Slowing Down

Warning!  This pushes the limits of every thermodynamic term and principle ever published.  I tend to leap ahead and skip steps I consider obvious.  That is not good for explaining things, but great for solving puzzles.  So let's take a step back and slow down.

If you have two objects in an insulated box that are in thermodynamic equilibrium with each other, they will be in thermodynamic equilibrium with the ambient conditions outside of the box.  If 50% of the objects are at one temperature or energy level higher than the rest, they determine the steady state condition of the thermodynamic equilibrium.  So if the energy flux from the warmer half  to the cooler half is 100Watts, the energy flow from the total of the interior to ambient will be 100Watts.  You can vary the percentages anyway you like, the warmer will still determine the steady state condition if the system is in equilibrium.  If you add insulation to the box, the energy flow from warmer to colder will increase proportionally to the decrease in energy flow to ambient until equilibrium between the interior objects is restored.

Why is that statement correct?  If the two objects are in thermodynamic equilibrium, removing the insulation would not change their equilibrium for a finite period of time.  If there was 100Wm-2 flowing from one to the other, there would still be 100Wm-2 flowing once the insulation is removed.  Removing the insulation would cause both objects to emit more energy elsewhere, but they would remain in equilibrium with each other.  The steady state flow rate would gradually decrease if they had large thermal mass, more quickly if they had small thermal mass, but the equilibrium would remain.  This is conditional equilibrium or equilibrium dependent on balanced steady state conditions.

The chart above is the sensitivity of that box to an addition of 3.7Wm-2 of additional insulation equivalent.  The higher the highest temperature, the lower the impact.

Slowing Down Part II

Why is the Sensitivity 0.8 Degrees

UPDATE:  Fishing accomplished



I started this blog because I was posting climate stuff on my energy blog.  The reason for the climate stuff was that alternate energy was becoming less of a hot topic.  A shame, because there is some very interesting alternate energy options out there.  When I started looking at the climate science, I noticed some things that just did not fit.  Global warming is just one big ass thermodynamics problem.  Thermodynamics involves a lot more than just infrared radiation.

The first thing I noticed is that the term down welling long wave radiation is used.  DWLR is nothing more than the temperature of the sky which can be used as an indication of the resistance to outgoing infrared radiation.  Pretty much anyone that has ever insulated something knows that radiant heat loss is an issue, but conductive heat loss also has to be considered.  If you insulate a wall with a dry, still air space it will lose less heat.  Most don't know that if you add a radiant barrier, it will lose 1/3 less heat.  A complete radiant barrier increases the resistance to energy flow by 50% meaning it is responsible for 1/3 of the energy savings.  2/3rds of the heat loss would still be due to conductive initiated energy flow.  Radiant barriers do not stop conduction so there is not perfect insulation or combination of insulation types.  There will always be heat loss, you can only reduce the amount.

Since heat loss is a given, you can figure out about how efficient your insulation may be, by seeing how much adding some more would change things.  To do that, you need to know where you are first.  The Earth has an average of 240Wm-2 of heat loss.  The average surface temperature is around 15 degree centigrade, so the interior heat is around 390Wm-2 on average.  The difference between what is retain and what is lost is 240Wm-2 minus150Wm-2 equaling 90Wm-2.  Since space is at near zero degrees absolute, that difference seemed a little higher than it should be.  About the most heat that out atmosphere should be able to retain should be half of the 150Wm-2 or 75Wm-2.

The reason it is higher is because the upper atmosphere also can gain and lose heat.  Since we have more heat retained, there must be a lower surface energy sink.  The coldest region inside the atmosphere is the tropopause.  It has a temperature that varies, but since the Earth is retaining more energy than it should, the tropopause should have a temperature that radiates 75Wm-2 which is about -82.5 degrees C.

While there are dozens of ways to estimate what flows should balance what temperatures in equilibrium, the Earth is not a simple box, it is a complex dynamic system.   Still there are some ways to simplify.

With the thought experiment there are 10 objects inside the insulation.  Seven are radiating 425Wm-2.  They represent the oceans with an average temperature of 294 K degrees.  Three are radiating at 308Wm-2 representing the land areas at 271.5 K degrees.  These are close to the average temperatures currently.  Note that 271.5K is just a little below freezing, roughly at the freezing point of salt water.  The latent heat of fusion of the masses of sea ice buffer the lower temperature.  While the system is dynamical complex, the freezing point of water, adjusted for the salt content, stabilizes the lower temperature range.  Since there is a large seasonal change in solar radiation, the sea ice rebuilds each winter.

The difference in the energy of the water and land mass on average produces an average flux from warmer to colder.  Since these two surface are enclosed in a common insulating blanket, the energy flow out from the combined masses is equal to the flow from the warmer oceans to the cooler land, which is 117Wm-2.  Since the total energy of the interior is 390Wm-2 with 117Wm-2 instead of 240Wm-2 at the top of the atmosphere, the difference would the radiant energy of the sink for the heat from the interior.  240-117=123Wm-2 This energy level is equivalent to the average tropopause temperature of -57.2 C which has an energy of 123Wm-2.

The sensitivity to an additional restriction to energy loss of 3.7Wm-2, the approximate forcing associated with a doubling of CO2 would vary base on the local energy.  By taking the ratio of the forcing 3.7Wm-2 and the surface energy flux at any reasonable temperature, this chart provides estimates of the sensitivity.

The curve intersects 288K, the average surface temperature around 1.0, 294K the average ocean temperature around 0.9 and decreases as temperature rises to approximately 0.8 at 305K or 32 C degrees, the high average temperature of the tropical oceans.  That sensitivity, 0.8C would be the approximate no feedback climate sensitivity to 3.7Wm-2 forcing by any cause.  The higher the ocean temperature in the tropics increases, the lower that sensitivity will become.

Proving why will require more work, but a simple model can produce interesting results.

Forgive any typos, but fishing comes before proofing.

BACK FROM CATCHING:  So if you have read this far you see some numbers but nothing that blows any wind up your skirt.  It really should.  The 271.5K average temperature of the land mass portion happens to be the freezing point of salt water within a small margin of error.  As salt water freezes, it has to release more heat, the latent heat of fusion, providing a feedback to the atmosphere.  With the enormous volume of water on Earth, this provides a long term feedback, on the order of  thousands of years.  When the Salt water freezes it forms fresh ice.  The melting point of fresh ice is 273.15 K degrees or about 1.65 C warmer which would limit the radiant heat gain set point by 7.56Wm-2.  So during an inter glacial period, there would be less fresh ice, the controlling temperature would be closer to 271.5K and during a glacial period, the controlling temperature would be closer to 273.15K.  That greatly limits the variation in "Average" Earth temperature.  Since the overall feedback is negative, as in sensitivity increases with decreasing temperature, this tends to erase the "faint sun" paradox and plays hell with the Green House Gas theory.

It also would pose some problems with ice core proxy reconstructions.  In the Antarctic where temperatures never exceed 273.15K degrees, the results would be totally different than in the Arctic where some eras the ice would never thaw and other eras where the surface layer of the ice could thaw.  Depending on the amount of thaw, the gases trapped in the ancient ice would not represent the conditions when the ice was deposited, but the conditions where the surface ice layer thawed.

Now you can have a long laugh at this outlandish claim, but I am afraid there are a few errors in Climate Science that are significant.

Back to Basics - Thought Experiment

Here is the problem, you have an insulated box emitting  240Wm-2 through the outer insulation layer.  You peak inside the insulation and see that there are actually ten objects under the insulation, 7 or 70% of the objects are emitting 425Wm-2 and 3 or 30% are emitting 308Wm-2 for a total emission felt at the inside of the insulation of 390Wm-2.  Insulation is added so that 3.7Wm-2 of added resistance to flow is uniformity distributed around the box.  How much additional energy is stored in each  of the ten objects in the interior?

Since the objects in question are not at the same energy state and enclosed in the same insulation blanket there is a variety of ways at looking at the problem.  You could ignore the individual objects and just look at the total energy.  390Wm-2 inside, 240Wm-2 outside leaves 150Wm-2 of resistance to energy flow.  Increasing the resistance by 3.7Wm-2 would increase the resistance by 3.7/150=0.025 so 1.025*390=399.75Wm-2 would be the impulse increase in the energy of the object.  The problem doesn't state that there is constant energy in the insulated part or that the energy through the insulation has to remain constant.  If you just magically increased the resistance to energy flow, there would be some thermal inertia which would increase the energy in the insulation to 399.75Wm-2 for some brief moment in time if the thermal mass were small.  The energy could overshoot this value and then drop or slowly sneak up on it, but there would be an increase toward 399.75Wm-2.

Another way to look at the problem is that some objects in the box are warmer.  There would be energy flowing from those objects to the cooler objects.  Since there is energy flowing through the insulation, the warmer objects are losing more energy to the environment.  With the warmer at 425Wm-2 and the colder at 308Wm-2, there would be 117Wm-2 net energy flowing from the warmer to the colder.  The net flow from the warmer to ambient would be 308Wm-2 matching the flow of the cooler object to ambient.  With 308Wm-2 average energy trying to escape and only 240Wm-2 escaping the restriction to flow would be 308-240 or 68Wm-2.  Adding 3.7 to 68 would increase the resistance to flow by 3.7/68=0.054 resulting in 1.054 *(.7*425+.3*308)=1.054*390=411Wm-2 as the value that would be approached.

Which one makes the most sense?

Think about if the colder objects are surrounded by the warmer objects.  The objects all radiate the same energy in all directions.  So now the warmer objects would emit a net flux of 117Wm-2 inward, 425Wm-2 outward which would be restricted by the insulation allowing only 240Wm-2 to escape.  425-240=185Wm-2,  Adding 3.7Wm-2 of resistance would decrease the rate of flow by 3.7/185=0.02 leaving 1.02*425=433.5Wm-2.

At 433.5Wm-2 the temperature via S-B would be 295.7 C degrees.  The initial temperature of the 425Wm-2 objects was 294.25 C degrees, the increase in temperature would be 1.45 C degrees.

Now let's change the state of the objects.  Let's make the warmer objects 300K degrees which would radiate 459Wm-2.  459-240=219, 3.7/219=0.0168 resulting in 1.0169*459=466.8 Wm-2 which would be a S-B temperature of 301.2 K degrees.  The warmer the warmest object, the less impact increasing the insulation has.


UPDATE:  Since a few people are scratching their heads.  Here is something else about this simple problem.

By specifying that the objects inside the insulation are in conditional equilibrium, the energy flow from the warmer to colder objects, 117Wm-2 takes on a whole new meaning.  If they are in equilibrium with that flow rate, then the inside of the box is in equilibrium with the outside.  That would mean that the ambient heat sink would be 117Wm-2.  But wait you say, the flux to ambient is 240Wm-2!  Nope, it would be 117Wm-2 which would mean that there is 240-117=123Wm-2 difference.  That would be the true effective sink or ambient flux which is a temperature of 57.2 degrees C or 215.8K degrees, the temperature of the tropopause.  Some of you may find that interesting.

Now if you were into abstract logic, you would realize that 123Wm-2 is an odd number in more ways than one.  Let's see if you can figure out why?  If you go back through the calculations above, you may find a hidden surprise.