In the ensuing discussion on Does Back Radiation “Heat” the Ocean? – Part Four, the subject of the cool skin of the ocean surface came up a number of times.
It’s not a simple subject, but it’s an interesting one so I’m going to plough on with it anyway.
The ocean surface is typically something like 0.1°C – 0.6°C cooler than the temperature just below the surface. And this “skin”, or ultra-thin region, is less than a 1mm thick.
Here’s a diagram I posted in the comments of Does Back Radiation “Heat” the Ocean? – Part Three:
There is a lot of interest in this subject because of the question: “When we say ‘sea surface temperature’ what do we actually mean?“.
As many climate scientists note in their papers, the relevant sea surface temperature for heat transfer between ocean and atmosphere is the very surface, the skin temperature.
In figure 1 you can see that during the day the temperature increases up to the surface and then, in the skin layer, reduces again. Note that the vertical axis is a logarithmic scale.
Then at night the temperature below the skin layer is mostly all at the same temperature (isothermal). This is because the surface cools rapidly at night, and therefore becomes cooler than the water below, so sinks. This diurnal mixing can also be seen in some graphs I posted in the comments of Does Back Radiation “Heat” the Ocean? – Part Four.
Before we look at the causes, here are a series of detailed measurements from Near-surface ocean temperature by Ward (2006):
Note: The red text and arrow is mine, to draw attention to the lower skin temperature. The measurements on the right were taken just before midday “local solar time”. I.e., just before the sun was highest in the sky.
And in the measurements below I’ve made it a bit easier to pick out the skin temperature difference with blue text “Skin temp“. The blue value in each graph is what is identified as ΔTc in the schematic above. The time is shown as local solar time.
The measurements of the skin surface temperature were made by MAERI, a passive infrared radiometric interferometer. The accuracy of the derived SSTs from M-AERI is better than 0.05 K.
Below the skin, the high-resolution temperature measurements were measured by SkinDeEP, an autonomous vertical profiler. This includes the “sub-skin” measurement, from which the sea surface temperature was subtracted to calculate ΔTc (see figure 1).
The existence of the temperature gradient is explained by the way heat is transferred: within the bulk waters, heat transfer occurs due to turbulence, but as the surface is approached, viscous forces dominate and molecular processes prevail. Because heat transfer by molecular conduction is less efficient than by turbulence, a strong temperature gradient is established across the boundary layer.
Ward & Minnett (2001)
Away from the interface the temperature gradient is quickly destroyed by turbulent mixing. Thus the cool-skin temperature change is confined to a region of thickness, which is referred to as the molecular sublayer.
Fairall et al (1996)
What do they mean?
Here’s an insight into what happens at fluid boundaries from an online textbook (thanks to Dan Hughes for letting me know about it) – this textbook is freely available online:
The idea behind turbulent mixing in fluids is that larger eddies “spawn” smaller eddies, which in turn spawn yet smaller eddies until you are up against an interface for that fluid (or until energy is dissipated by other effects).
In the atmosphere, for example, large scale turbulence moves energy across many 100′s of kilometers. A few tens of meters above the ground you might measure eddies of a few hundreds of meters in size, and in the last meter above the ground, eddies might be measured in cms or meters, if they exist at all. And by the time we measure the fluid flow 1mm from the ground there is almost no turbulence.
For some basic background over related terms, check out Heat Transfer Basics – Convection – Part One, with some examples of fluid flowing over flat plates, boundary layers, laminar flow and turbulent flow.
Therefore, very close to a boundary the turbulent effects effectively disappear, and heat transfer is carried out via conduction. Generally conduction is less effective than turbulence movement of fluids at heat transfer.
A Note on Very Basic Theory
The less effectively heat can move through a body, the higher the temperature differential needed to “drive” that heat through.
This is described by the equation for conductive heat transfer, which in (relatively) plain English says:
The heat flow in W/m² is proportional to the temperature difference across the body and the “conductivity” of the body, and is inversely proportional to the distance across the body
Now during the day a significant amount of heat moves up through the ocean to the surface. This is the solar radiation absorbed below the surface. Near the surface where turbulent mixing reduces in effectiveness we should expect to see a larger temperature gradient.
Taking the example of 1m down, if for some reason heat was not able to move effectively from 1m to the surface, then the absorbed solar radiation would keep heating the 1m depth and its temperature would keep rising. Eventually this temperature gradient would cause greater heat flow.
An example of a flawed model where heat was not able to move effectively was given in Does Back-Radiation “Heat” the Ocean? – Part Two:
Note how the 1m & 3m depth keep increasing in temperature. See that article for more explanation.
The Skin Layer in Detail
If the temperature increases closer to the surface, why does it “change direction” in the last millimeter?
In brief, the temperature generally rises in the last few meters as you get closer to the surface because hotter fluids rise. They rise because they are less dense.
So why doesn’t that continue to the very last micron?
The surface is where (almost) all of absorbed ocean energy is transferred to the atmosphere.
- Radiation from the surface takes place from the top few microns.
- Latent heat – evaporation of water into water vapor – is taken from the very top layer of the ocean.
- Sensible heat is moved by conduction from the very surface into the atmosphere
And in general the ocean is moving heat into the atmosphere, rather than the reverse. The atmosphere is usually a few degrees cooler than the ocean surface.
Because turbulent motion is reduced the closer we get to the boundary with the atmosphere, this means that conduction is needed to transfer heat. This needs a temperature differential.
I could write it another way – because “needing a temperature differential” isn’t the same as “getting a temperature differential”.
If the heat flow up from below cannot get through to the surface, the energy will keep “piling up” and, therefore, keep increasing the temperature. Eventually the temperature will be high enough to “drive the heat” out to the surface.
The Simple 1-d Model
We saw a simple 1-d model in Does Back Radiation “Heat” the Ocean? – Part Four.
Just for the purposes of checking the theory relating to skin layers here is what I did to improve on it:
1. Increased the granularity of the model – with depths for each layer of: 100μm, 300μm, 1mm, 5mm, 20mm, 50mm, 200mm, 1m, 10m, 100m (note values are the lower edge of each layer).
2. Reduced the “turbulent conductivity” values as the surface was reached – instead of one “turbulent conductivity” value (used when the layer below was warmer than the layer above), these values were reduced closer to the surface, e.g. for the 100μm layer, kt=10; for the 300μm layer, kt=10; for the 1mm layer, kt=100; for the 5mm layer, kt=1000; for the 20mm layer, kt=100,000. Then the rest were 200,000 = 2×105 – the standard value used in the earlier models.
3. Reduced the time step to 5ms. This is necessary to make the model work and of course does reduce the length of run significantly.
The results for a 30 day run showed the beginnings of a cooler skin. And the starting temperatures for the top layer down to the 20mm layer were the same. The values of kt were not “tuned” to make the model work, I just threw some values in to see what happened.
As a side note for those following the discussion from Part Four, the ocean temperature also increased for DLR increases with these changes.
Now I can run it for longer but the real issue is that the model is not anywhere near complex enough.
Further Reading on Complexity
There are some papers for people who want to follow this subject further. This is not a “literature review”, just some papers I found on the journey. The subject is not simple.
Saunders, Peter M. (1967), The Temperature at the Ocean-Air Interface, J. Atmos. Sci.
Tu and Tsuang (2005), Cool-skin simulation by a one-column ocean model, Geophys. Res. Letters
McAlister, E. D., and W. McLeish (1969), Heat Transfer in the Top Millimeter of the Ocean, J. Geophys. Res.
Fairall et al, reference below
GA Wick, WJ Emery, LH Kantha & P Schlussel (1996), The behavior of the bulk-skin sea surface temperature difference under varying wind speed and heat flux, Journal of Physical Oceanography
Hartmut Grassl, (1976), The dependence of the measured cool skin of the ocean on wind stress and total heat flux, Boundary Layer Meteorology
The temperature profile of the top mm of the ocean is a challenging subject. Tu & Tsuang say:
Generally speaking, the structure of the viscous layer is known to be related to the molecular viscosity, surface winds, and air-sea flux exchanges. Both Saunders’ formulation [Saunders, 1967; Grassl, 1976; Fairall et al.,1996] and the renewal theory [Liu et al., 1979; Wick et al.,1996; Castro et al., 2003; Horrocks et al., 2003] have been developed and applied to study the cool-skin effect.
But the exact factors and processes determining the structure is still not well known.
However, despite the complexity, an understanding of the basics helps to give some insight into why the temperature profile is like it is.
I welcome commenters who can make the subject easier to understand. And also commenters who can explain the more complex elements of this subject.
A Heat Transfer Textbook, by Prof Lienhard & Prof Lienhard, Phlogiston Press, 3rd edition (2008)
Cool-skin and warm-layer effects on sea surface temperature, Fairall, Bradley, Godfrey, Wick, Edson & Young, Journal of Geophysical Research (1996)
Near-surface ocean temperature, Ward, Journal of Geophysical Research (2006)
An Autonomous Profiler for Near Surface Temperature Measurements, Ward & Minnett, Accepted for the Proceedings Gas Transfer at Water Surfaces 4th International Symposium (2000)