Three Compartment Ocean

Long term settling times that can appear to be oscillations or weakly damped decay curves just drive the Climate Science minions nuts.  After being spoon fed the milquetoast basics with simplistic control theory they just can't grasp how a system can be stable but swing around on different time scales.  I ran into this situation way back in the 1980s with a first for us HVAC monitoring system with a brand new just released D to A converter on a S100 bus board which we hooked up to a 30 pound Compaq lug-able with the red plasma screen.  Woo Hoo, we were cooking with high tech gas!  The "Project Manager" skimped on the laser trimmed resistors and installed 1% Radio Shack "precision" resistors to set the range for the 4 to 20 milliamp pressure and temperature transducers which I was to install.  One of the pressure transducers was for the discharge static pressure in constant volume central AC system which would never vary much.  After explaining how the "precision" resistors truncated the range of the 4-20 milliamp sensors requiring software calibration, we started our data logging project.  The system worked fine and maintained temperature and humidity within tolerances, but the "project manager" got completely wrapped up in the discharge static pressure data.  It was all over the place he thought.  Nope, it was just noise once I got him to adjust the range.  The system pressure was 0.75 inwc and varied by 0.025 inwc in time with the fan RPM.  That 0.025 inwc variation bugged the hell out of him though.

This brings me to a two compartment model by Steven Schwatrz with the Brookhaven National Laboratory.  Dr. Schwartz use a simple RC two compartment model with the atmosphere/ocean mixing layer as the smaller compartment and the bulk of the oceans the second compartment.  The way he divided the specific heat capacities he ended up with a roughly 8 year time constant for the atmosphere/ocean mixing layer and a roughly 500 year settling time for the bulk of the oceans.  The object was to determine climate "sensitivity" and based on his rough model he came up with a ballpark of around 2C per doubling.  Nice simple approach, nice solid results, nice simple model.  The ~8 year time constant would be the equivalent of the noisy discharge static in terms of actual energy.  The bulk of the Oceans would have about 800 times the capacity of the atmosphere/ocean mixing layer compartment.

In the Sketch above, I have a three compartment model for the bulk of the oceans.  I am not concerned with the noise, just the energy.  Since the southern oceans can more easily exchange energy, their time constant would be close to the 500 years that Dr. Schwartz figured.  The northern hemisphere oceans cannot exchange energy as well with each other and thanks to the Coriolis effect, can't exchange energy that well with the southern oceans.  As a rough estimate, the time constant for the northern Atlantic would be about 125 years and the time constant for the northern Pacific about 250 years based on just area and common equatorial forcing.  With the northern Atlantic "charging" first, it would be the first to start a discharge by what ever convenient path it can find with a "likely" harmonic of tau(Atlantic)/2 or 62.5 years.  The northern Pacific would "likely" have a 125 year harmonic and the southern hemisphere a 250 year harmonic.  The noisiest signal would likely be the north Atlantic 62.5 year "oscillation".  It doesn't matter what external forcing is applied, with unequal areas and limited heat transfer paths there will be some "oscillations" around these frequencies and the magnitude of the oscillations would be dependent on the imbalance between compartments.  Most of the world land mass drains into the Atlantic, that energy varies with season and precipitation/ice melt, there will be constant thermal "noise".

Not that complex.  Look at the big picture not the noise. 

The Global Gore Effect

While everyone waits impatiently like kids on Christmas Eve for the Fifth Assessment Report on Climate Change and/or Carbon Pollution, the lack of Global Warming for the past few years has created a bit of a situation for the members of the Intergovernmetal Panel on Climate Change (IPCC).  The problem is that every since Al Gore got involved, climate hasn't done that much changing.  Temperatures peaked for the most part in 1998 when Al Gore Symbolically sign the Kyoto Protocol.  Since that symbolic signing, the United States has been one of the few nations to symbolically meet the Kyoto emissions limits.  You could say that Former Vice President of the United States symbolically tamed climate all by himself proving that the pen is more powerful than the United Nations.

Saves a lot of work downloading all sorts of data, all you need is GISTEMP from 1998.  You don't have to worry about all those "adjustments" and paleo stuff, because the Gore Effect is the strongest climate forcing known to man.  Al Gore has saved the world just by picking up a pen, symbolically of course. 

Convection Cells - Sensible Impact

One of the smaller discrepancies in the Earth Energy Budgets is the sensible or "thermal" heat loss/gain where the K&T budgets have a lower 17 Wm-2 and the Stephens et al. budgets uses 24 Wm-2.  That is a large difference considering that anthropogenic forcing is estimated to be around 4 Wm-2 if you include all radiant impacts.  Thermals are an adiabatic process.  Air expands as it rises and compresses as it falls and by assuming that no energy is exchanged with the environment, the net impact is zero provided the starting and ending pressures are the same.  Using sea level as a reference, convection starting at sea level and returning to sea level would have zero net impact but convection starting at sea level and ending at some higher elevation would have a cooling impact, compression would not be able to complete an adiabatic cycle.  With the "average" environmental lapse rate at ~6.5C per kilometer, the air ending at a higher elevation would be about 0.65C cooler per 100 meters of elevation.

The average elevation of global land masses is about 680 meters above sea level.  Air rising from the oceans and ending on land would be ~4.4C cooler than that returning to sea level on average.  Land covers ~30% of the surface of the Earth, so if all evaporation took place over the oceans, the rain falling on land would be about the same temperature of the air carrying that moisture and ~30% would be cooler by ~4.4 C degrees if it fell on land.  Just as a rough estimate, 30% or 4.4 is 1.3 degrees gross cooling if averaged globally.

If the average temperature of the global ocean surface is 290C, the impact of precipitation on global "surface" temperature would be  an ~1.3 C reduction to 288.7 C degrees.  In terms of energy, the net global impact would be on the order of 7 Wm-2 for this crude illustration.  There is more to it than that of course.

Since water vapor makes things complicated, HVAC uses a number of rules of thumb to simplify estimated.  One is the sensible heat ratio or the sensible heat divided by the total heat loss/gain in a moist air process.  With an estimated SHR of 0.59 and a latent heat loss of 88 Wm-2, the total heat loss would be ~214 Wm-2 with sensible loss being 126 Wm-2.  In HVAC you are not generally concerned with what portion of that sensible heat loss is due to conduction, convection or radiant transfer, just that heat loss is not latent.  Using the same rough approximation of land area, 30% of the 126 Wm-2 of sensible would not return to the source, oceans, resulting in approximately 38 Wm-2 of net loss on a "Global" average from sea level.  The HVAC SHR rule of thumb is at a constant pressure so it does not include the compression loss.  Including both results in 45 Wm-2 total sensible heat loss from the oceans to the land.  If the average temperature at sea level is 290C which has an effective energy of 400 Wm-2, the effective energy of the land area would be 355Wm-2 or 45 Wm-2 less.  70% of the surface of the Earth at sea level would be ~17C and 30% of the Earth not at sea level would be ~8C degrees.  Global average surface temperature would be about 14.3 C degrees using the rough estimates of sea surface temperature (SST) from the pre satellite era, the HVAC rule of thumb with just a bit of correction for compression produces a reasonable rough estimate.  You can call it a gut or sanity check if you like.

The actual average SST is more complicated.  In the northern hemisphere, SST is closer to 20 C and in the southern hemisphere it is closer to 17 C degrees.  More of the evaporation in the northern hemisphere is likely to fall on land because of the most of the land is in the northern hemisphere.  It would take a fairly detailed analysis to get more than a rough estimate, but the HVAC rule of thumb indicates that there is a fairly large amount of sensible heat loss to be considered.

All of hat sensible heat is not completely lost.  It is transferred to a higher elevation where eventually it can work its way back to sea level.  The longer the moisture associated with the sensible remains on the land masses, the more significant the sensible loss will be.  Snow, ice, ground water and lake reservoirs hold that energy in a lower state for a longer period of time making precipitation records and reconstructions a valuable tool for determine past climate conditions. Some though can be lost radiantly which the HVAC rule of thumb ignores.

There is a radiant rule of thumb though that is useful.  That sensible heat is transferred to a higher average elevation where the energy can be emitted in all directions.  Assuming that up/down is the most significant radiant impact, approximately half of the sensible heat loss would be "true" loss and not "reflected" back to the surface.  Half of the 45Wm-2 would be 22.5 Wm-2 which is very close to the sensible impact estimated by Stephens et al. in their version of the Earth Energy Budget and when you include their margin of error, +/- 7 Wm-2, the HVAC plus radiant rule of thumb contender, performed rather well as ballpark estimates.

The trillion dollar question is how accurately the sensible impact can actually be determined and the time scale required for returning to the mean.  Say hello to sea level.

This graph of sea level recorded at Key West is from the NOAA Sea Levels on-line site.  I picked Key West because it is close to me, it is a coral island reasonable well removed from areas of seismic activity and has a fairly long record for the US.  Since sea level change would be a proxy for precipitation retained on the land masses, it would be a reasonable proxy for both thermosteric impact, warming of the oceans and land mass sensible heat retention.  I doubt the two can be completely separated.  The graph indicates that sea level has risen by ~0.2 meters in the past century which is almost 8 inches in typical Redneck units.  There appears to have been more variation from 1925 to 1950 than from 1970 to present which would indicate that there is not much if any acceleration in sea level rise.  One would imagine if CO2 is causing everything, that there would be some signature, acceleration beginning ~1950 or sea level rise so we could all agree that CO2 done it and move on.  But it doesn't.

Instead we have what appears to be an underestimation of sensible heat loss by the old guard climate alarmists of ~8 Wm-2, roughly the average adiabatic compression difference between sea level and land elevation which is a natural variability consideration.  Where the rain falls depends on the atmospheric and ocean cycles that can have, based on the sea level at Key West, century long trends or better.

Now you should have a question about how I estimated the SHR.  By comparing the energy budget estimates with absolute temperature and humidity estimates.  It is not carved in stone, it is just an initial estimate and it most likely will vary with time and natural oscillations that vary the percentage of rain that falls on the elevated plains.  If you have a better one, whip it out. 

What Sign was that Again?

The great thing about Thermodynamics is you can change your frame of reference.  From the correct reference, you get useful answers which can be transferred to another frame to learn more about the system and also check your work.  You can get some really screwy answers if you pick the wrong reference.  Since climate science started with less than stellar references, a top of the atmosphere with is actually the middle of the atmosphere, a surface that is actually a kilometer or two above the real surface and use averages of air temperatures a couple meters above the surface for land and about 10 meters below the surface for the oceans, there are all sorts of opportunities for climate scientists to really end up looking like dumbasses.

Just for fun I thought I would compare the BEST "Global" land "surface" temperature average with the Atlantic Multi-decadal Oscillation and the Houghton NH land use "carbon" estimates, INVERTED.  Why inverted?  Well a little back ground first.

The Houghton land use carbon study is an estimate, nothing wrong with that, but the depth of the estimated soil carbon loss is rather shallow.  Along with losing soil carbon, land use tends to increase soil moisture loss, erosion and soil average temperature by a degree or two.  Since Carbon is the focus of every thing climate related, the land use carbon estimate is nearly useless as a land use carbon estimate.  It can be off by nearly 100% in some areas where deep rooted plants where the norm like Steppe, I thought I would look for a relationship of any kind.

Land use is consider a negative forcing.  The climate scientists are certain that cutting down trees to create pasture for goats to over graze is good for the "climate".  Never mind the occasion screw up that causes a dust bowl here and there or a fresh water sea to become a salt flat, land use cools the environment.  Wet land cause warming with all that water vapor feed back so they are not good for climate either.  Minions of the Great and Powerful Carbon look to the land that is warming, but should be cooling, because of all that land use change, to show just how bad things are becoming because mankind is addicted to Carbon.

Since the Atmospheric Boundary Layer (ABL) is the real greenhouse, what cools the true surface warms the ABL which is fixed to roughly 0 C provided there is water vapor.  No water vapor then the physics change.  You get less deep convection without water vapor and the lapse rate increases.

I have mentioned for a while that the impact of land use looked completely screwy, but have been constantly reassured that the sign is correct.  Never mind intense farming in high plains tends to be stressful on the soil as evidenced by the US dust bowl and the USSR version in the 1960s, land use cools the "Global" land. 

Inverting the Houghton land use carbon data seems to produce an unusual correlation with the most recent three decades of "Carbon Pollution".  Of course the data is not suited for the purpose I used it for and obviously further study is required, the climate science code for SEND MO MONEY!

But I thought some might get a chuckle out of the possibility that climate scientists have screwed up yet again because of their fanatical Carbon done it bias. 

It is Greenhouses all the way Down

Dr. Roy Spencer is doing a redo of the redos of the Woods greenhouse experiment.  It would seem that after more than 100 years of Greenhouse gas theory and more that 100 years of actual greenhouse use that people would tire of reinventing the wheel so to speak.  One of the problems Dr. Spencer will have is his greenhouse experiment will be conducted in a greenhouse.  Woods had the same problem and installed a layer of glass above his experiment so Woods had a greenhouse in a greenhouse in a greenhouse.  The drawing above attempts to illustrate one of the atmosphere's greenhouses, the Atmospheric Boundary Layer (ABL).

Solar in yellow on the left is based on our current best estimate of the actual average annual energy absorbed during the day portion of our 24 hour day.  The orange on the right is based on our current best estimate of the purely thermal or infrared portion of the energy transfer during the night portion of our 24 hour day.  The blue lines sloping down represent the ABL.

While the total energy absorbed in the ABL by all sources is large, the net energy, what really matters, averages about 88Wm-2 or about the amount of the 24 hour average of the latent energy transferred from the actual surface, the floor of the ABL greenhouse to the roof of the greenhouse the ABL capping layer.  You should noticed that I have divided the net energy of the ABL into 39 up and 39 down with a question mark in the middle.  That question mark is about 20 Wm-2 or about the range of estimates for the total latent energy transferred to the atmosphere, 78Wm-2 to 98 Wm-2.  That is how well we understand our atmosphere.

This graphic, borrowed from an Ohio State University server which unfortunately doesn't have a good attribution, the author remains nameless so far, though he does thank Nolan Atkins, Chris Bretherton and Robin Hogan in the at least three versions that pop up while Googling atmospheric boundary layer inversion capping, has a neat graphic that I plan to critique in an educational way.  "The Stable boundary layer has stable stability" is something that might be better worded, but makes a fair tongue twister.  There, critique over.  I need to be careful because the course is on lightning, I don't want sparks flying because of my questionable use of intellectual property. 

The power point presentation that this graphic was lifted from looks like it has good potential to simplify explanation of the complex processes that take place in the ABL convective mixing layer, so I hope the author fine tunes and publishes since most of the other discussions I have seen are dry as all hell.

The  gist of the graphic for my use right now is the transition from an entrainment to inversion capping layer.  During the day mode, moist air rises with convection mixing the layer between surface and capping layers.  As the moisture begins to condense, buoyancy decreases at a stable capping surface where further cooling, mainly radiant, increases the air density which lead to subsistence or sinking air mass that replace the mass that convected from the surface.  As night falls, the thermal energy driving the convective mixing decreases leaving an inversion layer that produces the true surface greenhouse effect.  For those less than radiantly inclined, the temperature of the roof is greater than air above and below producing a higher than "normal" sink temperature for the greenhouse floor source.  The ABL "roof" gets most of its energy from solar, the 150 and floor latent and sensible energy the 224 in the first drawing.

The reason I have "Day" values for the solar powered portion is because the ABL can only contain so much energy.  The ABL expands upward and outward increasing the effective surface area allowing greater heat loss to the "space"/atmosphere above the ABL capping layer.  That expansion can be towering deep convective deep in summer or just clear skies with a little haze, but the ABL "envelop" expands in the day and contracts at night producing what is known as a residual layer between the entrainment layer and the stable nocturnal layer.  If there is advective or horizontal winds below the capping layer, the impact changes.  A sea breeze is a good example that tends to cool sometimes and warm others, lake effect another and then you can have massive fronts move through which can destroy the ABL stability layers all together.  Considering all those possibilities is a challenge, so let's stick with a static version so heads don't explode.

If you look at the orange arrow with the 59 and thin 20 arrow, that is the current best estimate of annual average radiant surface cooling, where that surface is the floor of our greenhouse.  That 20 Wm-2 represents the imperfection of our greenhouse.  If the average final or lowest average floor energy is 335 Wm-2 which would be a temperature of about 4 C degrees, then the greenhouse floor would start the night at about 355 Wm-2, about 8C and ramp down to about 4C producing a 4C range of temperature.  If the 20 Wm-2 were less, the range would be less and either the start temperature would be lower or the end temperature higher.  Since the ABL has a limited capacity, the initial temperature would tend to be about the same and the final temperature would increase reducing the diurnal temperature range of our ABL greenhouse.  If the 20 Wm-2 window was completely shut, the capacity of the ABL would still limit the total amount of initial warmth, just the diurnal temperature range would approach zero.

Now let's imagine we reduce the 20 Wm-2 by 4 Wm-2.  Our final energy would be about would be about 339Wm-2 which has an effective temperature of 4.9C or about 0.8 to 0.9 C warmer than the less efficient ABL greenhouse at the lowest point of operation.  That increased efficiency would likely increase the latent heat loss a little during the day mode, increasing the initial temperature of the ABL greenhouse by about 0.8C.  The overall impact would be about 0.8C warmer conditions or less.  Nothing is perfectly efficient so the 0.8 -0.9 C per 4 Wm-2 would be an upper limit for the ABL greenhouse.

The ABL greenhouse though is inside a free atmosphere greenhouse.  Adding the 4 Wm-2 at the ABL roof may impact the performance of the free atmosphere greenhouse.  What would keep the free atmosphere greenhouse from impacting the ABL greenhouse and vice versa?  When the roof of the ABL greenhouse is produced by water vapor which has a limited temperature of condensation and set freezing point, adding energy doesn't change the temperature only the rate of energy transfer.  The ABL volume has a limited heat capacity so convective mixing would increase with added energy expanding the ABL envelop more or producing more deep convection loss if the ABL capping layer becomes less stable.

So why is the globally averaged annual floor of the ABL greenhouse about 335 Wm-2 or about 4 C degrees?  If the roof is limited by the condensation or freezing point of fresh water, 0C or about 315 Wm-2 and the efficiency of the ABL greenhouse is limited by the 20 Wm-2 of window radiant energy, what else would it be? 

It Depends on How Hard You Look - Golden Ratio

The Golden Ratio is at the boundary of Science and Pseudo-science.  A. M. Selvam has published quite a body of work on self-organized criticality and non-linear dynamics using the Golden "mean" and the Penrose tiling pattern to "predict" patterns in just about everything.  Her work tends to make sense even though it shouldn't make sense.  In my opinion, it does because there are simply more natural patterns that can be reduced to irrational numbers than to rational whole numbers.  We tend to think in whole number where nature doesn't think.  Not everything in nature falls into a Golden ratio pattern, there is no reason everything should, but there is some logic to why the Golden ratio at least appears to dominate along with Pi, e and various roots. Nature doesn't do base 10.

Pi, e and various roots are commonly used to describe things in nature that are more common or ordered like circles, spheres, decay curves because we live in a "not a box" universe.  Phi, the Golden ratio, is a bit like the red haired stepchild of the irrational number gang though.

The probable reason is Phi doesn't exactly fit anything.  It is a close mean to a lot of things but it is inexact.  Natural arches on Earth vary around the Golden mean and if every material had the same strength the Golden mean would be irrelevant.  The Golden mean nearly fits more things on Earth and in the Solar system than it would if we lived around some other star.  Fate makes the Golden mean somewhat relevant to us Earthlings. 

Fate is not a scientific term, but chance is.  The probability or chance of some object forming that has some approximation of a Golden dimension is greater than "normal".  If you look hard enough you can find more examples.  If you want to dispute the significance of Phi you can find plenty of examples to call Phi Phans nuts.

If I were to say that Earth is not a perfect sphere, folks would agree but Pi is here to stay even though it is not a perfect fit in nature, because it is a closer fit to nature.  When we need more "exact" measure Pi is the guy.  But when there is more irregularity we get all flustered and forget that Phi  is a better general fit for all the stuff that isn't as ordered as a sphere or a curve influenced by gravity or the inverse square law.  We need that order and better "fits" between our perception of nature and our construction of math.  Had we kept base 60 as our math concept, Phi would be Phine.  With base 10 and metrics, our perception of the universe just gets more biased to a nonexistent "normal".  US units of measure, inches, feet, furlongs, bushels and peaks actual fit what we perceive instead of forcing things to fit plus requires some thought which is a good thing.



So let's think about Phi, 1.6180339887....  That is close to Pi/2,   1.5707963268  +/- 3 percent.  Earth's orbit isn't perfect, it is off by about 3 percent. 



What about e? 2.718281828 , since Phi = (1+(5)^.5)/2, Phi plus 1= 2.6180339887.... or 3.8% more than e. 

Phi is a pretty decent approximation for most everything but not exactly equal to anything.  How can you not "see" Phi relationships in nature and how can you deny Phi is relevant to nature?  It is right on the boundary of science and pseudoscience.

Math purists, who tend to be extremely anal, will devise hundreds of statistical methods to allow for uncertainty in nature that are built into fractals approximate with Phi.  Over billion of years of random erosion, adaption and evolution, things are not perfect and never will be, Phi is just a good estimate of the mean degree of imperfection.

Now which is the pseudoscience?

Sea Dog Wagging the BEST Tail

The Berkeley Earth Surface Temperature (BEST) project has updated and is still updating its site.  A discussion of the pluses and minuses of the revised products is going on at Climate Etc. among other places and has finally brought to the forefront the issue of Land Amplification.  The minions of the Great and Powerful Carbon tend to miss the subtle issues of a mainly land located in the northern hemisphere, "Global" temperature series and what drives the temperatures of the majority of the land in that land only data set, the northern oceans.  So in yet another soon to fail attempt I have plotted the Reynolds Oiv2 SST for the Northern Extra Tropical oceans from 24N to 70N latitude.  This time though I thought showing the BEST Tmax and Tmin instead of Tave might be better.

Since the Oiv2 data only starts in November of 1981 and has seasonal variation that needs to be removed to see the ~0.4 C shift starting in 1985 thanks to volcanic forcing plus a Pacific Decadal Oscillation (PDO) mode swing, I used the monthly averages for the 31 full years common to the data sets for the baseline and seasonal cycle removal.  That should be pretty clear to anyone that halfway follows the surface temperature debate.  BEST, being predominately northern hemisphere data has a strong northern hemisphere seasonal cycle.  While my approach may be less than ideal, at least there are 31 years and I explained what I did.

Pretty much anyone, other than the minions of the Great and Powerful Carbon, should notice that there is a strong correlation between the satellite measured northern extra tropical oceans and the BEST "Global" land surface temperature data.  Most would notice that the correlation is better with the Tmin than the Tmax.  Most would notice that the northern extra tropical oceans are curving back toward the mean prior to both the BEST Tmin and Tmax.

The minions of the Great and Powerful Carbon manage to have the land data wagging the sea dog tail when the opposite would appear to be the case.  As I have pointed out before, Land Amplification should be considered and that because of land amplification, the northern Atlantic region (AMO) makes a damn good proxy for "Global" land and ocean "surface" temperatures.  That means that the Central England Temperature record makes a pretty good proxy for "Global" "surface" temperature and since the Indo-Pacific Warm Pool correlates well with the longer term average north Atlantic SST, the Indo-Pacific Warm Pool  makes another pretty damn good proxy for "Global" "Surface" temperature anomaly.  All because of land amplification.

Figure 53. This figure shows the amplification ratio between 30N and 60N (roughly from the middle of Texas to the bottom tip of Greenland) compared to the amplification ratio in the Arctic. The observed value from Berkeley Earth is shown in red and the GCMs are in blue. The GCMs tend to overestimate the amplification at the pole and underestimate the amplification in the mid-latitudes.

BEST has become the last great hope for the alarmingly high "sensitivity" that the minions of the Great and Powerful Carbon need to sell their Fear Overconfidence and Confusion which requires drastic extraordinary measures to save mankind from ourselves as only they are capable of doing.

Remarkable isn't it?

UPDATE:

While we are at it let's consider some baseline dependence issues. 

Since roughly 1990 the instrumentation for the surface stations have been various digital sensors.  The sensors required a good deal of adjustment to produce reliable data.  Unlike analog, liquid in glass, the digital instruments can tend to have a bias, typically on the warm side.  There is no reason to believe that the adjustments didn't correct things, but the adjustments impacted at an inopportune time.  Since the surface and satellite instrumental generally agree, a modern era baseline should be as good if not better than an arbitrary baseline.  The plot above use the same baseline as the first graphic with the NOAA ERSSTv3 20N 90N data that is readily available at this site.  This time seasonality was not removed which may be a minor issue.

With this baseline, the BEST Tmin starts at the lowest initial condition with Tmax more closely tracking the northern extra tropical SST.  The "Global" diurnal temperature trend would have decreased until circa 1980 then started increasing roughly around 1985.  The majority of the warming was due to Tmin and from the start of the data until about 1960 then more uniform warming took place.  Just a different view of the same old data. 

The Madness of Reductionist Methods

This is a comparison of the Steinhilber et al 2009 Holocene TSI reconstruction with the Oppo et al. 2009 Indo-Pacific Warm Pool temperature reconstruction.  While there is a correlation just eyeballing, there are lots of exceptions that would need to be explained by "other" stuff or lags, so it is not a pretty correlation required by reductionists. 

Comparing the TSI recosntruction to the Holocene portion of the Monnin et al 2001 Antarctic Dome C CO2 reconstruction, there is also a less than ideal eyeball correlation.  The same explanations for "other"and lags would be required, but CO2 started rising around 7000 years ago and the reconstructed Total Solar Insolation near the same period. 

Because the reductionist models do not allow for longer term impacts due to cumulative heat transfer between various complex ocean layers with variable inertia, solar of course cannot have a significant impact but diffusion into and out of simple slab models can be used to "explain" hitches in the reductionist model correlations. 

You could call this blinded by the Enlightenment.  The 10Be isotope used to construct the Holocene TSI is collected at the true surface of the Earth, in the Steinhilber et al. case, the Greenland Glacier and the CO2 reconstruction of CO2 at the Antarctic ice cap.  The general correlation would be indicative of "Global" forcing and the exceptions, internal variability between the poles.  There is no simple reductionist "fit" because the systems, Earth and the Solar system plus Earth - Atmosphere and Oceans have their on response times and "Sensitivities".  So this solar precessional cycle impact that could include actual Top of the Atmosphere TSI, TSI incidence angle, Atmospheric and Ocean tidal forces, Volcanic forcing, Ocean heat transport delays as well as atmospheric forcings, provides enough degrees of freedom to paint any picture of past climate one wishes.

The reductionists are convinced their way is best even though their model of Earth climate requires constant "adjustment" to appear to be useful.  Like a bulldog they cling to an "elegant" theory and ignore the growing number of paradoxes created by that theory. 

To explain away the Solar CO2 relationship for the past 7000 years they only have to select enough noisy proxies to average away any solar signal.  Instead of looking for the more difficult to answer correlations, they just avoid them. 

That "Benchmark" Thing

I have discussed the "Benchmark" used by Science of Doom a number of times.  The "Benchmark" is the estimated Planck response or zero feedback sensitivity for the "surface" temperature of Earth.  From the Science of Doom post, Measuring Sensitivity, "

If somehow the average temperature of the surface of the planet increased by 1°C – say due to increased solar radiation – then as a result we would expect a higher flux into space. A hotter planet should radiate more. If the increase in flux = 3.3 W/m² it would indicate that there was no negative or positive feedback from this solar forcing (note 1).

Suppose the flux increased by 0. That is, the planet heated up but there was no increase in energy radiated to space. That would be positive feedback within the climate system – because there would be nothing to “rein in” the increase in temperature.

Suppose the flux increased by 5 W/m². In this case it would indicate negative feedback within the climate system.

The key value is the “benchmark” no feedback value of 3.3 W/m². If the value is above this, it’s negative feedback. If the value is below this, it’s positive feedback.

Without adding mass to the atmosphere, there is no reason to expect that "Benchmark" to change, but who exactly was that "benchmark" value drifted into?

For a planet to exist, Energy in has to Equal energy out, in simple terms, work has to equal entropy if you think of a Carnot Engine that can be perpetually stable.  If there is more than one stage, the entropy of the first process could be used by a second process leading to a variety of efficiency combinations.  The "surface" then could not be perfectly 50% efficient, Ein=Eout if any of the surface input energy is used by a second stage.

The leads interestingly to three states, less than 50% efficiency most likely, greater than 50% efficiency not very likely and 50% ideal efficiency, impossible.  So what does this have to do with the "benchmark"?

This is a plot of required specific gas constant for an atmosphere for a stable planet.  If a "surface" transfers waste energy to the atmosphere the atmosphere will need to find a happy specific heat content or some portion of the atmosphere with erode to space.  Using 1 for density and 1000 millibars for barometric pressure.  This is simply using the ideal gas laws solving for R(specific) with respect to temperature for a constant pressure.  I stopped the plot at 300C degrees which results in an R(specific) of 3.3 with units that should be Joules/K, which if I use time t=1 sec is equivalent to W-Sec/K.  The standard value for R is 8.3J/mol-K , where mol is moles of gas.  So for 300K degrees, there would be approximately 3.3/8.3=0.39 moles per cubic meter if the desired units are Wm-2/K for the "benchmark" sensitivity for an ideal gas at 1000 millibars with a density equal to one unit.  Earth happens to have a surface pressure close to 1000 millibars and the density of dry air at 300C is 0.616 kg/cubic meter. 

Earth's surface doesn't have much "dry" air and adding moisture to air actually decreases its density since H2O is light in comparison to O2 and N2.  The actual surface air density at 300C would be a little less than 0.616 kg/cubic meter. 

Using the "Benchmark" value, increasing "surface" forcing by 3.7Wm-2 would produce a 1.12 C increase in temperature, but the "benchmark assumes zero feedback.  With the "benchmark" limited by the specific heat capacity of air, any increase in surface temperature has to have a negative feedback if the surface efficiency is less than 0.5 percent meaning more energy is lost to the upper atmosphere and space than gained by the surface. 

The other cause that can exist is where at the surface more work is performed than entropy, Venus.  The surface density of Venus' atmosphere is about 67 times greater than 1 and the surface pressure is about 92 times greater than 1000 milibar.  With a surface temperature of 740K the Venusian "benchmark" would be 1.8 Wm-2/K, twice as efficient at retaining heat than Earth.  So if Earth is 39% efficient, 22% worst than 50%, then Venus should be 61% efficient, 22% greater than 50%.  If you compare the geometric albedo of both planets, Earth is ~37% and Venus ~67% with both having other energy inputs, geothermal, rotational, tidal etc.  Earth is lower likely due to some time in its past having an average surface temperature of 300K or greater causing loss of atmospheric mass and Venus having a more dense atmosphere retaining and likely gaining atmospheric mass. 

It is interesting in any case that the Earth "benchmark" sensitivity appears to be estimated to be for a surface temperature of ~300C or roughly 10C greater than the current average.  Since that requires greater atmospheric mass/density, we can't go back there anymore. 

Is a Picture Worth a Trillion Dollars?

Updated with GISS Global Temperature and the Charney estimates at bottom:

Once the minions of the Great and Power Carbon spread their faith to the economic community, the finest Economists the world has to offer discuss the discount rate that should be justified for saving the world from the greatest peril current rattling around in the minds of the minions.  If "sensitivity" is greater than 3C it will cost trillions of US dollars to save the world, over $30 per ton of Carbon must be charged.  If "Sensitivity" is approximately 1.6 C, the world can eke by on a measly trillion or so with Carbon taxed at about $3 per ton.  If "Sensitivity" is less than 1, the whole Great and Powerful Carbon Crisis should have never existed.

When BEST first published their land only temperature reconstruction they included a simple forcing fit.  Volcanic and CO2 forcing scaled to produce a simple fit to the land only data.  You can download the data for their fit from their quickly improving website.  Above are three "Sensitivities with the volcanic forcing on a 1985 to 1995 baseline so later, satellite era data can be used.

Using the NOAA ERSST3 tropical ocean data (20S-20N) with the same baseline, this is the fit for three "Sensitivites"  Green nada cash, Red a trillion dollars maybe and Orange multiple trillions.  The 1.6C, trillion maybe is the best fit.

Using the same "sensitivities" without the volcanic for simplicity, back to 1700 AD, 1.6 a trillion maybe is still the best fit but OMG trillions is coming on strong!

Starting at 900 AD, 1.6 C a trillion is still the best fit but nada, zilch, bagels 0.8C is making a showing, OMG TRILLIONS is falling back in the pack.

 Starting at 0 AD, nada, zilch, bagels, 0.8C takes the lead for good.  The minions of the Great and Powerful Carbon can smooth out the past from 1500 AD back, but not even "Dimples" Marcott can get rid of the dip near 1700 AD, the period formerly known as the little ice age.  So the next time someone says they have to collect taxes for the Great and Powerful Carbon, stick this in their ear. 

 Since everyone seems to have favorite data to use, this one compares GISS temperature with the two original estimates offered to Jules Charney in 1979, Hansen 4C and Manabe 2C.  The 0.8 C, my estiamte for the more realistic lower end is also included.  The 3C mean IPCC estimate is the average of the Hansen and Manabe estimates with an uncertain to 0.5 C on both ends producing the original 1.5 to 4.5 C sensitivity range.  The baseline is still 1985 to 1995 which is roughly the "initial" condition for the first IPCC report.  Manabe's 2 C is right on time with the 0.8 providing a reasonable lower bound and the 4C still in the hunt but showing signs of divergence based on the 1990 start date.  Hinecasting, the 4C wanders out of contention with both 0.8C and 2C maintaining contact with the instrumental.   Just in case you were curious.

What are the Odds?

The Climate Change policy advocates never discuss odds.  They have less descriptive "likely", "very likely" and "most likely" which provides ballparks and "fat tails", things that "could" happen.  I "could" win the lottery.  Earth "could" have an impact event in the next three months.  A nuclear reactor core "could" burn through the Earth to China.  Major alarmist Climate Scientists "could" be right.

Consider the upper range of climate change impact, 4.5C degrees per doubling of CO2.  From an interglacial starting point, that is where most of the glacial ice sheets have melted and sea level in high like now, for the past 1 million years, there is no point were the Earth temperature made it to 4.5 C higher than it is today.  The last time temperatures were 4.5C higher was ~ 30 million years ago and the last time there was a major impact event was ~2.7 million years ago.  Alarmist Climate scientists have and continue to use 4.5 C as an upper boundary for a doubling while the current rate per doubling is on the order of 0.8 to 1.6 C per doubling.  The odds of 4.5 C per doubling is likely on the order of an impact event.  An asteroid or comet crashing into the Earth disrupting the geomagnetic field and causing a magnetic field reversal, major climate shift and new evolutionary paths. 

"Sensitivity" is defined as the change in "surface" temperature per change in radiant "forcing".  The estimated range of "sensitivity" is 1.5 to 4.5 C per ~3.7 Wm-2 with the "benchmark" response estimated at 3.3 Wm-2 per degree C.  3.7/3.3 yields 1.12 C per 3.7Wm-2  From the start, even the minimum impact is overestimated by ~0.38C degrees. The "benchmark" is based on observation from arguably a cooler period caused by greater than "normal" volcanic activity and/or other natural factors.  A cooler object is easier to warm so the "benchmark" value is likely inflated, meaning the already inflated minimum "sensitivity" is even more inflated.  Now 3C per doubling has "likely" the odds of an impact event or me winning the lottery.

A simple estimate of the new "benchmark" can be made using the "average" estimated Down Welling Longwave Radiation of 334 Wm-2 +/- 10 Wm-2.  That produces a "benchmark" of 4.8Wm-2/C +/- ~0.4 or about 0.76 C per 3.7Wm-2 equivalent doubling.  The curious would note that the "average" temperature of the oceans is 4C which has an approximate energy of 334.5 Wm-2 which also produces a "benchmark" of ~4.8Wm-2.  Someone even more curious could look at the "environmental" lapse rate formula and notice that considering the specific heat of the atmosphere has a factor alpha ~0.19 which inverted is 5.25 Wm-2/C or should be if you work out all the units, though I have not done so.

You can even compare the ~0.8 C sensitivity to a 3.0 C sensitivity using reconstructed CO2 data to discover the potential impact of "guessing" that the 20th century was "normal" enough to use in determining the "benchmark".

The orange 0.8C per 3.7 Wm-2 of atmospheric forcing versus the ridiculously "ideal" 3.0 C per 3.7 Wm-2 forcing compared to a reconstruction of the Indo-Pacific Warm Pool.  The 3.0 C sensitivity requires feed backs to increase its efficiency to 375% of input.  To an engineer that is like saying you have not only met God, but slept with her and was on top. 

Each of these "discoveries" reduces the odds that "sensitivity" to 3.7 Wm-2 of atmospheric forcing will be high.  These "discoveries" also increase the possibility that alarmists Climate Scientists are whack jobs, cheese done slipped of their cracker, die hard "China Syndrome" DVD owners.  .

 

Sky Dragons versus the Brain Dead Zombies

I have written a couple of posts on the problem of the Sky Dragons using outdated and error filled previous "peer reviewed" Earth Energy Budgets to disprove any at all "Greenhouse Effect".  When I mention the same issues to the "Carbon Tax will save the world" geniuses, aka the brain dead zombies, they make the same type of errors only in the reverse.

The Brain Dead Zombies demand detailed physical derivations or else they don't listen to any other view.  Climate Science is not at that point.  Climate Science is at the accounting and organization stage of its infancy.  Older work like Lean et al. pre 2000 and others that don't include the majority of the new "global" satellite information are antiquated.  Models and paleo reconstructions that end prior to 2000 are useless or worse, misleading.  You can't produce any reasonable first principles argument other than delta T = ?*ln(Cf/Ci) plus ?.  That is pretty poor first principles to base saving the world on.

The largest problem is natural variability. 

You can difference any of the "global" surface temperature data sets by hemisphere and show the range of short term, ~60 year, natural variability.  Peak to peak is roughly 0.4C and despite arguments to the contrary, the net impact is not 0.1 C plus or minus a touch.  Since most of the variability is in the land dominate northern hemisphere, atmospheric and "Greenhouse" effects amplify the shorter term natural variability impacts.  I include the UAH NH and SH with regressions to show the range of "uncertainty" that should be considered.  If you follow the NH regression you might notice that it resembles the OHC slope that is currently used instead of "surface" temperature since "surface" temperature is not playing nice with the global ambitions of the Brain Dead Zombies. 

By picking a start date from the mid 1950s to early 1980s, the Brain Dead Zombies (BDZ) can produce the scary charts then mumble some nonsense about first principles and Occam's razor to baffle the lay public with bullshit.  Some of the more whacked out BDZs will even use the Best land only surface temperature data which is primarily NH because that is where the land is, mixed with idealized and unverifiable "physics" to "prove" we all should be wearing ashes and sack cloth for the next millennium.

In their latest effort to baffle, the BDZs promote the above graph from an unnamed source, i.e. they didn't provide proper accreditation other than the pnas.org in the link.  The graph ends in approximately 1998 cutting off the past 15 years of climate "pause"  knowing that their Brain Dead dihydrogen monoxide banning minions can't figure out what year it is anyway.  Adding the "pause" year, the peak to peak range would be approximately 0.8C with likely another 15years, thirty years total, of "pause" conveniently trimmed from their Carbon Tax sales pitch.  The chart appears to be one created by Tsonis et al where the instrumental record is the dark solid line, the instrumental with estimated natural variability removed is the dashed line and an exponential fit is applied, the thin solid line.  For some odd reason the BDZ think this is proof of some nonsense or the other.

This chart borrowed for Steve McIntyre's post on the Guy Callandar's simple climate model covers the same period up to present with the grren line being the Callandar model which has a "sensitivity" of approximate 1.6 C degrees, the lowest range of IPCC "projections".  Neither the Tsonis nor Callandar models consider that the start, ~1900, might have been below "average" due to the presistence of little ice age conditions.  Depending on what "average" is, the percentage of warming due to CO2 equivalent anthropogenic forcings would vary.

The Berkeley Earth Surface Temperature (Best) project also has a fit of estimated volcanic and human forcing on climated compared to their land only temperature product.  Since the average start temperature is approximately 8.25 C and the end point in 2012 is approximately 9.8C, you can use the Stefan-Boltzmann law to determine that the approximate change in "forcing" 7.9Wm-2 for 1.55C change or a "sensitivity" of 0.196C/Wm-2 but there is a lot more negative volcanic forcing prior to 1900 than after.

If you consider the peak temperature prior to the major volcanic forcing only ~0.5 degrees of the rise might be due to "industrial" forcing with the remaining ~1C due to recovery.  If you completely ignore the possibility that a significant portion of the warming is due to natural recovery, you get a high "sensitivity" and if you consider that 1900 started near the little ice age minimum ~0.9 C cooler than "normal", you get a lower CO2 equivalent "sensitivity.

Like this.  Using the Law Dome 2000 year reconstructed CO2 data I show the extremes.  The blue is 3.0C per doubling of CO2 and the red is 0.8 C per doubling of CO2, but the atmosphere responds to energy change at the surface even if there is no change in atmospheric composition.  0.196C/Wm-2 would result in ~0.8C for 4Wm-2 of CO2 equivalent forcing.  So you have two choices.  Thermogeddon, because nothing existed prior to James Hansen or most to the warming/cooling from 1750 to present was natural or at least not CO2 equivalent forcing related.

 This chart includes the Oppo et al 2009 Indo-Pacific Warm Pool SST reconstruction using the entire 2000 years as the anomaly baseline.  Which "sensitivity" do you think is a better fit with reality?

The Brain Dead Zombies avoid pre-industrial cooling like the plague.  If you mention what should be a simple observation they will switch topics to peak oil, Big Oil or just scream "At 35C all die!!", because what else would you expect from a brain dead zombie.  At least the Sky Dragons try to stay on topic.


Update: Since the issue is if CO2 is the majority share holder in climate change I decided to add this chart.

The Marchitto et al 2010 data and spreadsheet was downloaded from NOAA Paleo and the paywalled paper, Dynamical Responses of the Tropical Pacific Ocean to Solar Forcing during the Holocene (DOI: 10.1126/science.1194887)  published in Science Magazine is available in the embedded link.  From the abstract:


The early Holocene SSTs were also characterized by millennial-scale fluctuations that correlate with cosmogenic nuclide proxies of solar variability, with inferred solar minima corresponding to El Niño–like (warm) conditions, in apparent agreement with the theoretical “ocean dynamical thermostat” response of ENSO to exogenous radiative forcing.

Stott et al. 2004 is also available at the NOAA Paleo site and a free view pdf version of the article published in Nature magazine available here.

From the conclusions: Cariaco Basin sediments also contain evidence of higher rainfall in northern South America during the early Holocene, with increasingly arid conditions developing during the past 5,000 yr (ref. 18). These data all point to tropic-wide changes in the hydrological cycle that have been attributed to a more northerly position of the ITCZ during the early Holocene in response to changes in solar radiation associated with the precessional cycle. Data from other parts of the Pacific and Atlantic will now be required for an assessment of whether the changes in the hydrologic cycle affected the salinity gradient between the Pacific and Atlantic Oceans. If so, millennial to centennial scale changes in Holocene ocean thermohaline circulation would be directly affected by ocean–atmosphere processes that have occurred in the tropics

It is as Simple as Night and Day - a Day Night Budget Look

There are a few things that are very difficult to explain to both sides of the debate about the Earth Energy Budgets.  The Sky Dragons get lost in the averaging method used and others will mention that the "Greenhouse" effect is a 24/7 thing requiring averaging.  However you look at it, a budget should balance without too much forcing.  Of the budgets available, the Stephen's et al. appears to be the most accurate and the Kiehl and Trenberth budgets tend to have a common error that they for some reason are unwilling to admit.  This leads to a lot of confusion and unneeded debate. 

To highlight the errors I have used a Day Night version which is far from perfect.  Day would be energy in and night energy out and the two have to equal other than some small imbalance on the order of a Watt per meter squared or less at the Top of the Atmosphere, but possibly much larger at the "surface" due to the immense heat capacity of the oceans .  For the Day Night version most of the day values need to be doubled.

Here I have modified the Stephens et al. Earth Energy Budget produced to dispute some issues with the series of Kiehl and Trenberth +/- Fasullo Earth Energy Budgets.  On the Day side I have doubled the values for atmospheric and surface absorption, latent heating/cooling and sensible heating/cooling.  This assumes that the majority of sensible and latent energy flux are day energy related.   That is a very limited assumption but useful for this post.  The Night values are not doubled as they are based on 24/7 values. 

Considering just the solar energy absorbed, in the Stephens' et al. 165Wm-2 is absorbed by the true surface and 75 Wm-2 by the atmosphere producing 240Wm-2 absorbed over a 24 hour period.  Since the sun illuminates on the side of the Earth facing the sun for about a 12 hour period, the actual solar radiation absorbed is 480Wm-2 during that half day so the night side would have to lose 480Wm-2 during that 12 hour period if a steady state is maintained.  Looking at the problem this way 330 Wm-2 is absorbed by the surface and 150 Wm-2 by the atmosphere.  This produces a ratio of 150/330=0.45 or 45% of the solar energy relative to the "surface" is absorbed by the atmosphere.  For an ideal greenhouse effect, none of the solar energy would be absorbed by the atmosphere.  If the atmosphere were a perfect radiant shell, then about 50% of that energy would impact the "surface" and 50% would be lost to space or impact a higher "shell".  That would produce a surface energy for the Day period of ~405Wm-2 which would have an equivalent temperature of about 290.7 K degrees. 

At night the true surface would lose energy first to the atmosphere.  With the effective "surface" temperature of 290.7K and the effective atmospheric temperature of 226K initially (1-Based on the Stefan-Boltzmann law), the temperatures would decay with an initial Carnot efficiency(2) of 22% decreasing to a Carnot efficiency of 18% if the "surface" has enough thermal mass to maintain the atmospheric temperature.  Since the oceans have ~1000 times the thermal mass of the atmosphere, the limit is how efficiently the oceans can transfer energy to their "surface".  This doesn't involve any Greenhouse gas effect other than the "surface" is liquid/solid and the atmosphere is gaseous with a limited specific heat capacity.

The amount of solar energy absorbed by the atmosphere is dependent on the composition of the atmosphere.  For a perfect greenhouse effect there would be no solar energy absorbed in the atmosphere only heat energy leaving the surface would be absorbed.  With roughly 150Wm-2 of solar absorbed for a 24 hour average of 75 Wm-2 absorbed, at least 75Wm-2 of the "greenhouse effect" is actually an atmospheric effect.  Literature trying to present a simplified greenhouse effect analogy generally will mention that with a "surface" at 288K where it should be 255K, that there is 33C of "Greenhouse effect"  That is incorrect.  The difference in energy for that 33C is 390Wm-2 surface to 240 Wm-2 "theoretical surface" is 150Wm-2 of which 50% is solar energy absorbed above the "surface".  So if the "surface" is actually the atmosphere, then there would be no "Greenhouse effect".  This is the reason I stress "surface" in most of my posts.  Which "surface" or frame of reference you choose impacts the budget. Since the "surface" is just attempting to maintain the energy already absorbed by the sun in night mode the actual "greenhouse" portion of the atmospheric effect requires a little more attention to detail.

The first detail is the planetary boundary layer(3) which ranges from a 100 meters or so to a few kilometers, or roughly the bottom of the clouds.  This "skin" layer depends on turbulent mixing.  Over the oceans without buildings and terrain features, the planetary boundary layer is more stable.  The combination of higher thermal mass and a more stable planetary boundary layer reduces the diurnal temperature change. During mainly the day period, solar energy causes evaporation estimated to be 88Wm-2 for a 24 hour period or 176Wm-2 for the 12 hour Day period.  Along with the latent cooling associated with the evaporation there is an estimated 24Wm-2 of sensible/convective cooling for the 24 hour period and 48 Wm-2 for the 12 hour period.  Not all of this surface cooling occurs during the day so using the day night model you have to be a bit careful.  Note; that Stephens et al use the terms Latent Heating and Sensible Heating, indicating the importance of the impact on the lower atmosphere aka the planetary boundary layer. 

Including solar absorbed, the atmosphere gains 150Wm-2 solar, 176Wm-2 latent and 48Wm-2 sensible/convective during an approximate 12 hour period totaling 374 Wm-2.  Including the ~ 20 +/- 4 Wm-2 Stephens et al. estimate for atmospheric window energy or energy from the surface that does not interact with the atmosphere, there is a true surface energy of 394Wm-2.  This balances the Stephens et al Budget at the "surface" for Day mode.   K&T managed to double the atmospheric window energy by confusing "surfaces" in their day and night Earth Energy Budget cartoon and have to reduce latent and sensible in order to "close" their budget which amplifies the impact of the "greenhouse effect" in error. This is an important point, with the approximate total solar related energy absorbed by the atmosphere is equal to ~374 Wm-2, the "surface" contribution could be increase this by the  approximate atmospheric window value to ~394Wm-2. 

Now we have a completely confusing mess, Sky Dragons on one hand saying there is zero "greenhouse effect" and mainstream scientists doubling the "greenhouse effect".  Both sides wander down rabbet holes trying to justify their positions.  Depending on which "surface" the combatants select, they can come close to "proving" their points.  While neither side would agree with my day and night explanation, the nonaligned might find it beneficial, so let's look again at the basic numbers.

480Wm-2 Day must equal 480 Wm-2 Night is equivalent to the 240Wm-2 in equals 240Wm-2 out since both equal zero.  We are just assuming that day stuff mainly happens in the day and night stuff mainly happens at night.  With that 150Wm-2 would be the day atmospheric effect which would equal the night 150Wm-2 "greenhouse effect".  That results in a 24 hour averaged 75Wm-2 of each effect.  If the surface energy is 390Wm-2 averaged for 24 hours, then the "Greenhouse Effect" produces 75Wm-2 of the ~390Wm-2 leaving a no greenhouse effect surface energy of 315Wm-2.  Since 390Wm-2 is the energy of a surface at 288K and 315Wm-2 the energy of a surface at 273K, the "greenhouse effect" produces a warming of ~15C degrees.  Not 33C but 15C degrees and most of that due to water vapor with a caveat.

Without some variety of dry greenhouse gas the water vapor portion would reduce greatly which can lead to some justification of the 33C, but at the same time clouds would decrease changing albedo so the 33C is not all that convincing if seriously scrutinized.  Instead consider Steve McIntyre's at ClimateAudit revival of Guy Callandar's model of the greenhouse effect that actually agrees with current conditions. 

In Steve's post he plotted his model over the original graph by Callandar published in 1938.   As long as you start at some relevant point, CO2 could produce 50% of that 15C of greenhouse warming.  Without any CO2 there would still be other dry greenhouse gases like CH4, O3 and various other traces that would have some impact.  Even with Callandar's model the "surface" can still be questioned.


Consider all the energy transferred to the atmosphere again, 150Wm-2 solar, 176Wm-2 latent and 48 sensible for a total of 374Wm-2.  Ignoring the atmospheric window and the estimated radiant you can compare that total with the estimated Down Welling Longwave Radiation (DWLR) of ~340 Wm-2.  The difference 34 Wm-2 and considering the equivalent temperature for each energy value a temperature difference of 6.7C degrees.  From a "surface" actually located in the atmosphere approximately near the planetary boundary layer there should be a diurnal temperature change of roughly 6.7C with a change in energy of ~34 Wm-2.  That "surface" would have a "sensitivity" of 5.06Wm-2 per degree or 0.197C/Wm-2. If CO2 equivalent dry gases produce 4Wm-2 of forcing per doubling, the result would be ~0.8C of warming at the "surface" located near the planetary boundary layer.  That is about half of the ~1.6C per doubling estimated by Callandar.

 If you compare the radiant emissions OLR - DWLR from the Stephans et al. budget the net is 53 Wm-2 with up to 9Wm-2 of uncertainty which is 19Wm-2 greater than the diurnal change estimated.  Including the atmospheric window estimate of 20 +/-4Wm-2 the rough estimate for the Planetary Boundary Layer fits well with the Stephens et al. budget without estimating the surface OLR before hand.  It should fit because this is the real "Greenhouse Effect".  Water vapor transfers energy from the true surface to the Effective Radiant Layer (ERL) where the radiant properties of the atmosphere impact the rate of heat loss.  Increasing the dry well mixed greenhouse gas composition of the atmosphere will change the diurnal temperature range.  Since most of the energy contained in the atmosphere is due to solar energy absorbed directly and transferred by latent surface cooling and convection, adding ~4 Wm-2 to a total of 374Wm-2 has a nearly immeasurable impact at the true surface but ~0.8C above the planetary Boundary layer.   However, ignoring latent cooling of the surface, that 4Wm-2 would produce ~0.8C degrees of warming which combined DTR impact the ~1.6C estimated by Callandar. 

Effective Radiant Layer is a somewhat confusing term required by a somewhat confusing problem.  240Wm-2 (255K) is not an isothermal layer that envelops the entire surface of the Earth.  It cannot be a ideal radiant layer so it must be averaged for an effective value.  Since H2O, CO2, O3 and all the other gases that emit larger amounts of radiant energy have their on temperature relationships in the atmosphere they would each have their own effective radiant layers.  Stephens et al. by using the terms latent and sensible heating allow the selection of the lower atmosphere for either "surface" or ERL depending on your inclinations.  With 374 Wm-2 total atmosphere absorption in the Day mode and close to 405Wm-2 total absorption at the physical surface in day mode, combined  they are providing an approximate Tmax of 290.7K degrees and a Tmean of 288.7K implying a Tmin of 286.7K or a diurnal temperature range of ~4C degrees at the true "surface".


This sensitivity range, 0.8 to 1.6 C per CO2 equivalent doubling, would most easily be seen in the "global" diurnal temperature range.  Now the Climate Scientists have a problem.  "Global" average surface temperature is based on the average of land surface measurements of the maximum and minimum daily readings at various altitudes compared with estimates of sea surface temperature based on measurement below the true sea surface.  The diurnal change in SST is estimated to be ~1 C degree for ~71% of the "surface" and the land "surface" diurnal temperature range is estimated to be 11C for ~29% of the "surface".  That would produce an estimated "Global" Diurnal temperature range of 3.8 C degrees, about equal to the the range estimate based on "surface" temperatures but lower than the estimated 6.7 C degrees based on net surface radiant emission.  Why?

Other than the uncertainty included for the individual estimates, because a portion of the "surface" is neither land nor sea, it is sea ice.  About 20 million kilometers squared of the "surface"at any give moment is sea ice.  That is ~4% of the surface and a large part of the uncertainty.   Another part of the uncertainty is that nearly 48 million kilometers squared in winter is dark.  Having no diurnal temperature, the increase in CO2 equivalent gases would not have the same diurnal impact.  What impact there is would be dependent on the atmospheric circulations that bring energy to the polar regions which can result in in-phase or out of phase polar warming and cooling.  Yet another issue is the higher the altitude the lower the atmospheric effect.  By not having a fixed surface for reference the effective surfaces or radiant layers require considerable manipulation when calculating and "average" surface temperature and diurnal temperature range. Considering all these sources of uncertainty, 3.8C to 6.7C is not a bad estimate for "Global" diurnal temperature range considering either the true surface or the planetary boundary layer can be the effective surfaces.

The Climate Scientists picked the wrong metric and the wrong "surface" to monitor changes in the "Greenhouse Effect" while the Sky Dragons picked the wrong "surface" to disprove the "Greenhouse Effect".  That leaves the current debate in an unbelievable state of confusion.  Thankfully, there are still real scientists like Graeme Stephens that actually know how to add and old masters like Guy Callandar who knew how to keep it simple.  

The real story is likely to be told when the Berkeley Earth Surface Temperature project produces their version of "Global" diurnal temperature change with their combined land and oceans data set due on a climate blog near you hopefully in time for Christmas.  Note: the Stephens et al budget drawing and BEST land only DTR charts were purloined from  Here and Here.  Both are good links to follow.

Based on the data available, the BEST land only DTR, the range decreased from the start of the instrumental record until circa 1985.  Increasing DTR is not indicative of GHG forcing as WMGHGs would reduce the rate of heat loss during the Night mode of operation.  During the time period used to exploit 'Greenhouse Effect" impacts, there appears to be a substantial non-GHG related impact either not anticipated or at least poorly explained by the Climate Scientists in charge of public relations.  Land area is predominately in the Northern hemisphere where "most" of the warming is occurring and according to the BEST DTR, that "most" of the warming likely has causes other than WMGHGs if the "Greenhouse Effect" is properly explained.

While the satellite temperature record is short, it agrees well with the surface temperature record.  Comparing the temperature response by hemisphere the trend in the Southern Hemisphere is small in comparison with the Northern which has an increasing DTR inconsistent with impacts expected by WMGHG.  The period selected to promote the urgency to mitigate CO2 emissions just happens to be the maximum slope perfect for "selling" urgency.

If you were not "selling" urgency you might select a longer time frame to so that the impact of WMGHGs is less than half of the projected amount being "sold" by Climate Scientists that picked the wrong metric, doubled impacts and used poorly defined frames of reference.  The change in the slope of the "scary" northern hemisphere shifted circa 2000 which is requiring the Climate Scientist Mitigation Sales Staff to shift their metric to Ocean Heat Content which has increased at an "unprecedented" rate during the same period of maximum slope used initially to "sell" their cause., but with a lag to prolong "effect".

Steven McIntyre replicated Guy Callandar's model and compared it with the original "surface" temperature metric and one of the many Climate Models that are diverging from reality.  It appears that Climate Science, at least the science that is "sold" to stimulate a need for urgency, has regressed instead of progressed since 1938.  While the public hears the need for urgency, less publicized Climate Scientists like Graeme Stephens and company that can add correctly tend to agree with the model produced in 1938 which is outperforming the carefully "tuned" current era of climate models. 

In conclusion, the Sky Dragons are wrong, there is a greenhouse effect.  The Climate Science Urgent Action Sales Staff are wrong, the impact of CO2 equivalent gases is less that half the amount they are trying to sell.  There will be an impact due to CO2 equivalent gases in the range or 0.8 to 1.6 C based on the best available data we currently have indicating that "most" of the warming is due to long term recovery and solar energy absorbed in the atmosphere with CO2 providing ~25% of the impact plus amplification of the other climate influences contributing to the current Pause/Stall/Halt in global surface temperature warming described quite well by Syun-Ichi Akasufo of the university of Fairbanks.

Hat tip to BishopHill.

I am sure this post can use some proofing which I may or may not do in the future.  Until then have fun.  

(1) Wikipedia link on Stefan-Boltzmann Law.

(2) Wikipedia link on Carnot Efficiency. Note that Maximum and minimum temperatures should be used.  Average temperatures for source and sink are just a rough estimate. 

(3) Wikipedia link on Planetary Boundary Layer.

Principa Scientifica and the Kiehl and Trenberth Screw Up

Principa Scientifica is the home of the Sky Dragons, the total deniers of radiant atmospheric effects, or almost anyway.  What stuck in their craw was the idea of Down Welling Longwave Radiation (DWLR).  That is not a bad thing, the concept of DWLR was pretty much confused and abused by the Kiehl and Trenberth Earth Energy Budget Cartoons. 

First for the guys already calling me nuts, the early K&T budgets contained an error that impacted their estimation of DWLR.  The error of ~18Wm-2 was in atmospheric absorption in the Atmospheric window caused by their choice of "surface".  Water in the form of ice and droplets has a different radiant spectrum than water vapor.  That means most of the K&T error is associated with clouds which is still the largest uncertainty in the atmospheric system anyway.  In the newest of the Trenberth co-authored Earth Energy Budgets, that error was corrected and referred to as a "minor adjustment".  They admitted their error rather quietly, but they did admit their error.  They did not change their Cartoon though.

This is the cartoon from their most recent TFK 2009 paper.  You can see that the 40 Wm-2 from the "surface" appears to be passing through the clouds.  It doesn't pass through the clouds, it interacts with the clouds causing an approximately +/- 18 Wm-2 uncertainty in the surface of origin of the atmospheric window radiation.  The 0.9 Wm-2 net absorbed at the bottom should then be 0.9 +/- 18 Wm-2 which is a sizable margin of error.  If they are half as intelligent as they think they are they would know that.

Their, Trenberth, Fasullo and Kiehl, insistence on perpetuating the myth of confidence was noticed by several of their peers including Dr. Graeme Stephens who published a rebuttal Earth Energy Budget.

In the Stephens et al. Earth Energy Budget Cartoon the "All-Sky" Atmospheric Window estimate is 20W,-2 +/- 4 Wm-2 which is a more correct estimate and the Surface imbalance is 0.6 +/-17 Wm-2 reflecting the actual uncertainty.  The Stephens et al. Earth Energy Budget was discussed on Dr. Judith Curry's blog Climate Etc. and contains a link to the original version.

Since the Stephens et al. is a rebuttal, they used the same basic form used by TFK which still produces a misleading picture of what DWLR actually is supposed to be.

For example there is 26.6 +/-5 Wm-2 shown as DWLR from clouds.  There is ~75 Wm-2 of solar incoming energy absorbed by the atmosphere primarily by water/ice/water vapor.  That would have a net positive impact on the surface energy, technically being DWLR but not from an Out Going Longwave Radiation (OLR) source.  There would be OLR absorbed by the water/ice/water vapor as well which creates a bit of confusion. A better way would be to define the "surface" as the average cloud base so that DWLR has an actual meaning in physics.  Once latent and convective transfer are reduced enough that there can actually be radiant energy transfer isotropically, then you would have a meaningful DWLR value of approximately 220 Wm-2 +/- 20 Wm-2. 

For some reason, the critics of the Sky Dragons don't bother to point out that Principa Scientifica papers challenging crap are by default crap and that they should first note that TFK are not a valid scientific references and just move on since the minions of climate science don't have the gonads to criticize their own crap, like the TFK pseudo-scientific nonsense.   That leaves the rest of the world stuck with two groups of idiots that can't get past square one in what should be a constructive scientific debate.

What both groups should realize is that Climate Science is a field in its infancy with a lot of obsolete references that need to be weeded out and replaced with better estimates with realistic degrees of uncertainty.

Principa Scientific could take that first step, but don't hold your breath.