The Regression – Watts Up With That?

By Andy May

Introduction to the “Climate Oscillations” series

My last two posts, Musings on the AMO and The Bray Solar Cycle and AMO were fun to research and write, and they helped show that solar variations and cycles do have an impact on climate change regardless of what the IPCC says in AR6 WGI and their other reports.

From AR6 WGI Chapter 7:

“Changes in solar and volcanic activity are assessed to have together contributed a small change of –0.02 [–0.06 to +0.02] °C since 1750 (medium confidence).” (IPCC, 2021, p. 962)

They go on to say that the solar impact on global warming since 1750AD is negative (-0.01°C ± ~0.04°C) (IPCC, 2021, p. 961). They also admit that the ocean oscillations, like the AMO and PDO (which they rename AMV and PDV) are “unpredictable,” (IPCC, 2021, p. 197) meaning they are not reproduced by their models. They try to use this model failure to justify their conclusion that the oscillations are not a natural phenomenon but are simply random natural variability. This is despite statistical evidence that the oscillations are coherent and anything but random. Most of the oscillations can be traced back over 100 years using proxy evidence, this is well before humans could have influenced them (Biondi, Gershunov, & Cayan, 2001) and (Gray, Graumlich, Betancourt, & Pederson, 2004). Christopher Moy and colleagues have traced ENSO back 12,000 years using an Ecuadorian sediment record (Moy, Seltzer, & Rodbell, 2002). ENSO is closely related to several other important oscillations, especially the critical AMO and WHWP oscillations discussed in this post and the last two posts.

AR6 is not very consistent, the authors have medium confidence that anthropogenic and volcanic aerosols contribute to the “AMV” and other oscillations, but low confidence in how much they contribute. They have high confidence that the oscillations are natural variability but cannot explain their regularity and coherence (IPCC, 2021, pp. 427 & 504-506).

This is the first of a series of posts on many of the most important and well-studied ocean and atmospheric climate oscillations. I will try and provide the reader with evidence that each oscillation is natural and has been around since the pre-industrial period, or even earlier, and thus is natural and not random variability. Each post will have a title that begins with “Climate Oscillations” and a number so they are easy to search for. As we will see in this series, some of the oscillations appear to be influenced by the shorter 11-year Schwabe and 22-year Hale solar cycles.

The Regression

I did a regression analysis to see how the twelve oscillations (14 in the 1978 regression) I looked at correlated to the HadCRUT5 global mean surface temperature (GMST). GMST is not a very good indicator of climate or climate change, but it is a commonly used yardstick of climate model quality. Indeed, the terms “global warming” and “climate change” are typically illustrated with graphs showing the increase in GMST. Evidence that this warming is not a problem today is ignored (May & Crok, 2024).

Whether global warming is a problem or not is in dispute, but it is a fact that the world is warming, and some are concerned about it. What is the cause of the warming? Is it natural warming after the cold winters of the Little Ice Age? Is it caused by human emissions of CO₂? Most of the natural ocean and atmospheric circulation oscillations examined in this post are not modeled properly (some say not modeled at all) in current global climate models (Eade, et al., 2022). The IPCC AR6 report admits that the AMO (they call it the “AMV”) signal in the CMIP6 climate models is very weak, specifically on page 506:

“However, there is low confidence in the estimated magnitude of the human influence. The limited level of confidence is primarily explained by difficulties in accurately evaluating model performance in simulating AMV.” (IPCC, 2021, p. 504)

Some authors have written, based on model output alone, that the AMO is a result of volcanism and human emissions alone with no natural component (Mann, Steinman, & Miller, 2020) and (Mann M. , Steinman, Brouillette, & Miller, 2021), even though the statistical evidence of a natural AMO extending back to the 1600s is indisputable (Gray, Graumlich, Betancourt, & Pederson, 2004). Given the IPCC assessment of the accuracy of their models, there is clearly no reason to believe the AMO is due to volcanism and anthropogenic effects.

We don’t know exactly what drives the ocean and atmospheric oscillations or how they work together (the so-called “teleconnections”), just that they do exist and have been around as far back as we can see using proxies. My regression study, which included simple multiple regression and stepwise regression analysis analyzed the oscillations listed in Table 1.

All the oscillations in table 1 have good data back to 1950 except for the northern and southern hemisphere sea ice areas which only go back to 1978. Sea ice area is an important factor in climate since when it is large it traps more heat below the ice and when it is low more heat can escape and is sent to space, cooling the Earth. Yet, the overall global climate cycle has a period of 60-70 years, so the 1950-present period is important to study, and the 1978-present period is too short. So, I did two studies, one over each period.

1950 Regression study

Table 2 lists the significant oscillations in order of their importance in explaining HadCRUT5 from 1950 to 2021. As noted above, 1950 is a good starting date since Marcia Wyatt and Judith Curry have established that global climate oscillates between a warm phase and a cool phase on roughly a 60-70-year cycle (Wyatt & Curry, 2014) and (Wyatt, 2020).

The regression study was done with the R stepwise regression function “forward.” I included all 12 oscillations that had data back to 1950. Both NH_ice and SH_ice only had data to 1978, so they are examined in the “1978 Regression Study” section below. All regressions used the HadCRUT5 yearly mean global temperature as the dependent variable.

First I made a simple regression model of all twelve (14 in the 1978 regression below) oscillations and then I used stepwise regression, based upon the AIC statistic, to figure out which oscillations helped predict HadCRUT5 and which were not needed because they did not add anything to the regression. The list of variables in Table 2 are the only oscillations that contributed to the 1950 regression against HadCRUT5. All other oscillations either duplicated information in the already included oscillations or did not correlate with HadCRUT5.

It is important to remember that HadCRUT5 is not representative of global climate, it is just an average temperature. This means that the excluded oscillations are still important climate indicators, they just do not contribute to this regression. Another key point is that the AMO is always the most important oscillation.

The model illustrated in figure 1 only uses the AMO and it critically includes the change in the slopes of both the AMO and HadCRUT5 records that occurs during the 1970s. The change in AMO slope is more dramatic than the change in the HadCRUT5 slope, so the R² is only 0.58.

Adding more oscillations does improve the predicted HadCRUT5 1950 result. Figure 2 is the 1950 model created with all seven oscillations listed in table 2. The mismatch before 1970 in figure 1 is still present, but much less suggesting that the added oscillations are helping before 1970.

The model illustrated in figure 2 has an R², adjusted for the number of included variables, of 0.85, which is a large improvement over only using the AMO. However, adding more oscillations to those listed in table 2 does not improve the result.

There are seven oscillations in the model illustrated in figure 2 (listed in table 2), but the top three oscillations, AMO, WHWP, and SAM achieve an R² of 0.77, so the last four oscillations only add 8%. The AMO, WHWP, and SAM 1950 model is illustrated in figure 3.

As we will see in the following posts, the AMO and the WHWP are mostly located in the North Atlantic, Gulf of America, and Caribbean, although the WHWP does extend into the Pacific nearly to the Niño 3 region early in the year. The addition of the SAM (Southern Annular Mode or the Antarctic Oscillation) seems to supply most of the additional information needed to do a decent job of modeling HadCRUT5 from 1950 to the present. For whatever reason, the Pacific and Arctic oscillations are not important in predicting HadCRUT5, or don’t add much. Remember, the various oscillations are not independent of one another, they do influence each other to some unknown extent.

1978 Regression study

All by itself, the AMO explains 80% of the variance in HadCRUT5 in the 1978 to present regression. A plot of the AMO only regression model since 1978 is shown in figure 4.

The R² of the AMO model in figure 4 is 0.8, so it is a decent model, however, since 1978 both series have similar positive slopes and will always have some correlation. The AMO model to 1950 is not nearly as good as shown in figure 1. The other statistically significant oscillations used in the 1978 regression are listed in table 3, they add 11% to the R².

The resulting 1978 model using the seven variables listed in table 3 is shown in figure 5.

While the model shown in figure 5 is impressive, it only shows part of a climate cycle that is closely related to the upturn in the AMO oscillation earlier in the 1970s. It is easy to get a good correlation between any two series that are monotonically increasing due to autocorrelation.

Discussion

The remaining posts in this series will discuss each of the oscillations listed in table 1 and their significance, so we will not get into those details in this post. Here we just wanted to show which oscillations contributed to a HadCRUT5 model and which did not. Other key points:

1. Oscillations that can be traced into the 19^th century and earlier must have a significant natural component.
2. All multi-decadal and longer oscillations are important climatically, the fact that all do not significantly add to a regression model of HadCRUT5 suggests that they either duplicate information in other oscillations or that HadCRUT5 is not a good stand-in for global climate, or both. Probably both.
3. The fact that few (perhaps none) of these oscillations are successfully modeled by the CMIP6 climate models suggests that the models do not successfully capture natural climate change, thus the IPCC calculation of the anthropogenic part of climate change is seriously flawed (see figure 3 here).
4. The two most important oscillations in predicting HadCRUT5 are the AMO and the WHWP area. These are followed closely by the Southern Annular Mode (aka the Antarctic Oscillation) and the Northern Hemisphere sea ice area (1978 model only).

Finally, this is a regression analysis to predict HadCRUT5 with climate oscillations to try and detect the climate oscillations that best correlate to “global warming.” This is not a climate model, it is not an attempt to make a climate model, it is only a statistical exercise. Statistics and statistical analysis are not proof of anything, it isn’t even scientific analysis, they are just useful tools to sort through datasets. Just as AI is not intelligent, statistics is not science, both are useful tools.

What I think I have demonstrated is that long-term climate oscillations correlate with GMST reasonably well and that the oscillations have a large natural component. More evidence of the latter will be presented in subsequent posts. Figures 1, 2, and 3 show that the oscillations catch the critical change in HadCRUT5 slope during the 1970s. It is also shown, although not very well, in the CMIP6 models as shown in figure 6. The earlier change in slope in the 1940s is also not captured very well in the CMIP6 models.

Since the human influence on climate has never been observed, the guts of the AR6 case that nearly all recent warming is due to human activities is made by comparing climate model results to observations as is done in figure 6. Just as we do with climate oscillations they sort of capture the change in slope during the 1970s.

Two issues are apparent comparing figure 6 to figures 2 and 5. Doesn’t it seem the modeled “natural only” climate in green in figure 5 is too flat given that the critical oscillations trend up in the 1970s? The second issue is why is the modeled trend (in brown) between 1910 and 1960 so flat? The observations are not flat, there was a lot going on climatically in that period.

The AR6 case that nearly all the warming since 1950 is human-caused is very weak. Their case that the climate oscillations are mostly due to human activities and AMOC is confusing and weak (IPCC, 2021, 3.7.1, pp 504-506). They almost admit this when they state that they have low confidence in their estimate of the human influence on the AMO (IPCC, 2021, p. 506).

The following is from AR6 WGI, page 506:

“The evaluation is severely hampered by short instrumental records but also, equally importantly, by the lack of detailed and coherent long-term process-based observations …, which limit our process understanding. In addition, studies often rely solely on simplistic SST indices that may be hard to interpret … and may mask critical physical inconsistencies in simulations of the AMV compared to observations.”

I couldn’t agree more. We clearly do not know much about the oscillations or how they relate to climate change. In short, the “science” is not settled.

Download the bibliography here.

Download the data and the R code here.

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