SteveF and the PDO versus North Atlantic

SteveF is a fellow resident of the not as tropical as they once where Florida Keys.  SteveF is a smart guy with a lot more statistical savvy than I have, but that doesn't mean I agree with everything he comes up with.  Recently he had a guest post on Lucia Blackboard where he considered using accumulation of PDO influence on climate.  I personally think that the PDO or Pacific Decadal Oscillation is important, but since it is just a lag response to the ENSO or El Nino Southern Oscillation, that there are better ways to skin this particular fish.

I think we need a better index.  Looking at the Drake Passage and Bering Strait Choke points for ocean heat distribution I thought that he should use something like a PDO modified for absolute sea surface temperature or energy versus a NOA (North Atlantic Oscillation) also modified for absolute SST.

Above is a comparison of the North Atlantic SST with CRUtemp 4 land only temperature series.  The correlation between the two according to my spreadsheet is 55.4 percent with no lag consideration at all.  The comparison is just anomaly using the 1981.90 to 2013.083 monthly baseline which is all the Reynold's OI v2 data set I used had available.  55.4% correlation is not super great, but pretty darn close.  If it was better, I would be more suspicious of something, mainly me and my spreadsheet, being amiss.

Since the North Atlantic region is truly accumulative, it is provided additional energy by the THC mainly from the southern ACC region, I would think that the North Atlantic would make a better choice for a Global Temperature index than the PDO which is noisier and involves more inconsistent lags.

Comparing the North Atlantic to the MEI, I found there is an apparent lag of roughly 8 years with the Atlantic as a whole.  It may be fun to compare the MEI, PDO and this North Atlantic region.

Since his post has comments closed, I thought I would just post my thoughts here.

UPDATE:  With what appears to be a fair correlation between North Atlantic SST and Global Land temperatures I thought I would add this chart:

There is a little issue brewing about SST proxy reconstructions.  The depth of the core sample may cause the reconstruction to be less SST related and more actual depth related.  The core used in the blue, is MD99-2275:  66°33'N, 17°42'W, 470 m water depth while the orange is RAPiD 21-3K: 57°27.09'N, 27°54.53'W, 2630 m water depth.  I used anomaly instead of actual temperature because of the controversy, but with the variability of the shallower reconstruction being more than the deeper, is what one would expect both due to location and depth.

Just for grins, this includes the CRU4 Global and NH temperature series using the same 1880 to 1968 baseline used for the reconstructions.  It is apples and oranges, but since the satellite SST correlates to 55.4% with CRU4, it might make for interesting conversation.

Is Climate Chaotic or Not?

This is a classic argument, is climate chaotic?  My position has always been that it depends on the degree of accuracy you want.  Climate is chaotic in that is has unpredictable events over different time scales, but if you are just looking for a ballpark estimate, that is doable.  The above is a comparison of five Atlantic ocean paleo SST reconstructions.  The Kim and Reuhlemann reconstructions are in the tropical Atlantic on each side of the equator.  They are the most stable, but you can see there is an antiphase relationship.  Average climate based on those two would be extremely stable since their average is nearly constant.  The lower three include two for the Arctic region and one for the southern hemisphere ACC region.  They are more chaotic as in higher variance and comparing the two Arctic reconstructions, there is considerable phase shifting in a rather small region.  If you average them all out you would estimate a relatively stable climate, but there is more noise.

If you consider that noise climatic weather, then you can reasonably predict future climate.  You have to define what period should be called macro-weather or micro-climate.  30 years by these reconstructions would not be climate, but either the Macro or Micro version of your choosing.

This is just the three higher latitude reconstructions.  In the top two, there is roughly five degrees of temperature range, but there is northern hemisphere land mass that responds more dramatically to change versus the southern hemisphere when land and polar amplification is minimal.  So in the NH that +/- 2.5 C fluctuation could produce +/- 5 to 10 C higher latitude fluctuations depending on the magnitude and duration of the events.  That region is only 25% of the global area so with +/- 5 C fluctuation there, could be +/-1.25 C global climate fluctuations.  If you are predicting climate to +/- 1.25 C, then you could have reasonable confidence in your predictions.  The more precise you want your prediction to be, the less likely you would be correct.  

Now notice the roughly 5000 year upward curve in the SH reconstruction by Nielsen versus the roughly 4000 to 8000 year downward curve in the Bendle reconstruction.  At the end they become synchronized near the time of the Little Ice Age.  Now there are two polar regions which would have a combined climate impact that could exceed the +/-1.25 C range base solely on the NH region.  Now you would either need to increase your Macro or Micro time frames or expand the uncertainty margin for your predictions.  

There are physical reasons for the fluctuations, forcing and lags in distribution in a thermally asymmetrical planet.  As long as you allow for the proper lags at the proper times, you can improve your precision.   Ignore the lags in distribution and you are likely to get egg on your face.  

Your call, is climate chaotic or not?

UPDATE:  Those lags are pretty important.

That is the ENSO index normalized just to see fluctuations compared to the Atlantic SST.  98 months or just over eight years produces the best fit.  From 1990 to 2005 there was considerable NH warming.

Not too surprisingly, most of that warming was in the NH North Atlantic region.  Imagine that?

Zonal Flux using the Oceans

 The meridional flux changes started with the Drake Passage opening tend to drive long term climate change.  With the Choke points at the Drake Passage and the Bering Strait metering the equalization of zonal energy, the Atlantic Ocean due to the Thermao-Haline Current (THC) takes centuries and longer to rebalance with the rest of the global oceans (see Brierley & Fedorov 2010).  As estimated by the Toggweiler et al. ocean models and the paleo-ocean reconstructions by Nielsen et al., frequencies of 150 years and long should be common.  How much impact there is over the longer term is estimated at 3.2 C degrees for the meridional impact and 0.6C for the zonal impact of the ocean circulation changes some few million years ago.

The meridional "oscillations" or recurrent patterns over long time scales are fairly easily explained by the shift in the ocean thermal equator versus the physical equator.  The chart above shows the estimated total energy flux per 5 degree latitude band in blue versus the difference in meridional flux by latitude band.  With the Antarctic isolated by the ACC created with the Drake Passage opening and the lack of liquid ocean below the ACC, the mean altitude of the Antarctic ice cap (~2000 meters) produces nearly a 20 degree abrupt temperature gradient with the dry adiabatic lapse rate.  This high and dry region is approximately 9 percent of the total surface area of the Earth.  The Blue curve then is effectively the moist air/liquid ocean envelop that would produce the radiant impact of changes in atmospheric chemistry.  With the Antarctic high and dry, a dry air only model of CO2 impact would be required to produce reasonable estimates.

The zonal imbalances are more "weather like" in their impact.

This chart uses the Reynold's OI v2 data in 60 degree longitude bands to show the noisy relationship of zonal regions over the past 3 decades.  The anomaly is created be subtracting the SST data from the seasonal signal of each band.

This chart shows the raw data for each band in estimated Wm-2.  The Pacific and Atlantic zones show the seasonal sine wave with the India Ocean region (0-60E) show a more complex combination of signals.

The Eastern Pacific and the Middle Eastern Latitudes have the largest noise component (weather) of the zonal regions.  The Eastern Pacific has the great ocean area of these two regions and should have more climate impact because of the greater thermal mass.

The Western Pacific has less noise and would appear to be a better proxy to climate change instead of weather changes.  In this chart the warming from beginning of the data to 1998 is clear as is the "pause" or plateau in warming following the 1998/1999 El Nino climate shift.

With the Western Pacific as a control region, the Western Pacific minus the Atlantic, the longer term oscillation indicator, could be a good indication of zonal impact on climate.  From the ~1994 valley at -2 Wm-2 to the ~1999 peak at 2 Wm-2. global temperatures as measured by HadCRU increased by ~0.2 C degrees.  With virtually no change from the ~1999 period to the ~2012 period, there is likely more Atlantic influence than Western Pacific on the estimated "average" global surface temperature.

Focusing on the Atlantic band in this chart, the overall trend is 0.639 C per century likely caused by thermal energy transfer lag created by the Drake Passage and Bering Strait choke points.

It would appear there may be much more to climate change than well mixed greenhouse gases.

Update:

While I am more concerned with the energy imbalances many like to see temperature anomaly.  This compares the 0-60W Atlantic SST zone temperature to the HadCRU4 Northern Hemisphere surface temperature anomaly.   There is a pretty fair correlation as you can see and also there is a difference in the trends.

Atlantic Paleo SST - Another Nail?

" The dominant forcing factor appears to be precessional

insolation; Northern Hemisphere summer insolation correlates to at least the early to middle Holocene climate trend. Spectral analysis reveals centennial-scale cyclic climate changes with periods of 1220, 1070, 400, and 150 yr. The record shows good correlation to East Antarctic ice cores and to climate records from South Georgia and Bunger Oasis. However, the record shows out-of-phase behavior with regard to climate records from the western Antarctic Peninsula and the Peru-Chile Current; such behavior hints at a climatic divide through Patagonia, the 
Drake Passage, and between West and East Antarctica."

Nielsen, S. H. H. 2004 (2009)

This chart compares the Southern Atlantic reconstruction by Nielsen et al. with a tropical Atlantic (near Granada) by Ruehlemann et al. and Sub-Arctic reconstruction by Bendle et al.   all the data is available on the NOAA paleo site.

Since I am trying to find some better index for Global Climate to compare with various SST reconstructions, these are three of my more recent downloads.  By starting with the atlantic and using the satellite SST data by region, I should be able to come up with some reasonable latitudinal weighting system for the reconstructions.  It is a bit of a bear since the sample dates are so inconsistent, but so far it looks like I may be able to get about 400 years resolution, which is fine for my purposes, but not so great for chasing every 0.5 C tick in the instrumental record.  So far for the Atlantic at least, roughly 2500 BC was the warmest period, mainly because of the tropics and Arctic pulsed up together.  There is a smaller MWP Atlantic pulse and the rather sharp LIA decline following that.  How those work out on a global scale, I don't know, but so far most of the fluctuation is in the Atlantic with the NH having the largest volatility as should be expected.

Nielsen et al. is just my most recent paper that agrees with Manabe and the GFDL gang and strongly hints Hansen has screwed the pooh by underestimating long term variability.     

An Open Paleo-Climate Challange

JeanS, Steven McIntyre and other online "auditors" have had their way with the recent Shaun A. Marcott et al. Reconstruction of Regional and Global Temperatures for the past 11,300 Years.

The procedure that Marcott used appears to have lost more information than it gained in combining a variety of 73 paleo temperature reconstructions from around the globe.  Using the same procedure used for combining modern era instrumental data, the paleo reconstructions could have been more optimally interpolated to establish a procedure for combining various types of paleo reconstructions with different sampling frequencies, variation and record length.

With most of the same "skeptics" involved that led to greater confidence in the accuracy and limitations of the instrumental surface station record, "crowd sourcing" a paleo-climate absolute and anomaly temperature record regionally and globally should be a worthy project for the climate science junkies.

Food for thought.

Baseline Selection Again

With the current hubbub over the Hockey Stick Revisited I thought I would throw in my two cents.  SST reconstructions go with SST reconstructions, period.

The plots above show three Holecene period SST reconstructions for the Atlantic Ocean with the principle author's name and published data as listed on the NOAA Paleo website I used to download the data.  Since the freshest data should be the better data, I used the "present" value of 1950 to year zero for the baseline on the bottom chart and on the top chart I used year zero to -8000 as the baseline on the upper chart.  Which do you think is closer to reality?

The Kim 2002  data is specifically selected, because it shows just what I wanted it to show, that there hasn't been a heck of a lot of change in the Tropical Atlantic Ocean for some time.  The other two I just picked because they were in the North and South Atlantic because just about any reasonable paleo SST reconstruction will show a fairly large amount of variability as you approach the poles.  I can say with great confidence that today is about as warm as it has ever been in the past 8000 years.

I could dwell on the downtick of the Bendle 2007 reconstruction or the uptick in the Ruehlemann 1999 reconstruction, but that would just be picking nits since neither have the absolute accuracy over the entire record to discern a quarter of a degree one way or another.  The Bendle 2007 by the way is a much smaller ocean area than the others so it would require less weight and I didn't weight any of the reconstructions.

If I included a few noisy tree ring reconstruction, I could have a much more noisy plot with not a heck of a lot more information.  Since the Northern and Southern Hemispheres tend to be out of phase on various time scales, I could average all the information away.

Personally, I think there can be a lot more useful information gained from Paleo, if guys collecting the samples, calibrating the ages and calibrating the ranges actually provided the reconstructions.  The papers would likely be a lot more boring, but much more informative.

The 55S Catastrophe or Closer to the Real Deal

There is a world of difference between knowing what is wrong and proving it.  That is especially true when the mistake is so simple.  Starting at the wrong base assumption can spread like wildfire scorching every calculation afterwards.

This sketch represents Earth at its maximum insolation mode.  The slanted black line is the plane of the Earth with respect to the Sun.  If you can visualize the orbit of Earth with the missing southern polar region, this orbital mode actually provides the highest average solar insolation for the Body part of the Blackbody core.  The Shell portion would always receive uniform solar insolation since it does not have any portion of its surface thermally isolated from the rest.  The Shell and the Body receive solar insolation continuously.

In night mode, the body loses energy to the shell.  Since the active area of the body is less than the area of the shell, the active body region would provide energy both to the shell and inactive regions of the body.  With the inactive Antarctic region be approximately 9% of the total area of the Globe, 91% of the body energy would be transferred to the shell, less some smaller percentage transferred to the inactive Antarctic region.  If the Antarctic is truly thermally isolated, then the temperature and energy signature of the Antarctic should be very closely related to the shell temperature and energy characteristics.

Antarctic temperature data is by far the most suspect of all the surface temperature data available.  With the polar vortex dynamics causing occasionally radical transitions, the trends could be highly suspect, but there may be some information in the longer term mean values.  The Amundsen-Scott base at the South Pole has one of the longer records and is possibly less contaminated by polar weather.  Using the GISTEMP monthly station data you can compare the absolute temperature and Stefan-Bolzmann equivalent energy for the station.

	Max	Min	Average	Mean
Actual	218.49	102.40	144.73	148.39
Ratio	240.10	112.53	159.04	163.06

This table has the S-B equivalent energy values for the period from 1957 to 2012.  The Average is the simple average and the mean is the root mean squared for the 664 monthly values available.  The Ratio row is the actual values divided by 0.91 which is my estimate for the active region of the body of Earth's combination blackbody and shell.  The Max and Min values I would think should be suspect requiring a little more diligent treatment, but the Mean and Average should be fairly close to the "Greenhouse Effect" magnitude.

To take this one more step, the actual energy of the portion of the body providing the energy to the shell may be estimated.  If the actual average absolute energy of the active surface is 390Wm-2, then roughly 62% of the surface is active based on the Average value or slightly less with the Mean value.  With only 91% of the true surface likely to be active with the Antarctic isolated, then roughly 68% of the overall surface may be providing the blackbody energy for the shell and Antarctic regions.  That is close to the actual open ocean area of Earth.  This may seem somewhat circular,but albedo is not a factor in the energy flux out of the body, only the emissivity of the surfaces, with water being close to ideal.

It is a shame that the polar region data is so sparse, since it looks like the Antarctic has the potential resolving some of the more perplexing discrepancies.

The Isolation of the Southern Pole

One of the fascination I have with with the various theories of the ice ages is the Drake Passage and the thermal isolation of the southern pole.  When the Drake passage opened some millions of years ago it created the Antarctic Circumpolar current improving the heat sink efficiency of the southern oceans. The Arctic has the Bering Strait as its main circumpolar path, but due to the depth and orientation with the Coriolis Effect, it is not capable of keeping the regions oceans open or mainly free of ice.

Toggwieller et al. estimated that the Drake Passage cooled the Southern Hemisphere while warming the Northern Hemisphere with a net cooling of possibly 4 C degrees.  Depending on the actual average surface temperature used, that would be in the range of 16 to 20 Wm-2 of additional heat loss due to the thermal isolation of the southern pole.

The area for the region from 55S to the south pole is 46.4 million kilometers square or roughly 9% of the total surface area of the globe.  If the Drake Passage effectively removed that area from the thermodynamic workings of the globe, the global impact could be in the range of 16/.09 to 20/.09 or have an impact on a source average energy of 177 Wm-2 to 222 Wm-2 with a rough average of 199 Wm-2, which is the current range of the estimated Effective Radiant Layer (ERL) energy range.  This would shift the thermal equator northward by roughly 16 to 20 Wm-2.

-90 to -55	-90 to equ	-55 to equ	20S to 20N	Equ to 55	equ to 90	55 to 90
0.54	16.89	19.95	27.25	23.08	19.90	2.21

Since I have the nomads SST data, I determined averages by the zones about.  You can see the imbalance between the hemisphere, but if you notice the -55 to equ versus the equ to 90, the average temperatures are virtually identical.  The global meridional energy balance is shifted north just a Toggweiler et al. 2000 noted.

-90 to -55	-90 to equ	-55 to equ	20S to 20N	Equ to 55	equ to 90	55 to 90
318.15	401.29	418.50	461.72	436.67	418.24	326.07

Using the Stefan-Boltzmann equation, I used the absolute temperatures to estimate the effective energy of the same regions.  The difference between the non isolated southern pole and the new -55 to equ  is roughly 17.2 Wm-2 or 3.15C is you use the upper temperature table.

There have been a few more papers on the impact of the Drake Passage since Toggweiler et al.

The establishment of the modern meridional and zonal SST distributions leads to roughly 3.2 degrees C and 0.6 degrees C decreases in global mean temperature, respectively. Changes in the two gradients also have large regional consequences, including aridification of Africa (both gradients) and strengthening of the Indian monsoon (zonal gradient). Ultimately, this study suggests that the growth of Northern Hemisphere ice sheets is a result of the global cooling of Earth's climate since 4 Myr rather than its initial cause.  Brierley, C.M. et al. 2010

The "modern meridional and zonal SST distributions would be the result of the Drake Passage opening.

I think that 3.2 and 3.15 are pretty close considering the alleged inaccuracy of satellite temperature data.  

Shifting the thermal equator would require shifting the atmospheric radiant balance.  For the Earth to have a stable climate, you can't have major imbalances that are not compensated for in one way or another.

South pole to equ	North pole to Equ	South pole to equ. S	North pole to equ N
143.56	135.64	100.36	92.44

So in this table I compared the meridional flux relationships.  From the Equator, there is a larger southward energy flux than northward.  From the lower latitudes (equ S and Equ N) to the poles there is also and imbalance.  But the difference in both cases is exactly 43.20 Wm-2 or roughly the atmospheric window energy value.  

I didn't do this to prove Toggweiller et al. or Brierley et al. know what they are talking about, but to see roughly how much accuracy I could expect from the Nomads OI v2 data set.  I must say I am again impressed with the satellite data.  This was just a quick comparison so there may be more information available, but currently I am more curious about the zonal SST distribution and that 0.6 C that could be part of the longer term natural climate oscillations also estimated by Toggweiler et al. 1994.

Shell and Body Should not be Difficult to Grasp

It really puzzles me why this concept is so hard for some to grasp.  A gray body has two components, a shell and a body.  The shell by definition is isothermal, there cannot be any perpendicular transfer of energy, only in/out transfer.  To estimate the energy of a gray or black body from space, you use the simple relationship TSI*(1-albedo)/4 to determine Ein which since the definition of the body limits internal heat transfer will always equal Eout.

The shell is the part of the gray body that TSI*(1-albedo)/4 applies to, not the true "body" of the object.    Since the "body" has to have some degree of perpendicular heat flow, the average energy available at that surface is TSI*cos(lat)/pi times the Cos(lon relative to local solar noon)  Then allowance can be made for limits in transmittance to that point on the spherical body.

Anyone that has any interest in designing a solar pond is aware of the "average" insolation and the "peak" insolation for the pond location which are considered along with the thermal capacity and layer gradients to determine the "operating" temperature of the solar pond.

Once you move beyond the simplistic ideal approximations you can begin to actually understand the minimal gray body considerations that need to be made.

We Need a Better Index

The opening of the Drake Passage had a huge impact on the mixing efficiency of the global oceans.  The flow through the Drake Passage from the southern Pacific to southern Atlantic is on the order of 130 million Sverdrup.  Since the Northern Hemisphere doesn't have a passage with as much flow potential, there is a large imbalance in the efficiency of the hemispheres to equalize energy distribution.

Attempting to locate the cause of the long term pseudo-cyclic climate changes is difficult to say the least, having a better set of indexes for the modern era wealth of data would be a large help.  Since "weather" oscillations make up the bulk of indexes, trying to adapt regional indexes to hemispherical and global impacts is a lot like herding cats, I have been toying with what might be better "global" indexes based on ocean temperature differentials at the two most important transfer points.  The Drake Passage from 65S to 55S with the eastern region from 0W to 60W versus the western region from 60W to 120W.  In the north, the North America is in the way so the northern region is based on 55N to 65N with 0W to 60W as the eastern region and 120E to 180E as the western region.

This is the southern SST index using Atlantic minus Pacific temperature differential across the Drake Passage.

This is the northern SST index also using Atlantic minus Pacific regions which is the differential roughly across the Bering Strait, at least a close as satellite data can produce.

These are both non-standard indexes, so this post is just to describe what indexes I am attempting to use.  They could end up being totally useless, but since there are a large number of paleo ocean cores in both general regions, what the heck.

The energy flow through each of the passages is really what I am interest in, so a "global" index will require a little data massage.

This is after a little massage.  The standard deviation of the southern index is 0.164 C and the northern index sd is 0.582 which produces a ratio of 3.54 which is used to "normalize" the two hemisphere proposed indexes.  After the normalizing massage, the two index are nearly mirror images of each other.  The difference of the two produces the red "Global" curve with the 0.14  unitless trend per decade.

In order to be useful, the "global" index would need some reliable units to associate with the trend.  As both of the individual hemisphere indexes are Atlantic to Pacific differentials and the "global" is the difference of two differentials, allowing for a number of scaling options.

The reason for this attempt to develop a new set of indexes may not be apparent.  However, the impact of global ocean mixing seems to be grossly underestimated by some of the online climate change junkies and this approach might help to explain the complex thermal inertia of the oceans.

NOTE: The data used for the charts is from the nomads.ncep.noaa.gov OIv2 data set from 1981 to 2013.  I will try to post a spreadsheet after I clean up a few issues, but it shouldn't be difficult to replicate if anyone is interested.

Precessional Cycle and SST

I was curious about how much impact the precessional cycle of the Earth would have on Sea Surface Temperatures.  This chart is the cumulative contribution by latitude to allow for the different percentages of open ocean that would likely be available.  The two mean value lines show that there is a slight difference in total energy, but the main change is in the energy distribution.  Again, since I am only considering open ocean area, there is no albedo correction for the energy.  Because of the land area differences, there would be a large land albedo change, but not so much on the oceans I would think.

The two black arrows point out peaks that are just off center of the equator.  Since the Earth rotates, there is a Coriolis effect that tends to somewhat uniformly mix the two real hemispheres, but would tend to block mixing between the two hemispheres.  So there is likely to be a pretty big change in the internal heat transfer even though total energy is about  the same.

The precessional cycle is not fixed.  It is like a tire out of balance and can change how much weight is out of place.  The largest weight or mass imbalance is likely due to glacial mass, which we don't have a lot at this point in history.  If the precessional cycle is 21,700 years, then it would take about 10,850 years for the Earth to switch from the Southern hemisphere peak to the Northern Hemisphere peak with the orientation changing about 1 degree every 60 years.  In a full precessional cycle the thermal equator peaks would move to the extremes shown and spend more time located on the equator for two beats of the cycle.  Since the blue curve is the current orientation, Earth should be in the build glacial mass mode.

Because of the asymmetric distribution of land and oceans, the precessional cycle should have a four count beat.  SH max - Equator max - NH max - Equator max, producing 5425 year cycle in paleo climate records.  Oddly, there is a 4300 year cycle that is related to orbital precession.  That is a fifth, not a quarter, indicating that something else is involved in the paleo climate records.  That could be ocean mixing lag of 5425-4300=1125 years, but since the precesssional orbit is subject to fluctuation, kind of hard to verify.  Noticing that the SH max and NH max orientation would likely have different deep ocean mixing dynamics, there could be a range of lag times from the 1125 years that should be easy to spot to 1700 years that was determined by C14 isotope mixing.  (1700+1125)/2=2825/2=1412 years which is fairly close to the Bond event range.  Since precession progresses at roughly 60 years per degree, with a mean frequency of 1412 years, every 23.5 degrees there should be some reason for a perturbation if the Bond cycle is actually a cycle and not just unrelated events.  Since the timing is roughly right, it might be nice to figure that out here pretty soon.

The orange curve in this reconstruction shows that northern high latitude ocean surface temperatures tend to have the roughly 4300 year pulses when they are not covered with glacial period ice.  As I had shown before the equatorial region paleo reconstructions have a similar cyclic signature.

None that I have found so far have a clear signal of the 4300 or 1412 cycles as real cycles, just recurrent patterns from so not well known perturbations with solar forcing on its own not enough to trigger the events.  The internal imbalance with solar though may be able to explain some of the events.

The search continues.

Pi Day

Yesterday was Pi day, 3.1413, well close enough anyway.  I should have posted this yesterday, but I was wanting to do some double checking.

A blackbody is not a gray body.  A black body distributes is energy uniformly over its entire surface.  In order to produce a "blackbody" for experiments, the grand masters of radiant physics had to take a few liberties and just use a fraction of a surface that approximated a black body, a blackbody cavity.

The sketch is borrowed from wikipedia.  The grand masters used the little hole to isolate the spectrum they wanted to test.  Earth doesn't have a nifty little hole that provide just the spectrum we like, so we have to scratch our head a bit and figure how closely Earth can come to being a real blackbody.  Well, that should start with the furnace or inside of the box.

The Sun is very close to an ideal blackbody and provided the energy that goes into the cavity to stoke the furnace.  Instead of a slit though, Earth has pretty large oceans that allow the solar energy in and currents to slowly mix the energy.  Unlike the moon and asteroids, the liquid oceans allow for more uniform distribution of the energy so Earth can behave more closely to a true blackbody.

Without the subsurface mixing inside the box, the energy from the sun would be distributed based on the total energy available and the cosine of the latitude of spherical surface receiving that energy.  Since Earth has a fluid "interior", I speculated that the distribution would diffuse based on the Square root of the cosine latitude.  Then the average would be TSI*cos(L)/pi for the moon and TSI*SQRT[Cos(L)/pi] for the Earth, if it had ideal internal transfer.

I made this cute little chart to show the difference between a solid not so ideal blackbody in yellow and a liquid core more ideal blackbody in green.

While I don't have very good data on the ocean thermoclines which would be the most idea black body surface, I do have sea surface temperature data by latitude and an estimate of average insolation by latitude that I posted in Ideal versus Observation.

What I neglected to show in that post was the Ideal with mixing versus observations.

This compares the observations with the SQRT[Cos(L)/pi] annual average.  Again, since this is a long term average and since clouds are not fixed albedo factors, there is no consideration of albedo in this comparison.  You will note that the southern hemisphere is lower than average and the Northern hemisphere higher just like Toggweiler et al at the Geophysical Fluid Dynamics Laboratory have noted. If I compare the estimate average surface temperature of 399Wm-2 based on more current estimates to the ideal estimate, the emissivity factor would be 0.921 instead of the ~0.924 commonly used with the Stefan-Boltzmann Law.  While I am sure I may have a mistake somewhere, the fit is just plain remarkable and should be noted by skeptics of the use of Blackbody equations and deniers of natural ocean oscillations.

Now armed with this fine tuning of the blackbody baseline, I should be able to produce a more accurate static model with meridional flux values for a future post.

Ideal versus Observation

While the deep oceans should provide the effective black body source to mate radiant physics to my more mundane thermodynamics, the deep ocean data is not all that great.  That requires picking a less than desirable reference layer that has reasonably accurate observations.  So far, the what appears to be the most reliable is the the satellite derived Sea Surface Temperature (SST) data.  Since I am really more concerned with the sub-surface of the oceans, I am going to compare the average solar insolation by latitude using TSI time the Cosine of latitude divided by pi approximation.  I want to include the orbital eccentricity without getting to complicated, so I have set up a spreadsheet for winter, summer, spring and fall values to produce an average average insolation.

The Spring and Fall (S-F) curve in orange is based on 1361 Wm-2 Total Solar Insulation (TSI) is slightly greater than the Annual average in green.  Since I am using only the ocean areas most likely to be ice free most of the year, the range is from 65N to 65S.

Using the optimally interpolated SST data along with the actual area of ocean per 5 degree latitude band, this chart compares the observed SST to the "Ideal" SST using the average insolation shown above.  The values listed are cumlative contributions by band.  The sum of all the contributions for 65N to 65S is 350 Wm-2 for the Ideal model and 416 Wm-2 for the observations.  Note that the difference is 66 Wm-2 for them that have been regular blog followers. The blue line is the difference showing an average of 2.5 Wm-2 with a range of roughly 1.3 to 4.75 Wm-2 difference.  Considering all the uncertainty in the approximations, that is pretty darn close.

Remember, there is no albedo adjustment at all involved in this approximation. Since the area used is open ocean and clouds are not stationary, typically forming after peak insolation anyway, albedo is not as much a factor in the average energy absorbed by the liquid oceans of the planet.

I have to clean up my spreadsheet a bit, then I will do a post on the impact of orbital precession on SST which should be interesting.

Average and the Sub-Surface

The chart above is just distributions of incident energy on a sphere based on cosines.  The blue curve is the peak incident energy by degree of latitude, the orange is the peak incident energy allowing for meridional curvature and the yellow is considered the average incident energy, which would be roughly the average sub-surface energy.  If the sphere is made of solid material, the average sub-surface energy would be about 20% of the peak energy available.

If the sub-surface is fluid, or the rate of energy transfer in the sub-surface is greater than the loss of energy from the sub-surface, the sub-surface average would tend to spread into a more uniform distribution.  I used the SQRT(COS(pi())) to simulate a near optimum spread.  The actual efficiency of the spread would depend on the fluid properties and the rate of heat loss from the surface above the sub-surface.

The curves above just consider the power cycle.  If the sphere rotates at the perfect rate, the peak curves would be equivalent to a half rectified sine wave with 50% on and 50% off.  Then using the COS^2, the input "signal" RMS value would be COS^2/2.  If we consider the residual "average" we now have a range which depends on the mixing efficiency of the sub-surface layer.

There is some confusion over what is surface and sub-surface.  The layer with the most efficient mixing should define the sub-surface layer which would be the most effective ideal blackbody source.

On Earth, that sub-surface would be the oceans.  If Earth were a pure water world with near ideal sub-surface mixing efficiency, the average energy of the sub-surface would be approximately 23% of the input energy.  1361*0.23=313 Wm-2.  That average is slightly below the freezing point of fresh water and slightly above the freezing point of salt water with a salinity of ~35g/kg.  Since salt is reject when ice is formed, the minimum energy required for liquid brine should be considered which is -32 F, -17.7 C or 255.45 K degrees.  Since that mixing efficiency is less than ideal, the average subsurface energy is slightly higher, since roughly 8% of the polar regions are land mass not ocean.

Earth is blessed to have a fairly well mixed salt water ocean covering about 70% of the planet.  So blessed in fact that the number of coincidental factors that need to be considered are close to miraculous.  Earth hit a universal sweet spot and man caught Earth at just the right time.

The point of this post though is to highlight the importance of considering the sub-surface mixing efficiency.  If the rotation speed changes, the impact on the sub-surface would be huge.  If the location of the land masses reduce the mixing efficiency of the deep ocean currents, the impact can be huge.

Until  warmists begin to consider the real greenhouse, the global oceans, there will not be any progress made trying to understand the miraculous world we inhabit.

Update:  In case anyone would like to play with the sub-surface impact, here are a few numbers:

140.56 mkm^2 is the Northern hemisphere ocean area from the equator to 65N, average solar would be close to 1337Wm-2 for for the NH half year.  196.4 mkm^2 is the Southern hemisphere oceans from the equator to 65S with an average solar insolation of about 1385 Wm-2 for that half year.  There is more "under the ice" area in the NH but the THC mixing is predominately driven by the southern ACC which will require a little thought.  From the looks of it though, the sub-surface average is one of the few solar forcing estimates that actually makes sense.  With the total ocean area of 337 million km^2 of a total global surface of 510 mkm^2, the 66% typically open ocean area at roughly 311 Wm-2 would produce a "shell" ERL energy of 202 Wm-2.  This would seem to make the radiant "blackbody" work, but there is still a pretty large range of uncertainty.

On the Relative Importance of Meridional SST Gradients and Climate "Sensitivity"

Climate "sensitivity" is one of those curious subjects.  There should be A, singular, climate sensitivity, according to the greenhouse gas theory, that will eventually produce some degree of warming per increase in atmospheric CO2 concentration.  It is really simple, there is a natural log response per increase, and an exponential increase currently which will warm until some limit is reached after including various, positive feedbacks.  It is like being given a blank check with no clue what the account balance happens to be.  "Skeptics" want to know the balance and the "warmists" just want to run around preaching doom and gloom.

Well, finally, the conversation seems to be turning to real limits based on regional "sensitivities".  The chart above has some basic information based on Sea Surface Temperatures by 5 degree latitudinal bands.  There is the standard deviation of temperature, Areal Weight (degree C contribution by area) and the ordinary least squares linear trend by band.  I have included two "Sink Regions" which are areas of the ocean which have an annually averaged surface temperature less than or equal to 4 C degrees, the approximate "average" temperature of the total ocean volume.  Most of the standard deviation is due to the annual solar cycle that ranges from about 1313 Wm-2 in summer to about 1408 Wm-2 in winter with a mean of about 1361 Wm-2.  The sink region in the Northern Hemisphere is larger, based on latitude, due to the seasonal solar cycle, but due to the lower ocean surface area, the Northern Hemisphere ocean sink potential is lower.  The Northern Hemisphere is warmer than the Southern Hemisphere because the Southern Hemisphere has better mixing and more sink area than the North.

Since energy prefers the path of least resistance, the more efficient Southern Ocean Sink, the Antarctic Circumpolar Current, would be the more likely limiting factor for "equilibrium" climate impact of CO2 increase.

Since a real limit to the impact of CO2 may be lower than initially estimated, that realistic upper limit seems to be politically incorrect to discuss.  Instead, the "Fat Tail" of possible warming is the strawman tossed out by the "warmists".  At the "current" estimated rate of deep ocean warming, it will take 300 to 400 years to increase the "average" temperature of the oceans by 1 degree C, which is roughly the "no feedback" climate "sensitivity" to a doubling of CO2.  Since we live on a planet that rotates about 366.26 times in an Earth year, the hemispheres are somewhat isolated by the Coriolis Effect.  In order for the Northern Hemisphere warming to be felt in the Southern Hemisphere, CO2 has to back up NH cooling like a clogged toilet.  That requires the thermal mass of the NH to store twice as much energy as the thermal mass of the SH.  Since the Atmospheric thermal mass is limited by the specific heat capacity of the atmosphere and CO2 does not add a significant amount of thermal mass to the atmosphere, there is a physical limit to the amount of "damage" CO2 can do in terms of climate "sensitivity".  The heat has to be stored some where.

I put this post together for the master of simple diffusion since he has finally realized that the data he has been using is just not up to the task.  If he cares to, I have even put together a spread sheet with the current state of the art sea surface temperatures in 5 degree bands so he can double check to his heart's content that long term ocean oscillations will determine the ultimate climate "sensitivity" on a time scale of millennia.   5 degree SST for Web.  I am not sure how well that Google docs spreadsheet works, but he should at least be able to cut and paste the data.

For some light reading, Relative Importance of Meridional SST Gradients...

How to Handle Clouds

Clouds are one of the major PITA of climate science.  Below the clouds where we live, the uncertainty in measurement is huge, approximately +/- 17 Watts per meter squared.  Above the cloud the uncertainty is manageable, about +/- 2 Watts per meter squared.  I have become pretty convinced that the surface uncertainty is normal business as usual.  Clouds form in response to surface temperature and moisture.  Because of that, clouds have diurnal, seasonal and multi-decade patterns, probably longer.

Since I am more concerned with some expected "equilibrium" climate sensitivity than weather, instead of using a "fixed" input energy, I have been comparing peak energy input and RMS plus residual energy.  The RMS would be perfect for a pure resistance or "static" load, but since the ocean would be a complex load, resistance times capacitance, for the input and the atmosphere would also be a complex load for the oceans with the added bonus of the atmosphere intercepting some of the input energy as well, the period or time constant for the RC circuit would be important.

In an RC circuit, the energy decays or approaches values based on Eout=Ein*e^(-t/RC), which is simple enough, but since the Ein is noisy due to orbital and albedo fluctuations and the output load or atmosphere is also noisy with fluctuation due to the same plus different orbital forces, tides, Coriolis, assuming an "Average" is quick and dirty way around the complexity.  Still, there needs to be a reason for considering what time frame should be used for that "average".

The odd position of considering RMS plus residual is that for most situations, it is equal to the "Average".  All RMS plus residual does really is more heavily weight the equatorial band and de-weight the higher latitude bands.  The at "equilibrium" the input signal becomes more of a pulse width modulated square wave than a alternating signal considering time frames greater than one Earth year.  This is more important for the internal energy considerations since above the clouds, the "Average" is perfectly acceptable after allowing for a smaller residual energy absorbed directly from the energy source.  Depending on the altitude above the clouds and the thermal capacity of the atmosphere at that altitude, that residual can be on the order of 65 Wm-2 at roughly 100km above the surface, the Turbopause layer.  As I have noted before, the Turbopause is the limit of turbulent mixing which would produce a more "ideal" radiant "shell" to oppose the more "ideal" blackbody source, the oceans.

This ocean "blackbody" to Turbopause "shell" reference causes some confusion since the area of the "blackbody" is roughly 70% of the area of the "shell".  That would require approximately 30% of the blackbody energy advect or horizontally transfer to the less than ideal blackbody area between "surface" and "shell" to form the Effective Radiant Layer (ERL), for those into the pure radiant physics approach.  Since "global" albedo is estimated to be 0.3 or 30% there is a cause and effect issue.

That cause and effect issue is also muddied by the change in albedo with solar angle of incidence.  At latitude 60 for instance, the incident solar energy is 50% of peak but with the incident angle being 45 degrees, the normal albedo would increase due to reflection at the surface plus the energy that does penetrate would "bend" due to the refractive index.  These are somewhat small considerations that grow in significance with the desired degree of precision.

To reduce uncertainty, ignoring clouds should produce reasonable long time constant estimates that can be compared to more creative attempts to analyze the noisy troposphere.

Sweet Spots and Argiculture

This was posted on Watts Up With That.  I am re-posting because I agree, some some minor caveats.  The caveats are the sweet spots, those Goldilocks conditions that amaze, but tend to not last long.  There are cycles that are unavoidable and have to be adapted to when they arise.

Controlling soil carbon and moisture is key to limiting unwanted climate change.  Grasslands need grass and the herds are part of that cycle.  Forest need trees and glaciers need snow.  You can't convert everything to fields and parking lots and not expect climate change.  Got to find those sweet spots.

Sea Surface Areal Contributions

This is just a quick post to get some charts up for a future discussion.  Some of you might find it interesting though.

I have been playing with a static model that needs a good deal of work yet, but since there was a discussion on ocean oscillations and how best to use what for which, I thought I would get back to the battle of the hemispheres which is always going on and creates a lot of noise.  Using the NOMAD3 Optimally Interpolated Sea Surface Temperature data, (click the link if you want to play). I broke the global SST up by zonal bands.  Since I have a fairly good break down of ocean versus land area by 5 degree latitude, I used the two to create my own "Global"  average SST, with "Global" meaning from 65S to 65N.  Of course all the data sets have different bands they like to call regions, so this is not quite equivalent to the GISS regionals that use 24 degree zones, but fairly close.  This gives me a "mean" SST of around 19.5 C which is lower than AQUA, but then AQUA uses 60S to 60N.  There is no consistency it seems.  Anyway, "global" average SST appears to be higher than the 16 to 17 C thrown around if you consider only ice free oceans as oceans.

So this chart would not be as messy, I just used the NH and SH here with the absolute temperatures converted to Wm-2 using the standard Stefan-Boltzmann equation.  The point is to show that both NH and SH have fairly stable seasonal cycles that are nearly pure sine waves but a bit of a lag that produces the standard "Global" temperature average look.  With 65N-65S having a mean temperature of about 19.5 C, the "Global" mean energy is roughly 419 Wm-2 for the ocean surface with the SH providing about 240 Wm-2 and NH about 180 Wm-2.  That actual "average"  NH SST is about 2 C warmer than the SH, but due to the smaller area, it has a smaller contribution.

Because of the internal lags, there is a little frequency modulation going on which is why I tend to spend a good bit of time on harmonics and RMS values instead of the whole "average" thing most prefer.

60 degrees of Confusion.

There is a lot to consider in climate.  Internal heat transfer is the toughest since at the top of the atmosphere there is not much going on.  So while waiting this morning I though I would toss out a simple example of internal potential energy difference due to solar orbital variation.

Since the Earth is a sphere not a flat disc, you should allow for curvature when calculating surface irradiance.  At the nadir or the point on the Earth facing the center of the Sun, you could receive 100% of the energy emitted.  At 60 degrees, due to the angle of the surface relative to the Sun, that energy would be spread over an area twice as large.  Since the annual orbit of the Earth around the Sun is an ellipse, not purely circular, in winter the maximum energy is ~1410 Wm-2 and in summer it is ~1315 Wm-2.

At latitude 60S, since the Earth tilts ~23.5 degrees, the effective angle is closer to 45 degrees than the 60 degrees used to reference to Earths rotational axis.  Instead of 50%, 60S would receive closer to 70% of the maximum 1410 Wm-2 or 987 Wm-2.  At 60N, there is the same tilt impact but with the lower 1315 Wm-2 producing a maximum possible irradiance of 920 Wm-2.  The difference is ~67 Wm-2.  Since the length of day is longer in local summer, also due to our axial tilt, a smaller percentage of the globe would be able to gain more energy, think of it as pulse width modulation, adding a small but significant amount to the seasonal impact.

If you consider the range of peak values at the Equator, the maximum irradiant is 1293 in winter and minimum is 1205 in summer.  A difference of 87 Wm-2 between those seasons, but in spring and fall the maximum is roughly 1366 Wm-2 (it could be as low as 1360 Wm-2, so there is some uncertainty). That would produce a Southern Hemisphere imbalance wrt the Equator of roughly 70 to 67 Wm-2 and a Northern Hemisphere imbalance of roughly 155 to 161 Wm-2.

The axial tilt of the Earth is not fixed.  It drifts over a period of roughly 44 thousand years which would change the Equatorial imbalance by about 10 Wm-2.  Depending on what the actual absolute surface temperature is, that could produce a roughly a two degree C range of temperature.

The precession of the Equinoxes also changes in an irregular period averaging roughly 21,500 years.  The impact of that change requires considering surface albedo which would impact the percentage of solar energy absorbed and emitted, which can get complicated.  The point of this short post is that there is more than enough internal energy imbalance to offset a significant portion of a radiant impact dependent near isothermal or at least relatively stable conditions.  Speaking of which, Venus has the closest to a purely circular orbit with a day nearly equal to its year.  With no significant orbital or hemispherical imbalances, it has the conditions needed for a maximum radiant impact.  More on that later, right now I have to meet a man about a Tarpon.

Averages

I was discussing my thoughts on averages versus RMS the other day during happy hour.  I mentioned how the climate system was a lot like music.  I also threw in the Selvam Golden ratio implications.   I think that both went over his head, so I am making this quick post.  The chart above is just pure sine waves with the average of the full wave through the fifth or 5 times base frequency.  The average of all of the shapes is one.  The RMS value of all the pure waves is 0.707.  The RMS value of the average of all the pure sine waves, the blue curve, is 0.31569 +/- a touch since I only used 360 points in the spreadsheet for the sine waves.  With an RMS value of 0.707 and average of 1.0, there is a considerable range of variation possible depending on the length of time considered.  Adding this one section of time to that value, 0.707+0.31569= ~1, but it should be pretty obvious that during this one period of time, the apparent impact would seem much larger.

If I add a 45 degree lag to the base frequency, you can see the shift that would produce a step appearing function to the average wave shape.  The average value of all the pure sine wave curves is still one, the RMS values of all the pure sine waves is still 0.707, but the RMS and average value of the "average" blue curve changed, dramatically across the bifurcation point at zero.

I stopped at the fifth in these examples to show that the odd lower harmonics still have a noticeable impact while the even harmonics tend to cancel.


 Since energy has to move in any system, there will be delays in transfer and efficiency losses in the transfer and conversion of the energy.  For Earth there is a common 3 month lag.  3 months out of 12 months is a 1/4 lag pretty close to the 45 degree lag impact in the second graph.  Without knowing what is a true full cycle that would produce the "average", it would be better to consider RMS and Peak to Peak values as realistic limits.

This may seem counter intuitive since RMS is lower than average, but the summation of the harmonics and delays would produce the equivalent of a "constant" minimum value for any time frame.    In the second chart the "constant" is approximately 30% less than the "average" in the first half of the cycle.  This is without any capacity values, just internal lags.

So what to this have to do with the price of tea in China?  Variation is energy loss.  Compare an Earth year to a Venus year.  On Earth, there are 365.25 daily rotations per orbit with an eccentricity of 3.4% from peak to valley.  Venus has 0.92 daily rotations per orbit and an eccentricity of less than 1 percent.    With a Venus day nearly equal to a year and nearly no annual change in orbital forcing, there would be few harmonics and lags to consider at the surface, it would be nearly isothermal.  The "average" solar insolation calculation for both planets is still considered TSI/4 despite the huge orbital differences at their true "surfaces".  Earth's "surface" can likely never be isothermal, so it would always be cooler than "average" at its true "surface".

The Solar Constant?

A constant should be constant.  You can compare Total Solar Insolation reconstructions and find a lot of variation in the "constant".  Leif Svalgaard is a solar scientist I think that is now at Stanford University that has noted how climate scientists tend to pick and choose what value of the Solar "constant" they like for a particular purpose.  With my RMS versus "average" post, I seem to have stirred up some discussion of my sanity.   Why?  Because I think a constant should be a constant.

So here is the problem.  Because the Earth revolves making one rotation in 24 hours you could have what David Springer points out a half rectified sine wave.  The RMS value of a half rectified sine wave is half of the peak.  If Earth had a perfectly circular orbit with no axial tilt, the solar constant would be and the input power would be peak/2 period end of conversation.  Since the Earth orbit is far from perfect, peak/2 is an estimate.  I contend it would be a low estimate.

Does it matter?  If the estimate produces an insignificant error, it doesn't matter.  If it matters totally depends on the degree of precision you wish to obtain.  Since the subject is climate science, a one percent error is roughly equal to the impact of a doubling of CO2, so one percent error is my initial "baseline" for significance.

Due to the elliptical orbit alone, solar intensity varies nearly 100 Wm-2 at the true top of the atmosphere each year.  The typical RMS value of a pure sine wave is 0.707 times the peak of the sine wave,~50 Wm-2 or 35 Wm-2.  Because of axial tilt, the period of the sine wave applied varies by ~10% or 2.4 hours at latitude 45 degrees.  We no longer have a pure sine wave.  Now I contend we need to consider the "true" peak, which is actually the Peak-Peak value and the duration to come up with a more accurate estimate.  That would mean that up to 70 Wm-2 of energy is acquired internally that would have to be transferred with the typical losses in transfer and conversion along the way.

So what would this mean?  That TSI would need an ~70 Wm-2 (65 to 67 Wm-2 appears to be that actual value) DC component due to annual orbit variation.  That DC component is nearly 50% of the "Greenhouse Effect" impact and has absolutely nothing to do with atmospheric gases, only orbital variations.  

I could of course be wrong, but averaging averages is prone to produce errors.  Since the solar "constant" has been revised downward and the estimated "average" surface temperature based on the 1951-1980 also revised downward, it would be very easy to confuse the causes and effects.