Simple Radiant Model - Averaging

Since our rock has a few idiosyncrasies, like tilting and wandering around on that tilt, this use of the simple radiant model is show the subtle effects.  AS is Austral Summer, when the southern hemisphere is closer to the Sun and the Earth is also closer to the Sun.  Instead of 1361Wm-2, the solar energy in AS is close to 1410Wm-2.  That is about 3.6% greater than "average".  In AW, Austral Winter, the Northern hemisphere is tilted toward the Sun and the Earth if further away from the Sun.  The average solar energy during AW is about 1320Wm-2 or 3.6% less than "normal".  The model average is 344.8 for AS, 322.8 for AW then I have Average 1 and Average 2.  Average 1 is the annual average of just AS and AW for daylight.  Since half of the globe would be dark, the global average according to the Simple Radiant model would be half or 231 Wm-2.  That is a little lower than the 236 to 239 Wm-2 average used most calculations.  Then the Simple model is using exactly .30 albedo and rounding solar energy a tiny bit.

Average 2, is the average of the annual energy between AS and AW,  333.8 divided by 2 would mean 166.9 Wm-2, which is Summer Winter only average.  Cumulative, 667.6 for dayside or 333.8 Wm-2 global, is the cumulative peak value over one year.

Since the Earth is round, the simplest way to estimate "average" solar energy is TSI*(1-abedo)/4, where 4 is the ratio of the surface area of a Sphere to a Flat Disc.  With TSI = 1361 and albedo = 0.30, then "average" Solar energy available at the Top of the Atmosphere would be 238.2Wm-2 per day.

The Simple Radiant Model is less than perfect, but it should be consistent.  The SRM "average" is 231 versus 238, the cumulative average would be 334 and the simple average, 167 Wm-2.

If the energy loss from the surface was extremely fast, the global average energy would be close to the simple average.  If the energy loss from the surface was extremely slow, the global average energy would be close to the cumulative average.  If the Earth were an "ideal" blackbody, the global average would be 231Wm-2 based on the Simple Radiant Model.

This SRM is not supposed to provide exact number for any "average".  It is only designed to provide a reference.  Some may have noticed that no "Greenhouse Effect" is involved in any way with the SRM.  That is because, in my opinion, there are too many assumptions made of what "average" would be without a GHE.

Why use this Simple Radiant Model?

With energy provided mainly at the equator, internally, that energy has to be transferred towards the poles.  The Cosine function simply provides a visual tool.  Since the Earth has an equatorial radius of ~6371 kilometers, the Cosine of the latitude times the radius would be the radius of a parallel slice of Earth at that latitude.  At latitude 60, the Cosine is 0.5, so 50% of the equatorial "wall" would be available at latitude 60 to internal pole ward heat transfer if the "slice" were the same depth.  The altitude of the tropopause at the equator might be 20 kilometers, the the internal energy transfer were ideal, it would be 10 kilometers at the 60 degree latitude "slice".  It is not, but the difference between "ideal" and actual is meaningful.  By the same logic the slice at latitude 75 would be nearly 50% of  latitude 60 slice.  Just like the simple regulator, the area available for flow decreases as the height or radius of the section, decreases.

Simple Radiant Model with Degrees Kelvin

The Sun is a radiant source with a true average.  It uniformly emits energy isotopically or in all directions.  The Earth emits energy isotopically, but not uniformly.  In order to emit uniformly, internal energy transfer would have to be instantaneous.    That is physically impossible.   

So here is the simple radiant model again.  Ein TOA is 70% of 1361Wm-2 or roughly the solar energy available corrected for estimated albedo.  The mean distribution of that energy 603 Wm-2, shown with the blue mean value line and the 603.1 average of the blue curve.  The mean of that 603 curve is ~390 Wm-2.  The red curve is temperature determined using S-B (Wm-2/5.67e-8)^.25, the Stefan-Boltzmann relationship.

This simple model is not designed to resolve all the issues of climate change, only to illustrate the relationship of energy and its 4th power cousin temperature.  The transfer of energy poleward, is the key component of global "mean" temperature.  If earth had a denser atmosphere, it would be effectively isothermal.  If Earth had no atmosphere, it would get hot on the sun lit side and cold as all get out on the darkside.  That would require another simple model based on longitude.  It should not be necessary to merge two models to illustrate that the sunny side is uniformly warm and the variance in temperature for an ideal world starts increasing as the poles are approached.  If the energy is shifted north or south of the equator, the pole closer to the shift would have a more uniform temperature and the one further away a more radiacle change in temperature.  No change in global "forcing" is required to significantly change poleward temperature.

Location, location, location.  That is just to remind the radiant only affecionadoes that the density and composition of the "surface" has a huge impact on temperature distribution.

Now the model is for an ideal planet with no tilt, the energy is applied at the equator.  The Earth tilts at roughly 21 degrees and there is nearly 8% difference in the energy applied to the two hemispheres due to the  elliptical orbit around the Sun.

By shifting the peak energy South by 21 degrees latitude and increasing solar insulation, the simple radiant model produces a southern hemisphere "lobe"  of energy but the northern hemisphere temperature impact begins in noticably at the equator and drops off the chart at roughly 70 degrees north.  This is the Austral summer configuration.  If I were to combine this with an Austral winter snapshot, there would be two "lobes"  with a dip near the equator.  By merging those two charts, you would have a rough "ideal" Theta E of the atmosphere or potential temperature only in terms of energy Wm-2.

The "true" Theta E would depend on the rate of energy release from the surface.  Each layer, liquid, solid, and gas would have different energy transfer rates based on the physical properties of each layer.

Simple Radiant Model

Living on a close to spherical rock wandering through space we oddly have a flat perspective of the universe whizzing around.  Being able to visualize not only what we "see" but what nature "sees" requires a little imagination.  Communicating that vision in two dimensions is more of a challenge.  Simple models help.

Above is a simple radiant model.  Like all models it is not perfect.  The Earth is not a perfect sphere, so using the "average" would produce some error.  This model uses a simple cosine of latitude to show what energy visiting the Earth may "see".

The best estimate of the average solar energy available to Earth annually is ~239Wm-2, if that energy is uniformly distributed across the true surface of the Earth. The average energy available at the Top of the Atmosphere (TOA) is roughly 341 Wm-2.  Between the TOA and "true" surface, there is a lot of stuff going on, so how much can a simple model tell us?

By plotting the weighted average, or the 239 Wm-2 times the cosine of the latitude, we have the blue curve.  Averaging the blue curve produces 151.3 Wm-2, which is roughly the magnitude of the "Greenhouse Effect".  Adding the 151.3 Wm-2 to Ein, 239 Wm-2, results in 390.3 Wm-2 or the estimated average Stefan-Boltzmann equivalent surface energy.  Just using this simple model we can arrive at a very close approximation of the "Greenhouse Effect". No smoke, no mirrors, just a simple radiant model.

When I posted the Simple Regulator Note, I mentioned that visualizing the same type of shape in the atmosphere would be a little difficult for some.  The cosine curve in the plots are just a smoothed version of that simple regulator.  Energy applied at the equator, the peak of the curves, has to migrate toward the poles.  The resistance to flow of that energy by latitude would roughly follow the curves.  It is harder to exit from the equator and easier to exit at the poles.  Think about it, then you can bookmark this simple radiant model to impress your friends.

Simple Regulator Note.

This is about the simplest example of a non-linear flow regulator.  A right triangle opening.  Since the angles are equal, the area of the opening equals 1/2 the base times the height, the height and base are equal so area equals 1/2h^2.

This is the main part of the design of a number of fluid flow automatic controls.  By having a spring control the pressure required to change the value of "h", the controller can be calibrated for a range of flow control provide the pressure of the fluid is regulated.  If you consider the widest point of the base as the equator and the point one of the poles, you have one of the may control features of Earth's climate.  The blue line would be the thermal equator or the hemisphere mean.  As the average temperature of the hemisphere increases, the mean would shift toward the point or pole.

What may be harder to visualize is that there would also be a simple regulator in the atmosphere.  Because of gravity, the air density decreases with altitude, the resistance to flow decreases with altitude or h.  The atmosphere doesn't have an easy to determine base though.  It would have its narrowest base at the global thermal equator and its widest base at the closest pole.  Since the fluids vary from water to photons, what the fluid in question "sees" may not be what we might "see".  For the system to be stable, all the fluids would have to "see" the same average area.  So if you know what any one fluid "sees" you can estimate what all the other energy "fluids" would have to see on average, for the Earth to exist.  Since the Earth does exist, this simple regulator can be the main module of a climate model.

The Southern Ocean Oscillation

There are few locations on Earth that stand a chance of being representative of past climate better than Southern South America.  It is the Best Place to Start since it is highly influenced by the Humbolt Current and the Antarctic Circumpolar Current variations.  ENSO cycles on scales of hundreds of years influence climate and the Southern Eastern Pacific ocean is the best indication of the start of those cycles.

While it would be convinient to have all the answers to changes in forcing that impact climate, the fact is that climate is dynamic with long term settling times that appears as Unforced Internal Oscillation that cannot be dismissed.  Even the initiation of what may be the Atlantic Multi-decadal Oscillation appears in the southern oceans nearly three decades before the obvious shift.

Girma, an online denizen that frequents Dr. Judith Curry's Climate Etc. blog, obsessively points out that there is a repeatable pattern in the instrumental climate record.  What is missing is a way to identify the cause and predict the impact on future climate.

Instead of an Index, which doesn't correlate to actual temperature impact, the Southern Ocean Oscillation can be compared with regional data to estimate the timing and rough magnitude of the impact of the shifts in the oscillation.  While far from perfect, the pseudo cyclic oscillation appears to have more predictive capability than any other longer term oscillatory pattern.

So instead of taking my word for it, I recommend that those interested download a copy of the Neukom et al. Southern South American temperature reconstruction, average the reconstruction over the 1880 to 1995 overlap period and have at prognostication.  Pass it along to your friends and impress strangers with your new climate predictions.

Since the Neukom et al. 2010 link on the NOAA Plaeo site appears to have been altered, here is the original reference:
:
Southern South America Multiproxy 1100 Year Temperature Reconstructions
-----------------------------------------------------------------------
World Data Center for Paleoclimatology, Boulder
and
NOAA Paleoclimatology Program
-----------------------------------------------------------------------
NOTE: PLEASE CITE ORIGINAL REFERENCE WHEN USING THIS DATA!!!!!


NAME OF DATA SET:
Southern South America Multiproxy 1100 Year Temperature Reconstructions

LAST UPDATE: 3/2010 (Original receipt by WDC Paleo)
CONTRIBUTORS:
Neukom, R., J. Luterbacher, R. Villalba, M. Küttel, D. Frank,
P.D. Jones, M. Grosjean, H. Wanner, J.-C. Aravena, D.E. Black,
D.A. Christie, R. D'Arrigo, A. Lara, M. Morales, C. Soliz-Gamboa,
A. Srur, R. Urrutia, and L. von Gunten.

IGBP PAGES/WDCA CONTRIBUTION SERIES NUMBER: 2010-031

WDC PALEO CONTRIBUTION SERIES CITATION:
Neukom, R., et al. 2010.
Southern South America Multiproxy 1100 Year Temperature Reconstructions.
IGBP PAGES/World Data Center for Paleoclimatology
Data Contribution Series # 2010-031.
NOAA/NCDC Paleoclimatology Program, Boulder CO, USA.


ORIGINAL REFERENCE:
Neukom, R., J. Luterbacher, R. Villalba, M. Küttel, D. Frank,
P.D. Jones, M. Grosjean, H. Wanner, J.-C. Aravena, D.E. Black,
D.A. Christie, R. D'Arrigo, A. Lara, M. Morales, C. Soliz-Gamboa,
A. Srur, R. Urrutia, and L. von Gunten. 2010.
Multiproxy summer and winter surface air temperature field
reconstructions for southern South America covering the past centuries.
Climate Dynamics, Online First March 28, 2010,
DOI: 10.1007/s00382-010-0793-3

The GISS LOTI data can be obtained at GISTemp Zonal Means.

Weird Autocorrelation?

Update:  Okay, found out that there was a copy paste error in the spread sheet.  Still an interesting situation, see below:


Since I had the mess up I may as well take this chance to explain what I am trying to do better.  The impact of solar variation is estimated at ~0.2C degrees depending on the source.  That impact is complicated since solar is absorbed at different depths, impacted by cloud cover, impacted by heat capacity variation due to internal variability, it is just basically a bitch to accurately isolate all the impacts of solar.  The screw up in the original post below tends to indicate that some more information on solar longer term impacts may be in the data.  The formula I am trying to find just uses the quadratic equation to determine distance traveled from point A to point B per data point and compares that distance with the distant traveled for point A to point C, D or whatever.  Since solar has impacts with differing time delays, by using point A to B for 6 months, point A to C for 11 years I should be able to isolate the solar signal a little better.  I know that FFT would do the same job or I could download R and used canned routines, but there should be a simple approach that is pretty effective with just the basic spread sheet program.  

Autocorrelation is tool for finding a repeating pattern in a time series or signal.  The Durban Watson Statistic, is a test for auto correlation that is used in most statistical analysis.  The DW compares a value at time t with a value at time t-something, typically 1, and divides [e(t)-e(t-1)]^2 by e(t)^2.  The e(t) is normally a residual, of the variance from the mean of the regression or signal that the statistic is being preformed on.  If the "noise" or residual is truly random, the sum of all the e(t)-e(t-1) would be zero or darn close.

Looking at the new HADCRUT4 and the Svalgaard solar data, I got a wild hair and decided to do a simple "cheat" autocorrelation anaysis.  The "cheat" is:

                                                   [x(t)-x(t-4)]/[x(t)^2+x(t-4)^2]^0.5 

Just like the DW test, if x(t) and x(t-l) are truly random there will be no trend.  If the values of x(t) are greater than 1, the magnitude of the test value can fluctuate a good deal, but it is just a "cheat" test I am playing with.

 This is a test with just random numbers and no trend if the random number generator is truly random.

This is a test with a large trend added to the same random series.  This "cheat" test is not all that sensitive, but    it does the job and is quick in Openoffice.

Update:  In the chart above [x(t)*x(t-4)] not [x(t)-x(t-4)] was used, my bad.  So when I use the "cheat" with lag 3 on the HADCRUT4 data set and compare to the Svalgaard TSI, I get an interesting chart.  Notice that the 1910 to 1940 temperature rise is not evident in the chart and the cheat statistic appears to be inversely correlated to the longer term solar time series.  

I have no idea if the cheat is exceptional in any way or totally buggy, but that is pretty interesting.

I will have to brush up on my stats (arrgh!), but there is probably a more standard autocorrelation method that can fine tune that relationship.

Added:

This is the cheat with HADSST2 showing a pattern more like I was expecting with the lags and the ugly pre-1900 sh data.  

This is the [x(t)-x(t-4)] version of the CRUT4 data.  More on this in a moment.

This does a reasonable job, but is not much better than just plotting variance and I already know there is a reduction in variance, what I don't know is if that is an artifact of the crappy data or something that is related enough to solar to estimate impact.  

So to cut down on the noise what I done here is scaled the data before the operation.  I just found the minimum value, in the NH data series of course, and added that minimum to both the NH and SH data sets.  Solar appears to have a pretty good correlation, but there is not much more information than just eyeballing the curves.

So I am still stuck with this estimate of lags for solar forcing. There is no indication of a true lag in the tropics because of ENSO noise, but a hint in other latitudes.  Both highest latitudes are also so noisy that they are useless.

Playing with ENSO and Solar

Updated with all new chart at the end!

One of the guys crazy enough to listen to my theories wanted to know more about natural variability.  The chart above is a damped cosine with Tau = 54 months, another with Tau = 30 month and a sine wave for Solar TSI variation with 140 period and 36 month lag.  The 54 30 36 is the sum of those curves.  The background tropics is from HADCRUT4 since I had it on the spread sheet.  The delay in heat transfer from the tropics toward the hemispheres or how long it takes the atmosphere and currents to make that energy available in the higher latitudes varies.  This chart just gives a rough idea of what may be happening for this one particular event.  Every event will be different because the harmonic or resonance frequencies change for a variety of reasons.  One of the neater ones is ocean heat capacity.

When the oceans or one hemisphere relative to the other has different or lower than "normal" capacity, the rate of uptake or release of the ocean energy would of course change.  That change can be seen, if you look hard enough, in various data that is readily available.  Sea level is related to heat capacity, diurnal temperature differences  and of course the rates of change in surface temperature would be related, to ocean heat capacity. and the distribution of that capacity.  That simple means that "Sensitivity" changes.  It will decay toward some new "normal".

With everything changing, I thought I would use this unique view to illustrate how Solar and Climate are related but not very predictably.  I trended, or added a 0.8 C per century slope to the Svalgaard Total Solar Irradiance or Insolation (TSI) reconstruction instead of detrending the HADCRUT4 temperature record.  Early in the period, Climate was more sensitive to solar changes and as ocean heat content increased, the sensitivity to solar decreased.  There are CO2 and other forcings in there as well, but this tends to indicate than Solar is not negligible by any stretch of the imagination. Because Solar impacts a variety of "layers" of atmosphere and oceans, the solar energy in averaged over a longer time period and can create the steps in the temperature record.  The downward slope from these steps would be an indication of the ocean heat capacity relative to "normal" and the current "pause" is likely an indication of "normal" for the current conditions being reached.

I just thought a few folks might get a kick out of this non-standard view of Climate.

Since the change in the relationship of one region to another tends to highly shifts in climate better than the more slow changing "trends" this chart show the average solar from 1850 with the difference between NH temperatures, total and SST, minus the tropical temperatures.  This would be the similar to the AMO, though it would include northern Pacific variation.  The Holy Climate Shift! arrow is where Scandinavian temperatures jumped nearly 3 degrees and remained on that step.

Old Shocks in Climate

This chart is just for illustration so don't go nutz thinking the climate problem is resolved.  What is shows is  how different delays to a perturbations can sum to a response curve that doesn't resemble the perturbation.  I have said may times that the "noise" in climate is actually the more interesting "signal".  Schwartz et al. published a paper saying they had "found" THE lag time and were able to calculate climate "sensitivity"  Their paper was met with "YOU CAN"T DO THAT!"  Actually, you can, but you need to be BERRY BERRY CWARFUL how you interpret your results.

The truth is there is a roughly five year lag and it does give you a clue about climate sensitivity.  In this case there is likely a charge time for the upper oceans on the order of 5 years, but that 5 years is not a guarantee.

Equatorial heat is transferred to the northern and southern extra-tropics at different rates which change with the initial conditions of the northern and southern extra-tropics.  For example; if the northern hemisphere had been colder than normal, there would have been more sea ice than normal, that greater than "normal"sea ice would "dampen" the northern hemisphere response and vice versa.

The weakly damped ~5 year (currently) lag/decay has several "bumps" that can "synchronize" with a future perturbation, like solar.  Solar itself has a not so reliable cyclic nature, so the "synchronization" is pretty random.  Solar though is close enough to being "predictable" that a smart person with plenty of computer time on their hands could make a reasonable forecast a decade or two in advance.  However, this is just one of many weakly damped decay curves of likely hundreds.

Solar and weakly Damped Interactions

In the Sun!  It's not the Sun!  Come on guys, think.

Solar energy is absorbed by the atmosphere, the surface sink layer, the upper mixing level and the lower mixing level.  I am not going to look it up by something like, 20%, 25%, 45% and 10% respectively.

The delays would be months, months to a year, a year to 5 years and a 5 years to 15 years, for the atmosphere, skin layer, upper mixing layer and lower mixing layer.  A surface cannot emit energy any faster than energy can be transferred to the radiant surface, so there are lags.  Since the solar cycle is roughly 11 years and the lower mixing layer can delay energy release longer than 11 years at times, you have the wonderful harmonic or decay curve to consider.

Here is the Leif Svalgaard Solar TSI reconstruction with 5 and 15 year smoothing with ocean again an incorrectly labeled 11-5 which should be 15 yma minus 5 yma.  Open office has a nasty habit of not updating the second label for some odd reason.  PITA it is.

The 11 or 15 minus 5 is just a method of isolating a delay peak.  It is not to scale and likely inverted, but since the timing is the thing, it is useful.  The 15 year moving average illustrates the general impact that could be expected, the 5 year and "raw" data the noise that may be expected and the 11-5 of course, an estimate of the more noticeable impact.

The lower mixing layer absorption would be the biggest PITA.  Since the delay is not close to being reliable and depending on the currents, the impact may or may not be amplified by land/ocean thermal capacity ratio,  you have to be lucky to attribute any effect to the lower mixing layer absorption cause.  That would involve intimate knowledge of the internal natural oscillation causes and decay curves.

Weakly Damped Lost in the Noise

Natural internal oscillations appear to be weakly damped.  Since the forcings are not using the same dampening, that leads to fun "seeing" what is going on in the climate system.  To dig out some of the "signal" there are some simple ways that don't require a ton of work.

This chart is the HADCRUT4 detrended 30-30 or tropical data with 11yr moving average, 4 year moving average that is not labeled for some reason and the average of the two moving averages.  The 11 year averaging smooths the curve more than the 4 year moving average and the average of the two is not all that informative.  By subtracting the 4 year moving average from the 11 year moving average, you can highlight the differences and remove the trends.

This chart is the difference of the 11 and 4 year moving averages for the NH, Tropics and SH HADCRUT4 data.  We now have a signal envelop.  As you can see, the NH and SH do not respond the same to the forcing signal, likely the solar cycle variations.

By adding the Svalgaard TSI reconstruction you can see two points where solar is in phase with the internal oscillations and a box where the internal signal dramatically reduces.  The entry to the box, solar is 180 degrees out of phase with the internal signal and at the exit of the box, solar is nearly in phase with the internal signal.  This is likely due to the damening of the internal signal first being different between hemispheres and longer than the ~11 year solar cycle.

This chart is just a weakly damped sinewave.  When a solar cycle is in phase with the first peak, it would have the greatest impact, the second peak would have noticeable impact and the third peak may or may not be large enough to notice.  Since the solar cycle is only in phase every second to fifth oscillation, trying to isolate solar's true impact would be a major bitch.  Needless to say, assuming a 2 or 3 year lag without considering the internal dampening, would be pretty useless.

Thermal Capacity and Amplification of Measured Temperature

This table contains the area of water and land per 5 degree bands of latitude.  The right column, Gain is 4.2*Water/(4.2*Water-1*Land)  Where there is only water, the gain is one.  Where there is only land, the gain is complicated and negative.

The multiplier 1, for Land can vary from ~0.7 to ~3.0.  The multiplier, 4.2 for water, can vary from ~3.9 to ~4.3 depending on temperature and salinity.  The multiplier for ice, whether fixed to land or on the surface of water is ~2.0.

This gain is based on the thermal capacity differences between surface areas of the globe.  The Gain is unitless.  In the Table, the units for Water and Land are million kilometers squared.

This table is useful for illustration, but another table based on Longitude and Latitude to produce gridded values would be required for serious utility.

With the gridded gain, the distance between high heat capacity "cells" (low gain) and low heat capacity "cells" (high gain) could be used to determine the relative impact that thermal capacity has on local surface temperature.

For three dimensional use, the heat capacity of the atmosphere above the "cell" and the elevation or distance from the surface "cell" to the atmospheric "cell" would be used to determine "relative" gain.

That in a nutshell, is the basic building block of a model for determining the impact of internal variability on climate. The central module of a "moist air" or enthalpy model which would need to be compared to a "dry air" or radiant model.

The Pause that Refocuses

The title is blatantly stolen from the Climate Etc. Blog.  There is uncertainty and there is uncertainty or ignorance. The "Pause", is the climate shift that started in 1995 though it probably started in 1990 and was interrupted by Pinatubo.  So the "significance" of the "pause" is now the new rehash on Climate Etc.

Sequential Linear Regressions (SLR) is a way to "Gut Check" a trend significance.  Scientist don't like that kinda talk, they want peer reviewed proof, but once again into the lack of peer reviewed breach.

First, using just one data set and the "average" of that data set to boot, when determining the significance of a trend is just plain stupid.  So this rehash is another "Stupid" discussion.  Stupid is not always the same as ignorance.  The chart above has the 15year and 20year SLR for the new HADCRUT4 surface temperature data set.  The units on the y axis are decadal trends in degrees C for each point with the start date on the x axis.  The mean value for the "Global" series is shown which indicate a reliable "mean" regression slope from 1955 of ~0.12 for the 20 year and ~0.13 for the 15 year curves.  That should be pretty straight forward.

The difference between 0.12 and 0.013 is small, indicating that there is not enough statistical difference between 15 year trends and 20 year trends for this portion of the "average" of this time series, to worry about.

By hiding the "global" curves but leaving the mean value lines, you can compare the most noisy, NH means to the least noisy, SH means, which gives a range of ~0.08 to ~0.16, or a 0.08 range of uncertainty above and below the ~0.125 mean of the "average" "Global" temperature SLR.  Without knowing the physical processes causing that range of uncertainty, 0.08 to 0.16 would be your range of "ignorance".  Since the mean of the "average" is ~0.125 and there is a +/-0.04 ignorance range, you can be fairly certain that there is a trend of at least  0.085 but likely less than 0.165 for the HADCRUT4 (66% confidence) data from 1955 to present.

There are plenty of other "peer reviewed" methods that can be used, but this is a very simple, "gut check" method that is in keeping with, Exploratory Data Analysis (EDA), which is basically, LOOKING at the data.

Nearly forgot, the same SLR comparison from 1900 with 32 year regressions shows a mean slope of ~0.08 per decade, the current ~0.8C of total warming.  The difference between the 1900 to present ~0.08 and 1955 to present ~0.125 is 0.045 producing the roughly same 66% confidence level ( 0.08 to 0.17 instead of 0.16).

Decades of Heat Capacity Change

This is not really ready for prime time but it is an interesting view of climate change.  I am using the surface area of the oceans by 5 degree bands of latitude and temperature data to put together a profile view of heat capacity.  I am working more on the look than the accuracy right now, using GISS regional land and ocean data  instead of actual ocean 5 degree bands, but it looks pretty neat.

This is how it looks so far.  Estimated heat capacity of the surface layer or the oceans by latitude.  There are decade plots of average showing that there is not much to see.

This view is a lot better.   The plots are the decades (shifted up one year to include 2011) subracted fro the 1942 to 1951 decade which is the base period.  The oughts (00s) are the main story, but it is interesting that the 90s where not that different than the 40s except for the northern high latitudes.  The bump in the ACC region is obvious in all the plots, but the 70s, 80s and the 00s show the shift toward the northern latitudes pretty well.

Still a lot of work to do, but it will be fun to "see" heat capacity changes instead of the same old boring temperature anomaly stuff.

10 Raised to the 22nd is a Big Number

With the validity of temperatures trends being questioned the debate turns to Ocean Heat Content (OHC).  This is the area of the famous "missing" heat.

This table is estimates of the ocean by 5 degree latitude bands.  The Tave, or average temperature is from one of Bob Tisdale's charts posted by Roger Pielke Sr. when examining SST by latitudinal band.  Since the bands I am using are not the same as Bob Tisdale was using, this is an estimate.

The Water Area is in million kilometers squared (km^2), there are one million cubic meters in a km^2 of water one meter deep, there are one million grams of water in a cubic meter of water and this chart estimate 4.2 Joules per gram per degree C.  For negative temperatures, 4.2 is assumed to zero C degrees.  Above zero, each degree adds 4.2 joules per gram.  This is an estimate since salinity does impact the heat capacity and the 4.2 J/g varies with temperature.  This determined the One Meter Joules value.  The One Degree column is a "what if" temperature uniformly increased by a degree or the impact of one degree temperature change per 5 degree latitude band.

The top one meter of the oceans would contain roughly 2.78 E+22 Joules.  So to estimate the heat capacity of the upper mixing layer, should that be 100 meters thick, multiply by 100.  A simple tool to put in your bullshit detector toolbox.

While I have briefly checked the values in the table, I haven't gone nutz since there are several estimates made that I would like to make more accurate.  For general BS detector use, it appears to be close enough for government work.  Should anyone note a glaring error, let me know, but this is basically a rough draft from an ongoing project.

Like using the data to "see" global heat capacity.  Like here, the oceans are biased to the Southern hemisphere but the energy of the oceans is more uniformly "balanced" between the hemispheres.  I could use this base estimate and use decadal variations temperature by latitude to show the shifting balance.  That would be the climate "shifts".  The resistance of the atmosphere to radiant heat loss would change with the shifting internal "balance".  Since the southern hemisphere has the thermally isolated Antarctic, that "window" to space is more open.

How Would You Predict the Future?

The one truism about trends it that by the time you know one exits, it is too late to do you any good.

There are tricks to help locate trends.  This is "normalized" data for GISS LOTI regional.  Normalizing, or dividing the average (not RMS) by the standard deviation in this case, lets you compare the fluctuations of different data sets.  The green curve, 44S to 64S (legend should read 44-64S)  does not vary as much as the other data it is compared withIt has roughly the same "trend" but less variation.

This is the Green 44S-64S with Global, Northern Hemisphere and Southern Hemisphere data, no "normalization" this time.  The Green Curve is almost 100% ocean.  The Blue is about 70% ocean.  The Yellow is about 76% ocean.  The Red is about 35% ocean.  If you where thinking about predicting changes in the oceans, which would you use to predict the future?

Hint:  What is the color of money?

Tuggweilder and Samuels, 1994, Effect of the Drake Passage on Global Thermohaline Circulation



Abstract-The Ekman divergence around Antarctica raises a large amount of deep water to the
ocean’s surface. The regional Ekman transport moves the upwelled deep water northward out of
the circumpolar zone. The divergence and northward surface drift combine, in effect, to remove
deep water from the interior of the ocean. This wind-driven removal process is facilitated by a
unique dynamic constraint operating in the latitude band containing Drake Passage. Through a
simple model sensitivity experiment WC show that the upwelling and removal of deep water in the
circumpolar belt may be quantitatively related to the formation of new deep water in the northern
North Atlantic. These results show that stronger winds in the south can induct more deep water
formation in the north and more deep outflow through the South Atlantic. The fact that winds in
the southern hemisphere might influence the formation of deep water in the North Atlantic brings
into question long-standing notions about the forces that drive the ocean’s thermohaline circulation.

Is a must read if you want any insight into longer term global climate.  The drawing which is reproduced without permission, so should the holder of the rights be offended, I will remove, but it is a very educational drawing.   The Antarctic Convergence is more than just an ocean convergence, it is an upper ocean, deep ocean, atmospheric, thermally isolated Antarctic, radiant window to space convergence zone, which is modulated by the Drake Passage Current and southern hemisphere atmospheric and sea ice dynamics.  It is the cheese in the "big cheese" of climate regulation.  The source of the 4C deep ocean heat content borders a ~2C mixed ACC band with the mystereous <0 C source of the true abysmal depths sliding down the rock face of the continent of Antarctica.  Small changes in weather patterns and sea ice extent can cause a 2 C change in temperature from 55S to 45S in a fairly short time period.  That shift would change the average temperature and downward pressure on the 4C deep water supply for the THC with impacts that would be felt many decades in the future.

Enjoy

Sweets Spots, Apples and Frozen Oranges

Climate today is being compared to past climate to predict future climate.  Only one problem, the conditions in the past do not exist today and many unlikely to exist in the future.  So what drove the changes in the past will likely not have the same impact in the future.  This is the single most difficult point to explain in the climate debate.

The solar insolation typically used for "Ice Age" comparisons is 65N or in some studies 70S.  The chart above use Huybers et al. data for 30S and the 250Wm-2 threshold.  When both the Solar and either of the SST reconstructions (Herbert et al. 2010) are above a threshold or "Sweet Spot", there is a coordinated response.   Below a certain threshold, there is little or no response to solar.  The rise of the South China Sea from 250ka to 200ka was not inphase with the Eastern Pacific or the penultimate deglaciation would have occurred 20 to 40ka before it did.  At 150ka, the Eastern Pacific was below its threshold and the South china Sea was decreasing.  The decrease in the Eastern Tropical Pacific was likely due to Southern Hemisphere sea ice and circulation that changed the heat transfer efficiency in the southern oceans.

Once both the Eastern Pacific and South China Sea reached their peaks, prior to peak solar, the decline into the last glacial maximum (LGM) began, undoubtedly aided by Northern Hemisphere increasing ice mass.  The decline into the LGM took 100,000 years from the peak Pacific ocean temperatures.

The common thought process is that that cycle is repeatable.  With mankind claiming the vast expanse of lands that where covered by glacial ice in the LGM, it is unlikely that man would fall asleep at the switch for 100,000 years to allow the gradual accumulation of glacial ice.  So it is not productive to compare a response to solar forcing where glacial ice is a major feedback.  That would be comparing apples to frozen oranges.  Periods where ice extent are more inline with what "should" be expected, would be a better comparison if attempting to predict future climate.

Quite a few researchers have attempted to use paleo data to determine "climate sensitivity".  Using perfectly valid methods, they arrive at ranges from 0.7 to 9 C degrees per doubling of CO2.  The higher estimates are generally based on the most recent past 400,000 years where the would be nearly maximum ice albedo feedback and ice mass thermal feedback with ocean current impacts thrown in to boot.

By eliminating the Ice variable that impacts radiant forcing, the internal dynamics of the oceans relative to an expectation of future minimal ice expanse condition would allow not only a simpler, but more accurate prediction of impact due to various "pertinent" forcing combinations.

This confusion over where to focus attention is likely the largest stumbling block in the climate debate.  Multi-millennial land use impact cannot be ignored.

Sweet Spots Produce Amazing Results

Any Golfer, Baseball Player or Physicist knows about sweet spots.  Where the least amount of energy provides the greatest result.  In golf, many players pay big bucks to get frequency tuned shafts and cavity backed irons.  The oversize metal woods like the aluminum baseball bat have larger "sweet spots" where  less velocity produces greater distance that wooden clubs or bats.  One of the best, but somewhat difficult to master golf swings, is David Duval's in his prime.

Constant acceleration through the point of contact, SWEET!  If you over swing or under swing you just don't get the same results.

Climate also has its sweet spot or Goldielocks moments.  In Climate science you hear about forcings, conservation of energy and conservation of mass, but not much about conservation of momentum.  This plot of the Bintanja & van de Wal 45N termperature of the deep ocean and the estimated orbital precession shows a sweet spot.  The upswing in temperature was perfectly timed with the increase solar energy in the southern oceans while the southern ocean temperatures where developing momentum in a warming phase from a deeper than normal depressed temperature.  Now this plot is of the 45N ocean temperature, how would I know what the southern oceans where doing?

The Martin et al. bottom water temperatures don't cover the same period, but comparing the last two deglaciations shows what I am talking about.  The penultimate deglaciation had the Tropical Eastern Pacific BWT out of phase with the Atlantic BWT.  The energy collected by the Pacific was partically transferred to the Atlantic, but not with the proper timeing to over come the thermal inertia of the Atlantic waters.  In the last deglaciation, a synchronizing pulse circa 80 k years ago shifted the momentum of the Atlantic bottom water so that with the following solar pulse the sweet spot was hit.

The shift from 41 ka cycles to the current ~100 ka maybe cycle is due to changes in the internal harmonics of the global ocean heat transfer.  Bold statement, right?

This chart of the Pahnke southern ocean SST with estimated solar precession also shows how with in phase orientation, there is greater results for less energy applied.

Looking at the first chart again, the x-axis is scaled to 23ka years and shift to align with some of the more interesting peaks.  The precession frequency is not exact and the decay frequency or internal harmonics of the oceans are not exactly tuned to the precessional frequency.  The 4.3ka recurrent frequency of the ocean oscillations from precessional perturbation is not a perfect "fifth", it is a little out of tune.  The Oceans also have a ~5.8ka decay from the 41ka obliquity perturbations indicating they decay well before that next perturbations.  The oceans are current tuned to ~21.5ka cycles which drift allows to synchronize either with precession or with every second or third obliquity cycle.

Showing why there is a new tuning since ~800ka years ago is a challenge, but the precessional cycle has been in charge in the distant past.

Between 1800ka and 2000 ka years before present, the Earth's Geomagnetic field was also in the current orientation and developed the start of the `~100ka ice age cycles.  Even then the range of oceans temperatures was small with no hint of runaway climate.  In fact the short precession frequency produced a smaller range of variation.

Timing is everything in nonlinear dynamics, whether it is a golf swing or paleo climate.

Just Charts Waiting for a Story

Since I have had a few computers crash in the past two years likely due to humid Florida weather, I tend to post stuff on line for safe keeping.  Instead of trying to keep the stuff private, I just let it out there for all to see..  There are lots of Southern Hemisphere Ocean Cores to play with, so I will just post a few charts I think are keepers here from time to time.  References will be a little lax with mainly just the core ID posted unless someone complains, until I either use the charts in a semi-post or just move on.  Geomagnetic fans though might find this one interesting.

SUGGESTED DATA CITATION: Yamamoto, M., et al.  2007.
California Current 136KYr Alkenone Sea Surface Temperature Estimates. 
IGBP PAGES/World Data Center for Paleoclimatology 
Data Contribution Series # 2007-100.
NOAA/NCDC Paleoclimatology Program, Boulder CO, USA.

The Bintanja and van de Wal should make and excellent reference for past sea level.  This chart compares the Herbert et al. 2010 Tropical Eastern Pacific and South China Sea temperature reconstructions.  Opposite axis are used with the Herbert data shifted so the mean value of all three series for the period 0 to 3000 ka, where available, align.  The temperature scale is just roughly adjusted for fit near 2000ka.

This is the same chart from 1500 to 3000 ka with the rough adjustment period in the highlight box.  This is the period which had two closely space magnetic reversals followed by the longer Compass North orientation. 

The first part of the chart which shows the shift circa 900 to 920 ka which starts the rise in Tropical Eastern Pacific Temperature and sea level wide fluctuation range.

The shift in the highlight box not only change the slope of tropical Pacific SST, it appears to have accentuated the longer 400ka orbital cycle.  

The DSD607 is in the Northern Atlantic which provides a good comparison to the tropical eastern Pacific.  The same Herbert et al. 2010 for ODP846 and Lawrence et al. 2010 

Lawrence, K.T., S. Sosdian, H.E. White, and Y. Rosenthal. 2010. 
North Atlantic climate evolution through the Plio-Pleistocene climate transitions. 
Earth and Planetary Science Letters, Vol. 300, Issues 3-4, 
1 December 2010, pp. 329-342. 
doi:10.1016/j.epsl.2010.10.013 

Interesting take in the Abstract:

We propose that the expansion of the West Antarctic ice sheet (WAIS) across the MPT increased the production and export of Antarctic Bottom Water from the Southern Ocean and subsequently controlled its incursion into the North Atlantic, especially during glacial intervals. It follows that the early 100 kyr response of BWT implies an early response of the WAIS relative to the northern hemisphere deglaciation. Thus, in the "100 kyr world," both northern hemisphere and southern hemisphere processes affect climate conditions in the North Atlantic Ocean.

I wonder if they noticed the magnetic reversal coordination which could be due to Antarctic Ice Sheet movement.?

Tuning History - Climate Blues in A5

Orbital influences on climate can also be tuning influence of orbit on climate, power chords like fifths may resolve some to the mystery.

I studying the correlation of estimated climate change in deep ocean core samples I noticed that precession, the red haired step child of orbital parameters, appears strongly as an ~23,000 year response and that there appears to be a 4,300 year recurrent decay from the precessional impacts.  Obliquity and Eccentricity are considered the big orbital players in the climate band.

According to:

To tune or not to tune: Detecting orbital variability in Oligo-Miocene climate records

Cristian Proistosescu a,⁎, Peter Huybers a, Adam C. Maloof b


" A different behavior is observed for the 1/23 kyr−1 peak where, for a moderate amount of tuning, the significance of the peak increases dramatically. The robustness of the results for precession across testing configuration lead us to confidently conclude that significant precession band variability is present in the ODP 1218 δ18O record. This result is, to our knowledge, the first unbiased statistical test for orbital variability using orbitally tuned records."

and

"For ODP 1218 the estimated autocorrelation coefficient is ϕ=0.87 and the variance of the ∈ disturbances is 0.41 at a time step of 4.3 kyr."

A little "tuning" goes a long way as long as it is compared with untuned data.

This is not Earth shattering news for most, but the locating the potential source of Bond Events kinda blows wind up my skirt :)

"Global" versus the Oceans - Part Four

From the original installment, the "Global" versus to Oceans series has been intend to show the impact of the Antarctic Continent and Circumpolar Current on Global climate and magnetic orientation.  The potential instability of Antarctic Ice sheets to orbital and tidal forces can impact orbital and tidal forces.  A complex set of tens of millennial scale climate related geophysical interactions.

The Scaled EPICA CO2 and the Baseline provided by Bintanja & van de Wal provide a "standard" for comparison to various regional reconstructions of past ocean climate.

This series of comparisons adds the Herbert et al 2010 South China Sea SST anomaly and Eastern Pacific to the "standards".

 The period from ~800ka to present is tame compared to the more distant past.  The next chart shows the most recent magnetic field reversal.

There are many gaps to fill, but the use of the Scaled CO2 and 45N temperature of the deep oceans provides an interesting perspective of past "climate".  One of the more interesting is that it is unlikely that there is a single "sensitivity" of climate to carbon dioxide.  Then relative calm of the past 800 k years would indicate more sensitivity while the beyond 800 k years could produce any sensitivity one wished to find.  Since the 45N remains more closely related to CO2, it is very likely that land based ice has the greatest control over CO2 and Southern Ocean mixing the greatest control over land based ice.  At least, CO2 is less likely to influence geomagnetic field reversals than huge Antarctic Ice Sheets.

Note:  While I have reviewed the "Global" versus the Oceans posts, there are always chances to improve and correct.  Any volunteer review comments are always welcome.