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Tuesday, October 14, 2014

Why Pi?

When I mention that the subsurface temperature tends to the energy equivalent of TSI/Pi(), eyes roll.  I use it as a convenient approximation.  If I were to get into more detail, I would use the integrated incident irradiation  which would consider the azimuth of the sun by latitude and time of day with a day isolation factor that included seasonal variations.  Since I am more concerned with the ocean subsurface energy, I would also have to consider land mass and sea ice.

I find it easy to just assume that liquid ocean is most likely between 65S and 65N, then Io*Cos(theta) from -65 to 65 would be about 450 Wm-2 average while TSI/Pi() would be about 430 Wm-2 excluding the land mass.  Those would be average insolation values for the day time portion of a rotation.  If the insulation were close to perfect, these would be the more likely values of the subsurface energy actually stored.

Another reason I like this approximation is that if the oceans were never frozen at the poles, the angle of incidence over 65 degree would mean close to 100% reflection off a liquid surface anyway.  The only energy that would likely penetrate to the subsurface directly would be between roughly 65S and 65N except for a month or so in northern hemisphere summer.  It is a lot easier to say the subsurface energy will tend toward TSI/Pi(), than to carry out a lot of calculations which are about useless without knowing the actual cloud albedo at each and every location on Earth.  Roughly though, if you consider a noon band with a zero tilt and the average 1361 Wm-2 TSI, from 65S-65N the insulation could be as high as 910 Wm-2 versus 665 Wm-2 for 90S-90N for the oceans.  That should give you an idea of the difference between subsurface and surface solar forcing using average ocean land distribution.  There are of course central Atlantic and Pacific noon bands with nearly zero land mass between 65S and 65N that can allow much more rapid subsurface energy uptake.  So until I either take the time or determine a need for a more accurate estimate, TSI/Pi() is convenient.

Purist won't like that, but hey.

There are quite a few things that can bung up that estimate.  One is how well the subsurface energy is transferred pole ward.  If the transfer is slow, like before the Panama closure, the equatorial temperatures would tend higher which could increase the average or the Drake Passage could open which would decrease the average.  When the average changes the cloud cover percentage and extent would change making the puzzle a bit more challenging.  With a baseline, "surface tends tend toward TSI/Pi()", you can at least estimate the impact of changes in ocean circulation on average ocean energy.  It is far from perfect, but a convenient approximation.  It is also convenient to assume that albedo is fixed.  Subsurface versus surface energy provides a reasonable explanation why albedo may be some what fixed.

If you have a more elegant estimate, break it out.


Note:  This post is just an explanation in case some wants more detail about the TSI/Pi() approximation.  It may be revised or expanded as required.

Monday, October 13, 2014

Normal?











TSI Albedo Surface subsurf. App. Surf.





TSI/4 TSI*(1-1)/Pi() TSI*(1-1)/4 Sub-App Wm-2/K K/Wm-2
Winter 1410 0.215 4.00 3.14





Wm-2 352.50 352.32 276.71 75.79



Eff. K Degrees 280.80 280.76 264.31 16.45 4.61 0.22
Summer 1310 0.215 4.00 3.14





Wm-2 327.50 327.33 257.09 70.41



Eff. K Degrees 275.68 275.65 259.49 16.15 4.36 0.23


Based on the Forcing, Feedback, Response and other Mumbo Jumbo post here is a little table for the more realistic conditions on Earth.  All of these are still "ideal" estimates meaning take with salt, but if we didn't have an upper atmosphere reflecting sunlight and molecules getting t-boned by higher energy photons/particles, we might have the actual estimate Total Solar Irradiance (TSI) "felt" at some easily "seen" atmospheric level we will call the Top of Our Atmosphere (TOOA) not to be confused with TOA, another idealized estimate.  The App. Surf. is the Apparent Surface that some space ship tooling around would see.  In order for the Earth to exist when the space ship tourists arrive, the Energy in would need to be pretty close to the energy out.  With any luck the tourists measurements will suck as much as ours and they will say Ein = Eout and not worry about minor uncertainties.

If they arrive in Winter, they might be surprised that our planet is colder than they would expect and if they arrive in Summer they might think Earth is not going to be around much longer because it is over heating.  

You should note that in the chart, albedo is lowered to 0.215 from the conical 0.30.  I did that so the energy calculations for the surface and subsurface would be the same.  That would be an equilibrium and/or steady state condition required by a less than perfect black body with a semi-transparent fluid atmosphere/surface but still homogeneous by design .  In the real world, some portion of the albedo is provided by the cloud surface, some portion is provided by the physical surface and some portion provided by the above the cloud surfaces.  The majority, about 72% is provided by the base clouds, which are...?  That is right sports fans, a response to surface and sub-surface temperature.  

Since Earth has a less than perfectly circular orbit, there is a small difference between Winter and Summer and in the far left column you have a 0.22 and 0.23, K/Wm-2.  That would be the apparent "Sensitivity" in degrees K per Wm-2 observed.  Since the observed energy depends on the atmospheric response required to equalize Tsurface and Tsubsurface, the Ein=Eout requirement is co-dependent on the Esurf=Esubs requirement. 

Earth also has an orbital tilt peculiarity.   That means that TsurfNH and TsurfSH, for the hemispheres, would also need to find a happy place.  This is before considering all the issues with real estate location.  Our Ideal Model of Earth already has a number of co-dependent equilibrium/steady state conditions that must be met or no Earth as we know it would exist.  Most of the flexibility needed to meet the conditions is provided by the rapid climate response cloud team.  

While this isn't all that complex to me, some get confused by more than one equilibrium/steady state requirement and try to simplify (over simplify IMO) to a single requirement.  You need to be extremely careful with the likely long list of simplifying assumptions needed for that degree of reductionism because they are ASSUMPTIONS not facts.  Jumping in to debate issues with overly simplified models is a bit like arguing with a drunk, doesn't do much good.

If you aren't into arguing with drunks, a tad more complex model would include another "surface" located above the normal cloud base in the drier part of the atmosphere.  This would be the surface layer where increased CO2 would play a larger role.  To play with that layer, the Remote Sensing Systems (RSS) Temperature Lower Troposphere (TLT) data which is available in absolute temperature format with masking ability from Climate Explorer can come in handy.  This can provide an approximation of the subsurface for the dry air "surface" portion of our puzzle.

With a rough average of 272 K degrees, about one C below freezing, available "subsurface" energy at a minimum would be 310 Wm-2 and thanks to a very narrow atmospheric window, about 20 Wm-2 of extra energy "MAY" be available at any time if you would like to get more detailed.  Note that my mask is for 65-65 degrees or the portion of the surface that is actually illuminated year around thants to the peculiar axial tilt situation.  At the poles especially during winter, they would be part of the dry "surface" and in the Antarctic most of the area would be "dry" all year.  Trying to lump in these dry surfaces would tend to overly complicate this supposedly simple post on co-dependent thermodynamic states which doesn't "solve" anything, just introduces another way of looking at the same tired old problem.

When you have two or more co-dependent states with different response times, you can expect oscillations or hunting while the states try to find their happy place.  When you have several co-dependent states, you can expect more interesting hunting.  But if you know the preferred state, then you can make some progress without resorting to Chaos Math, which I consider an nice thing.

Sunday, October 12, 2014

Forcing, Feedback, Response and other Mumbo Jumbo

Now tell me, which came first,  the chicken or the egg?  Discussions of Forcing and Feedback can be about like that.  When some talk about the greenhouse effect they mention that the "Earth is 33C warmer than it would be if there were no Greenhouse Gases".  I guess they think the egg came first?

With no atmosphere, the Earth would have a "surface temperature" of about 4 C degrees based on TSI/4 or ~1361 Wm-2/2 = 340 Wm-2 which if you assume a very perfect black body, the Stefan-Boltzman Law would give you an effective temperature of about 4 C degrees.  If the Earth were a less than perfect but close black body, the "subsurface temperature" with no atmosphere would be about TSI/Pi=433 Wm-2 which by the S-B law would be a temperature of about 22.5 C degrees.

The subsurface temperature would be due to one and only one radiant surface, the assumed to be ideal surface, that would produce an average of ~4 C degrees.  Instead of an atmosphere insulating the surface, a few meters of assumed uniform soil of some sort provides insulation.  There is a page on Lunarpedia related to lunar temperature you can check if you like.  If the actual absolute "surface" temperature of the Earth is 15C, then Earth's "surface" temperature would fall right in the range of an "ideal" black body surface and subsurface.  If our atmosphere thickens or becomes a better insulator, the temperature would increase to closer to the subsurface 22.5 C and if it thins, closer to the 4 C surface temperature.

No where have I mentioned clouds or CO2 or anything forcing/feedback related.  This is what I consider the egg.  This is why I continually ask for a better definition of the "surface" folks are talking about in reference to Global Warming or the Greenhouse Effect.

The actual Earth doesn't have a uniform "ideal" surface/subsurface it has oceans.  The "average" temperature of the ocean subsurface is about 4 C degrees.  That is likely due to a variety of "lucky breaks".  The first lucky break is water has a weird maximum density at 4 C degrees.  Even though that is for pure water, the salty oceans still are influence by the 4 C density phenomenon and the ~0 to -2C freezing point of the current blend of fresh to salty water.  The second lucky break is that water which is close to an ideal black body provided it isn't frozen or evaporated, would tend toward the ideal black body temperature related to TSI/Pi.    That's right sports fans, if there were no clouds the oceans average temperature would be close to 22.5 C degrees.  The third lucky break is that as the briny oceans saturate with salt, the freezing point can drop to about -18 C degrees.

If you have ever looked into solar ponds, a heavy brine subsurface with a stratified fresh water lens makes one hell of a solar energy collector.  That makes it very difficult for Earth to remain a "snowball" for any length of time as long as there is the sun and salt limits in the equatorial oceans.  It also means that there will be considerable water vapor if the oceans are not frozen over.

With warm equatorial oceans there will be water vapor in the atmosphere.  Water vapor is also a greenhouse gas, but it is limited to a more narrow temperature range of roughly -43 C in a "normal" atmosphere but in a very clean atmosphere with very few cloud condensation nuclei (CCN), the limit could be as low as -100 C degrees depending on the overall concentration.  How much impact water vapor all alone would have on "surface" temperature I have no clue.  The atmosphere of the Earth also contains oxygen which in strong solar irradiation reacts to form ozone mainly near the equator.  I have seen estimates that tropical ozone and water vapor advected towards the poles increase the temperature of the highest latitudes by about 50 degrees in a very critical region.  So we have two greenhouse gases, ozone and water vapor that exist due to solar irradiance, atmospheric composition and oceans that are responses to the circumstances, "lucky breaks", that are not easily classified as forcing or feedback.  Changes in water vapor and ozone can be feedback or forcing or more realistically responses to general system conditions.  You would have to define "normal" in order to pigeonhole the changes.

With warm oceans and some CCN, there would be clouds which tend to reflect solar irradiance.   That in my opinion is a response which can become a forcing or feedback depending our your perspective i.e. frame of reference.   Since the subsurface depends on the solar insulation at the surface, clouds a few kilometers above the surface would tend to reduce the solar impact.   Remember that if the actual albedo of  the ocean area is 0.23, then the subsurface temperature would be 4C using the (1-a)*TSI/Pi approximation.  Try that on your own just for kicks.

This is were climate science in its "Global Warming" mode went wrong in my opinion, they assumed a normal instead of considering a range of normal that would be related to the surfaces selected as references.

As it is, additional CO2 would increase the atmospheric insulation potential and the impact would always depend on the current conditions.  The largest of the current conditions would be the average temperature of the oceans which have that tendency toward a 4 C average as a relatively clear liquid subsurface.

So now go figure out what "discrepancy" there might be in "surface" temperature.