In Part One we looked at how solar radiation and DLR (or “back radiation”) were absorbed by the ocean. And we had a brief look at how little heat would move by conduction into the deeper ocean if the ocean was “still”.
There were some excellent comments in part one from Nick Stokes, Arthur Smith and Willis Eschenbach – probably others as well – take a look if you didn’t see them first time around.
We will shortly look at mixing and convection, but first we will consider some absolute basics.
The First Law of Thermodynamics
How does the ocean sustain its (high) temperature? Every second, every square meter of the ocean is radiating energy. The Stefan-Boltzmann relationship tells us the value:
j = εσT4, where ε is the emissivity of the ocean (0.99), σ = 5.67 x 10-8 and T is the temperature in K
- if T = 20°C (293K), j = 415 W/m²
- if T = 10°C (283K), j = 361 W/m²
Now, many people are confused about how temperatures change with heat imbalances. If, for some reason, more heat is absorbed by a system than is radiated/conducted/convected away – what happens?
More heat absorbed than lost = heat gained. Heat gained leads to an increase of temperature (see note 1). When the temperature of a body increases, it radiates, conducts and convects more heat away (see note 2). Eventually a new equilibrium is reached at a higher temperature. It is important to grasp this concept. Read it again if it isn’t quite clear. Ask a question for clarification..
Questions are welcome.
A Simple Model
It’s easy to find the basic equilibrium point using the first law of thermodynamics. All you need to know is the energy in, and the equation which links energy radiated with temperature.
For radiation, this is the Stefan-Boltzmann law cited earlier. The starting temperature for the ocean surface in this example was set to 300K (27°C). Depending on whether solar and back-radiation or just solar is heating the surface, here is the surface temperature change:
Notice the difference in the temperature trends for the two cases.
Now the model doesn’t yet include convective heat transfer from the ocean to the atmosphere (or movement of heat from the tropics to the poles), which is why in the first graph the temperature gets so high. Convection will reduce this temperature to a more “real world” value.
The second graph has only solar radiation heating the ocean. Notice that the temperature drops to a very low value (-15°C) in just a few years. Clearly the climate would be very different if this was the case, and the people who advocate this model need to explain exactly how the ocean temperature manages to stay so much higher.
By the way, if we made the “well-mixed layer”, dmixed, of the ocean deeper it would increase the time for the temperature to change by any given amount. That’s because more ocean has more heat capacity. But it doesn’t change the fact of the energy imbalance, or the final equilibrium temperature.
The model is a very simplistic one. That’s all you need to demonstrate that DLR, or “back radiation” must be absorbed by the ocean and contributing to the ocean heat content.
Turbulence and the Mixed Layer
Let’s take a look at a slightly more complex model to demonstrate an important point. This simulation has four main elements:
- radiation absorbed in the ocean at various depths, according to the results in Part One
- conduction between layers in the ocean
- convective heating from the ocean surface to the atmosphere, according to a simple model with a fixed air temperature
This model is not going to revolutionize climate models as it has many simplifications. The important factor – there is no convection between different ocean layers in this model.
Now conductivity in still water is very low (as explained in Part One).
The starting condition – the “boundary condition” – was for the temperature to start at 300K (27°C) for the first 100m, with the ocean depths below to be a constant 1°C.
The model is for illumination. Let’s see what happens:
The wide bars of blue and green are because the day/night variation is significant but squashed horizontally. If we expand one part of the graph to look at the first few days:
You can see that the day/night variation of the top 1mm and 10cm are significant.
Look back at the first graph which covers four years. Notice the purple line, 10m depth, the blue line, 3m depth; and the red line, 1m depth.
Why is the ocean 1-10m depth increasing to such a high temperature?
The reason is simple. This model is flawed– these results don’t occur in practice. (And yes, the ocean would boil from within..)
The equations that make up this model have used:
- the radiation absorbed from the sun and the atmosphere (as described in part one)
- the radiation emitted from the surface layer (the Stefan-Boltzmann equation)
- conductivity transferring heat between layers
If these were the only mechanisms for transferring heat, the ocean 1m – 10m deep would be extremely hot in the tropics. This is because the ocean where the radiation is absorbed cannot radiate back out.
For a mental picture think of a large thick slab of PVC which is heated from electrical elements within the PVC. Because it is such a poor conductor of heat, the inner temperature will rise much higher than the surface temperature, so long as the heating continues..
The reason this doesn’t happen in practice in the ocean is due to convection.
If you heat a gas or liquid from below it heats up and expands. Because it is now less dense than the layer above it will rise. This is what happens in the atmosphere, and it also happens in the ocean. The ocean under the very surface layer heats up, expands and rises – overturning the top layer of the ocean. This is natural convection.
The other effect that takes place is forced convection as the wind speed “stirs” the top few meters of the ocean. Convection is the transfer of heat by bulk motion of a fluid. Essentially, the gas or liquid moves, taking heat with it.
Price & Weller (1986) commented:
Under summer heating conditions with vanishing wind, the trapping depth of the thermal response is only about 1m (mean depth value), and the surface amplitude is as large as 2ºC or 3ºC. But, more commonly, when light or moderate winds are present, solar heating is wind mixed vertically to a considerably greater depth than is reached directly by radiation: the trapping depth is typically 10m, and the surface amplitude is reduced in inverse proportion to typically 0.2ºC. Given that the surface heating and wind stress are known, then the key to understanding and forecasting the diurnal cycle of the ocean is to learn how the trapping depth is set by the competing effects of a stabilizing surface heat flux and a destabilizing surface stress.
Here are the results from a model with another slight improvement. This includes natural convection. The mechanism is very rudimentary at this stage. It simply analyzes the temperature profile at each time step and if the temperature is inverted from normal buoyancy a much higher value of thermal conductivity is used to simulate convection.
The “bumpiness” you see in the temperature profile is because the model has multiple “slabs”, each with an average temperature. This could be reduced by a finer vertical grid.
During the early afternoon with peak solar radiation, the ocean becomes stratified. Why?
Because lots of heat is being absorbed in the first few meters with some then transported upwards to the surface via convection – but while the solar radiation value is high this heat keeps “pouring in” lower down. However, once the sun sets the surface will cool via radiation to the atmosphere and so become less buoyant. With no solar radiation now being absorbed lower down, the top few meters completely mix – from natural convection.
I did have a paper with a perfect set of measurements to illustrate these points. It showed day/night and seasonal variation. Sadly I put it down somewhere. Many hours of hunting for the physical paper and for the file on my PC but it is still lost..
Note that the large variation of surface temperature (4-5°C) is just a result of the convective mixing element in the model being too simplistic and moving heat much faster than happens in reality.
Kondo and Sasano (1979) said:
In the upper part of the ocean, a mixed layer with homogeneous density (or nearly homogeneous temperature) distribution is formed during the night due to free convection associated with heat loss from the sea surface and to forced convection by wind mixing.
During the daytime, the absorption of solar radiation which occurs mostly near the sea surface causes the temperature to rise, and a stable layer is formed there; as a consequence, turbulent transport is reduced.
Daily mean depth of the mixed layer increases with the wind speed. When the wind speed is lower than about 7-8 m/s, the mixed layer disappears about noon but it develops again in the later afternoon. A mixed layer can be sustained all day under high wind speeds..
The subject of convection and oceans is a fascinating one and I hope to cover much more. However, convection is a complex subject, the most complex mechanism of heat transfer “by a mile”.
There are also some complexities with the skin layer of the ocean which are worth taking a closer look at in a future article.
This article uses some very simple models to demonstrate that energy radiated from the atmosphere is being absorbed in the ocean surface and affecting its temperature. If it wasn’t the ocean surface would freeze. Therefore, if atmospheric radiation increases (for example, from an increase in “greenhouse” gases), then, all other things being equal, this will increase the ocean temperature.
The models also demonstrate that conduction of heat on its own cannot explain the temperature profiles we see in the ocean. Natural convection and wind speed both create convection, which is a much more effective heat transport mechanism in gases and liquids than conduction.
Diurnal Cycling: Observations and Models of the Upper Ocean Response to Diurnal Heating, Cooling and Wind Mixing, James Price & Robert Weller, Journal of Geophysical Research (1986)
On Wind Driven Current and Temperature Profiles with Diurnal Period in the Oceanic Planetary Boundary Layer, Kondo and Sasano, Journal of Physical Oceanography (1979)
Note 1 – For the purists, heat retained can go into chemical energy, it can go into mechanisms like melting ice, or evaporating water which don’t immediately increase temperature.
Note 2 – For the purists, the actual heat transfer mechanism depends on the physical circumstances. For example, in a vacuum, only radiation can transfer heat.