse gases in shifting probabilities and intensities.

The heat dome was a natural weather pattern — correct.

Some daily and annual records from the 1930s persist — also correct.

But framing March 2026 as “nothing new” or purely alarmist ignores that it produced the largest monthly temperature anomaly in 132 years of U.S. records, set dozens of new March-specific benchmarks across the West, and occurred against a clear long-term warming background.

Natural variability and human influence both play roles; the data show their interaction is pushing extremes further.

The Dust Bowl prompted major reforms: the Soil Conservation Service (now NRCS), shelterbelts (tree windbreaks), and better dryland farming techniques. These reduced vulnerability to future droughts.

In the context of today’s climate discussions (e.g., comparing 1934/1936 heat to March 2026’s record U.S. warmth): The 1930s extremes were real, regionally intense, and driven by natural ocean patterns + poor land management—not global greenhouse gases. Many individual daily/summer records from that era still stand, especially in the Plains. However, the 1930s warmth was not part of a sustained global trend like the post-1970s warming; it was more localized and amplified by the dust/soil feedback loop.

Today’s background warming (~1.1–1.5°C globally since pre-industrial) raises the baseline temperature, so the same weather patterns (like heat domes) now produce hotter outcomes. March 2026’s +9.35°F national anomaly was unprecedented for any month in 132 years of records—but it was an early-spring event, unlike the Dust Bowl’s peak summer heat/drought. Both eras show how drought + heat interact with land surfaces, but the drivers and global context differ.

The Dust Bowl remains a powerful case study of how human decisions can worsen natural variability—and why soil conservation and climate awareness matter.

_____________________________________________________________________________________

Update:

Les Hatton’s exact conclusions

“Is a 1.1°C Rise in a Century Unusual?” published in Science of Climate Change (Vol. 6.1).

The analysis is fully reproducible because it uses the publicly available EPICA–Vostok ice-core dataset (deuterium-based temperature proxy, century-sampled over ~800,000 years).

The Vostok Ice Core data contains numerous interesting features which can be confirmed by anybody as the data is open. We can conclude the following:

A rise of 1.1°C in a century is not unusual in the current interglacial. In fact 16% of the centuries since the end of the last Ice age show a rise at least as big as the current century and none of these could have been affected by anthropogenic action.

A rise of 1.1°C in a century would have been considered unusual any time more than 200,000 years ago. For some unknown reason nothing to do with us, the temperature has become more volatile in century on century changes in the last 200,000 years. Whether this is a physical effect or an artifact of isotopic smoothing with time is unknown although there is no evidence for the latter on the peaks of the last four interglacials. And there is an abrupt change in magnitude of about 4°C in between the last 5 interglacials and the preceding 4 which is atypical of a continuous smoothing process.

The current interglacial is nothing special. It is currently still more than 3°C cooler than the peak of the last one about 130,000 years ago (which was by assumption entirely free of anthropogenic effect) and the degree of variability in this data is much the same now as then.

Given then that a rise of 1.1°C is quite commonplace in this current interglacial and that none of the earlier occurrences could have been affected by anthropogenic activity, this raises the question of why we are trying to attribute the current rise to anthropogenic effects as if it was unusual.

https://doi.org/10.53234/scc202603/05

Click to access SCC-Vol.6.1-Hatton.pdf

Hatton’s data-driven approach is a useful reminder that climate has always varied, sometimes rapidly, on natural timescales. It challenges simplistic claims that any warming above a certain rate must be human caused. At the same time, it does not directly disprove a substantial anthropogenic contribution today — attribution studies (using models, fingerprints like stratospheric cooling, tropospheric warming, etc.) still play a role in quantifying that.

See also:

Shocking News: 3 Million Years CO2 Not Driving Temperatures

Does the Global Sea-Level Rise Have a Sinusoidal Variation

The question “Why does the Global Sea Level Rise have a sinusoidal variation with a period of about 26 years?” was asked in the comments to one of my papers in 2023. My reply pointed out that the satellite coverage was only 95% and so what was happening in the other 5% may be relevant. In my follow up paper “Measuring and Analysing Sea Levels using Satellites during 2023 – Part 2”. I analysed the Tidal Gauge results of 9 ports in the northern regions of the Atlantic Ocean and above up to the Arctic Ocean.

A scenic view of ocean waves crashing against each other under a bright blue sky filled with fluffy white clouds.

From Watts Up With That?

By Kip Hansen

An Investigation using Tidal Gauge Data Part 1 – Preliminary Analysis

by Dr. Alan Welch FBIS FRAS — 2 December 2025

Note: This paper will be published in two mutually-dependent parts, this part and the second to follow in day or two, depending on the publishing schedule here.

Introduction

The question “Why does the Global Sea Level Rise have a sinusoidal variation with a period of about 26 years?” was asked in the comments to one of my papers in 2023. My reply pointed out that the satellite coverage was only 95% and so what was happening in the other 5% may be relevant. In my follow up paper “Measuring and Analysing Sea Levels using Satellites during 2023 – Part 2”. I analysed the Tidal Gauge results of 9 ports in the northern regions of the Atlantic Ocean and above up to the Arctic Ocean. The analysis was very simplistic but showed promise so now a more detailed analysis will be carried out using procedures and methods developed more recently.

Before proceeding another question could be “so what?”. The graph is basically almost linear (R2 = 0.99) with fits using quadratic or sinusoidal adding very little on this. But in 2018 Nerem et al produced their paper concentrating on a quadratic curve, using the small quadratic coefficient to be representative of an acceleration. If they had contained this to the confines of the data all would have been acceptable, but they proceeded to extrapolate for over 80 years and release their paper. The paper as still being used as a reference in many papers each month. Over the 8 years it has been used to create dramatic scenarios of flooded cities and frighten all the children. The investigation of a sinusoidal curve has tried to balance the picture. A point overlooked in using the quadratic curve is that if the calculations had been started in 2008, they would now show a deceleration. What paper would Nerem et al then write?

The paper is in two parts.

Part 1 contains preliminary analyses in which each Tidal Gauge is processed up to the Spectral Analysis stage.

Part 2 carries out Curve Fitting in which residual values (Actual values minus values on a best fit curve) are judged against a curve that is the combination of 2 or 3 sinusoidal curves using peak periods derived from the spectral analyes.

Preliminary Analysis

This study makes more use of Tidal Gauge data than NOAA data but uses Spectral Analysis.

The 9 locations are Reykjavik – Iceland Torshavn – Faroe Islands

Aberdeen – Scotland Lerwick – Scotland Bergen – Norway Barentsberg – Svalbard Narvik – Norway Murmansk – Russia Tiksi – Russia

Only Aberdeen and Bergen have datasets spanning more than 100 years, with Torshavn covering only about 50 years.

Before analysing these 9 ports the results for Brest will be studied as this covers over 210 years although there are a couple of sizeable breaks in data. This work was carried out earlier, but some aspects will be of interest. The data are shown in Figure 1.

Graph illustrating the mean sea level at Brest, France, from 1800 to 2006, showing a trend with fluctuating data points represented in blue, and a smooth green line indicating the overall trend.
Figure 1

The usual curve fitting is carried out as shown in Figure 2. Again, possibly excessive precision has been used to be on the safe side. This is not in order to indicate accurate fitting but with possible high values on the “x” axis power terms might need this extra precision.

Graph showing curve fitting analysis for Brest Tidal Gauge data, with plotted black points representing measured sea level data and a green curve indicating the fitted model.
Figure 2

A Spectral Analysis was carried out on the data and Figures 3 and 4 show the outcome for long and short periods.

Graph showing the spectral analysis of Brest data, with period years on the x-axis and amplitude on the y-axis. Notable maximum value of 525.87 at a period of 1429 years is highlighted.
Figure 3
Graph showing the spectral analysis of Brest data, illustrating amplitude variations over different period years, with labeled peaks for periods of 26.3, 42.8, 54.4, and 76.1 years.
Figure 4

Figure 3 indicates a peak (barely a peak) at a period of 1429 years. Most other Tidal Gauges show much higher periods, but it would be interesting to see how sinusoidal curves with periods in the region of 1000 years would compare with the quadratic fit.

Curve fitting was carried out for curves with periods of 1000, 1100 and 1200 years. The equations are shown in Excel Format.

= CONST + AMP * SIN(((SHIFT + 2 * A1)/PERIOD) * PI()) (Equation 1)

CONSTAMPSHIFTPERIOD
mmmmyearsyears
7341.5406.51409.01000
7371.2437.51575.41100
7430.1496.91731.41200

Figures 5,6 and 7 compare the quadratic curve with the 3 sinusoidal curves, together with comparisons of slope and acceleration.

Graph comparing different fitted curves for Brest tidal gauge data over the last 240 years, showing quadratic and three sinusoidal curves with periods of 1000, 1100, and 1200 years.
Figure 5
Graph showing Brest slopes in mm/year, comparing quadratic fit with sinusoidal curves of 1000, 1100, and 1200 year periods, plotted against time since 1800.
Figure 6
Graph showing acceleration in millimeters per year squared with curves representing 1000, 1100, and 1200-year periods alongside a quadratic fit, plotted against date minus 1800.
Figure 7

The next part may be good lateral thinking or a bit more La La Land!!

Using the 1200-year curve and extrapolating from 500 BC to 2500 AD results in the following.

Graph depicting Brest Sea Levels over a 1200-year curve, showing periodic fluctuations with key historical periods labeled: Roman Warm Period, Dark Ages Cold Period, Medieval Warm Period, and Little Ice Ages.
Figure 8

The indicated periods may be arguable. It surprised me that the last Thames Ice Fair occurred as late as 1814. A more worrying interpretation of this graph, if it is remotely indicative, would be that the sea levels (and associated Temperatures) do not peak until about 2450. Could events be as bad as that? How hot were the Roman and Medieval Warm Periods?

Finally with respect to Brest Figure 9 shows the residuals, that is the actual values minus the values on the quadratic curve and Figure 10 the spectral analysis of these residuals.

Scatter plot showing residual values for Brest, measuring deviations from a quadratic curve over years after 1800, with marked axes and data points distributed around zero.
Figure 9
Chart showing the spectral analysis of Brest residuals with period years on the x-axis and amplitudes on the y-axis, highlighting dominant periods of 17.1, 28.2, 86.1, and 92.8 years.
Figure 10

The periods of the peaks vary from those on the full data spectral analysis, and it is not very easily seen on figure 9 that there may be a decadal oscillation of about 93 years. This was

investigated by creating data files of random values, one set as straightforward random values and one set as random numbers with a standard variation. Many cases were run and figures 11 and 12 show one case from each series.

Scatter plot of random values on the left and a spectral analysis graph on the right, showing frequency response.
Figure 11
Scatter plot showing data points and variations over time on the left, and a line graph indicating spectral analysis results on the right.
Figure 12

First impressions are a bit worrying as they indicate curves with periods in the range 10 to100 years but closer inspection shows these all have small amplitude (labelled theta on these plots) of about 2 whereas in the actual tidal gauge plots these are between 10 and 30 for the residuals. These Theta values are relative values and do not indicate actual physical values.

(I may not have described the process clearly, and may not have described it correctly, so if anyone out there can help I would be very grateful)

Turning now to the 9 Tidal Gauge datasets they will be considered starting with the longest period of measurement and then in roughly an order of reducing period. But before proceeding the following 9 small figures (in Figure 13) show the outcome of the earlier curve fitting exercise of a 26-year period curve to plots of the residual values, that is the actual values minus the value on the quadratic fit. Whilst a roughly 26-year period curve fits in many positions there is evidence of other, usually, longer period components as can be seen in the Aberdeen plot where a larger 85ish year variation is obvious. The larger spectral analysis peaks will refer to primary modes, but shorter ones may be other primary modes or secondary modes. One problem with these 9 analyses was that the data plotted is a moving average based on 101 data points. With no breaks in data this equates to just over 8 years but as there are several gaps in the data this may distort matters. Averaging removes most of the short-term frequencies and makes it easier to perceive the general form.

Three graphs depicting tidal gauge data analysis, with sinusoidal and quadratic curves overlaid, showing fluctuations in sea level.
Aberdeen .. Bergen .. Narvik
A comparison of tidal gauge data featuring three graphs displaying sinusoidal curve fits for the locations of Reykjavik, Murmansk, and Bergen, illustrating fluctuations in sea levels over time.
Reykjavik .. Murmansk .. Barentsburg
Three graphs depicting tidal gauge data for locations: Lerwick, Torshavn, and Aberdeen. Each graph shows time series data with green data points, red trend lines, and a grid background.
Lerwick .. Tiksi .. Torshavn

Figure 13

Each of the 9 Tidal Gauges will now be looked at showing the initial data from NOAA Web Site, processed data showing best fit quadratic curve, residuals (actual value minus value on best fit curve), spectral analysis plots and tables of results. The tables are basically values from the software’s original use, which was variable star analysis. The first column is Frequency

(1/Period) in cycles per year. Time is the Period at which this Frequency occurs in Years. Theta has been referenced in this paper as Amplitude.

At this stage no curve fitting was carried out as in most cases there are 2 or more peaks. The Amplitudes used on the Spectral Analysis (amp) and the Amplitudes of the Sinusoidal Curves (AMP) have been studied for known multi sinusoidal curves and it has been found that the Amplitudes for a pair of curves, 1 and 2, are related by the equation

AMP2 = AMP1 * SQRT(amp2/ amp1) (Equation 2)

Using this it can be estimated the relative dominance of each curve shown on the Spectral Analysis graphs.

Chart showing mean sea level data for Aberdeen, UK, including a main graph with trend line, NOAA Tidal Gauge Data, and spectral analysis results.

Bergen

Graph showing NOAA data for Bergen, Norway, with a trend line for sea level change over time.

Narvik

Graph depicting mean sea level data for Narvik, Norway, including NOAA data, tidal gauge data, residuals, and spectral analysis results.

Narvik (reduced data set)

The data before 1947 has been discarded due to the large gap in readings and the suspicious initial data values close to the beginning of the data.

A series of graphs depicting the Narvik Tidal Gauge data over time, showing a trend line, residuals, and spectral analysis results, alongside data tables for full and residual spectral analysis.

Reykjavik

Graph showing NOAA data for Reykjavik, Iceland, with a trend line indicating sea level rise.

Murmansk

Graph showing NOAA data for Murmansk sea level, with a trend line indicating change over time.

Barentsburg

Graph showing mean sea level data for Barentsburg, Norway, with trend lines and residuals.

Lerwick

Graph showing historical sea level data for Lerwick, including NOAA data, with a trend line and fluctuations over time.

Tiksi

Graph showing sea level trends over time with NOAA data, including Tidal Gauge data and residuals analysis. Contains plots for full data, residuals, and spectral analysis results.

Torshavn

Graphs showing NOAA data, tidal gauge data and results for Torshavn, including full data and residuals with spectral analysis results.

Coming Soon:

Having applied spectral analysis to a number of Tidal Gauges, Part 2 will use the findings to derive sinusoidal curves.

Measuring and Analysing Sea Levels using Satellites during 2024

This report presents and analyses the sea level data for 2024.  The year 2023 finished with the strong El Niño still causing faster increasing sea level rises but during 2024 the El Niño reduced considerably.  The rate of rise is now more stable at about 3.3 mm/year and the so called “acceleration” has resumed its downward trend.  The analysis carried out now uses software to carry out Spectral Analysis and to converge on a best fit sinusoidal curve using an iterative approach.

ChatGPT

From Watts Up With That?

Guest Essay by Dr. Alan Welch FBIS FRAS

Summary.  This report presents and analyses the sea level data for 2024.  The year 2023 finished with the strong El Niño still causing faster increasing sea level rises but during 2024 the El Niño reduced considerably.  The rate of rise is now more stable at about 3.3 mm/year and the so called “acceleration” has resumed its downward trend.  The analysis carried out now uses software to carry out Spectral Analysis and to converge on a best fit sinusoidal curve using an iterative approach.

Preamble – Some thoughts regarding “acceleration”

A term that appears many times in sea level reports is acceleration.  I feel that unfortunately it has been misused in situations where no clear acceleration exists, but a quadratic curve has been fitted.  These curves yield a coefficient for the t2 variable that have the same units as acceleration but need to be applied with caution.  Extrapolation is very misused, especially over many decades.  For these reasons I have called the resulting acceleration “acceleration” generally throughout the text but have found it useful in using its changing value with time to judge different models.

I must be careful not to create a “pot calling the kettle black” situation as my work involves using sinusoidal curves and prediction.  The sinusoidal curves are now backed up by spectral analysis, which has also showed short period cycles due to El Niño effects, longer periods from decadal oscillations and possible very long periods (c1000 years) in some Tidal Gauge data.  The prediction item involves showing how the sinusoidal curve would show the variation of “acceleration” with time over a 70-year period up to about 2060 and comparing this with “acceleration” assessments every month or so.

Main Findings.

Data releases via the https://climate.nasa.gov/vital-signs/sea-level/ web site were made during 2024 for January, June, July, August, October and November but although all were analysed this report uses the latest, January 2025, data.  The Figure 1 shows the data with linear and quadratic best fits and shows how the term “residuals” is defined.

Figure 1

The residuals (measured values minus linear values) were plotted in Figure 2 together with a quadratic best fit curve and the standard deviation of the errors added.  To check this process is carried out correctly the quadratic term is compared with that for the full data and the linear fit checked as being y = 0 x + 0.

Figure 2

Next in Figure 3, the residuals were plotted together with a sinusoidal curve having an amplitude of 4.2 mm and a period of 26 years.  The value of 26 years has been used for a couple of years having been originally eyed in.

Figure 3

The standard deviation has improved over the quadratic fit from 3.13 to 3.06.  The period of 26 years has been retained so as not to keep changing but a possibly higher value may be more appropriate hence the above figure was repeated but with a period of 29 years and the standard deviation reduces further to 2.99 as shown in Figure 4.  Part of the improvement in the standard deviation is also due to the -0.4mm constant in the equation.

Figure 4

The choice of 29 years followed on due to the introduction of two other analytical techniques. Firstly, the fitting of a sinusoidal curve using a convergence process where the four parameters in the equation (constant, amplitude, shift and period) are changed by small steps and an error criterion  (square root of the sum of the squares of the differences) reaches a minimum.  The process does not guarantee this is the absolute minimum but starting with different parameters may help to confirm this and/or using diagonal small increments by combining two of the parameter increments in pairs.   Secondly the use of spectral analysis has been introduced details of which can be found in an Appendix.  There are many spectral analysis methods and whilst that used (CLEANest method) may not be the most suitable, checks were performed on a range of simulated curves to judge the suitability of the chosen approach and how to interpret the graphs produced.  

Inspection of Figures 3 and 4 shows a tendency for the fitted curve to be similar to a quartic polynomial.  Figure 4A shows the result of applying a quartic curve and whilst the SD is now reduced from 3.13 for a quadratic to 3.01 it is still slightly higher than the 29-year period.  A danger with polynomials is that near each end of the data the graph can become influenced excessively by the highest order term.  Not obvious in this case but extrapolators extrapolate at your peril!!

Figure 4A

Figure 5 shows the result of the spectral analysis for the residuals in the NASA analysis.  The amplitudes are best judged as relative amplitudes indicating the impact of various periods.  (I must thank Tonny Vanmunster of the CBA Belgium Observatory for help with his software.  Asking him what the term “theta” used in the program on the y axis is  he replied “Related to CLEANest, and the “theta” value shown on the Y Axis: In the CLEANest method described by Foster (1995), the Y-axis of the periodogram represents the power of the signal at each frequency (or period) — but it’s important to note that this is not the same as a classical Fourier power.    Instead, the Y-axis in a CLEANest periodogram reflects the amplitude of the cleaned spectral component at each frequency, after the iterative removal of sidelobes caused by uneven time sampling (spectral window effects). You can interpret it as a “debiased” or “cleaned” amplitude, where aliasing has been largely suppressed.  So, I would suggest to call it the amplitude or CLEANest amplitude.”

It is the Periods of various peaks that are most useful.

Figure 5

As shown in the appendix when sinusoidal periods involved are nearly close to the period covered by the data the highest point on the spectrum fits quite well but is followed by a long, sometimes slowly descending, tail.  Figure 6 homes in on the periods below 12 years where the effects of the El Niños and La Niñas are mainly seen.

Figure 6

Figure 7 shows the El Niño index covering the NASA data range the data being extracted and processed through the Spectral Analysis program producing the spectrum shown in figure 8.

Figure 7
Figure 8

With a peak  amplitude between 10 and 11 years what role can sunspots have on this.  The migration of sunspots towards the equator over the solar cycle and changes in size combined with the sunspot number produces a daily “Total Solar Irradiance”  (TSI) as shown in figure 9 which covers the period of the satellite readings.

Figure 9

The Spectral Analysis of this portion of the TSI resulted in the following.

Figure 10

We need some HUMOUR at this stage.  Following the lead of 97% of Climate experts I have fitted the quadratic curve shown above and then extrapolated it to 2100.  Get a good supply of suntan lotion in!!

Figure 10A

The following graphs, Figure 11 and Figure 13, are probably, in my mind, becoming the most important ones as they progressively grow over time.  They plot the “acceleration” values against the date they were determined based on the data from the start of 1993 up to that date.  Prior to 2012 the “accelerations” were more chaotic due to the shorter time periods and large swings in data.  From 2012 onwards there is a more settled form to the graphs superimposed on which are several “S” shape deviations each occurring because of an El Niño and the effect of which diminishes with time. These occurred in 2015/16 (Very Strong), in 2018/19 and 2023/24 (Strong) and even a weak effect in 2021 is just discernible.  Since about 2017 there has been a steady decrease in “acceleration” with short increases over a year at each large El Niño.  These combine to result in an average reduction in “acceleration” of about 0.002 mm/year2 per year.

Figure 11

Having stated that I think these graphs are very important I have only found one similar example of this graph (figure 15).  This was in a paper by R. S. Nerem, T. Frederikse, B. D. Hamlington (Ref 7) dated March 2022.  Unfortunately,  the data only goes up to the end of 2020 and uses superseded data.  In my paper (Ref 5) I discussed this change in data where some historical data, as far back as 1993, has increased by over 8 mm for some, as far as I know, unexplained reason.  Three of the figures are reproduced below to show those changes together with a predicted curve based on a 26-year cycle.

Figure 12 Before changes 
Figure 13  After changes
Figure 14 Changes in data

The change of 8 mm is about 2.5 times the annual increase in sea levels.  The graph, in Ref 7, was, not unreasonably at the time, used to substantiate the statement that “…the acceleration coefficient becomes stable after 2017” but it would be interesting to see it updated.  One thing I have noticed is that whereas a couple of years ago the “accelerations” were quoted in the form 0.083 +/- 0.025 mm/year2, which represented 1σ, they are now quoted in the form 0.09 +/- 0.09 mm/year2 to 0.08 +/- 0.06 mm/year2 representing a 90% confidence interval.  These changes now lead to a much lower projected limit.  At least this lower limit is in line with my work and the Tidal Gauges.

The quoted slopes, accelerations and comments are from Ref 6, “The rate of global sea level rise doubled during the past three decades”.  The note 1 below the values are from ref 6.

“Table 1 Changes in rates and accelerations during the altimeter record

End DateRate (mm/year)Acceleration (mm/year2)2020–2050 Sea Level Change (mm)
2017.993.3 ± 0.40.09 ± 0.09171 ± 77
2018.993.3 ± 0.40.09 ± 0.08168 ± 71
2019.993.3 ± 0.40.09 ± 0.08174 ± 64
2020.993.3 ± 0.40.09 ± 0.07169 ± 60
2021.993.3 ± 0.30.08 ± 0.07165 ± 57
2022.993.3 ± 0.30.08 ± 0.06158 ± 55
2024.003.3 ± 0.30.08 ± 0.06169 ± 52
  1. Rate and acceleration estimates for different lengths of the satellite altimeter record. The start year is fixed in 1993 but the end year of the record used varies from 2017.99 to 2024. The last row indicates the rate and acceleration estimates over the current full record. Uncertainty estimates denote the 90% confidence interval. Additionally, the extrapolation of the measured rate and acceleration is used to project the sea level change from 2020–2050.”
Figure 15

If the residuals had followed a sinusoidal variation based on the 29-year sinusoidal curve an equivalent set of “accelerations” could have been determined.  Figure 16 shows the “accelerations” as at the end of Jan 2025 with the “accelerations” calculated using quadratic curve fitting to a set of data obtained from a 29-year curve and extended to 2065.  Compared with the previous 26-year curve this slightly extends the prediction of when “accelerations” will reach values similar to long range Tidal Gauge data of between 0 and 0.02 mm/yr2.  This is shown as occurring  at about 2035.  The curve as calculated is asymptotic to 0 but it will probably converge on a slightly higher value in line with Tidal Gauges.

Should I pop my clogs before, say, 2030, it would be nice to think someone out there keeps adding new “acceleration” values to Figure 16.  My grand kids are only 11, and have not yet acquired the spreadsheet bug, so not quite ready yet to take up the mantle.

Figure 16

Conclusions

The slope of the data has settled down to about 3.3 mm/year.

The “accelerations”, having peaked at just over 0.09 mm/year2 during the period 2017 to 2020, has now reduced to nearly 0.07 mm/year2 in early 2023 at which stage an El Niño caused a short-term blip back up to 0.08 mm/year2 before resuming a downward trend.  With time the effect of future El Niños on the “accelerations” would gradually reduce.

The introduction of the spectral analysis and iterative determination of a sinusoidal curve has been a great benefit.  Because of this the process has been extended to a much wider range of data, but as yet this has not all been analysed.  This amounted to over 50 times the amount of work (spreadsheets and figures) as needed when analysing the NASA data.  Therefore, I have spreadsheets coming out of my ears(!) but to fully present it all will need a large amount of extra compiling of results, producing figures, discussing and finalising the conclusions. 

The datasets include the following.  As and when each dataset is finalised, I intend to issue a report.

NOAA data

The site https://www.star.nesdis.noaa.gov/socd/lsa/SeaLevelRise/LSA_SLR_timeseries.php issues the Sea Level Data every few months.  The sets being processed are those with Seasonal Signals removed as measured by the Topex, Jason-1,-2,-3 and Sentinel-6MF Satellites.  The data files analysed were from 1993 to approximately the end of September 2024 although a more recent set of data takes the values up to the end of 2024.  They cover the global data and the data for 24 sub-areas from the Pacific Ocean down to small seas such as the Adriatic Sea.  An interesting presentation is to plot values like “acceleration” or phase shift for each sub-set on an easterly basis.  Any trends may help to make judgements on the legitimacy of the derived “accelerations” as being meaningful or mainly a manifestation of the method of determination.

Tidal Gauge data

There are hundreds of Tidal Gauge datasets and those selected include very long sets, such as Brest, those recently discussed on WUWT, such as the NY Barrage and odd ball ones with negative slopes and/or negative “accelerations”.  The general approach adopted was similar as that used for the satellite data except that with longer date ranges involved. With this longer (> 100 years) curve the residuals are calculated with respect to this curve.   Also, whereas the NASA data used the spectral analysis only for the residuals, for the Tidal Gaude data it will also be applied to the full data to possibly pick up very long-term curves.

North Atlantic, North Sea and Arctic Sea data

These Tidal Gauge datasets were used in Ref 5 to investigate the theory that the Global Sea Levels had an “acceleration” because the satellite coverage was only 95% and the main areas missing include large areas of the North Atlantic, North Sea and Arctic Sea.  If these had a decadal oscillation this may show up as a sinusoidal variation.  At that time the sinusoidal curve was judged by eye to be about a 26-year period but now a more accurate assessment can be made.

All nine Tidal Gauges will be considered.

Appendix – Spectral Analysis Program

A recent addition to the analysis tools has been the use of spectral analysis software.  The program used is called Peranso, described as  Light Curve and Period Analysis Software and used mainly in the analysis of variable stars.  It was written by Tonny Vanmunster at the Center for Backyard Astrophysics Belgium & Extremadura.  As such it has features that are specific to variable stars but can be used to analyse general sets of data.

Due to star magnitudes being such that brighter stars have magnitudes that are more negative the y data for non-astronomical values must have their signs changed.  Also, the system refers to Julian Days which may not be relevant and can be changed to Periods in Years.

To use for a general set of x y data an excel file can be set up with x (time) values in the A column, a set of commas in the B column and the variable, with a changed sign, in the C column forming a CSV type file.  This data is then copied into a Clipboard.

Nine cases of data input were produced as shown below (Figure A1) to investigate how the system responds and to investigate the suitability for the type of data found in sea level studies.

Figure A1

The top line is for a single oscillation with the longest period, the second line 2 oscillations and the third line 3 oscillations.   The first column is all main long-term oscillations, the second column adds an intermediate oscillation and the third column an extra short-term oscillation.  The resulting spectral plots are shown below in figure A2.

Figure A2

The “long tail” on the upper row come about from the fact that all the much longer period curves have a very similar RMS error.  It requires about 3 oscillations before a more definite peak period is obtained as is shown in row 3.

A further case involved using a very short section of a 1000-year curve.  The figures are taken from the Peranso screen and show the input (Figure A3), and spectrum obtained (Figure A4).  The peak is shown as at a period of 1111 years and is hardly discernable.  This slightly higher period generally occurs when the input is a short portion of a much longer curve.  As a peak it is not very obvious, a large range of long period curves would fit nearly as good.

Figure A3
Figure A4

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References (Not all references appear in this report but may appear in follow on reports)

1. https://wattsupwiththat.com/2022/05/14/sea-level-rise-acceleration-an-alternative-hypothesis/

2.  https://wattsupwiththat.com/2022/06/28/sea-level-rise-acceleration-an-alternative-hypothesis-part-2/

3. https://wattsupwiththat.com/2023/05/02/30-years-of-measuring-and-analysing-sea-levels-using-satellites/

4.      Nerem, R. S., Beckley, B. D., Fasullo, J. T., Hamlington, B. D., Masters, D., & Mitchum, G. T. (2018). Climate-change-driven accelerated sea-level rise detected in the altimeter era. (full text .pdf)  Proceedings of the National Academy of Sciences of the United States of America, 115(9).  First published February 12, 2018

5. https://wattsupwiththat.com/2024/04/06/measuring-and-analysing-sea-levels-using-satellites-during-2023-part-2/

6. B. D. Hamlington,  A. Bellas-Manley, J. K. Willis, S. Fournier, N. Vinogradova, R. S. Nerem, C. G. Piecuch, P. R. Thompson & R. Kopp. The rate of global sea level rise doubled during the past three decades. https://www.nature.com/articles/s43247-024-01761-5

7.   R. S. Nerem, T. Frederikse & B. D. Hamlington.   Extrapolating Empirical Models of Satellite‐Observed Global Mean Sea Level to Estimate Future Sea Level Change    https://repository.library.noaa.gov/view/noaa/54199

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The Atlantic Is Cooling at a Mysteriously Fast Rate After Record Warmth

So they do not have a clue why the Atlantic has suddenly got colder, but they think they know that global warming made it hotter in the first place, even though there is no physical for the claim that a slightly warmer atmosphere can make any measurable difference to ocean temperatures!

From NOT A LOT OF PEOPLE KNOW THAT

By Paul Homewood

For over a year, surface temperatures in the Atlantic Ocean hit new highs, but that trend has reversed at record speed over the past few months, and nobody knows why.

In June, temperatures in the Atlantic were 2 to 5 degrees Fahrenheit (1 to 3 degrees Celsius) hotter than normal in much of the ocean, with some areas getting as much as 9 degrees F (5 degrees C) warmer than average. Those temperatures weren’t a one-off, as the Atlantic had regularly seen record-breaking levels since March 2023. That year marked the fourth in a row that the world’s oceans set new heat records.

The hot water was partially a result of human-caused climate change, but it was also due to a particularly strong El Niño in 2023 and 2024. But that system appears to have passed, according to the National Oceanic and Atmospheric Administration.

NOAA data shows Atlantic sea surface temperatures have cooled at a surprising rate since May. Since June began, temperatures have been a degree or two Fahrenheit colder than normal for this time of year. That means El Niño will likely be replaced by its counterpart, La Niña, a weather system that allows cold water to rise to the surface of the Atlantic, some time between September and November. Both El Niño and La Niña are complex systems driven by trade winds, solar heating, and rainfall in the tropic regions, and can be difficult to predict. Still, the sudden shift in Atlantic temperatures has been puzzling, and nobody seems to know why it’s happened so quickly.

“We’ve gone through the list of possible mechanisms, and nothing checks the box so far,” Frans Philip Tuchen, a postdoctoral student at the University of Miami, told New Scientist.

https://gizmodo.com/the-atlantic-is-cooling-at-a-mysteriously-fast-rate-after-record-warmth-2000488967

So they do not have a clue why the Atlantic has suddenly got colder, but they think they know that global warming made it hotter in the first place, even though there is no physical for the claim that a slightly warmer atmosphere can make any measurable difference to ocean temperatures!

They also get their knickers in a complete twist stating that El Ninos in the Pacific raise SSTs in the Atlantic!

The inability to explain what has happened underlines how little scientists really do know about the way our oceans work. And it is these oceanic cycles which are at the heart of long term global climate cycles, because of the immense thermal capacity they store.

We know little, but we do know that large and sudden temperature shifts have occurred in the Atlantic in the past, as seen in the AMO:

https://climexp.knmi.nl/getindices.cgi?WMO=UKMOData/amo_hadsst&STATION=AMO_hadsst&TYPE=i&id=someone@somewhere

This latest cooling episode, along with the preceding warming one, is merely just a part of that long term pattern.

NOAA’s Graph Provides Best Evidence That Solar Heating Is Warming the Oceans, Not CO2

However, their regional changes in heat content are much more consistent with solar heating than from greenhouse theory.

From Watts Up With That?

Jim Steele

NOAA’S Climate.gov’s Ocean Heat Content presents an illustration (graphic A) of changing ocean heat content with this accompanying narrative. “Rising amounts of greenhouse gases are preventing heat radiated from Earth’s surface from escaping into space as freely as it used to. Most of the excess atmospheric heat is passed back to the ocean.” However, their regional changes in heat content are much more consistent with solar heating than from greenhouse theory.

Although greenhouse theory describes rising CO2 as acting like a blanket across the globe that keeps more heat in the ocean, graphic A perfectly depicts asymmetric heating that we would expect from solar heating and ocean circulation (graphic B). The greatest increase in heat content happens along the east coasts (highlighted by red ovals), especially in the Kuroshio Current off Japan, and the Gulf Stream.

Why such regional differences from the same CO2 blanket?

Graphic C, from peer reviewed research (Huang 2015), describes the net heat flux in and out of oceans. The red and yellow colors represent where more heat enters the ocean than leaves, yet NOAA shows cooling in those regions. The blue colors in graphic C, show where more heat is ventilating back to space than that region absorbs, yet NOAA’s graph shows those regions warming!  Observations completely contradict NOAA’s greenhouse warming narrative.

net surface heat flux

The most plausible explanation is based on well-known ocean science. For example, greatest amount of heat flux into the ocean happens in the tropical eastern Pacific, where La Nina-like conditions cause upwelling of cooler waters that reduce cloud cover that increase solar heating! Solar radiation penetrates several meters into the eastern ocean where it can be stored for various lengths of time. That stored solar heat is then transported into the western Pacific where much is then deflected northward along the Kuroshio Current where it ventilates. During La Ninas that heat transport is greater, explaining why NOAA’s observed increase in the regions from 1993 to 2022 correlates with the switch to more La Nina-like conditions during the past 3 decades.

A similar dynamic happens in the Atlantic, where stored tropical heat ventilates from the Gulf Stream and moderates Europe’s winter. Not all the Gulf Stream’s heat ventilates allowing much of the salty warm solar-heated waters to enter the Arctic Ocean, creating a reservoir of warm water between 100- and 900-meters depth, and capable of melting all the Arctic’s sea ice (Polyakov 2017).

In contrast to the fact that CO2 infrared only penetrates the ocean by a few microns, solar heat penetrates several meters. Due to subsurface saltiness that inhibits heat convection back to the surface, some heat is trapped for entire seasons to many decades and centuries. As illustrated in Graphic D, the science of solar ponds demonstrates how the sun heats the subsurface oceans.  Despite air temperatures averaging 68°F, solar ponds can fantastically triple temperatures in their bottom layer to over 190°F.  For more details explaining the different dynamics that explain why ocean warming is due to solar heating, watch Science of Solar Ponds Challenges the Climate Crisis

40 years of expert failure: New NOAA STAR satellite temperatures only show half the warming that climate models do

An all new reanalysis of the STAR satellite data finds markedly lower temperature trends for the last 40 years. The big deal about this is that this third dataset suddenly supports the original UAH satellite data, not the other RSS system, and not the “surface thermometers” sitting near hot tarmacs and absolutely not the climate models.

From JoNova

By Jo Nova     h/t Cohenite

New NOAA STAR Satellite system gets a major correction and suddenly agrees with UAH satellites, not RSS

An all new reanalysis of the STAR satellite data finds markedly lower temperature trends for the last 40 years. The big deal about this is that this third dataset suddenly supports the original UAH satellite data, not the other RSS system, and not the “surface thermometers” sitting near hot tarmacs and absolutely not the climate models.

The warming trend in the troposphere was only half of what the expert models predicted. From the paper:

Santer et al. (2021) reported that the multi-model averages for the TTT trends from CMIP5 and CMIP6 were 0.28–0.29 K/decade during 1979–2019. The total TTT trend found in this study was only one-half of the climate model simulations during the same period.

The authors admit that this has strong implications for the models, and supports a paper by skeptics Ross McKitrick and John Christy: Ross McKitrick replied in the Financial Post:

An important new study on climate change came out recently…

Zou’s team notes that their findings “have strong implications for trends in climate model simulations and other observations” because the atmosphere has warmed at half the average rate predicted by climate models over the same period. They also note that their findings are “consistent with conclusions in McKitrick and Christy (2020),” namely that climate models have a pervasive global warming bias.

Zou et al from NOAA is a bit of a blockbuster. Certainly a surprise. Skeptics have long favoured the original UAH satellite data set that consistently showed far less warming than climate models and for good reasons (see below) — especially because UAH agreed with 28 million weather balloons. A second satellite set called RSS gradually showed warmer trends than UAH did. A third satellite set was collected by NOAA and called STAR and it agreed with RSS — at least until a few weeks ago. Now suddenly it’s been re-worked thoroughly and the trend is almost identical to the UAH one.

As Roger Pielke Jnr says “if true — this is very scientifically important”:

He quotes Zou et al who are agreeing that their results support the skeptics

This is consistent with conclusions in McKitrick and Christy (2020) for a slightly shorter period (1979–2014). Possible reasons for the observation-model differences in trends may include climate model biases in responding to external forcings (McKitrick & Christy, 2020), deficiencies in the post-millennium external forcings used in model simulations (Santer, Fyfe, et al., 2017), phase mismatch in natural internal climate variability (Po-Chedley et al., 2021; Suárez-Gutiérrez et al., 2017), and possible residual errors in satellite data sets.

Pielke Jnr: Read that again, especially the last sentence. [They] are suggesting the possibility that either observations of global warming are flawed, that climate models are flawed, or maybe both. These possibilities would — if true — be very scientifically important.

Here’s now different the satellite datasets were in 2018

UAH was called the outlier, but all the other datasets used similar methods to RSS. They all continued to use a satellite called NOAA-14 even though its calibration was drifting. They also used similar strategies for diurnal drift adjustments. In Roy Spencer’s words “ Thus, NOAA and UW are, to a first approximation, slightly altered versions of the RSS dataset.”

Figure 2. A comparison of warming trends from 1979 to 2015 for the radiosonde data and the three global satellites. from Roy Spencer (Christy et al 2018)

Ross McKitrick explains the history of these differing satellite temperature sets. This is a battle that’s been waging for thirty years.

Ross McKitrick:The important climate study you won’t hear about 

 Special to Financial Post

[John] Christy and his co-author, Roy Spencer, invented the original method of deriving temperatures from microwave radiation measurements collected by NOAA satellites in orbit since 1979. Their achievement earned them numerous accolades, but also attracted controversy because their satellite record didn’t show any warming. About 20 years ago scientists at Remote Sensing Systems in California found a small error in their algorithm that, once corrected, did yield a warming trend.

Christy and Spencer incorporated the RSS correction, but the two teams subsequently differed on other questions, such as how to correct for the positional drift of the satellites, which changes the time of day when instruments take their readings over each location. The RSS team used a climate model to develop the correction while the UAH team used an empirical method, leading to slightly different results. Another question was how to merge records when one satellite is taken out of service and replaced by another. Incorrect splicing can introduce spurious warming or cooling.

The climate modelers have been seeking some kind of endorsement of their models from satellites for decades, but the gap has grown wider instead of narrowing. STAR was a lifeline for the modelers, now it’s not:

In the end the two series were similar but RSS has consistently exhibited more warming than UAH.  Then a little more than a decade ago, the group at NOAA headed by Zou produced a new data product called STAR (Satellite Applications and Research). They used the same underlying microwave retrievals but produced a temperature record showing much more warming than either UAH or RSS, as well as all the weather balloon records. It came close to validating the climate models, although in my paper with Christy we included the STAR data in the satellite average and the models still ran too hot. Nonetheless it was possible to point to the coolest of the models and compare them to the STAR data and find a match, which was a lifeline for those arguing that climate models are within the uncertainty range of the data.

Satellite show the models are wrong:

This below is the graph in McKitrick and Christy (2020) that the new STAR analysis essentially supports. The best tropospherein the world are running too hot, predicting a lot of warming that isn’t happening.

They overdo the warming in the lower troposphere and in the mid-troposphere in the tropics and all over the globe. After 40 years and massive emissions of CO2 the models are wrong. The modelers don’t know what drives the climate.

From 2017:  Five reasons UAH is different (better) to the RSS global temperature estimates

I explained why UAH was scientifically much more respectable than RSS

Five reasons UAH is different to RSS

  1. UAH agrees with millions of calibrated weather balloons released around the world. RSS now agrees more with surface data from equipment placed near airports, concrete, airconditioners and which is itself wildly adjusted.
  2. In the latest adjustments UAH uses empirical comparisons from satellites that aren’t affected by diurnal drift to estimate the errors of those that are. RSS starts with model estimates instead.
  3. Two particular satellites disagree with each other (NOAA-14 and 15). The UAH team remove the one they think is incorrect. RSS keeps both inconsistent measurements.
  4. Diurnal drift probably created artificial warming in the RSS set prior to 2002, but created artificial cooling after that. The new version of RSS keeps the warming error before 2002, but fixes the error after then. The upshot is a warmer overall trend.
  5. UAH uses a more advanced method with three channels. RSS is still using the original method Roy Spencer and JohnChristy developed with only one channel (which is viewed from three angles).

The latest corrections by Zou 2023 were intricate and involved. This is just one eye candy graph of many (below). But we get some idea of how many satellites were involved in the last 40 years. In this case the adjustments were different over land and ocean for each satellite.

Figure 5: Inter-satellite difference time series for satellite pairs between those from TIROS-N to RTMT after the frequency adjustment for (a) over the global ocean and (b) over the global land. Zou et al

It’s a testament to the work of John Christy and Roy Spencer that the new detailed corrections suggest they were probably mostly right all along — despite the immense pressure on them to “find” results and adjustments like the other teams.

It’s a credit to Zou et al and the team at NOAA for publishing what appears to be conclusion that they  might have preferred to ignore.  Though they do suggest that the warming has accellerated lately:

Remarkably, the total tropospheric trends during the latest half period were nearly doubled the earlier half period over the global ocean.

But there is more discussion from Ross McKitrick at Judith Curry’s site on why the claimed “recent acceleration” in this paper is short term, not significant and dependent on picking the right break point.

In sum, based on a preliminary analysis the new NOAA data do not support a claim that warming in the troposphere has undergone a statistically-significant change in trend. The Global and Tropical TTT series show no support for the claim. The Global MT series appears to show support but only if the break data is placed in a specific interval in the early part of the last decade, and more recently the tests do not support acceleration. Finally, all of these results are biased towards finding evidence of a trend break due to the treatment of g. Robust critical values could be generated, which I might get to someday if no one else does it first.

REFERENCES

Christy, J. R., Spencer R.W., Braswell W.D. & Junod, R. (2018) Examination of space-based bulk atmospheric temperatures used in climate research, International Journal of Remote Sensing, 39:11, 3580-3607, DOI: 10.1080/01431161.2018.1444293  [ResearchGate]

McKitrick, R., & Christy, J. R. (2020). Pervasive warming bias in CMIP6 tropospheric layers. Earth and Space Science, 7(9), e2020EA001281. https://doi.org/10.1029/2020ea001281

Zou, C. Z., Xu, H., Hao, X., & Liu, Q. (2023). Mid‐Tropospheric Layer Temperature Record Derived from Satellite Microwave Sounder Observations with Backward Merging Approach. Journal of Geophysical Research: Atmospheres, e2022JD037472.

Satellite image: By NASA