Dr. Roy Spencer’s Global Warming Blog
Roy W. Spencer, Ph.D.
Summary of key points
By choosing the “best” models and estimates of CO2 fluxes (those which best explain year-to-year changes in atmospheric CO2 content as measured at Mauna Loa, HI) for the period 1959-2023 as provided by the Global Carbon Project, a multiple linear regression of yearly Mauna Loa CO2 changes against those “best” estimates of sources and sinks leads to the following alterations to the “official” Global Carbon Project estimates of the sources and sinks result in the observed increase in atmospheric carbon dioxide. (Note: As a statistical exercise, this does not constitute a “proof”… These are just some areas that carbon budget modelers may want to study when adjusting their models):
- The global anthropogenic CO2 emissions seem to be 30% higher than reported (I find it hard to believe… Again, statistics don't necessarily prove it).
- The drop in carbon dioxide is underestimated on average by about 25%
- Seawater tanks of carbon dioxide are overestimated by about 20% (I don't know if they include carbon dioxide).
- The land use source of carbon dioxide (mainly biomass combustion) is overestimated about 2 times (very uncertain)
- Cement carbonic acid sinks have been underestimated about 7 times (very uncertain)
- During the 1959-2023 period, the remaining unknown CO2 tanks averaged 0.2 ppm/year (this may be just a residue of other statistical errors).
background
Many researchers have taken their careers to estimate various global sources and sinks of atmospheric carbon dioxide. The main net sources are man-made emissions (including cement production) and land use (mainly biomass combustion). The main CO2 sinks are land (vegetation and soil storage), ocean (stirring the “supple” atmospheric carbon dioxide downward… bio-intake remains very little) and cement carbonization (old cement absorbs atmospheric carbon dioxide).
The Global Carbon Project (GCP) periodically summarizes various estimates of these sources and sinking and produces easy-to-access data spreadsheets. I want to make a political stopgap (don't insult your peers), the GCP (as IPCC does with climate models) estimates almost all estimates of CO2 fluxes and averages them together to produce a single “best” estimate for a specific flux every year. For example, they have an average of 20 (!) different land models that cause annual net carbon dioxide fluxes to enter the land surface (I say “enter” because the current atmosphere “over-over” of CO2, about 50% higher than pre-industrial levels, making land and oceans the net sinking amount of CO2).
What did I do
However, since I am not part of the global carbon budget research community, I can choose which models and data-based estimates I use. Some of these models are better than others than others to explain the annual increase in atmospheric carbon dioxide in Mauna Loa in Hawaii, where I will use only the best estimates to provide the analysis.
(Now, some researchers think that the average of all estimates will be better than any personal estimate. I don't believe it… nor should you. As a simple example, you can't estimate something better by averaging good estimates and bad estimates.)
So what I did is examine how each individual model estimate (or sometimes observational estimate) helps explain the annual CO2 increase in Mauna LOA. I then chose the best and averaged them together. I then attribute the annual carbon dioxide changes in Mauna LOA to these averages. As shown in Figure 1, this produces a much better estimate for the MAUNA LOA CO2 record based on all available estimates from various sources.

To be fair, part of this better protocol comes from statistical regression. The GCP estimation (very admirable) uses all available estimations based on physics and parameterization and then see how well the results match the Mauna LOA record. They even include annual “residues” in spreadsheets to show how well the model fits the data (or how bad). honor.
But I used the best model and estimates and then used multiple linear regressions to see how well the data fits with Mauna LOA observations. Similarly, the annual changes in carbon dioxide concentration observed are statistically related to the sources and sinks of carbon dioxide from (1) anthropogenic emissions, (2) land use emissions, (3) land plant and soil absorption, (4) ocean absorption, (4) ocean volume, (5) cement carbonic acid (old cement removes CO2 from the atmosphere).
The results give the total regression model with an explanation of 81%. The regression coefficient tells us whether or not the individual CO2 budget clauses (the source and sinking of CO2). If the term equals +1 (for source) or -1 (for receiver), the model estimates for the annual CO2 source and sink are fair (average) in the explanation of annual CO2 changes in Mauna LOA.
I again emphasize that such statistical results can be misleading. An error in a term regression coefficient may result in error in other term coefficients. But regression analysis can sometimes reveal insights about what physics may be missing. I've seen both of these calculations for 40 years.
Here is the result:
Global artificial emissions: coefficient = 1.3 (+/- 0.22) This indicates that anthropogenic emissions are underestimated by about 30%. I find it hard to believe. Energy use is well known. Perhaps the cement production source is underestimated?
Global land use: Coefficient = 0.43 (+/- 0.45) This indicates that land use emissions have been overestimated (but the coefficient is very uncertain). Similarly, if a term has little skill, the coefficient will be lower due to the “mean regression” effect. This result shows me that annual land use as a source of carbon dioxide remains very uncertain.
Global landing: Coefficient = -1.26 (+/- 0.16). This suggests that the sinks of the land (mainly vegetation) are underestimated by 25%. The error is that the coefficient is small, so I think this result is important.
Global Marine Trough: coefficient = -0.80 (+/- 0.49), which indicates that seawater sinks have been overestimated (but have great uncertainty) about 20%. I haven't considered whether these ocean models include temperature rises (with minimal effect) or whether they include CO2 models. I don't believe this coefficient is significantly different from 1.0, and this is the case if the model is not biased against the estimation of seawater sinks.
Cement carbonated water tank: (-7.3 +/- 4.9) This indicates that the CO2 absorption of old cement has been greatly underestimated (but with great uncertainty). This is a surprising number and I don't know how to do it.
I don't believe most of these conclusions except for the model underestimated CO2 vegetation sinks. Recently published papers found that some vegetation absorption processes were underestimated by the model.
The underrated global sources of artificial emissions are also interesting. 1.3 coefficient is greater than 1, and if the annual anthropogenic emission estimate is poor, we will get the opposite from the regression. So, I tend to believe that this is true.
Anyway, it's a quick exercise. Maybe it was my 4 hours. You can access the GCP data spreadsheet here.
PS I'm sure someone will ask about adding various natural factors: for example, global surface temperature (land and/or ocean). Yes, it can be done.
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