## Tuesday, January 15, 2019

### Are Underwater Volcanoes Causing Ocean Warming?

There's important climate news in the last week -- ocean warming has been found to be 40% higher than was given five years ago by the IPCC 5th Assessment Report, bringing it in line with climate model predictions. And Antarctic ice melt is six times greater than it was in the 1970s.

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....

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

so
where

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

α = 4.7 × 109 ≫ 1
and
ΔT = 3 × 10-7 K/yr

so tiny, as expected. Converting this to a ocean heat gain gives

ΔQ = 1 × 1018 J/yr = 4 × 1010 W → 1 × 10-4 W/m2

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?

Layzej said...

So undersea volcanoes only contribute ~0.1% of the ocean's heat gain.

And that assumes there was no undersea volcanic heat prior to industrialization?

This Nature paper has some interesting thoughts on how undersea volcanos may be contributing to antarctic sea ice melt: Based on the observed 3He excesses, the mantle-derived heat at the front of the ice shelf cavity is 32 ± 12 J kg−1 of seawater. This excess heat is small compared to the heat content of CDW20 (ca. 12 kJ kg−1), demonstrating that volcanic heat does not contribute significantly to the glacial melt observed in the ocean at the front of the ice shelf. This interpreation is consistent with our understanding of melt dynamics beneath the Pine Island Ice Shelf - that most of the basal melt occurs within the cavity, as a result of ocean heat supply20. Yet, the relatively dilute volcanic heat source may be much more concentrated at the time of contact with the ice sheet, and the magnitude more significant when compared to the background geothermal heat supply to the grounded glacier. We infer the heat flux to the ice sheet using observations of the cavity circulation at the ice shelf front (Eq. 3).

David Appell said...

The heat gain is per year, and of that gain, volcanoes are ~0.1%.

But you're right, those volcanoes have been there all along. Since the ocean was in equilibrium before the industrial era (at least, let's assume that), it was losing whatever heat the volcanoes (plus other sources) were putting in.

Do you mean in that case undersea volcanoes really aren't contributing anything to the observed ocean heat gain in the anthropogenic era?

David Appell said...

Layzej: Thanks for pointing out that Nature paper. Probably coincidence, but they find a kinda similar ratio to the global one:

(mantle derived heat)/(circumpolar deep water heat) = 32 J/12 kJ = 3e-3

which is not too huge of a difference from my global number of 1e-4.

Granted, I didn't include heat vents in my calculation.

Layzej said...

Do you mean in that case undersea volcanoes really aren't contributing anything to the observed ocean heat gain in the anthropogenic era?

It probably depends on how undersea volcanic activity has changed over the last 100 years... right? Maybe there has been a drop in volcanic activity?