A Mixed Up Mixed Layer

Guest Post by Willis Eschenbach

A recent post here on WUWT entitled “Claim: Marine heatwaves becoming more intense, more frequent” referenced a study as saying:

When thick, the surface layer of the ocean acts as a buffer to extreme marine heating–but a new study from the University of Colorado Boulder shows this “mixed layer” is becoming shallower each year. 

Those who know me know that I take the UK Royal Society’s motto, “Nullius In Verba”, very seriously. So I went off to find out what I could about the mixed layer.

I figured that my best bet was the data from the Argo floats. These are amazing man-made ocean-dwelling subsurface creatures. They sleep down 1000 metres under the surface. Then every nine days, they wake up, sink down another 1000 metres, then slowly rise to the surface collecting data. Once on the surface, they call home like ET, report their findings, and then sink down again and go back to sleep.

Now, when I looked at the Argo float mixed-layer data, what I found was a curious thing. I hadn’t known that there are no less than four different methods for calculating the mixed layer depth— the temperature threshold, temperature algorithm, density threshold, and density algorithm methods. Always more to learn. The threshold methods are described here, and the algorithm methods are described here.

With that as a preface, here are the global results for the two threshold methods.

And here are the results for the two algorithm methods.

I note that the algorithmic methods give shallower average mixed layer depths than the threshold methods. And the range between the four methods is about ten metres out of sixty or so, very large.

So … is the mixed layer getting shallower? Well, it depends on which method you prefer. Here are the trends for threshold methods.

Note that before about 2004, there weren’t enough Argo floats deployed to give us good data. Looking at the post-2004 data, neither one of the threshold methods shows any trend. Next, here are the algorithm methods.

Ya pays yer money and ya takes yer choices … the algorithmic methods both show a slight decrease in the mixed layer depth of about 250 mm/year. However, after allowing for autocorrelation neither of the algorithmic methods shows a statistically significant change.

Next, is the claimed shallowing of the mixed layer due to the slight rise in temperature? Unknown. The authors of the study say:

… it is clear that large internal climate variability complicates the detectability of the forced MLD signal in observations

And speaking of “large internal climate variability” here is another look at the density algorithm method, this time with a gaussian smooth instead of a trend line:

You can see that the mixed layer depth got slightly deeper from 2004 to 2011, shallowed until 2016, and has deepened slightly since then … internal variability indeed.

Net result? I’d say that we don’t have enough data to say either that the mixed layer is shallowing, or that the cause is the slight ongoing global warming.

Lovely rain here, best of a wonderful world to everyone.


PS: As is my wont, I ask that when you comment you quote the exact words you are discussing, so we can all know both who and what you are talking about.

[UPDATE: A commenter asked for a Eurocentric view of the globe, and although I suspect this might indicate some kind of hidden climate-based scientific systemic racism, we’re a full-service website …


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Ron Long
February 2, 2021 10:28 am

You do a great job of presenting actual data, Willis, however you’ll never get any funding, so enjoy the lovely weather and view.

Phil Rae
Reply to  Ron Long
February 2, 2021 11:21 am

Yes! I think we can all agree on Willis’ wonderful ability to find, extract and condense vast swathes of data into simple easily-understandable graphics.

He cuts through the fog and lets us all see a clear view of the information, for better or worse. Always a pleasure to read an article from Willis.

Reply to  Ron Long
February 2, 2021 12:38 pm

I agree with you Ron, Willis does a wonderful job of presenting actual data. However, I think many of us underestimate the amount of work and coding new algorithms that Willis does to present the data so well.

Thank you Willis for all your work and insights.

Reply to  Willis Eschenbach
February 2, 2021 9:02 pm

You have been quite successful for a very long time.

Curious George
February 2, 2021 10:34 am

“When thick, the surface layer of the ocean acts as a buffer to extreme marine heating.”
I wonder if this is true. The claim only appears in the press release, not in the referenced study.

Reply to  Curious George
February 3, 2021 1:06 pm

The oceans adsorb most of the Sun’s IR which breaks the hydrogen bond between the water molecules in the water – resulting in the heat being carried away as water vapor – which eventually becomes rain water.

Robert of Texas
February 2, 2021 11:05 am

So I was STILL confused by what they are trying to measure – this “mixed layer” – and went digging into Wilis’s references: (https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2004JC002378)

“A striking and nearly universal feature of the open ocean is the surface mixed layer within which salinity, temperature, and density are almost vertically uniform. This oceanic mixed layer is the manifestation of the vigorous turbulent mixing processes which are active in the upper ocean. The transfer of mass, momentum, and energy across the mixed layer provides the source of almost all oceanic motions, and the thickness of the mixed layer determines the heat content and mechanical inertia of the layer that directly interacts with the atmosphere.”

Well isn’t THAT rather random? It seems to mean the thickness of the mixed layer only depends on the amount of energy used in mixing it. Therefore, if the wind energy (and other sources of mixing) does not change, neither should the thickness of the mixed layer. So if the mixed layer is thinning, there must be less energy being used to mix it. Therefore, they are claiming that global warming is causing less mixing, and therefore should be causing fewer and less violent storms???

Reading on…”The concept of the mixed layer is arbitrary, and can be based on different parameters (e.g., temperature, density, salinity), and may represent averages over different time intervals (e.g., day, month).”

“Arbitrary” – You can say that again. They are measuring an arbitrary concept using various arbitrary methods and parameters to cause alarm about something that has no well-defined meaning. But they think it is changing and therefore HAS to be bad and HAS to be caused by global warming. Such brilliant scientific minds.

Thanks again Willis, you have advanced at least my understanding a small notch forward.

Reply to  Robert of Texas
February 2, 2021 4:13 pm


The paragraph on “arbitrary” was the results of those scientific minds meditating. What they wrote is simply called “sunyata”

February 2, 2021 11:08 am

Thanks again for more rational insights Willis.

I’m guessing you don’t sit expectantly by your phone waiting for a call from WAPO, NYT or The Guardian with any clarifying questions before they scramble to publish this additional info for their always open-minded readership?

(I jest of course)

Stay dry and warm.

Hans Erren
February 2, 2021 11:15 am

Willis, please add atlantic centered maps for the Europeans.

Ben Vorlich
Reply to  Willis Eschenbach
February 2, 2021 3:00 pm

Thank you Willis, as a European looking in Europe’s backyard is always my first step in items covering the globe. I suspect this is no different from anywhere else

Wim Röst
Reply to  Ben Vorlich
February 2, 2021 11:22 pm

The new maps show more clearly that the North Pacific is the outlier: a much shallower deep water layer. Supposedly there are as many storms in the North Pacific as in the North Atlantic but the salinity of the North Pacific surface water is much lower which results in less deep mixing. Buoyancy depends on temperature and salinity.
comment image
Source: https://www.weather.gov/jetstream/seawater

The southern oceans around Antarctica show a deep mixed layer while having an ‘in-between’ salinity for that latitude. The most stormy weather in this region enhances mixing.

Last edited 22 days ago by Wim Röst
Ben Vorlich
Reply to  Wim Röst
February 3, 2021 12:25 am

Thanks for that interesting post Wim. My poor use of my own language, I was really talking about people being more interested in what is happening locally before looking globally.

Wim Röst
Reply to  Ben Vorlich
February 3, 2021 6:34 am

My mistake Ben. I thought I was replying to Willis.

Like you I am also interested in ‘the Atlantic view’. Looking at Climatereanalyzer I often make use of the possibility to switch between the Pacific and the Atlantic view. Both have their advantages.

Annette Huang
Reply to  Ben Vorlich
February 3, 2021 8:51 am

It was pleasing to me to New Zealand on a global map for a change. We’ve usually dropped off the bottom of the world.

Hans Erren
Reply to  Willis Eschenbach
February 2, 2021 10:39 pm

Thank you Willis, there are more people living on 0 degrees length than on 180 degrees length.

Richard Patton
Reply to  Hans Erren
February 2, 2021 6:30 pm

When you are talking about what the oceans are doing a Pacific centered chart more clearly depicts that since the Pacific has most of the Earth’s oceans.

Hans Erren
Reply to  Richard Patton
February 2, 2021 10:37 pm

Richard, Although the Pacific covers a large chunk of the world and hence is the largers contributer to the global average, it’s the Atlantic oscillation that dictates the regional climate in Europe.

Robert W Turner
February 2, 2021 11:28 am

When thick, the surface layer of the ocean acts as a buffer to extreme marine heating”

Says who? Do they have any clue at all what they are talking about? How do “journalists” maintain a permanent concussion? So many questions, so little time.

Gordon A. Dressler
Reply to  Robert W Turner
February 2, 2021 1:30 pm

Right on! “Thick” as used in this context denotes above-average convection-mixing of the upper layer of the ocean . . . in turn this would imply above average heating of marine waters and be inconsistent with use of the word “buffer”.

Above and beyond this, heat conduction through water is always occurring due to the average temperature difference between warmer surface waters and colder, deep waters as reflected in the thermocline delta-T. While wind/wave-driven convective heat transfer rates may be much higher over a depth to as much as 200m, the conductive heat transfer rates occur continuously independent of sea state conditions and thus cannot be ignored as an important factor establishing sea surface layer temperatures . . . there is a TREMENDOUS amount of heat capacity below the thermocline.

It’s all about energy-in versus energy-out.

Reply to  Gordon A. Dressler
February 2, 2021 4:13 pm

Very good point, not sure what you mean by “there is a TREMENDOUS amount of heat capacity below the thermocline”.

En liu the mixed layer is a blanket above the thermocline underneath which heat not easily transfer hence is a buffer to the (deep!) marine waters.

The word I am reacting to is “capacity”. Absolutely agree the capacity is tremendous but I have a problem with it in relation to the thermocline which I (parhaps falsely) believe amounts to a “brick wall” which the heat can not pass over shorter timeframes (albeit heat will transfer at the rate of the Ocean Conveyer Belt time frame).

Not least as the depth of said thermocline depends on the depth of the mixed surface layer.

Care to elaborate on “capacity”?


Gordon A. Dressler
Reply to  Oddgeir
February 2, 2021 5:14 pm

The world’s oceans have an average depth of about 3,690 m (12,100 ft).

So, compare the typical 60 m depth of the “mixed layer” of the world’s oceans—as Willis documents in the above article using Argo data—to the average ocean depth. That is a ratio of about 60/3690, or about 1.6%

Thus, whatever heating/mixing happens in the “mixed layer” of the world’s oceans pales to insignificance compared the amount of additional heat the deeper parts of the ocean can absorb via that heat capacity.

As an exercise, take an average thermocline delta-T of 9 °C over 800 m depth of seawater (see https://oceanservice.noaa.gov/facts/thermocline.html ), and using the average surface area of the world’s oceans and the thermal conductivity of sea-water calculate how many terrawatt-hours of energy is being dumped into deep (>1000 m below surface) ocean waters each and every day.

The thermocline in the oceans is definitely not a “brick wall” to vertical heat transfer in the oceans via pure thermal conduction, but instead shows that that very process is happening.

Last edited 22 days ago by Gordon A. Dressler
Gordon A. Dressler
Reply to  Gordon A. Dressler
February 3, 2021 12:52 pm

BTW, the answer to the above “exercise” is that about 0.6 TW-hr is conducted across thermoclines to lower ocean depths every single day, given the above assumptions.

Gordon A. Dressler
Reply to  Gordon A. Dressler
February 5, 2021 8:28 am

Ooops . . . my bad! I slipped two decimal points due to incorrectly doing a units conversion. The correct answer to the above exercise is about 59 TW-hr per 24 hours.

Last edited 20 days ago by Gordon A. Dressler
James Donald Bailey
February 2, 2021 11:48 am

Any trends in the figures are definitely smaller than the displayed regular variations. And there isn’t really enough data to be able to make meaningful claims. But my eye is drawn to what appears to be a step function increase. Not that my eyes are scientific tools.

Could be that I just took a Rorschach test and I am exposing the depths of my psyche. Anyone else see a step function?

The step is more in the upper part of the variation. There also seems to be a larger, rhythmic variation emerging from the lower parts of the graph. Both things can skew long term averages based on poor sampling or insufficient data.

Steve Case
February 2, 2021 12:10 pm

Don’t forget this one:

Correcting Ocean Cooling 
NASA Earth Observatory

Reply to  Steve Case
February 2, 2021 4:44 pm

“The oceans are absorbing more than 80 percent of the heat from global warming,” he says. “If you aren’t measuring heat content in the upper ocean, you aren’t measuring global warming.”

Rain cools landmasses, the heat transfers to the oceans. No one should have any problems with this; It is physics.

I am however having a problem that NASA does not quantify the alleged warming… Can be found to be -7,5-10 is 17.5*10^22 joules.

Which over the timeframe of 1957-2005 amounts to ~18000 as compared to 21 million barrels of oil worth of energy per second or 0.089%, a little less than 1/10-th of 1% (fits ~80% of an increase in insolation with 1.25 W/m2…)

“Net flux is the difference between the energy absorbed by the Earth and the energy the Earth reflects or releases as heat. If net flux is positive (red), more energy is coming in than is going out. Most of the excess energy is stored by the oceans.”

Aren’t we building a crust on this planet of ours anymore then?

“By the end of the period, about 1.4 watts per square meter more energy was entering the Earth system than leaving it.”

Also about 1/10th of 1%, absolutely in line with credible variations in insolation…


Reply to  Steve Case
February 2, 2021 5:34 pm

Ah yes, the character who devised a temperature graph using allegedly measured increases that are well within the error bars of the equipment…

Rud Istvan
February 2, 2021 12:47 pm

WE, fine work with ARGO. Debunks the article thesis.

I have a larger problem with the study you linked to, which triggered the article. It purports to be findings about the Northeastern Pacific, not the world. Your ARGO data (figures 1-4) shows the mixed layer there varies between about 50 to 90 meters. Quite large natural variation, about 1.8x.

The SI reveals that the ‘findings’ are based only on mixed layer ocean slab outputs from a selection of CMIP5 models. This raises two grave issues. First, regional downscaling of GCM’s are well known to be notoriously poor compared to observations, and here the observations themselves vary by almost 2x.
Second, CMIP5 runs way hot as Christy pointed out to congress, for example by more than 2.5x in the tropical troposphere.

There is zero reason to think, as this papers authors did, that a regional downscaling would ever accurately simulate a regional change in an ocean mixed layer that observationally varies by ~2x since 2004. Shows just how poor ‘climate science’ and the reporting on it really is.

Rud Istvan
Reply to  Willis Eschenbach
February 2, 2021 4:27 pm

Best. Small amend. The article claim about the paper was global, but NOT the paper itself. Further makes your and my basic point.

February 2, 2021 12:58 pm

It’s my impression that if someone put those graphs on top of each other, ignoring the horizontal straight-tilted-wiggly lines, the vertical lines might line up. Don’t see a lot of differentiation in any of those charts, but maybe that’s just me.

Abolition Man
February 2, 2021 1:04 pm

Please, please consider putting out a compilation of your posts here on WUWT! You have a knack for explaining and illustrating studies and theories that may be unclear to the layman.
I would prefer a book, but I know that is asking a lot!
Your writing style reminds me very much of Jim Steele’s who’s book is sitting by my recliner waiting to be finished. Enjoy the rain on this glorious Groundhogs Day!

Abolition Man
Reply to  Willis Eschenbach
February 3, 2021 8:32 am

Completely understood, but I am old school; I’d much rather have a hard copy that I can reread at my leisure and I think there is pretty convincing evidence that too much time online causes severe mental problems! Of course, that would be more from social media sites, not truth and fact sites like WUWT!

February 2, 2021 1:28 pm

But, but, but the authors at U of Colorado Boulder as so sure of themselves…

Chris Hanley
Reply to  rickk
February 2, 2021 1:57 pm

Confirmation bias = observer bias + funding bias.

February 2, 2021 1:28 pm

Good post Willis!

In looking at the maps we can see that the depth of the mixed layer is a function of the (solar) forcing and the underlying ocean turbulence (currents). Thus, the thinnest mixed layers occur where the forcing is highest, between the tropics, and the turbulence is least, in the shadow of the continents.

What is interesting in the graphs, showing the evolution in time, is the variations in the yearly maximum depth (i.e. the bottom peaks). These seem to follow the solar cycle.

Rud Istvan
Reply to  dh-mtl
February 2, 2021 5:10 pm

Actually, the mixed layer is mostly a function of wave action. So depends on weather, not climate. The mixing is mainly by wind driven wave action. And typically is about half of the ocean photic zone where photosynthetic life thrives because of sunlight penetration plus food (CO2 from above plus nutrients from below).

February 2, 2021 2:04 pm

Excellent presentation again Willis .
A + B = C , all being variables
A data (selected) + b grade climate scientist = climate Crisis .
Interpreting All data By statistical anaiysis = Common sense .
MSM luv a crisis .
Common sense cannot be taught .

Wim Röst
February 2, 2021 2:05 pm

WR: Looking at the seasons the global mixed layer on average is deepest in July/August and shallowest around December. Summer heat and summer Sun on the NH in July/August coincide with the deepest mixed layer. NH winter circumstances diminish the average depth, only partly compensated on the SH by the SH summer.

More summer heating by sunrays results in a thicker mixed layer for the NH summer. Winter cold and the lack of sunshine diminishes the thickness of the mixed layer, again more on the NH than on the SH.

I remember some of Willis’ graphics showing the relationship between Sea Surface Temperatures (SST) and Cloud coverage respectively Cloud optical thickness – showing the possibility for sunrays to enter the oceans. Around 25 degrees the cloud coverage / optical thickness is the lowest. As the Intertropical Convergence Zone is mostly found on the NH, most surface area with SST around 25 degrees will be on the NH. And so we will find most insolation over NH oceans, warming the deeper surface layers and causing a thicker summer mixed surface layer over the NH than over the SH.

We also find the gyre with the highest salinity on the NH, in the North Atlantic: after high evaporation during NH summer more very saline and relatively warm water will go down, thickening the mixed layer.

I would say there is a relationship between cloud coverage and the thickness of the mixed layer.
comment image?w=688&ssl=1
comment image?w=693&ssl=1

Both graphics from:

Julian Flood
February 2, 2021 2:06 pm

 if the wind energy (and other sources of mixing) does not change, neither should the thickness of the mixed layer.”

If the ocean surface is polluted with oil, surfactant or phytoplankton lipids then the wind will engage less with the surface and the mixing will be less.


February 2, 2021 2:32 pm

Another fine post and thanks for the link to your previous posts up to 2018.
I can pick up the subsequent posts easily enough.
I have sent an email today to support@argo.net asking the single question, “what is the decadal increase in world ocean temperatures since the inception of the Argo Buoys (in~2004)?”
I know that you and Dr.Roy Spencer and Andy May have addressed this question and given your estimates but at argo.net the emphasis is on how many zettajoules of warming have occurred in the oceans,which is not enlightening to the lay person.
Andy May has wished me good luck in my quest but is not sanguine about my getting a meaningful response.
AR5 tells us that 93% of the world’s energy system warming has occurred in the oceans so it is reasonable to ask,‘how much’, as identified by the Argo buoys.

Rud Istvan
Reply to  Herbert
February 2, 2021 4:45 pm

H, just an observation. The reason for Zettajoules is that the Joule is a relatively small unit of energy, and the oceans are vast, high heat capacity, and cold. This hides the fact of minute changes in temperature sometimes beyond ARGO instrument capacity. See my guest post here some time ago on whether ARGO is mission capable. Yup, if you wait at least 10 years.

Reply to  Rud Istvan
February 2, 2021 6:11 pm

Thanks. I have just read your post “Argo-Fit for Purpose?”from two years ago.
It was most informative.

February 2, 2021 2:36 pm

Phd presentations related to my own or closely related fields of work have surprised me. I get the sense that either nobody asks them questions or they turn a deaf ear.

February 2, 2021 3:19 pm

On what basis are these Colorado gals and dudes claiming that “shoaling” (becoming shallower) of the thermocline means warming?

I guess that anything changing must mean warming and wereallgoingtodie, right? I mean – like – how can it, like, not?

Well, easily, in fact. It turns out that shoaling of the thermocline – in the long term at least – is associated with cold, not warm. (Shoaling means getting shallower.) This paper by Fabienne Regoli and colleagues from France and Belgium used fossil plankton and Ca/Mg ratios to work out the Pacific thermocline depth over the last 800,000 years, ie over the last 8 glacial cycles. They found shallower thermocline (lower boundary of the mixed layer) during glacial periods (that’s colder) and a deeper mixed layer during the warmer interglacials. And as glacial periods got colder, the thermocline got shallower, not deeper.


Our stratification record shows a systematic shallower glacial thermocline, whereas sea surface temperatures are characterised by precessional forcing. The record is indicative of a progressive long-term shoaling of the thermocline during the glacial stages during the late Pleistocene.

So here’s some advice for our Colorado kissing cousains. Want a warming story from shoaling of the thermocline? Then follow the example of Mike Mann and his Finnish friends and turn your charts upside down. Make the mixed layer get deeper, not shallower. That’s what warming should look like.

February 2, 2021 3:50 pm

A look at the maps suggest that the depth of the mixed layer is linked to storminess and not temperature. The deepest mixed layer is found in the stormiest parts of the North Atlantic, and the stormiest parts of the Southern Ocean, neither is exactly known for a hot climate.

Now this is not exactly unexpected, more and stronger storms obviously means deeper mixing and consequently a shallowing mixed layer suggests less stormy weather.

David A
Reply to  tty
February 2, 2021 5:27 pm

And we just had a report that it has gotten more stormy, a claimed increase in hurricanes.
( So who is right, I say neither)
Same old, same old, frogs getting bigger, frogs getting smaller, all CAGW climate porn

Joel O'Bryan
February 2, 2021 5:47 pm

The problem of course with Argo data is with both the short time period and the fact that the density of floats was still low prior to 2005. That second problem, low density coverage, is most certainly the cause of the wide excursions (variance) seen 2000-2004.

Additionally, at least in the equatorial Pacific, ENSO cycles of El Nino and La Nina have a major influence on the mixed layer depth, which has zilch to do with the climate scam.

February 2, 2021 5:51 pm

Willis, I’m so glad that you’re stuck at home with little to do but analyses such as this. I’m lying about the “stuck at home”, but not with the analyses (;

Keep it up. And I’m envious, you more northern CA folks got a nice rain. We in the south bay area, not much ):

February 3, 2021 12:50 am

Probably the result of all the energy from the air currents being extracted to generate electricity. Slower wind means less ocean mixing.

Or maybe not! But the energy to drive turbines has to come from the atmosphere. Now there is an unintended consequence. More turbines gives less mixing. I think that would reduce the energy content of the oceans.

February 3, 2021 5:49 am

I see what the authors did. Counting on the rest of the world to be too busy/lazy, they didn’t miss out on the opportunity to tell folks what to think.

Steve Z
February 3, 2021 7:49 am

All the graphs of mixing layer depth as a function of time seem to show annual cycles, which would indicate seasonal variation based on insolation.

It is not known from Willis’ article what procedure is used to obtain an “average” mixing depth, and how the Argo buoys are distributed over the world’s oceans–are they evenly distributed, or are there more Argo buoys per million km2 in certain areas of the ocean, and less in other areas?

One would expect that the mixing depth would vary seasonally at any given point (particularly in temperate regions), since the high sun angles during spring and summer would allow solar radiation to penetrate deeper into the ocean than the low sun angles (and shorter days) during autumn and winter.

Even if the Argo buoys are evenly distributed over the world’s oceans, the total ocean area in the Southern Hemisphere is much higher than in the Northern Hemisphere, so any global averages would be skewed toward the seasonality of the Southern Hemisphere.

Reply to  Steve Z
February 3, 2021 8:29 am

“One would expect that the mixing depth would vary seasonally at any given point (particularly in temperate regions)”

You mean like checking out the number of good looking bikinis at the beach between summer and winter? You don’t suppose there’d be a grant in it do you? Maybe I could work in the effect of climate change on gender spaces or some such-
Women’s toilets in Australia: the writing is on the wall (theconversation.com)

Dave Andrews
Reply to  Steve Z
February 4, 2021 7:04 am

I believe there are currently about 3900 Argo floats deployed but the number will vary as floats fail and sink and individual countries/agencies deploy their own numbers. The world map at the Argo site shows dots apparently covering the entirety of the world’s oceans but given how large the oceans actually are the buoys are in reality few and far between.

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