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Sunday, September 29, 2013

The Tropical Oceans and Solar Forcing

This is a basic sketch of the complex interactions near the tropical ocean surface.  Solar energy is absorbed in the Atmospheric Boundary Layer and the surface with some penetration to depth.  The ABL has a short time constant Tau, while the ocean surface has a longer time constant.  The ABL time constant after interaction with the surface was estimated to produce a roughly 9 month lag (Spencer et al.) and the upper ocean mixing layer a longer lag of approximately 8.5 years (Schwartz et al.).  The deeper ocean has variable lags on the order of decades to centuries.  Since there is considerable asymmetry, the combinations can become quite complicated.  In the tropics, volcanic and CO2 forcing have less impact with solar forcing and cloud response the stronger forcing.

Using the G. Kopp TSI reconstruction available at SORCE spliced to the TSI satellite composite the Comp. Kopp series was constructed as shown and averaged into a 8.5 year trailing series to simulate the ocean mixing layer impact plus a 37 month centered average with 9 month lag to simulate the surface ABL interaction.  The 8.5 year and 37 month series where combined with 1 and 0.5 scaling factors respectively.  Alternating solar cycles are enhanced with this combination producing a Hale Cycle (~21 year) pulse that match the ERSSTv3b tropics (20s-20N) SST time series.

With enough degrees of freedom you can make about any fit you like, but this particular fits indicates that a "pause" in the tropical oceans may have started as early as 1980 had there not been volcanic noise. 

Wednesday, September 25, 2013

How to Deal with Recovery from the Little Ice Age?

The Little Ice Age wasn't a true ice age since there was no massive glaciation, but it is generally recognized as a cooler than normal period, mainly in the Northern Hemisphere, but with some global impact.  The northern hemisphere is more sensitive to most types of climate forcing and feedback mainly because between 30N and 90N there is roughly a 50-50 split between oceans and land mass.  In the southern hemisphere from 30S to 90S there is an 85 to 15 Split with a large amount of the land mass poleward of 70 degrees south.  Oceans tend to dampen response to climate forcing and with little mid-latitude land to hold snow, there is less feed back.  Because of the differences in land/ocean ratio, the northern hemisphere above latitude 30 degrees, which represents about 21% of the global surface containing about 20% of the global oceans and about 48% of the global land mass is much more variable as far as temperature goes than the rest of the world.  Global Warming is supposed to be the issue but due to the 30N-60N sensitivity, regional changes can have a pronounced global impact. A large portion of the global population lives and farms in the mid latitudes of the northern hemisphere so it is worth a little special consideration, but it is a small fraction of the global climate picture. 

Since the Berkeley Earth Surface Temperature was published it has become a bit of a default "alarmist" data set because the land surface temperatures are amplified.  The revised BEST website have even made a point of showing how much the mid northern latitudes have amplified warming, something that seems to be a bit of a surprise to climate modelers, and the Arctic polar amplification which is a bit less than estimated by the climate modelers.  BEST has even provided comparisons of their data to various models showing quite a few differences that should be addressed.  A lot of the discrepancy is likely due to recovery from the Little Ice Age and "hyper" sensitivity of the  region to volcanic and aerosol forcing.  Without a better estimate of the LIA impact the situation is not likely to improve.

"Globally" the LIA is estimated to have produced approximately 0.9 C of cooling peaking around 1700 or 1850 AD depending on the source.  The slide into the LIA started around 1400 AD depending on region and today's global temperatures are approximately the same as prior to the LIA.  The BEST land data has warmed more than 0.9C and the North Atlantic ocean from 20N to 70N used as the AMO reference has also warmed by 0.7 to 0.9 C depending on your choice of minimum.  Using 0.9 as a first estimate of the LIA "global" impact, I removed that portion from the BEST global temperature trend.

This is what that looks like.  The smoothing is 17 month moving average run twice.  Using the BEST combined CO2 and Volcanic forcing estimate available on their Summary of Findings page, with "sensitivity" set to the No Feedback estimate higher end of 1.5 C per doubling I included a rough fit.  The fit leaves a bit to be desired, but is just intended as a reference to no feedback sensitivity plus estimated volcanic forcing. As you can see though, the volcanic forcing tends to do its own thing which could be due to inaccurate estimates or other factors.  Climate can have lots of other factors.  Solar is another fact that once upon a time was a major factor.

Back in the day you would see plots of Solar Sunspot Numbers (SSN) that were scaled to show how the sun drove climate.  That changed in the late 1960s along with a lot of other things in society.  Now that correlation is nearly meaningless because the new climate geniuses decided that all forcings are created equal.  A more efficient application of energy has never been on the same level as a less efficient application until climate science gathered steam.  The Kopp, G. TSI reconstruction is available from LASP Colorado which I have converted to anomaly using a 1950 to 2010 base line.  That puts 1700 AD at a 1 Wm-2 deficit or negative imbalance without adjustment.  Since solar is "applied" primarily in the equator region where there are plenty of oceans to suck up the energy, the actual imbalance allowing for atmospheric scattering is about 0.8 Wm-2.  The geniuses would use TSI/4, considering a perfect bowling ball surface getting 240Wm-2 on average instead of the steamy tropics that get closer to 1000Wm-2 peak on average.  Because of the averaging, solar just doesn't have the umph it had back in the heyday of thermodynamics.  Still, over 50% of the surface varying from 1000Wm-2 peak to 999Wm-2 peak is a small variation of only 1 Wm-2 which just happens to be about the magnitude of the current energy imbalance.

Volcanic forcing also impacts the incoming energy more than the outgoing and unfortunately impacts the northern latitudes more than the southern making things a bit complicated.  That creates a hemisphere imbalance that involves inconsistent atmospheric and ocean transport of energy on extremely difficult to model time scales to restore. 

When I add the Best volcano forcing estimates with a 1.0C CO2 forcing to the Solar, I get the comparison above.  Still not perfect and likely it will never be since there would be albedo and more of the other factors to consider.  Things do appear to be moving the right direction in any case.  CO2 has some impact close to its no feed back estimates, Solar appears to have a larger than currently estimated, more like formerly estimated impact and the volcano data still leaves a lot to be desired.  I could play with the scaling to get a better fit, but there is really not much point.   It does look like I could remove the BEST detrending since the NH is so much more sensitive.  I will leave that for later.


Here it is with no detrend of BEST and the Solar scaled down to 0.8.  Solar scaled to 0.8 would be about 0.4C for the global oceans which is a bit higher than most estimates but not outrageously high.  Due to land amplification, it is a better fit to BEST.

I just thought I would throw this out there for the Solar and Little Ice Age fans.  Y'all can pretty it up any way you like. 

Tuesday, September 24, 2013

Attack of the Lowess Form

Tamino, the proprietor of the Open Mind blog has a knack for twisting statistical reality.  Despite its limitations, Tamino has grown fond of Lowess or Loess Smoothing aka Local Regression

"LOESS makes less efficient use of data than other least squares methods. It requires fairly large, densely sampled data sets in order to produce good models. This is because LOESS relies on the local data structure when performing the local fitting. Thus, LOESS provides less complex data analysis in exchange for greater experimental costs." per the Wiki link. 

Okay, what the deal is Tamino got wind of someone saying the "Global" warming was as bad or worse prior to 1940.  There was a little ice age after all and things had been thawing out slowly for some time according to pre "Global" Warming, Climate Change, Climate Disruption, Carbon Pollution, climate scientists got involved.  Getting rid of the little ice age required a bit of novel statistical methods and even then there was still a nasty ~1C of dip in the way of serious Anthropogenic impact due to the Greenhouse Gas Effect theory.

As the Wikipedia quote states, Local Regression is not the first tool in the box that one should dig out for data that has already been averaged, scaled, weighted and other wise combined into a simple time series.  No method can predict the future of the time series so it is best to leave something to the imagination.

So here is a simple look at the situation.  Using the ERSSTv3b data for the normally liquid portion of the oceans, 1910 to 1940 had a pretty serious up tick in temperature. Since 1910 was about the coldest point in the instrumental data, the series uses 1910 to present as its baseline which you can easy see results in the zero mean blue line.  1910 to mean is about the same as 2013 to mean.  I could pick 1998 and get a little more up tick, but not much, the two periods are still about the same.  The slope from 1910 to 1940 is greater than the slope from 1976 to 2013 and would still be greater than 1976 to 1998 or any other point using 1976 as a starting point.  It may be somewhat inconvenient, but that is just the way it is.  There is no multiyear moving average, Loess smoothing or anything other than the annually resolved data from ERSST. 

I could use just the northern hemisphere data in the light red to juice the slope a little, but that didn't really move above the mean until 1983.  Then if I use less than 50% of the globe, I can get a little scarier.  By including the land I could get the slopes closer, but the difference between 1910-1940 and 1976-2013 just isn't enough to write home about, possibly a tenth of a degree with a margin of error greater than the difference.  But it is nice to see just how Loess some will stoop to continue the "Global" warming tradition. 

Sunday, September 22, 2013

CO2 Signature?

There are still quite a few people that believe CO2 has not impact what so ever on climate.  It does, but since CO2 is a bit player you have to really hunt of a hint of a CO2 signature in all of the noise.  CO2 also has a greater impact is the dryer portion of the atmosphere and over land mass since that is a drier portion of the surface.  To dig out a "signature" you can difference the satellite temperature data for the land and ocean.  That removes a bit of the noise that just a part of climate.  Then using a satelite era baseline with the least noise, 2000 to 2012 for example for both the land-sea difference and Mauna Loa CO2 you can compare the slope.  0.8 C should be the CO2 impact based on the Kimoto energy balance method so here is the comparison.

Is that definitive proof?  There is no such thing, but the expected trend is in the expected data using a reasonable, at least to me, method. 

Saturday, September 21, 2013

Surface Albedo and the Liquid Water Greenhouse Effect

The Earth Radiant Energy Budget (ERBE) monthly albedo for the period 1986 to 1990 is shown above.  Dark blue is low albedo and dark red high albedo.The red region in the southern hemisphere begins approximately in the 60S latitude range.  In the northern hemisphere the higher albedo starts closer to 50N latitude.

Due to land mass in the NH and winter snow cover the season variation in albedo becomes significant near latitude 40N an peaks near latitude 60N.  According to the Climate Data Information website, that change is roughly 0.3 or a 30% seasonal change.  In the southern hemisphere the more critical region, 40S-60S is mainly ocean and there is little seasonal variation.  Sea ice extent is part of the seasonal albedo change, but due to snow cover on land, small in comparison.

There is nothing particularly astonishing about snow and ice cover albedo being a major factor in climate change.  It is after all the more likely reason Earth has the currently glacial/interglacial periods and why the 65N solar insolation variation in the Milankovitch cycles is considered the most likely trigger for deglaciation which would have a large impact on "surface" temperature, but not ocean energy necessarily.  To get an estimate let's have a little thought experiment. 

What if there were no land mass to hold the snow and ice at a higher altitude where it is harder to melt in season?  With liquid oceans, the northern hemisphere albedo would be the same as the southern and if it weren't for the solar precessional cycle the surface albedo would still be high starting in the 60 to 90 latitude band at both poles.  That is due to the reflection of solar insolation a the low angles of incidence off of water.  If the oceans where perfectly calm, the surface albedo would be very close to the 25% to 30% range.  For fresh water, the critical angle of reflection is close to 53 degrees.

This figure from the Wikipedia article on total internal reflection is a good illustration of what needs to be considered for a calm mirrored surface.  Clouds scatter sunlight allowing solar insolation to be absorbed at lower angles and wave action increases the effective angle as well, increasing the effective critical angle to roughly 64 degrees or the Arctic circle latitudes.  Since the oceans are capable of holding the most energy, a water world should have more total energy than a mixed land and ocean world and a higher average temperature. Assuming there is no precessional cycle and ignoring cloud albedo since it both reflects and scatters energy, you can estimate the amount of energy likely to be totally internally reflected in the oceans.

The average energy available at the surface from latitude 60S to 60N would vary from a peak of 100% at the equator to 50% at latitude 60.  From horizon to horizon at the equator the insolation would vary from 0 near dawn and dust to 100% at noon.  The total average insolation experiencing total internal reflection would be greater than 50% of the total insolation available while the average for the entire surface would be exactly 50% neglecting scattering and refraction in the atmosphere.

If you consider only the area likely to experience total internal reflection you would have a spherical cap.

The energy entering that spherical cap would be the 24/7/365 energy entering the oceans.  You could change the rate of rotation, but the energy in would always be equal to the energy entering that cap area where it would be totally internally reflected and leave based on the thermal properties of the surface boundary.

For the cap, h would be the r*cos(60) and a r*sin(60), with r~6370km; a=6370*.866=5516km and h=3185km  The area would be pi()*(a^2+h^2) or pi()[(5516)^2+(3185)^2]=62.3 million square kilometers.

With 1361 Wm-2 of solar insolation available the average insolation for the cap would be 0.866*1361=1178Wm-2.  Correcting for average surface albedo of approximately 0.1, the approximate cap insolation would be 1060Wm-2 which with a total global area of 510msqkm would be ~130Wm-2 average energy totally internally reflected.  If you allow for the actual area between 60S and 60N of ~440msqkm, the average insolation would be 150Wm-2.  So you have a peak insolation of ~1060Wm-2, a diurnal average of 130-150 Wm-2 and a day only average of 260-300 Wm-2 that can be totally internal reflected versus a "global" average of 1361/4=340Wm-2 corrected for approximate "global" albedo or 0.30 results in 340*(1-.3)=238 Wm-2 for the full sphere.  Using the higher estimate, 150/238=63% of the energy available is likely to be totally internally reflected or fully absorbed and 37% likely reflected.

The 37% reflected in this case would be equivalent to the geometric albedo. Geometric albedo depends on the type of surface.  With water having a critical angle for total internal reflection it would also have a narrower range of angles for emission of energy.  A more up/down orientation.

This table from the linked Wikipedia article lists estimated bond and geometric albedos for objects in our solar system.  You will notice that there is considerable differences between Bond and Geometric albedo and that the quick estimate for Earth oceans agrees rather well with the table value.

If you assume that the entire surface of Earth can be estimated by using the Bond albedo but up to 63% of the energy is subject to total internal reflection requiring geometric albedo, you could have a significant error. In Earth's case .37/.30=1.23, up to a 23% error which could be called the liquid water greenhouse effect.

Friday, September 20, 2013

Seasonal Impact on Baseline Selection

I have taken the ERSST3 regional data, Tropics, 20N-90N and 20S-90S and used a short 2000 to 2012 baseline just to show how baseline dependent the temperature data can be.  The 1950-1980 "normal" baseline period is circled.  Just prior to 1950, SST data took a 0.2-0.4 C nose dive and these three regions shifted phase relationships.  Except for the period from ~1955 to 1998, the regions are close to be in the same phase.  Is the drop in the 1940s real?  Dunno, but the data is what it is, but using this baseline, the 20N-90N SST caught up to the rest of the oceans amplifying the most recent warming.  Using the southern ocean data 20S-90S though, there is a more consistent temperature rise from ~1910 with a hint of a peak value being approached, but is 2000-2012 the right baseline?

The Reynolds optimally interpolated SST data may have some clues.  Above it is converted to anomaly using the 2000 to 2012 baseline and seasonal cycle removed.  The variability in the NH data 20N-90N is much greater outside of the baseline range.

If you use the early part of the Reynolds SST data the variability shifts to the end of the record.  The most obvious cause is the volcanic activity in the early part had a greater impact on the northern oceans which have a smaller area and transfer energy to a much larger percentage of land mass.  Volcanic sulfate have a greater impact on radiant forcing than atmospheric forcing so the impact is greater in warming season.  The data has a seasonal baseline dependence that impacts "natural" variability.

Anyone working with the data knows this and knows that baseline selection impacts attribution, but not very many explain why they select a baseline only that others are cherry picking if they select a different baseline.

Odd that?

UPDATE:  The seasonal sensitivity can impact which year is the warmest EVAH.  That is always great fun.

Tuesday, September 17, 2013

OMG! It is Worse than We Thought!

With the Climate Change/Disruption/Carbon Pollution thing falling apart, the faithful are growing ever more desperate to find some link to cling to.  A couple of years ago I mentioned Land Amplification.  Land has a lower specific heat capacity than water so it tends to amplify warming in the oceans.  The oceans provide the energy for the planet's "night mode" of operation while water vapor and CO2 in the atmosphere regulate the energy leakage.  Unlike CO2, water vapor transports a lot of energy.  CO2 just interacts with the available energy since it is not a condensable gas at normal atmospheric pressure.  Specific heat capacity aka thermal mass is where the energy is, so follow the thermal mass.

Because land amplifies the ocean energy in night mode and solar in the day mode, land warms and cools much faster than the oceans.  Land temperature makes up only 30% of the global "surface" temperature average, but because of the amplification factor it has ~ 60% impact.  Temperature is not a particularly good indication of energy without a reference thermal mass.

Trying to show the brain dead zombies that specific heat capacity has to be carefully considered is like trying to teach a dog to use the toilet.  I am sure it is possible, but why bother, get a cat.

So in the chart is have the ERSST "surface" temperature data for the northern hemisphere oceans and the mid-latitude land region where most of the agriculture, industry and human beings lived happily until 1979.  In 1979, people started realizing they were screwing something up and set to start fixing the problems.  Instead of looking at the obvious, water, they had to get more creative.  The chart shows that the difference in specific heat capacity directly base on water is a significant contributor to "global" warming.  1.8 Joules per gram is the rough specific heat capacity of moderately dry soil.  If you reduce the moisture content of soil it gets warmer quicker but holds less total energy.  Climate is all about changes in the rates of change, low specific heat capacity changes the rate of change.  Then should you use the maximum temperature and minimum temperature average, you get a bigger change than you would if you measure the mean temperature of the soil a few inches below the surface.  The ocean "average" surface temperature is based on the "average" energy below the surface.  Mixing the two creates a fruit salad.

The Minions of the Great and Powerful Carbon somehow got it in their heads that water vapor increasing will amplify the impact of CO2 in the atmosphere.  Way up in the atmosphere where there is just water vapor and just CO2, they are both effectively non-condensable gases so that is true, but near the surface water has a starring role as a temperature regulator.  If there is more surface water, there is more thermal mass, there is less temperature change for the H2O and CO2 in the dry part of the atmosphere to interact with, i.e. reduce energy leakage. 

Now it gets to be really fun.  You can completely blow off radiant physics in the lower atmosphere, between the surface and the cloud/water vapor saturation boundary aka the Atmospheric Boundary Layer (ABL) because the radiant net energy flux is small relative to the latent and sensible energy flux.  The "global" average net radiant flux at the true surface is ~20Wm-2 of a total of 100+ latent and 35+ sensible.  20/135=.148 or approximately 14.8 percent of the surface outgoing energy impact is radiant and 85.2% is just plain old thermodynamics.  Because of confusing, the Head Minions of the Great and Powerful Carbon incorrectly estimated that to be ~30% or twice as much.  Ya think they are in a rush to correct that mistake?

I don't think so.  Now they are on about how the tail, low specific heat capacity air mainly centered over the mid-latitude is magically wags the Dog, causing warming in the southern hemisphere oceans pretty much like Northern Hemisphere Chlorofluorocarbons magically shot to the Antarctic Ozone layer.  They are preparing an exit strategythough,

Regardless of whether or not scientists are wrong on global warming, the European Union is pursuing the correct energy policies even if they lead to higher prices, Europe’s climate commissioner has said.

h/t WUWT

So it doesn't matter how wrong they are, Minions will stay the course.  Priceless.

Tuesday, September 10, 2013

Just for Grins - How not to Boil Water

The boiling oceans due to down welling long wave infrared demon radiation from hell myth will not die!  It is pretty funny.  There are still "experiments" mainly thought experiments because anyone actually thinking would do an experiment before commenting, being mentioned on the internet, to "prove" that DWLR heats water.

Dr. Strangelove (his chosen alias) recommended one that was pretty reasonable and easy to do at home should you become seriously bored.  Slightly modified the experiment goes like this. Take a glass of water filled to an inch below the rim and set an iron on top.  Most folks have water, real glass glasses and access to a dusty electric clothes iron.

Now Dr. Strangelove defined two hypothesis, 1) the water would evaporate and 2) the water would boil.  I recommend 3) you will become bored to death watching not much of anything happen.

So let's look at a little thermo.  Each gram of has a specific heat capacity of about 4.2 Joules/(gram*K) if you have a large liter glass or bowl, you can fill with one liter (1000grams) of pure water and have about a half inch of room at the top.  Assuming room and water temperature are about 25C degrees, you would need to add about 4.2 J/(gK) times 1000grams times 75 K degrees to raise the water to its boiling point which is a total of 315,000 Joules or 315 KJ.  That is all the energy required provided you have 100% ideal heat transfer just to get the water to the boiling point.

The world in a less than ideal place so there will be issues.  First would be convection, second would be evaporation and third would be radiant heat loss.  The glass at 25C just sitting on the counter minding its own business is exchanging energy with its surroundings.  If the water is at 25C and the air temperature at 25C the net transfer is near zero, but there is still some water evaporating unless the glass is sealed or the room is at 100% relative humidity.  Each gram of water that evaporates has to absorb about 2260 Joules of energy in order to change phase to water vapor.  As the water warms the saturation vapor pressure increases, increasing the rate of evaporation and each gram of water lost takes with it 2260 Joules plus 4.2 Joules for each degree it is above the initial 25 C degrees.  Now you can figure the total energy required to evaporate all the water.  2260 times 1000 plus the 315KJ just to sensibly raise the temperature to the boiling point.  That is a total of 2575 K Joules boil all the water off.

It actually takes less energy to get the water to the boiling point than it takes to evaporate all of the water provided convection and evaporation is limited.  The main concern is rates of heat transfer or thermal efficiency. 

Heating from above the surface is counter the direction of convection thanks to gravity.  Warm moist air rises and the warmer the air the more moisture it can contain.  Since we have an initial temperature of 25C(298K) and an iron we can assume is approximately 200C(473K) on the cotton setting, the maximum heat transfer can be estimated using Carnot Efficiency = 1-Tc/Th= 1-298/473 = 0.37 or 37% of the energy under ideal conditions is the best you can hope to transfer.  Using the Stefan-Boltzmann law with a source temperature of 473K degrees the effective energy under ideal conditions would be 2838 Wm-2 and the sink energy at 298 K being 447 Wm-2 the difference is 2391 Wm-2 times 37% equals  884 Wm-2 ideal Carnot efficiency transfer.  That efficiency decreases as the sink or liter of water temperature increases, so the maximum energy that the water can be raised to based on boiling at 100C (373K) 1-373/474=0.21 or 21 percent efficiency 368 Wm-2 energy transfer using the Carnot efficiency.

Imagine that instead of radiantly heating from over head, we can immerse the iron in the water.  The iron is rated at about 1000Watts or 1 kWh which converts to 3,600,000 Joules per hour.  The iron as an immersion heater could take "as little as" 60(2.575/3.6)=43 minutes to boil out the water where radiantly, under ideal conditions, (2,575,000/368)/60= "up to" 116 minutes to "evaporate" the water out, since efficiency decreases with increased temperature in both cases, much less in the first though. 

The fun part about the over head radiant heat is that water vapor has a strong IR spectrum.  As water evaporates the moisture absorbs radiation above the surface locally heating the air and blocking a portion of the IR energy from reaching the true surface.  This localized warming stimulates convection reducing the effective surface pressure increasing the rate of evaporation. We have a situation where evaporative cooling is stimulated so the bulk of the water in the glass may not warm at all with direct long wave radiant heat applied, not just the "back radiation".  With cold water in the bowl and less water vapor in the air, the direct IR radiation should be more efficient and actually do a little warming. 

If you decide to do this experiment at home remember firstly that I am irresponsible er not responsible for any domestic situations that may result and that you should not be surprised if the water temperature in the glass/bowl never gets over the 30 to 35 C range without conduction being involved.  I haven't had the patience to do this experiment, so let me know how things work out and let me know if you find any typos/errors that hinder your scientific creativity.


Error Cascade - Murky Waters in Climate Science

Kyoji Kimoto published a paper, On the Confusion of Planck Feedback Parameters in the somewhat controversial journal Energy and Environment.  A pre-print pdf copy is in the embedded link.  Kind of ironically the paper discusses errors and conflicts in past peer reviewed papers that may have caused the Intergovernmental Panel on Climate Change (IPCC) to over-estimate the surface temperature impact of increase atmospheric carbon dioxide.  It is ironic because one of the peer reviewed climate science paper Dr. Kimoto selected for reference also had a major error which caused the good doctor's paper to have a major error.  That paper with the Kiehl and Trenberth 1997 (K&T97) Earth Energy Budget.  The K&T97 error was approximately 20 Wm-2 of energy from the true surface that was absorbed by clouds and due to the mixed phase that clouds can have when moisture is super saturated, is re-emitted in the water/ice spectrum at the top of the atmospheric boundary layer.  Since the atmospheric window energy in the K&T97 budget was assumed to be fixed, the error cause a number of other errors during the process to "close" the budget.

Those that have followed my ramblings know that this is one of my more fun "discoveries".  It is a simple "bookkeeping" error, not something that involves higher level math to "prove", just one of those things where you should be able to say check your numbers again and everyone agrees and redoes the basics.  Climate Science doesn't work that way.  The ability to add is not a requirement for a career in climate science.  To get these Prima Donnas to admit an error is like pulling teeth.  You have to have a "peer reviewed" paper on the potential discrepancy that may lead to a minor over estimation of potential impact and that paper has to run the gauntlet of good old boys defending climate science.  You get fired or belittled if you mention such controversial things as math errors and are limited to controversial journals like E&E which are controversial because the climate science cadre say so.

So aside from the Kimoto error in the paper and where the paper is published, is there anything to learn from this situation?  Pooh pooh occurs or no one is infallible. 

This is the error.  Stephen's et al. produced a revised Earth Energy Budget with more realistic ranges of error and included more surface atmosphere interaction than the simplistic K&T97 budget used by Kimoto.  For example surface evaporation is closer to 88Wm-2, atmospheric absorption is closer to 75 Wm-2 and "back radiation is closer to 335 to 345 Wm-2.  The "back radiation" value is higher because water and ice in the atmosphere and clouds absorb close to 20Wm-2 which is directly added to the "back radiation" .  Simply the "Greenhouse Effect" is about 20Wm-2 closer to saturation than previously estimated at the true surface of the Earth.  K&T Budgets have gone through a number of revisions, but that ~20Wm-2 error has never been corrected so the Planck response is still over estimated by about 50%.  A simple way of determining the approximate Planck response is just by comparing the more accurate "back radiation" value of ~340 Wm-2.  340Wm-2 is effective energy of a surface at 4C (277K) which would be the approximate average surface temperature of an "ideal" black body with the current "average" solar energy provided.

If you want to double check, you can use the cloud base as your "surface".  Energy in still has to equal energy out and the lower the specific heat capacity of the "surface" the less you have to be concerned with lags or delays. 
This is an example of using an atmospheric "surface" or frame of reference.  If the Night and Day values bother you, you can even do a day/night version.

Energy in day equals energy out.  There is a limit to the "precision" of course, but +/-17 Wm-2 for a whole planet is not bad and the All-Sky atmospheric window in the red box is still the number to watch, not 40 Wm-2 with no true indication of error provided in the K&T energy budgets.  Face it if your numbers are off by 50% on the most crucial part of the budget, it is pretty much useless.  At the Top of the Atmosphere (TOA) were no one lives, accuracy is nice, but who lives at the TOA?

With cloud impact being the single highest source of uncertainty, how can the cadre ignore such a major error?  It all depends on the cumulative assumptions made.  This is where things get extremely messy.

The first assumption is equilibrium.  Earth is at best a quasi-steady state system, there is diurnal temperature range, seasonal temperature range, decadal temperature range, pick any time frame and there is some "average" temperature range.  To make life simpler, the TOA, where ever that is actually defined to be, has an equilibrium requirement, Ein=Eout based on an "average" Ein of ~1361Wm-2 which varies by a little over 3 percent between winter and summer.  While that is varying, the surface albedo varies seasonally and cloud albedo varies seasonally.  With all this constant variation, what is "normal" or "average" is highly debatable.  The one thing that remained constant in the K&T energy budget is the 40Wm-2 window energy.  It is an assumption required to estimate an "equilibrium".  It just happened to be a poor assumption.

So let's compare the impact of that assumption using Kimoto's equation,

OLR(K&T97)=390 + 78 + 24 + 67 - 325 = 235
OLR(Stephens)=398 + 88 + 24 + 75 - 345 = 240

From 1997 to 2012 the estimated Ein and Eout at equilibrium increased by ~ 5Wm-2, surface energy increased by 8 Wm-2, evaporation increased by 10 Wm-2, thermals/sensible stayed the same, atmospheric solar absorption increased by 8 Wm-2 and "Back Radiation" increased by 20 Wm-2.  Stephens et al. specifically point out the K&T error, Kimoto's paper was published prior to Stephens et al so Dr. Kimoto's paper is irrelevant due to bad input, garbage in garbage out.  Has nothing to do with the journal.

If you like, you can revise the Kimoto calculations with more current data and find that it results in a "Planck Response" of 7.05Wm-2/K, about the same value determined in the Ramathan et al. 1981 study cited in the Kimoto paper.

A 7.05 Wm-2/K Planck response would indicate that a 3.7Wm-2 CO2 equivalent forcing would produce ~0.52C of "surface" warming.  This is somewhat confusing because of the latent and sensible "surface" cooling that is included in the calculation.  That "surface" cooling is transferred to the atmosphere where it improves the atmospheric "insulation" efficiency which would in turn increase the surface radiant energy absorbed which K&T assume is "constant".  Now Kimoto's equation has difficulties that are a little more involved.

Equation 18 is a linear estimate of Stefan-Boltzmann Law which has to be restricted to a small range of change if it is going to be useful.  That will require a good estimate of the absolute temperature of the surface being impacted.  Assuming that the oceans are the more important surface.  the current best estimate of the "global" sea surface temperature is 18C degrees with of course a margin of error which can be argued for decades.  With a surface at 18C and no evaporation/convection, the energy flux change per degree would be 5.60Wm-2/K degrees meaning that the latent and convective cooling would have to be 7.05-5.6=1.45 Wm-2 for 7.05 Wm-2 of additional forcing to produce only one degree of warming.  Since the approximate value of 4 used in equation 18 implies 4Wm-2/K for an ideal surface with no latent or convective cooling you can compare the estimated latent and convective impact by considering that 4Wm-2/K is the ideal condition and 4Wm-2 plus 1.45Wm-2 the latent and convection approximation result in an actual 5.45Wm-2/K  and compare that to the actual 5.60Wm-2/K at 18C.  That difference is reasonably small considering that the actual absolute surface temperature is likely more uncertain.  In other words, the Kimoto approximation is in the right ballpark.

Now how to deal with the difference in "back radiation"?  Assuming half of the total impact of 7.05 Wm-2/K is "back radiation" related,  adding 4Wm-2 of energy at the surface would produce 6Wm-2 of total forcing,  6/7.05=0.85 degrees impact for Wm-2 of forcing.  You could assume all surface impact is reflected resulting in 8/7.05=1.13 degrees impact for 4Wm-2 of forcing.  Then comparing the Stephens et al OLR and "back radiation" you have (398+88+24)/345= 510/345=1.488 implying that adding 4Wm-2 of "back radiation" would produce 5.91Wm-2 of surface forcing or approximately 1.06 degrees of warming with no increase in latent and convective cooling.  Some portion of the latent and convective cooling transferred to the atmosphere would be returned to the surface, but with only a 20Wm-2 window down and a 40 Wm-2 window up, it would be less than 50 percent. 

I will leave a more rigorous dissection to others, but the cascade of errors tend to always result in higher than observed climate "Sensitivity" while a little more attention to detail indicates a lower than observed "sensitivity" or in other words, more longer term natural variability than most are willing to admit given the over estimations. 

I may come back to clean this up a bit, but as is it may inspire some to take a new look at Kimoto, K. 2009.

Saturday, September 7, 2013

Land Modification Impact on Global Climate

For those of you that like to play amateur climate scientist at home while waiting on some serious college football action to begin, here is a neat little "global" analysis you can do in a few minutes during commercials.  Using the ERSSTv3 data you can compare the northern and southern hemispheres with and without land.  LO is the Land and Oceans monthly data and O is the Oceans only monthly data.  N and S are the hemispheres north and south using the 0 to 90 data sets that are easily download.  If there is no land modification impact, there would be no significant change in the LO-O for Land and Ocean (LO) temperature imbalance or differential between hemispheres and O, Ocean only temperature differential during the instrumental period.  On the right axis scale, the differential increases from approximately -0.2 in late 1800s and near 1960 to approximately 0.1 C during 2000 to 2010.  There is an approximately 0.3 C impact which would produce between 0.15C and 0.3C "Global" impact depending on choice of data set, smoothing and start-end dates.  There is no way to separate out glacial melt from UHI to agriculture, but there is a significant impact due to some modification of land area.

When I was playing around with the Houghton Land-use carbon estimate which I had inverted just for grins, I noticed the odd shape of the curve in the above chart.  The "Green Revolution" started in roughly 1960,

"Green Revolution refers to a series of research, development, and technology transfer initiatives, occurring between the 1940s and the late 1960s, that increased agriculture production worldwide, particularly in the developing world, beginning most markedly in the late 1960s.[1] The initiatives, led by Norman Borlaug, the "Father of the Green Revolution" credited with saving over a billion people from starvation, involved the development of high-yielding varieties of cereal grains, expansion of irrigation infrastructure, modernization of management techniques, distribution of hybridized seeds, synthetic fertilizers, and pesticides to farmers."

The correlation between the green revolution and the land modification impact on global climate is at least interesting except for the most devoted minions of the Great and Powerful Carbon.  The is other land use data available, but the data is very coarse, just decade averages in most cases.  I may see if I can add some of that during half time.

UPDATE:  Since many seem to be in love with the Berkley Earth Surface Temperature data here is a comparison of the BEST NH land only with the ERSST3 Northern Oceans 20N-90N which shows more variation than the full hemisphere data.

As you can see the land temperatures started gaining on the SST during the "cooling" or flat period that was supposedly due to northern hemisphere aerosol forcing.  The dust and black carbon portion of the aerosols plus the expansion of farm lands, massive airport build outs and hydro projects would have had some impact on land temperatures with less on ocean temperatures. 

Just to show how baseline dependent BEST is, this chart uses Tmax and Tmin with the 2000-2012 baseline and produces a new Tave.

Friday, September 6, 2013

More Recovery Response Stuff

This is kind of cool.  The Kaplan Atlantic Multidecadal Oscillation with the Oppo Indo-Pacific Warm Pool Reconstruction.  When I first came across the Oppo reconstruction I noticed that the binning seems to have a decade off due to the 50 year average of the samples.  I could be wrong, but in this chart Oppo 2004 is shifted one bin (10years) and the noisy AMO has 21 year smoothing which seems to match pretty well.

Oppo 2004 is a 2000 year reconstruction but I am just using from 1400 in the plot to show the gradual decline into the Little Ice Age and the gradual recovery.  There is only about 0.8 C of depression based on the 50 year smoothed and 10 year binned Oppo data.  The monthly AMO data in the back ground shows the huge range of variability for such a small 21 year averaged trend. From the period 1400 AD to 2012 AD, there is very little trend.

If I highlight just the AMO from 1910 to 2009 it is easy to see the century trends.  The secular trend, 0.2C per century based on the 1856 to 2012 AMO data is a close match for the Oppo data from 1700 AD.  Depending on your choice of smoothing, the natural variability trend can be up to 0.7 C per century and if you are really anal, you can take the trend from 1976 to 2010 and eke out 0.8C in 34 years or a century trend of 2.4C.  There is basically a factor of 10 range available for those that wish to manipulate data and public opinion.  We of course don't know anyone that might be so inclined.

"Well, that is just the AMO!" they cry.

Is it just the AMO?  Share this with a Minion of the Great and Powerful Carbon you may know and love. 

Some Guys are Just so Silly

When I discuss the impact of asymmetry with some of the guys on line, there are a few so totally clueless they can grasp the concept.  When I extend the discussion on the impact of asymmetry to the radiant "shells", they get totally lost.  First, the radiant shell is just a shape with uniform temperature which can be considered an isothermal "layer", but it has a real shape, not an assumed flat surface or disc that can be integrated over a surface of any assumed shape.  A black body cavity is a chamber where all radiant energy that enters is internally reflected until the entire cavity is at a single uniform temperature.  So a black body cavity is perfectly uniform in temperature and the shell containing the cavity would be at a perfectly uniform temperature.  No ideal black body or shell exists, it is just a "model" of perfection.  There is a difference between the two that needs to be understood.  The source of the energy in the cavity is not critical, only the temperature.  For the shell, exactly the same amount of energy that enters must leave or the shell is not stable.  Micheal Fowler with the University of Virgina has a nice tutorial for those inclined.

Since the oceans on Earth are the closest thing we have to an ideal black body cavity, the energy actually absorbed by the oceans which would have very long absorption path lengths with critical internal reflection, just like a black body, needs to be considered differently than energy that is reflected from the surface or absorbed but not deep enough to experience the critical internal reflection that leads to maximum absorption.

So consider this case where the tropics and mid latitudes are low albedo oceans and the upper latitudes are either reflective or absorptive, but the energy is not directly transferred into the oceans.  If the ocean extends from 45N to 45S, 70.7% of the energy can be absorbed versus only 50% if the oceans extend to the poles.  If the Ocean extended to 60N and 60S, because of the angle of incidence, more of the solar energy would be reflected as you approach 60 degrees. 

Consider this case where all of the oceans are below the equator and all of the land is above the equator.  The oceans would absorb less than half the energy in the first case even with roughly equal areas.  The lower portion of the blue ocean here, 60S to 90S would have high reflection due to incidence angle.  Assuming a uniform surface when there is not, would leads to error.

 These are extreme examples, but Earth has ideally a 7:3 ocean land ratio.  In the first example because the extreme polar regions receive such a small amount of solar insulation, the effective ratio can be 4:1 with ice having roughly the same specific heat capacity as land.  With another orientation, the ratio could approach 1:1 if all the land is near the equator.  You have two extreme limits.

In HVAC, system components like fans can have  regions of instability.  With the same RPM and Total Static Pressure and fan can deliver 5000 or 7500 Cubic Feet per Minute of air flow.  Limiting the "system performance curve" to one or the other operating point simply requires limiting the airflow through the system at some stable static pressure.   If you don't, the system can operate at a stable RPM and CFM with the static pressure oscillating between the two extremes which has been known to destroy a few things.  So it is a good idea to know the limits before setting up the system/problem.

For some reason this is a totally foreign concept in Climate Science where finding upper limits appears to be an after thought and lower limits are disregarded.  For example, water vapor is assumed to be a constant with respect to temperature.  If temperature rises then water vapor rises uniformly while clouds which require water vapor find the absolute worse case in order to produce the maximum possible positive feedback to temperature.  That is an upper limit.  Where do they assume water vapor doesn't optimize but minimize the impact of rising temperature?  That is a perfectly logical assumption, that water vapor, clouds and precipitation produce negative feedback to temperature in order to maintain stability.  Since water vapor can, the "sensitivity" range should include the full possible range of water vapor feedback.

The current "pause" was completely missed by all the climate models because they share a common flaw, poorly defined limits. 

Consider that the water vapor extends or expands the liquid water black body cavity.  Now the atmospheric water, ice and water vapor absorb a portion of the energy provided by both the sun and the surface.  The current ratio is approximately 2.2:1 ocean atmosphere for the solar energy absorption.  You now have a black body cavity containing a black body or a near perfect black body cavity, the liquid oceans and a less than perfect black body cavity with a porous "shell".   The total energy emitted from the porous shell is approximately 315Wm-2, the effective energy of water at its fresh water freezing point.  That means the total energy of the cavity has to be twice or 630 Wm-2.  If there is only 480Wm-2 entering the porous shell, then 150Wm-2 of energy must be provided by the inner more ideal black body cavity.  If you want to rotate the system just divide the energy by 2, but the inner black body still has to provide 150Wm-2 based on the peak absorption rate since the black body cavity stores energy until an equilibrium is reached then the atmospheric shell begins to form to maintain that energy.  If the oceans did not have the ability to change phase, there would be no clouds and atmospheric water vapor and the surface would be have an ideal emission of 340Wm-2 and a subsurface energy of 680 Wm-2, because the measured emission is always half of the total energy.

Since the actual total energy is 630Wm-2 versus and ideal 680Wm-2, the Earth black body and water vapor shell is 630/680 = 0.9264  or 92.64% efficient plus or minus a touch, just like the Stefan-Boltzmann correction or fudge factor for real black bodies. 

You can divide by two for rotation, but the percentage remains the same.

I don't expect the Minions of the Great and Power Carbon to understand that, after all it is their models that are screwing the pooch, but they love their pooch and will defend it forever despite its obvious flaws, but there may be some that find this more than just "word salad".   

Monday, September 2, 2013

Solar Mysteries

Solar impact on climate is both obvious and mysterious.  Without the sun there would not be a climate debate, but the solar cycles vary so little in terms of total energy that it is hard to explain anything but a small impact.  "Global" temperatures of the past correlate well with solar until recently leading many to ignore the Sun's contribution in favor of more tangible "forcing" elements that can be made to "fit" different periods using different metrics.  There are Eureka moments almost daily as someone finds a new pattern that appears to match a new data source at a different location looked at in a slightly different way.  Welcome to a chaotic system, it aims to please.

The reality is that a complex system has so many feedback functions with varying amplification factors that anyone can get completely lost in the noise.  In trying to explain, I have used a variety of static models that indicate you can only get so close with the information available and that it is probably better just to accept the limits and focus on longer and longer time frames to reduce some of the noise.  The Three Compartment Ocean Model indicates that there are likely settling time frames or constants of at least 500 years with shorter pseudo-cyclic patterns on the order of 62.5 years just due to the size and limited flow rate between ocean basins.  Near the surface of the oceans, shorter time frame settling noise with periods of 5 to 10 years produce much of the "weather" which may be isolated from climate, zeroing out over a limited period, or an indication of longer term climate, awfully hard to tell one way or the other.  Still, chaos theory implies that there is self similarity of the patterns on all time scales.  Theories are theories though, not laws, just suggestions.

To figure out how small variations in solar can impact climate I have played with the TSI data from Sorce and the satellite data.  There is an obvious solar impact, but correlations never are completely convincing.

For example the solar TSI and lower stratosphere data provided by UAH show an obvious correlation, less than perfect, but obvious at least to my eye.  The lower stratosphere from what I have been able to determine tracks the ocean heat content well, but the stratosphere doesn't have the thermal mass to impress most climate junkies.

Comparing the northern hemisphere oceans, the detrended Atlantic tropics (0-20N, 20E-80W) minus Pacific tropics (80W-20E) indicate why the solar/climate relationship is so hard to quatify, threshold sensitivity.  The "pause" or plateau is an actual solar plateau at -0.25 Wm-2 roughly based on this scaling.  The differences between ocean basins settle quickly, ~2 to 3 years, but there is a response when the threshold is crossed.

Kind of interesting.  A longer term "staycation" on either side of the threshold should cause a gradual change in "climate" as far as surface air temperature and sea surface temperature are concerned.  Only one problem, solar reconstructions of the past are worse than most of the temperature reconstructions.

At the start of the IPCC series of reports, the solar "constant" was about 1366 Wm-2 and reconstructions by scientist like Judith Lean indicated that past solar variability was enough to drive climate until roughly 1950.   Since then, the solar "constant" has become 1361.1 +/- 0.1 Wm-2 and past variation is only +/- 1 Wm-2, about the same as then maximum estimated energy imbalance.  With the new and improved data, solar just can't do the job.  ENSO though, that natural internal variability can have some impact on climate but no one can agree on how much and since ENSO is an "oscillation", it doesn't much matter anyway, it will average out.  However, the comparison of of solar TSI and the imbalance between the northern Atlantic and Pacific oceans seems to indicate that solar can cause about 0.4C of variability with just the 11 years cycle so a prolonged solar minimum or modern solar maximum should be able to do about the same thing. 

The typical way that solar impact is determined is TSI/4 since the Earth is a rotating sphere.  The tropics though don't require half of that 4 divisor,  about 1.414, the square root of two is more relevant to the tropics.  In day mode, the ~1 Wm-2 of solar variation would be felt as ~0.7 Wm-2 of change at the ocean surface in the 30N to 30S latitude band.  That is still a small amount, but compared to an ocean only imbalance of ~0.3 to 0.6 Wm-2, significant.  "Proving" that solar drives ENSO or more realistically the tropical ocean regional imbalances is not a slam dunk, but there is enough evidence and close enough energy available to mark a fair argument to that effect.  So what is the major malfunction?

Well, comparing two of the Solar "TSI" reconstructions, we don't have an agreement on what "Top of the Atmosphere" and "Surface" really is.  The Svalgaard TSI reconstruction used above is scaled to the mean of the Bard et al. 1810 to 1966 mean value.  The blue line is the "modern" mean and the orange would be the past 1200 year mean.  Svalgaard's mean is actually 1361 Wm-2 +/- a touch which would be below the minimum chart value.  The Solar "Constant" has dropped nearly 5 Wm-2 since the start of the CO2 mania.

The Bard et al. estimated "TSI" is based on "surface" impact of solar variation using Carbon 14 and Beryllium 10 isotope ratios, per the Bard et al. abstract:

Based on a quantitative study of the common fluctuations of 14C and 10Be 
production rates, we have derived a time series of the solar magnetic 
variability over the last 1200 years.  This record is converted into 
irradiance variations by linear scaling based on previous studies of
sun-like stars and of the Sun's behavior over the last few centuries.  
The new solar irradiance record exhibits low values during the well-known
solar minima centered about 1900, 1810 (Dalton), and 1690 AD (Maunder).  
Further back in time, a rather long period between 1450 and 1750 AD is 
characterized by low irradiance values.  A shorter period is centered 
about 1200 AD, with irradiance slightly higher or similar to present 
day values.  It is tempting to correlate these periods with the 
so-called "little ice age" and "medieval warm period", respectively.
An accurate quantification of the climatic impact of this new 
irradiance record requires the use of coupled atmosphere-ocean 
general circulation models (GCMs).  Nevertheless, our record is 
already compatible with a global cooling of about 0.5 - 1 C during 
the "little ice age", and with a general cooling trend during the 
past millennium followed by global warming during the 20th century 
(Mann et al. 1999). 

So one measures "surface" impact of solar variation and the other a "constant" at some point in the atmosphere that has changed for whatever reason since 2000.  I am sure both groups are competent at their jobs, but which is more relevant to climate science, actual surface impact or potential impact at some not all that well defined "surface"?