Antarctic Bottom Water doesn’t fully explain the deep ocean warming acceleration

I thought Antarctic Bottom Water had a real chance of surviving this one.

The observational signal looked like a really good match at first glance. The warming sits in very dense abyssal water. When I stopped looking at the ocean only in fixed pressure layers and followed the actual evolving density structure instead, almost all of the apparent vertical isolation disappeared.

So, I kept following the heat.

I traced the dense water structure, checked the Antarctic export pathway, rebuilt the ECCO heat budget, fixed the pressure coordinate accounting, and finally got to the question that actually matters:

Can Antarctic Bottom Water and deep overturning move enough heat to produce the observed 4 - 6 kdbar warming acceleration?

The answer is no.

AABW and overturning appear to contribute to the structure of the signal. They even produce warming acceleration in the correct direction in the abyss.

They just don’t produce nearly enough of it.

On matched observational support, ECCO produces only about 2% of the observed 4-6 kdbar warming acceleration. That’s far below the quantitative threshold I set before seeing the answer. The final result is:

AABW/overturning fails as the dominant quantitative explanation for the observed abyssal warming-acceleration signal.

What exactly am I trying to explain?

The observation I’ve been testing is the positive warming acceleration in the deep ocean, especially around 4,000-6,000 dbar, as observed by Johnson [1] and Desbruyères [2].

For this analysis I stayed with the same observational reconstruction I’ve used throughout this entire project. The profile archive is built from World Ocean Database CTD observations and Deep Argo, mapped into the same pressure bin framework used to reconstruct the Johnson abyssal warming result.

The temperature variable is Conservative Temperature, so reversible pressure warming from adiabatic compression is already removed. For the ECCO comparison, I restricted the analysis to the common period:

February 1992 through November 2017

That gave me the period where I could compare the observational acceleration against a dynamically complete ocean state estimate.

The observational target was not “the entire deep ocean.” I first identified the 4-6 kdbar cells that were both warming and accelerating over that period, then mapped those targets into ECCO. There were 278 original observational targets and 266 passed the final deep-ocean ECCO mapping and estimator-support requirements. All 266 had complete support for the final acceleration comparison.

The acceleration itself came from the same quadratic temperature fit used throughout the observational analysis.

CT(t) = c₀ + c₁(t − 2005) + c₂(t − 2005)²

a = 2c₂

So the quantity I’m comparing isn’t just “warming”, it’s the change in the warming rate:

a = d²CT / dt²

K yr⁻²

At first, AABW actually looked pretty good

Before testing the whole energy budget, I tested something simpler. If Antarctic Bottom Water were carrying the warming into the abyss, I’d expect the deep signal to remain connected to the dense water structure somehow. We should see that pattern.

Initially that looked questionable.

About 46.9% of the 4-6 kdbar target volume appeared vertically isolated when I compared it against the overlying 3-4 kdbar layer in fixed pressure coordinates.

That could’ve been a serious problem for AABW. But, fixed pressure is not the same thing as following a water mass. So, I reconstructed the full temperature and salinity profiles, calculated σ₄, and followed the dense water surfaces instead.

That changed the result dramatically. Of the volume that had appeared isolated in pressure space:

98.925% became connected in density space.

None of the adequately supported volume remained demonstrably isolated. About 1.1% was untestable.

So, I couldn’t reject AABW because the abyssal warming was disconnected from the dense water. It wasn’t. The apparent isolation was mostly a coordinate problem. That was a strong reason to keep testing.

Then, I checked whether the Antarctic pathway was actually there

Next, I used ECCO to ask whether the density linked targets were dynamically connected to Antarctic dense water export and downstream overturning.

That result was more mixed. :( It was partially supported.

About 65.6% of the positive observational signal fell into regions with partial pathway support. Roughly 24.2% was inconsistent and 10.2% was untestable. None of the regions cleared my stricter “fully supported” lag/pathway criterion.

So by this point the story was: The water mass pattern fits. The abyssal signal is not actually isolated from the dense water structure. There is a plausible Antarctic/deep overturning pathway.

But the pathway evidence wasn’t perfect. So, I kept testing it quantitatively.

The hard part: how much heat does overturning actually deliver?

This was the part that took forever… :’(

ECCO gives the native ocean heat budget terms, including horizontal and vertical advection, diffusion, and forcing. But, my observational layers are defined by pressure: 3-4 kdbar and 4-6 kdbar.

A fixed pressure surface can cut straight through an ECCO model cell. At first, I tried interpolating the native vertical heat flux onto 3,000, 4,000 and 6,000 dbar.

That was wrong. :(

Those fluxes are integrated over ECCO’s native model faces. An arbitrary pressure surface inside a cell is not another native face, so interpolating the flux doesn’t conserve the model’s heat budget.

I replaced that with an exact conservative cut cell operator derived from the discrete native divergence.

The full period operator ultimately validated to essentially numerical precision. The maximum pressure operator error over the full run was only 0.07 W, while the physical terms are on the order of terawatts. The remaining monthly closure residuals were traced directly back to the native ECCO heat budget residual rather than the pressure transformation.

So, at that point I finally had a pressure layer heat budget I trusted. whew

One more trap: acceleration has to be calculated the same way

There was one last issue. I initially compared the linear trend in ECCO’s monthly heating rate against the quadratic acceleration of the observed temperature state. Those sound interchangeable.

For a perfectly quadratic, noise free signal they basically are. For a finite, varying ocean time series, they aren’t the same estimator… So, I changed the calculation again.

For every monthly heat-budget component I converted heat transport into temperature tendency:

dT / dt = Q̇ / (ρc_pV)

where

ρ = 1029 kg m⁻³

c_p = 3994 J kg⁻¹ K⁻¹

Then I integrated each monthly heat rate contribution through the actual time intervals:

ΔT_n = [Q̇_n / (ρc_pV_n)] Δt_n

That gave me a budget implied temperature trajectory. Then, I applied the exact same quadratic acceleration fit to that trajectory that I used for the observational temperature data.

This worked.

The reconstructed ECCO state and the budget derived state agreed essentially perfectly.

The volume weighted state acceleration was:

2.079628 × 10⁻⁵ K yr⁻²

The independently reconstructed budget acceleration was:

2.079627 × 10⁻⁵ K yr⁻²

The remaining closure contribution was only:

1.39 × 10⁻¹¹ K yr⁻²

So the heat budget and the temperature state finally agreed to numerical precision. That is the number I was waiting for. :)

And it isn’t enough

On the exact same observational support, the observed 4–6 kdbar acceleration is:

1.021216 × 10⁻³ K yr⁻²

ECCO produces:

2.079627 × 10⁻⁵ K yr⁻²

So:

R = a_ECCO / a_observed

R = 0.02036

Or about, 2.04%. Before running this calculation I had already defined the quantitative sufficiency range as:

0.33 ≤ R ≤ 3.0

Anything below 0.33 was magnitude insufficient.

The result is nowhere close.

0.020 is about 16 times below even the lower sufficiency boundary.

The formal classification is therefore: MAGNITUDE_INSUFFICIENT

and the combined mechanism result is:

AABW_TRANSPORT_DIRECTIONALLY_CONSISTENT_MAGNITUDE_INSUFFICIENT

Where does the ECCO abyssal acceleration come from?

This part was interesting, too. The modeled 4 - 6 kdbar acceleration is mostly produced by vertical transport.

Vertical transport contributes:

1.947 × 10⁻⁵ K yr⁻²

Horizontal/lateral transport contributes:

1.322 × 10⁻⁶ K yr⁻²

So the vertical contribution is roughly 14.7 times larger. Breaking that apart further:

Vertical advection:

+9.20 × 10⁻⁶ K yr⁻²

Vertical diffusion:

+1.03 × 10⁻⁵ K yr⁻²

Horizontal advection:

−5.56 × 10⁻⁵ K yr⁻²

Horizontal diffusion:

+5.69 × 10⁻⁵ K yr⁻²

Those last two almost cancel each other. Geothermal forcing contributes essentially zero acceleration, as expected from a nearly static geothermal field.

So ECCO absolutely does generate a physically real positive abyssal acceleration.

It just generates a very small one compared with the observation.

The vertical structure isn’t a perfect match either

ECCO produces:

4-6 kdbar:

+2.08 × 10⁻⁵ K yr⁻²

3-4 kdbar:

−3.56 × 10⁻⁷ K yr⁻²

So ECCO does reproduce the idea that the deepest layer behaves very differently and has a much stronger positive acceleration.

But the modeled 3-4 kdbar acceleration is slightly negative, while the observational 3-4 signal is positive.

I classified that as: VERTICAL_STRUCTURE_PARTIAL.

The regional budgets are messy, too. In 19 of the 21 4-6 kdbar regions, vertical and lateral contributions oppose one another.

That’s not necessarily surprising in a global overturning circulation. Water enters, leaves, mixes and redistributes.

But again, it doesn’t rescue the magnitude.

So what does this actually rule out?

This analysis shows that Antarctic Bottom Water does affect abyssal warming.

The warming follows the evolving dense water structure really well. The apparent vertical isolation mostly disappeared once I followed density instead of pressure. ECCO contains a plausible deep overturning pathway. And, ECCO generates a positive abyssal acceleration with a strongly vertical transport contribution.

So, AABW is physically relevant.

But relevance is not enough.

When I finally asked how much acceleration the modeled transport can supply, the answer was only about 2% of the observed requirement.

That is why I’m closing this mechanism as:

AABW / deep overturning — closed as the dominant quantitative explanation

It survives as a contributor. It survives as part of the water mass story.

It fails as the mechanism capable of explaining the magnitude of the observed 4- 6 kdbar warming acceleration.

I could’ve stopped when the original pressure layer comparison looked disconnected and said AABW failed.

That would’ve been wrong.

Following the density structure actually made the AABW case much stronger.

It took the full transport and energy calculation to break it.

That’s the result.

Next mechanism.

References

[1] Johnson, G. C. (2026). Observed Multi-Decadal Acceleration of Globally Averaged Abyssal Ocean Warming. Geophysical Research Letters, 53(14), e2026GL124104. DOI: 10.1029/2026GL124104. This is the paper that reports the accelerating 4,000 - 6,000 dbar abyssal heat uptake using historical shipboard CTD and Deep Argo profiles.

[2] Desbruyères, D. G., Purkey, S. G., McDonagh, E. L., Johnson, G. C., & King, B. A. (2016). Deep and abyssal ocean warming from 35 years of repeat hydrography. Geophysical Research Letters, 43(19), 10,356–10,365. DOI: 10.1002/2016GL070413. This is the earlier repeat hydrography analysis showing the strongest warming in the 4,000-6,000 m abyssal layer, particularly in the Southern and Pacific Oceans.