In my previous post I claimed that global warming showed no statistically significant signs of acceleration. In this post I remove the natural influences on temperature and find that there may indeed be a change in the warming trend, and that there may be some underlying causes.
Results
A straight trend from 1980 through to the end of 2023 goes from a warming rate of 0.196℃ per decade down to 0.188℃ per decade once the natural influences (discussed later) are removed. You’ll note that the standard deviation was also decreased by 27%. But…
The astute will note that several months from 2015 onwards fall above the 2σ confidence range. This causes the concern that the warming trend has increased. So let’s look at trends before and after each month, and their commensurate confidence ranges, to see if there is a breakpoint in the data.
2012 looks to have a statistically significant break. Let’s examine this more closely:
There is certainly a statistical likelihood that that the data after 2012 can be better explained by a larger trend than just a straight line from 1980. However, note that the trend line begins in a cool period (compared to trend) from 2012 to 2014. This accentuates the trend and is reminiscent of the Climate Escalator, except in reverse. It’s a problem when you use too short a period (< 15 years) to estimate climate trends.
Despite that problem, let’s look at the trend from 2015, when the data isn’t influenced by a cold period.
It still fails the Chow test for a continuous data model, but comparing the slope confidence ranges directly shows that there is still room for error.
Lastly, I looked at what would happen if the reduced residual just replicated the period from 2016 to 2019, for the period 2024 to 2027. This is the period after the last large El Niño in 2015/16 and may be more representative of what we’re going through now.
So it’s possible that this is a temporary slight warming period, just as 2012-2014 was a slight cooling period. We need to wait a few more years to be certain which it is. However…
Driving Forces
One concern is that the Ocean Heat Content, Cheng, Abraham, et al (2023), does show an uptick in heat absorption from 2010.
(a) 0-2000m (b) 0-700m
Another concern is that the Annual Greenhouse Gas Index is showing a stronger forcing rate from around 2012 onwards. This normally takes about 20 years, Caldeira and Myhrvold (2013), for most (60%) of the effect to show up, due to the effect of the ocean heat sink. But some of it will show up within a few years. I’m not yet sure if this increase is enough to fully explain the warming we’ve seen since 2015
Final Thought
In the end, I’m not completely convinced of an increase in the warming trend, but it is plausible. There just isn’t enough data to justify a certain stance. Not to mention that we may have reached peak fossil fuel consumption and that will result in a deceleration of warming (CO₂ forcing only goes up logarithmically, and it’s only our past exponential growth in emissions that causes temperature to trend upwards linearly). At the very least, I expect 2025 to drop to roughly the temperature expected by the trend—1.31℃ above pre-industrial, or 0.4℃ below the peak in September 2023. Fingers crossed!
Natural Influences
The three main natural influences on global temperature are solar, volcanic dust in the stratosphere, and the El Niño Southern Oscillation (ENSO). Together these account for about 50% of the month-to-month variability in the temperature deviation from the underlying warming trend. By removing these influences, we should be able to get a truer idea of the temperature trajectory.
While a direct fit to the residual temperature (temperature minus the trend) does reduce the variance of the data, a better fit comes from slightly smoothing the influence data, and delaying (lag) when it is applied.
Smoothing comes from an exponential decay model where the warming is applied over several years in an exponentially decreasing amount. This was used in Haustein, Otto, et al (2019). I did a simple search to find the coefficient in exp(-t/r) that minimizes the variance of data when each influence is removed.
Lag considers that there may be a delay from the index value to when it shows up in the temperature record. I again did a search to minimize variance, similar to Foster and Rahmstorf (2011). Where I differed from the previous two papers is that I combined smoothing and lag.
The third approach I took was to use Locally Weighted Scatterplot Smoothing (LOWESS, or sometimes LOESS) to remove the larger trend variations before minimizing the data variance. This is slightly different than using a straight-line trend to get the residual. Once the residual is reduced by removing the natural influences, it is added back to the LOWESS curve for additional analysis.
The resulting lag and decay rates are:
exp lag result
vol 0.8000 6 0.7296
solar 0.1000 1 0.7296
enso 4.0000 1 0.7296
The result heading here is reduced standard deviation relative to the original. The lag is in months.
A direct comparison to the residual data shows a clear correlation:
Although the adjustments are fairly subtle, an important concern is whether I am over-specifying the natural influences to force a correlation. There is a correlation even without the adjustments, and the influences used have obvious causal relationships with global temperature. The adjustments themselves derive from ocean warming and the delay for a local effect (volcanic eruption) to spread to the greater hemispheric area (see Haustein, Otto, et al (2019) above). And consider that removing all variation would require a complete physically-based climate model, and the great complexity involved.
Code
All code to reproduce these charts are on my GitHub page: https://github.com/dneuman/Projection/blob/main/projection.py
Data Finds 
Leave a comment