Henrys Law

 

Understanding Global Warming

Henrys Law

Figure 1. IPCC Carbon Cycle AR5. Simplified schematic of the global carbon cycle. Numbers represent carbon mass and exchange fluxes in Gt (Pg) carbon per year – hyperlink. The enclosed part [our highlighting] shows a chain of circles connecting the atmospheric carbon with that of the sea - quite to the sediment on the ocean floor. A total upward flux of 207,1 GtC is indicated.

According to Henry’s law, a balance must be maintained between the concentration of CO₂ in the atmosphere and in the ocean’s surface layer. As chemical and biological processes remove CO₂ from surface waters and transport it to deeper layers, space is created for additional CO₂ uptake at the surface. However, this downward transport introduces a delay in the system’s overall response.

Consequently, only an amount of CO₂ roughly equivalent to half of the fossil fuel emissions is absorbed by the oceans on an ongoing basis. An amount corresponding to the remaining emissions stays in the atmosphere, gradually increasing the atmospheric concentration of carbon dioxide.


As a result, the oceans absorb only a quantity equivalent to about half of the CO₂ emitted from fossil fuel combustion. The remaining portion stays in the atmosphere, where it gradually increases the atmospheric concentration of carbon dioxide

Water vapor and carbon dioxide are greenhouse gases that, figuratively speaking, form a blanket that keeps the Earth warm. That blanket does not heat and get heated. The heat comes from the sun. It is not the air that heats land and sea. It's sunshine and it varies quite a bit. As an example, Denmark received 25% more sunshine at the end of the 20th century, raising the temperature 1.7 ^oC.

Henry’s law illustrated. CO2 removed from the atmosphere will be replaced by CO2 from the sea. Gt C = Gigaton Carbon.

William Henry (1774 –1836) was an English chemist. He developed what is known as Henry's Law. It is a gas law that states that the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid. The proportionality is temperature dependent.

Between carbonized water and its headspace, there is an equilibrium determined by the partial pressure of the gas and the temperature. Henry's law applies offshore as well. The partial pressure of atmospheric carbon dioxide has risen since measurements began in 1958. The same goes for sea temperatures. The exchange of carbon dioxide between air and the sea skin is instantaneously.  It takes time to exchange CO₂ with the deep sea through upwelling, chemical and biological carbon cycles. These carbon cycles are vertical chaining (IPCC, AR5):

Carbon dioxide in air	↔	Carbon dioxide in sea	↔	Bicarbonate (HCO3−)	↔	Carbonate (CO32−)	↔	Sediment
829 Gt C	80 Gt	190 Gt C		33.820 Gt C		3.990 Gt C	0,2 Gt	1.750 Gt C

Literally air and sea can be considered communicating vessels where the above chain connects carbon in the air with sediment at the ocean floor in a reversible manner – hyperlink.

At the equator strong sunshine causes the sea to emit (outgassing) the most carbon dioxide. The North Atlantic acts as a sink (ingassing) with carbon dioxide going the other way. The IPCC has illustrated how carbon dioxide circulates between the air and the sea and the land. Summer/winter atmospheric CO₂ varies 10 ppm ~ 20 Gt C. Large amounts - well over 200 Gt of carbon - are exchanged every year. Of this, CO₂ from combustion makes up 8 Gt (4%). In a final steady state ~ 95% of the carbon will be in the oceans.

Henry's Constant for seawater

The constant for temperatures above zero is according to Plummer and Busenberg (1982) and below Zero is acc. to Neal Bailey et all. - Link  - Thermodynamic Henry's Law constants (KH) for CO₂ under low temperature and high salinity conditions.

Plummer and Busenberg (1982),  

logK_H = 108.3865 + 0.01985076T – 6919.53/T – 40.45154logT + 669365/T² where temperatures in K.

The lead author Neal Bailey  of "Henry's Law constant for CO₂ in aqueous sodium chloride solutions at 1 atm and sub-zero (Celsius) temperatures" -  Link - private correspondence 29.01.2021:

The rate of change in the Henry's Law constant varies with temperature, and so the overall release varies according to what the initial and final temperatures are. If you're looking for warming of the Arctic Ocean, with a mean surface water temperature of around 271 K, the results in our paper only extend to 272 K, in which case the Henry's Law constant decreases from .101 to .0887 mol(kg water)^​-1 atm^-1 when moving from 271 to 272 K. For temperatures higher than this, we rely on Plummer and Busenberg (1982),  

Extending an expected warming to 276 K, or 5 degrees, we find K_H  = 0.069679. This is a change of about (.101-0.069679) = .0313 mol of CO₂, which has a molar mass of 44.01 g, so that's 1.38 g of carbon dioxide released to the atmosphere per kg of water for a 5 degree warming. Note that this is kg of pure water, not salt water. Salinity 35 water at 271 or 272 K is going to be denser than pure water at 298 K. Using a density of 1025 g/L, we find 990 g/L or 990 kg H₂O per m³ of S 35 seawater. The surface area of the Arctic ocean is about 14,000,000 km², which is 14*10¹² m², thus you wind up with: (1.38 g/kg)*(990 kg/m³)*(14*10¹²m²) = 1.91*10¹⁶ g of CO₂ released per m depth of water. That's 1.91*10¹⁰ tons (19.1 GT) for a 5 degree increase from 271 to 276 K, to a depth of 1 m. 

The oceans, with a surface area of 361.000.000 km² and an average surface water temperature of 17 degree Celsius, will in a similar calculation push 6 GT C into the atmosphere for each degree of temperature rise, but such extrapolation is not valid. Ocean surface water to a depth of one meter corresponds to 361.000 km3, less than one per mille of the total amount of water. Equilibrium under these circumstances hardly occurs.

NOAA's National Geophysical Data Center estimates that 321,003,271 cubic miles (1.338.000.000 km3) is in the ocean.

Peter Stallinga in "Signal Analysis of the Climate: Correlation, Delay and Feedback" - Link - finds the Henry’s Law hypothesis can easily explain all effects. Using K_H= 10,5 ppm/K and a characteristic ocean outgassing time of τ = 600 year he can reproduce past temperature/carbon dioxide correlation.

Understanding Global Warming, Oversigt - LINK