On May 11 you reposted a blog from Dr. Roy Spencer, where he suggests that much of the increase in atmospheric CO2 could be due to warming of the oceans, and where he presents a few graphs that he claims are consistent with ocean surface temperature change contributing more than 80% of the measure increase in CO2 since 1958. Dr. Spencer’s suggestion is contradicted by many published studies of absorption of CO2 by the ocean, with some studies dating from the early 1960’s, long before “global warming” was a political issue. In this post I offer a simple model that shows why net absorption of CO2 by the ocean is most likely the main ocean effect.
If the rise in CO2 is being driven by human emissions, then the year-on-year increase in atmospheric CO2 ought to be a function of the rate of release of CO2, less any increase in the rate of removal of CO2 by increased plant growth and by absorption and chemical neutralization of CO2 by the ocean. Both ocean absorption and plant growth rates should increase with increased CO2 concentration in the atmosphere. To simplify things, I focus here only on ocean absorption.
On the other hand, surface temperature changes ought to have a relatively rapid effect, because the surface of the ocean is in contact with the atmosphere and so can quickly absorb or desorb CO2 as the water temperature changes. In fact, the ocean surface continuously absorbs CO2 where the temperature is falling, mostly at high latitudes, and emits CO2 where the water is warming, mostly at lower latitudes. Cold upwelling water from the deep ocean warms at the surface and desorbs CO2, while very cold water at high latitudes absorbs CO2 before it falls to the deep ocean. An increase in average ocean surface temperature will cause more CO2 to be emitted from surface water, but this effect is limited to a very small volume fraction of the ocean. Effects due to rapid temperature changes (annual time scale and less) are limited to a relatively thin layer, while the gradual absorption/neutralization process takes place at a rate controlled by ocean circulation and replacement of the surface water with upwelling (and “very old”) deep ocean water.
Any change in sea surface temperature should add to or subtract from the atmosphere’s CO2.
Annual change = (Annual emissions) – K1 * (CO2 – 285) + K2 * (delta SST)
Where “CO2” is the atmospheric concentration, K1 is a unitless “ocean uptake constant”, and K2 is a sea surface absorption/temperature constant, with units of PPM per decree C. Delta SST is the year-on-year change in average sea surface temperature. K1 is related to how quickly surface water is replaced by deeper water, and it should be a relatively small number, since ocean circulation and mixing are slow. K2 should be a relatively large number, since surface water temperature changes are relatively fast and we know that there is a strong short-term correlation between the rate of change of CO2 concentration and SST changes.
The model performs an iterative calculation (a step-wise approximation of integration) of the evolution of CO2 in the atmosphere. Each year a change in CO2 is calculated using the above equation, that change is added to the atmospheric CO2 concentration from the previous year, and the process is then repeated. The calculation starts with 1959, using a starting CO2 concentration of 315 (the value from Mauna Loa in 1958).
Measured CO2 values and measured year-on-year changes are from Mauna Loa. Average SST’s are from GISS. CO2 emissions, expressed as PPM potential increase in CO2 in the atmosphere, are based on worldwide carbon emissions (according to CDIAC at Oak Ridge) converted to an equivalent weight of CO2, divided by an assumed atmosphere weight of 5.3 X 10^9 million tons. This result was scaled by a constant factor of 0.7232, which is 28.96/44 = 0.6582 (to convert weight fraction CO2 to volume fraction), multiplied by 1.099 to match up with the range of CO2 emissions that Dr. Spencer used in his May 11 blog post. Note that nobody really knows the total carbon emissions, so different sources offer different estimates of total emissions. The final two years of CO2 emissions I had to estimate beacause the CDIAC data ended in 2006. I assumed an equilibrium ocean CO2 level of 285 PPM. I optimized K1 and K2 by hand so that the model had a reasonable fit with the data; the values were 0.0215 for K1 and 5.0 for K2. So the model equation is:
Annual change = (Annual emissions) – 0.0215 * (CO2 – 285) + 5.0 * (delta SST)
The graph titled “Annual Increase in CO2” compares the measured and calculated year-on-year changes along with the potential increase from fossil fuels.
The graph titled “Correlation: Model Increase vs. Mauna Loa Increase” shows that the model does a decent job of capturing the year-on-year temperature driven change in atmospheric CO2.
I suspect that if the model used monthly data and the 6-month lag between SST changes and CO2 changes that Dr. Spencer used, then the model fit would be better.
The graph titled “Measured CO2 versus Ocean Uptake Model” shows the final result of the calculation.
The evolution of CO2 in the atmosphere calculated by the model between 1958 and 2008 is reasonably close to the Mauna Loa record. The model suggests that about 2.15 PPM equivalent of emitted CO2 is currently being absorbed, or about half the total emissions.
My only objective is to show that the CO2 released by human activities, combined with slow ocean absorption/neutralization and sea surface temperature variation, is broadly consistent with the measured historical trend in atmospheric CO2, including the effect of changing average SST on short term variation in the rate of CO2 increase. Temperature changes in ocean surface waters cause shifts of a few PPM up and down in the rate of increase, but surface temperature changes do not explain 80% to 90% of the increase in atmospheric CO2 since 1958, as suggested in Dr. Spencer’s May 11 post. Because of its relatively high pH, high buffering capacity, enormous mass, and slow circulation, the ocean is, and will be for a very long time, a significant net sink for atmospheric CO2.
With a bit of luck, continuing flat-to-falling average surface temperatures and ocean heat content will discredit the model predictions before too much economic damage is done.