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Monday, January 14, 2013

Tale of Two Greenhouse part deux

The oceans really should be the key for determining the impact of change in any condition that would impact long term climate.  Shorter term climate, is little more than weather, it just what is considered "short term".

A good analogy for the oceans would be a battery.  If the oceans were perfectly well mixed, based on the current best estimates, the temperature would be 4 C degrees.  If the oceans completely covered the planet, then the average surface temperature of Earth would be 4 C degrees, for some time period.  How long doesn't matter for this example.

With a hypothetical atmosphere free planet, the effective radiant layer of the Earth would emit 334 Wm-2.  Since that surface on average receives ~340 Wm-2, the emissivity of the surface if both number were correct would be 334/340 = 0.98235 a unit less value for this example.  The Earth would be effectively a perfect black body.  The Earth though is not 100% cover with water and that water is not perfectly mixed, but let's continue with this example.

Since only 70% of the surface is covered with water that we are assuming is well mixed, that portion would emit at 334 Wm-2 but the total emitted, provided the remaining 30% land area does not emit, would be 70% of 334 or ~234 Wm-2.

I have previously posted that the Faint Young Sun Paradox is not, if you consider that the oceans can absorb more energy that they can emit until the total open water area increases enough to allow equilibrium.  This is due to the truism, that a radiant surface cannot emit energy any faster than energy can be transferred to the radiant surface.

Update: Since I tried to be too brief and mis-typed.  
More on the Static model

Sunlight penetrates the ocean surface and is absorb at depths of over 100 meters in small amounts. Surface water that cools becomes more dense and sinks.  The combination of solar warmed deeper water rising with cooling surface water sinking produces one or more uniform isothermal layers know as a thermoclines.  These isothermal layers limit heat gain from the surface and heat loss from below, creating an insulating layer where only the deeper penetrating solar short wave energy can warm the depths.  Until the rate of heat loss at the surface equals the rate of heat gain from solar at depth are equal, the oceans continue to gain energy.    Since time is not a factor for Earth, all it takes is a slight imbalance over enough time to produce the Earth as we know it today.

Had "Climate Science" started with this basic line of reasoning, life would have been simpler.

Since the Earth does have an atmosphere and does not have a nearly perfect black body surface that covers the entire "surface" it is easy to wander behind the little animals wondering how the Earth can be as warm as it is with as little energy that it appears to receive. This is aided by not thinking of the battery analogy.  While the entire "surface" may not be receiving as much energy, once a battery is charged, it does not require as much energy to maintain that charge.  Since the oceans can receive more than 1000 Wm-2 near the equator on a cloudless noontime,  the temperature of the equatorial oceans is limited by the rate that the ocean battery can accept a charge.  The deeper penetrating short wave energy from the sun, trickle charges the depths, but is insulated from surface heat diffusion by the direction of convection.

With an "average" sea surface temperature of approximately 21.1 C which would have a radiant energy of ~425 Wm-2 between the more stable 4 C "average" temperature of the deeper oceans, the "equilibrium" flux from the surface to the "average" would be 425-334=91 Wm-2 +/- a touch.  There are a lot of quote marks in that sentence.  The use of "equilibrium" is in the eye of the beholder.  I use a "static" model to determine stable conditions, so this would be my use of equilibrium.  Since the energy is flowing, you could call it a steady state or you could limit the "model" and call it a "conditional equilibrium" or "conditional steady state".  Whatever floats yer boat.  The "average" is in quotes is because it is an approximation.

Some of you will now complain that there is not enough math to justify my choices so far.  Well, 95% of solution is in setting up the problem.  If there are those hell bent on some kick butt math, why don't they take another look at that 91 Wm-2, "equilibrium" flux.  That just happens to be approximately the latent heat flux from the "surface".  The loss of that latent heat would create a new "surface" which when "averaged" across the total true surface produce the ~234 Wm-2 "surface" viewed from space in the infrared.  Earth is not a perfect black body, but 70% of it is close.

From this point things begin to be complicated.  Now the atmosphere with its water, ice, water vapor, ozone, CO2 and O2, absorb solar energy. There is a temperature inversion starting at the tropopause much like the temperature inversion below the Earth's surface.  With the static model, any change above the ocean surface has to be matched, eventually, below the ocean surface.  With either change, the energy flow from the equator to the poles would also have to change, to regain the "static equilibrium".  It may be a simple model, but it does have rules.  The oceans are more dependent on the "peak" energy available and the atmosphere, which does not hold a charge well, the "average" energy.

There should be a part three before long.  This ends here since it is part of an explanation for a denizen on another blog.

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