Arctic Ocean sensible heat loss

This post is quite long but stay with it. It shows how large some of the heat exchanges going on in the polar oceans can be.

The picture above shows an iceberg through mist rising from the sea.

It is pretty, but it is also showing is a vast heat flux of hundreds of watts per m2 from the ocean to the atmosphere...


I have talked before on this blog about how the sea ice moves, and how the International Arctic Buoy Programme provide some lovely movies of the buoy tracks which show this.  I also pointed to Eric Larsen's video of the ice moving too.

But what does this ice movement mean for the climate?

As the ice moves it fractures, and the cracks extend over wide areas. These cracks are responsible for the "water sky" I talked about previously.

A recent MODIS satellite image from the Aqua satellite  posted at the NASA earth Observatory shows one of these cracks (we call them leads) opening up.

A lead in the Arctic Ocean
A modis image showing a lead and sea smoke in the Arctic Ocean May 2013. From the NASA EO

From the scale bar on the bottom left you can see that the open water is ~18 km wide, and the lead is more than 100 km long. More than enough to get a ship through!

What is most interesting from my point of view is the "sea smoke"1. You can see above the open water in the picture it is labelled Fog.  The NASA www page describes the image and has this to say about the fog:


"Fog, caused by the difference in temperature between the water and atmosphere, is also visible along parts of the lead. “Condensation occurs when water from the relatively warm ocean transfers to the cooler atmosphere and condenses into water droplets,” explained Walt Meier, a scientist at the National Snow and Ice Data Center. “It’s the same process that gives us steam when you boil water, but the temperatures in the Arctic are quite different than those in your kitchen. The ocean water here may be on the order of 0 degrees Celsius, while the atmosphere may be -20 degrees Celsius.” "

So the fog is condensation caused through heat loss from the relatively warm ocean, to the cold air above.

And heat transport above the open water that leads to the condensation?

Let's work it out.

We always talk about how the ocean is moving heat around the planet. What amount of heat is the ocean losing to the atmosphere through the crack in the ice?

The full heat budget (that is what the ocean is gaining and losing from all the sources you can think of)  is pretty complex, so I will just look at one component, the so called sensible heat flux. This is when heat energy is transferred from the Earth’s surface to the atmosphere by conduction and convection, so here it is the flux of heat from the sea surface to the atmosphere.

The so called bulk formula to work it out is straightforward, and there is a good description in Marshall and Plumb (2008) (they have an excellent companion www site as well). Equation 11.6 from their text is:

{{Q}_{sens}}={{\rho }_{air}}{{c}_{p}}{{c}_{s}}{{U}_{10}}\left( SST-{{T}_{air}} \right)


{{Q}_{sens}} is the sensible heat flux from the ocean to the atmosphere,

{{\rho }_{air}} is the density of the air at the surface,

{{c}_{p}} is the specific heat of the air,

{{c}_{s}} is a stability dependent bulk transfer coefficient,

{{U}_{10}} is the wind at 10 m height,

SST is the ocean temperature and {{T}_{air}} the temperature of the air at 10 m height.

Where do we get the data to use in this equation?

For a couple of them I will use "standard values". For {{c}_{p}} I am going to use 1004.83 j kg-1 k-1. This means that it takes 1004.83 joules of energy to raise 1 kg of air above the lead, by 1 degree Kelvin. For {{c}_{s}} I am going to use a typical value of 0.00175 from McPhee (2008).

For the SST - the sea surface temperature I am going to use a constant value of -1.9°C which is a typical seawater freezing point at the surface. (It actually depends on the salinity - the more salt the lower the freezing point, but this will do for here).

For the temperature of the air?

For this I am going to temperature data from the Arctic Ocean from Figure 8.8a of Serreze and Barry (2009). The data that made the picture below are actually from the Russian North Pole program.


Arctic Ocean Atmospheric temperature cycle
Annual temperature cycle at the North Pole after Serreze and Barry (2009)

I also use a simple empirical formula to calculate the density of the air using temperature.

The only thing I do not have now to calculate the sensible heat flux from the ocean to the ice is the wind speed. If we look at the recent North Pole Environmental Observatory you can see that wind speeds of 5 ms-1 are not unusual, and storms with much stronger wind speeds are common.

So below is the heat lost by the ocean for four wind speeds: 0.5 ms-1 (black dashed), 2.0 ms-1 (back solid) 3.0 ms-1 (blue) and 5.0 ms-1 (red).

Sensible heat flux
The annual cycle of sensible heat flux from the ocean to the atmosphere for 4 different wind speeds.

So what have we got here?

Heat losses from the ocean to the ice in winter of 2-400 Wm-2 are the norm.

What does that mean physically? Think about it in terms of the output of a very bright 100 Watt light bulb, then that part of the ocean is losing the energy of  2-4 bright bulbs every m2.

But in the satellite picture at the top of this post which is just a small segment of the Arctic, there is more than 2000 km2 of open water.....


How about a "back of the envelope" calculation...


The wind speed I used was almost certainly low, but assume a 300 Wm-2 heat loss when the satellite image above was taken.

Then the heat loss over the 2x109 m2 of open water in that image is a massive 600 GW - yes that is Giga Watts - 600 x 109 Watts.

If you want to be really inappropriate then in 2 hours, that part of the ocean lost more energy than it takes to run the London Underground for one year2.

Remember that is just one component and not the full heat budget - which is partially why it is inappropriate. For the full budget we have to include latent heat flux, long wave radiation, short wave radiation, energy changes through state changes when ice grows and decays, and so on. Also large heat fluxes lead to rapid sea ice growth which then insulates the ocean from further heat loss.

Given that the lead in the picture above is only a fraction of the length of the lead in the full image, I hope it gives you impression of how large the heat budget components can be in polar climates3.

Sea smoke rising from the Southern Ocean
Sea smoke rising from the Southern Ocean



1. The sea smoke Wikipedia is going on my list of things to tidy up - it is not as good as it should be

2. The annual power usage of the London Underground is 1,163 Gigawatt hours.

3. With data from experiment in 1992 called LEADEX, a team of scientists calculated heat losses from similar Arctic open water to the picture above as being 250 Wm-2, so you can see the simple bulk formula is fairly good.


Marshall, John, and R. Alan Plumb. Atmosphere, ocean, and climate dynamics: an introductory text. Vol. 93. Academic Press, 2008. (This is a really excellent and straightforward textbook).

McPhee, Miles G. Air-ice-ocean interaction: turbulent ocean boundary layer exchange processes. Springer New York, 2008. (This is another excellent work - but many will find the mathematical treatment tough going).

Serreze, Mark C., and Roger Graham Barry. The Arctic climate system. Vol. 22. Cambridge University Press, 2009. (A standard work).