But I feel like blogging about the skeptical conjecture that underwater volcanoes are causing the observed ocean warming. For example, the radio host Lars Larson, whose show I was on last summer, conjectured that recently on Twitter:
Could this be causing ocean warming? Seems unlikely....It’s those darned underwater volcanoes and hot water vents.— Lars Larson (@FlushRivet) January 8, 2019
1) these volcanoes and vents didn't suddenly flare up during the Industrial era or in the 1970s -- they've been there for, what, billions of years at mid-ocean ridges where tectonic plate spread apart?
2) But let's do a little back of the envelope calculation to estimate their influence -- for underwater volcanoes, at least. (Plus it's always fun to get a chance to make LaTeX equations again.) Here's what I found:
"About 5 cubic-miles of lava erupt every year along the mid-ocean ridges and submarine fault systems associated with subduction zones...." (Forbes)
The lava is at a certain temperature TL, and the ocean at (an average of) TO. As the lava pours into the ocean, it gives up heat to the ocean, raising the temperature by ΔT. The final temperature of the lava will be TO + ΔT. Then by energy conservation, the heat gained by the ocean is the heat lost by the lava:
where M is mass and C is specific heat. Then
Here are the numbers I found for lava:
where 1200°C was the maximum value in the given range. For the ocean:
(The initial temperature of the ocean doesn't matter much, since TL is over an order of magnitude larger.) So
so tiny, as expected. Converting this to a ocean heat gain gives
over the Earth's surface area. Compare that to the trend found in the first paper mentioned above of about 0.60 W/m2.
So undersea volcanoes only contribute ~0.1% of the ocean's heat gain.
(I think it's hard to imagine just how huge the ocean is. For example, it's 1.5 times more massive than Ceres, the largest body in the asteroid belt, with a diameter of almost 600 miles.)
Anything I missed?