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Monday, August 5, 2013

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.

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