This post is about proving that CO2 changes in response to temperature changes, not the other way around, as is often claimed. In order to do that we need two datasets: one for measurements of changes in atmospheric CO2 concentrations over time and one for estimates of Global Mean Temperature changes over time.

Climate science is unsettling because past data are not fixed, but change later on. I ran into this previously and now again in 2021 and 2022 when I set out to update an analysis done in 2014 by Jeremy Shiers (discussed in a previous post reprinted at the end). Jeremy provided a spreadsheet in his essay** Murray Salby Showed CO2 Follows Temperature Now You Can Too **posted in January 2014. I downloaded his spreadsheet intending to bring the analysis up to the present to see if the results hold up. The two sources of data were:

Temperature anomalies from RSS here: **http://www.remss.com/missions/amsu**

CO2 monthly levels from NOAA (Mauna Loa): **https://www.esrl.noaa.gov/gmd/ccgg/trends/data.html**

**Changes in CO2 (ΔCO2)**

Uploading the CO2 dataset showed that many numbers had changed (why?).

The blue line shows annual observed differences in monthly values year over year, e.g. June 2020 minus June 2019 etc. The first 12 months (1979) provide the observed starting values from which differentials are calculated. The orange line shows those CO2 values changed slightly in the 2020 dataset vs. the 2014 dataset, on average +0.035 ppm. But there is no pattern or trend added, and deviations vary randomly between + and -. So last year I took the 2020 dataset to replace the older one for updating the analysis.

Now I find the NOAA dataset starting in 2021 has almost completely new values due to a method shift in February 2021, requiring a recalibration of all previous measurements. The new picture of **ΔCO2 **is graphed below.

The method shift is reported at a NOAA Global Monitoring Laboratory webpage,** Carbon Dioxide (CO2) WMO Scale**, with a justification for the difference between X2007 results and the new results from X2019 now in force. The orange line shows that the shift has resulted in higher values, especially early on and a general slightly increasing trend over time. However, these are small variations at the decimal level on values 340 and above. Further, the graph shows that yearly differentials month by month are virtually the same as before. Thus I redid the analysis with the new values.

**Global Temperature Anomalies (ΔTemp)**

The other time series was the record of global temperature anomalies according to RSS. The current RSS dataset is not at all the same as the past.

Here we see some seriously unsettling science at work. The purple line is RSS in 2014, and the blue is RSS as of 2020. Some further increases appear in the gold 2022 rss dataset. The red line shows alterations from the old to the new. There is a slight cooling of the data in the beginning years, then the three versions mostly match until 1997, when systematic warming enters the record. From 1997/5 to 2003/12 the average anomaly increases by 0.04C. After 2004/1 to 2012/8 the average increase is 0.15C. At the end from 2012/9 to 2013/12, the average anomaly was higher by 0.21. The 2022 version added slight warming over 2020 values.

RSS continues that accelerated warming to the present, but it cannot be trusted. And who knows what the numbers will be a few years down the line? As Dr. Ole Humlum said some years ago (regarding Gistemp): “It should however be noted, that a temperature record which keeps on changing the past hardly can qualify as being correct.”

Given the above manipulations, I went instead to the other satellite dataset UAH version 6. UAH has also made a shift by changing its baseline from 1981-2010 to 1991-2020. This resulted in systematically reducing the anomaly values, but did not alter the pattern of variation over time. For comparison, here are the two records with measurements through December 2022.

##### Comparing UAH temperature anomalies to NOAA CO2 changes.

Here are UAH temperature anomalies compared to CO2 monthly changes year over year.

Changes in monthly CO2 synchronize with temperature fluctuations, which for UAH are anomalies now referenced to the 1991-2020 period. As stated above, CO2 differentials are calculated for the present month by subtracting the value for the same month in the previous year (for example June 2022 minus June 2021). Temp anomalies are calculated by comparing the present month with the baseline month.

The final proof that CO2 follows temperature due to stimulation of natural CO2 reservoirs is demonstrated by the ability to calculate CO2 levels since 1979 with a simple mathematical formula:

For each subsequent year, the co2 level for each month was generated

CO2 _{this month this year} = a + b × Temp _{this month this year} + CO2 _{this month last year}

Jeremy used Python to estimate a and b, but I used his spreadsheet to guess values that place for comparison the observed and calculated CO2 levels on top of each other.

In the chart calculated CO2 levels correlate with observed CO2 levels at 0.9985 out of 1.0000. This mathematical generation of CO2 atmospheric levels is only possible if they are driven by temperature-dependent natural sources, and not by human emissions which are small in comparison, rise steadily and monotonically.

##### Previous Post: What Causes Rising Atmospheric CO2?

This post is prompted by a recent exchange with those reasserting the “consensus” view attributing all additional atmospheric CO2 to humans burning fossil fuels.

The IPCC doctrine which has long been promoted goes as follows. We have a number over here for monthly fossil fuel CO2 emissions, and a number over there for monthly atmospheric CO2. We don’t have good numbers for the rest of it-oceans, soils, biosphere–though rough estimates are orders of magnitude higher, dwarfing human CO2. So we ignore nature and assume it is always a sink, explaining the difference between the two numbers we do have. Easy peasy, science settled.

What about the fact that nature continues to absorb about half of human emissions, even while FF CO2 increased by 60% over the last 2 decades? What about the fact that in 2020 FF CO2 declined significantly with no discernable impact on rising atmospheric CO2?

These and other issues are raised by Murray Salby and others who conclude that it is not that simple, and the science is not settled. And so these dissenters must be cancelled lest the narrative be weakened.

The non-IPCC paradigm is that atmospheric CO2 levels are a function of two very different fluxes. FF CO2 changes rapidly and increases steadily, while Natural CO2 changes slowly over time, and fluctuates up and down from temperature changes. The implications are that human CO2 is a simple addition, while natural CO2 comes from the integral of previous fluctuations. Jeremy Shiers has a series of posts at his blog clarifying this paradigm. See** Increasing CO2 Raises Global Temperature Or Does Increasing Temperature Raise CO2 **Excerpts in italics with my bolds.

*The following graph which shows the change in CO2 levels (rather than the levels directly) makes this much clearer.*

*There are big swings in the amount of CO2 emitted. Taking the mean as 1.6 ppmv/year (at a guess) there are +/- swings of around 1.2 nearly +/- 100%.*

*And, surprise surprise, the change in net emissions of CO2 is very strongly correlated with changes in global temperature.*

*This clearly indicates the net amount of CO2 emitted in any one year is directly linked to global mean temperature in that year.*

**For any given year the amount of CO2 in the atmosphere will be the sum of**

*all the net annual emissions of CO2**in all previous years.*

*For each year the net annual emission of CO2 is proportional to the annual global mean temperature.*

**This means the amount of CO2 in the atmosphere will be related to the sum of temperatures in previous years.**

*So CO2 levels are not directly related to the current temperature but the integral of temperature over previous years.*

*The following graph again shows observed levels of CO2 and global temperatures but also has calculated levels of CO2 based on sum of previous years temperatures (dotted blue line).*

##### Summary:

The massive fluxes from natural sources dominate the flow of CO2 through the atmosphere. Human CO2 from burning fossil fuels is around 4% of the annual addition from all sources. Even if rising CO2 could cause rising temperatures (no evidence, only claims), reducing our emissions would have little impact.

##### Addendum:

Roland Van den Broek makes the valid point in his comments below that any two data sets generally trending positive will show a high degree of correlation, not proving any causation. Certainly, UAH reports rising GMA (Global Mean Anomalies) and MLO reports rising CO2. Note however that Δ GMA predicts Δ CO2 with a correlation of 0.9985. For comparison, I generated GMA from CO2 differentials, resulting in a lower correlation of 0.6030. I conclude that Δ CO2 ⇒ Δ GMA is spurious, while Δ GMA ⇒ Δ CO2 is real.

##### Resources

##### For a possible explanation of natural warming and CO2 emissions see** Little Ice Age Warming Recovery May be Over**

##### Resources:

**Fearless Physics from Dr. Salby**

In this video presentation, Dr. Salby provides the evidence, math and charts supporting the non-IPCC paradigm.

Climatologists are engaged in criminal fraud. This whole CO2 forcing nonsense cannot be right if the analysis here is correct.

LikeLike

Reblogged this on Tallbloke's Talkshop and commented:

Not forgetting that CO2 is only a minor trace gas, at ~0.04% of the atmosphere.

LikeLike

Reblogged this on Climate Collections.

LikeLike

Thank you that is very good, It his was also explained by Professor Ian Clarke at the Canadian Senate Hearings in 2016. There is another simple way to prove that the GE does not warm anything in that if pressure was lower the Atmosphere would be larger and the thermal energy per unit volume lower and so the temperature. This alone proves that the ATE is set by the degree of gravitational compression not the GE, as required by the AGW. Accordingly, temperature variations are due to changes in net insolation as always.

LikeLike

Thanks, Pete. I recall watching a video of that 2016 hearing with appreciation. Though I don’t remember Clarke’s part specifically.

LikeLike

It is a spurious correlation.

You’ll get the same correlation with any temperature (or other) series that has a linear trend.

It is explained in detail here:

https://www.science-climat-energie.be/2023/03/24/derivee-du-co2-et-anomalie-de-temperature/

Look for example at §5.1 where we obtain exactly the same correlation by changing the sign of the temperature series.

The article is in French, but Google translate produces good results.

LikeLike

True as a gross generality. But co2 rates go down as well as up.

LikeLike

In that graph it is not the co2 that goes up and down, but its annual growth rate. It’s not the same thing.

LikeLike

Yes, it is the derivative, change rate, that correlates up and down. Necessarily so, since it is the accumulated effects from multiple CO2 sources/sinks.

LikeLike

I do not deny the correlation between the co2 derivative and the temperature.

The problem is that this will always be the case with any fictitious linearly trending temperature series, regardless of its slope. Cases 1 to 5 of my article show this clearly.

In reality, these are just temporal correlations in which time is disguised as temperature.

LikeLike

Let’s see what happens when things cool down in coming years.

LikeLike

I believe the increase in co2 is mostly (about 80%) due to temperature increase, but not for the reasons you mention.

Redo your calculations by changing the sign of the temperature series.

You will see that your coefficient b also changes sign, but the correlation is unchanged. How can you explain this?

LikeLike

Roland Van den Broek makes the valid point in his comments below that any two data sets generally trending positive will show a high degree of correlation, not proving any causation. Certainly, UAH reports rising GMA (Global Mean Anomalies) and MLO reports rising CO2. Note however that Δ GMA predicts Δ CO2 with a correlation of 0.9985. For comparison, I generated GMA from CO2 differentials, resulting in a lower correlation of 0.6030. I conclude that Δ CO2 ⇒ Δ GMA is spurious, while Δ GMA ⇒ Δ CO2 is real.

LikeLike

That’s not what I meant.

What I want you to understand is that with your calculation technique

CO2(this month this year) = a + b × Temp(this month this year) + CO2(this month last year)

You can always find coefficients a and b which faithfully reproduce the co2 data with any linear series of temperature, whether its slope is positive or negative.

This is exactly what cases 1 to 5 show in the full article.

See https://qblog-rcli.netlify.app/posts/derivee-co2-temp/

It must be concluded that it is not the temperature which is the cause of the co2 growth rate, but the time.

LikeLike

You are mistaken. a and b have no effect on the correlation value. They only adjust the appearance of the series on the graph. To say that time is a causal variable is to ignore physical factors in play.

LikeLike

I take your words:

“Jeremy used Python to estimate a and b, but I used his spreadsheet to guess values that place for comparison the observed and calculated CO2 levels on top of each other.”

It is therefore these parameters that cause the correlation.

Repeat the same operation by changing the sign of the UAH series.

Your coefficient b will also change sign, and the coefficient a will be unchanged.

You will get exactly the same CO2 estimate.

Your figure titled “Observed and Generated CO2 levels to 12/2022” will look exactly the same.

It follows that the temperature cannot be the cause of the annual growth rate of CO2.

Your b-coefficient matches the average slope of the temperature to that of the CO2 derivative.

Your coefficient a allows you to translate the temperature trend multiplied by the coefficient b so that it is superimposed on that of the CO2 derivative.

This operation can be reproduced with any linear trend series.

Carefully review §4 in https://qblog-rcli.netlify.app/posts/derivee-co2-temp/.

You should understand that by replacing temperature with its trend over time, time disappears from your equation and only a temporal correlation remains.

It is not rocket science.

LikeLike

Roland, I estimated a and b by trial and error. At no time did the correlation value change. And as my final graph demonstrates, the data was not replaced with a trendline. I’m done with this Roland. Let’s leave it there.

LikeLike

I’ve linked to this and another your article in my article https://pi-alpha.org/Nature_Loves_CO2 with a sentence:

»Some scientists have rather shown, that CO2 changes follow temperature rise (while that may instead show the feedback loop on top of persistent CO2 increase, showing the feedback is not alarming at all), and that temperature is not rising uniformly as CO2 levels do, but in distinct steps following El-Nino episodes, most probably caused by submarine volcanism…«

In January I’ve been suspecting, that the time-delay in CO2 reaction on temperature is introduced by subtracting previous year value, but then I instead verified your conclusion using different statistical technique (subtracting trend and average yearly cycle), publishing my chart on Tallbloke Talkshop: https://tallbloke.wordpress.com/2023/01/06/temps-cause-co2-changes-not-the-reverse-2023-update/#comment-181643

But while spending time on this, I noticed, that this variation of CO2 depending on temperature is just a vibration on top of 2ppm/yr increase, and thereby you may not nullify our human merits on CO2 release by showing, that some of it is caused by something else, like a feedback from temperature fluctuations…

Anyway thank you for your amazing work…

πα½

LikeLike

Thanks PA. I’m preparing a rpost with evidence that CO2 may actually function as a negative feedback to temperature rise, which would explain why earth’s climate varies between such tight limits.

LikeLike

Isn’t it rather thus? :

1. Higher temperature (SST) brings more water evaporated from oceans

2. More water in atmosphere means more clouds

3. More clouds bring lower temperatures

Which seems quite logical…

Or may it be multiple effects combined…?

(I’m looking forward to see your post, when it comes…)

πα½

LikeLike

It’s here PA

LikeLike