INTERACTIVE COMPANION · METHODS · EQUILIBRIUM CHEMISTRY

The Seawater Bench

A live model accompanying "Solving Seawater"

Two calculators sit below, and both run the same solver the article does. The first takes a parcel of surface seawater and tells you what is dissolved in it. The second draws the plot that explains why the answer comes out the way it does. Nothing here is a lookup table: every number is a fresh root of the quartic, found in your browser while you drag the slider.

Model 1. What is dissolved in this water?

Four things go in: the atmospheric carbon dioxide the water is in equilibrium with, its temperature, its salinity, and its total alkalinity. Everything else comes out. The solver converts the dry-air mixing ratio to a fugacity by subtracting water vapour pressure and applying the virial correction, multiplies by the Henry's law constant to get dissolved carbon dioxide, then finds the one positive root of

F(h) = K₁C/h + 2K₁K₂C/h² + K_BB_T/(K_B+h) + K_w/h − h − A_T = 0

by safeguarded Newton iteration. Every term in F′(h) is negative, so the function is strictly decreasing and the root is unique.

–pH, total scale

–Ω aragonite

–carbonate, µmol/kg

–DIC, µmol/kg

Atmospheric CO₂ 420 ppm Start at today's 420. Drag back to 280 for the pre-industrial atmosphere and watch pH climb to 8.18; drag to 180 for the last glacial maximum. The club's headline number is the ratio of the hydrogen ion concentrations at 420 and 280, which is a rise of 39.80 per cent, not the 30 per cent usually quoted. Try 385 to see where the 30 per cent figure actually lives. Temperature 18.0 °C 18 °C is roughly the area-weighted mean surface ocean. Drag down to 2 °C for polar water and watch the saturation state collapse while pH barely moves. That is the whole reason the Southern Ocean is the first place this becomes a problem. Salinity 35.0 Open-ocean surface water runs about 33 to 37. This is the gentlest of the four controls: salinity shifts every constant a little and mostly cancels. Push it to 30 and see how little happens compared with a two-degree temperature change. Total alkalinity 2300 µmol/kg The conservation law that holds the whole system together. Raising it raises pH and carbonate together, because alkalinity is the ocean's stock of proton acceptors. This is the knob that ocean alkalinity enhancement proposals are aiming at, and dragging it will show you both how well it works and how much of it you would need. Mineral Aragonite is what corals, pteropods and many molluscs build with, and it is the more soluble of the two. Switch to calcite and every saturation state rises by about half, which is why coccolithophores and foraminifera have more room before they are in trouble.

CO₂(aq): – HCO₃⁻: – fCO₂: – Ω = 1 at: –

–

Model 2. The plot that explains the answer

Strip alkalinity out entirely and ask a simpler question: at a given pH, how is the dissolved carbon divided between the three species? That depends on nothing but K₁, K₂ and the hydrogen ion concentration, which is why this plot moves when you change temperature or salinity and stays put when you change carbon dioxide or alkalinity. The vertical marker is wherever Model 1 currently sits.

Show the pre-industrial marker Leave it on and set Model 1 to 420 ppm. The gap between the two vertical lines is the entire industrial acidification signal, and it looks tiny on this axis. Then read the carbonate curve at each of them and notice that the tiny gap has cost you a fifth of the carbonate. Carbonate axis Switch to the expanded axis to see what the carbonate curve is doing in the range seawater actually occupies. On the full axis it looks flat. It is not flat.

pK₁: – pK₂: – fraction as CO₃²⁻: –

What would break this

The honest failure modes deserve naming, and there are four worth stating. The parcel is in instantaneous equilibrium with the air above it, which no real mixed layer ever is, and that makes this bench report more acidification than an ocean still catching up. Every constant is at one atmosphere, so nothing here applies below the surface, where the solubility products rise with pressure and the saturation horizon lives. Alkalinity is held fixed, which is right for dissolving a neutral gas and wrong over the centuries in which sediment dissolution and weathering move it. And the alkalinity definition here carries only carbonate, borate, water and the free proton, so this bench should not be pointed at an estuary.

Try this. Set temperature to 2 °C, salinity to 34 and alkalinity to 2300, then walk carbon dioxide up from 280. The saturation state crosses one somewhere below 650 ppm, which is a level several emissions scenarios reach this century, and it does so while the pH is still above 7.85. Nothing dramatic happens to the pH readout at that moment. The thing that matters crosses a line quietly.