The Solar Precessional Cycle and Ocean Heat Uptake

I posted this work in progress tropical ocean reconstruction with the red precessional cycle curve on a blog and received a comment that you don't see solar insulation curves on most paleo reconstructions.  You don't because there is a 65N maximum insolation bias.  Glacial and interglacial  cycles hinge on ice and 65N maximum insolation has the largest impact on ice which tends to accumulate up around 65N.

That is fine.  However, we are not in a 65N maximum solar insolation cycle we are closer to a maximum 65S solar insulation cycle or about 10,000 years later in the game.  With the exception of the poles where the "endless day" effect of axial tilt creates a large variation in "average" solar intensity, no one much cares since the equatorial average doesn't vary much.  That would go back to the TSI/4 A$$trophyicist TOA insolation estimate.  As I have pointed out before, TSI/4 is perfectly appropriate for TOA or a rock planet, but not so much for a liquid planet.  For a liquid planet you need to consider subsurface penetration which leads to a TSI/pi() alternate approximation.  TSI/pi() is a thermodynamic consideration which needs more consideration for a more accurate estimate.  If the surface loses energy at a very high rate, you may as well go with TSI/4, but if there are sufficient lags in heat transfer, TSI/pi() is more accurate.  You basically have a valid range if you consider both.

 I wasn't going to get into this, since I am having more fun with the cloud regulation thing but this chart is based on ocean area and the precession of the equinox.  For a 30 degree insolation cone you would have maximum solar intensity on the largest area of ocean mid- precessional cycle.  For a 60 degree cone, maximum is closer to the southern tropics.  The 60 Degree cone, +/-30 degrees would have a minimum insolation of 87% of maximum and the 30 degree cone 97% of maximum.  You of course have cloud response which would reduce local insolation, but you have potential values in any case.  If the absorbed solar takes longer than a year to work its way out of the system, the peak solar insolation is what you need not "average".

You can look up density gradient solar pond design to get all of the things needing to be considered, but on a planetary scale, TSI/pi() is close enough for a rough estimate.  Then how much lower actual temperature is compared to TSI/pi() gives you an estimate of all those other considerations that some will say you were too lazy to figure.

As a by the way, when glacial mass is at a maximum, open ocean area is at a minimum.  Most of the world beaches have a gradual slope so if sea level is 100 meters lower, you would lose a lot of ocean area.  This would change correlations a bit.

In a high sea level world, "global" surface temperature would correlate more closely to tropical SST.  In a low sea level world, "global" surface temperature would correlate more closely with glacial area i.e. northern hemisphere surface temperature.  This is the main reason that high latitude tree rings are a waste of time if you are looking for "current" global temperature proxies.  They would be the go to proxy close to 65N max insolation, but not 65S max insolation.

Lat	1410Wm-2	°C	1361Wm-1	°C	1312Wm-2	°C	d(wm-2) max	dT max
25	352.0	7.6	339.8	5.1	327.6	2.5	24.5	5.0
20	376.8	12.4	363.7	9.9	350.6	7.3	26.2	5.1
15	397.1	16.1	383.3	13.6	369.5	11.0	27.6	5.2
10	412.0	18.8	397.7	16.3	383.4	13.6	28.6	5.2
5	423.5	20.8	408.8	18.2	394.1	15.6	29.4	5.2
0	434.1	22.7	419.0	20.0	403.9	17.4	30.2	5.3
-5	444.2	24.4	428.7	21.7	413.3	19.0	30.9	5.3
-10	449.4	25.2	433.8	22.6	418.2	19.9	31.2	5.3
-15	448.8	25.1	433.2	22.5	417.6	19.8	31.2	5.3
-20	442.1	24.0	426.7	21.4	411.4	18.7	30.7	5.3
-25	432.3	22.3	417.3	19.7	402.2	17.1	30.0	5.3

Using the area percentage and TSI/pi() you can make a table of Sea Sub-Surface Temperatures.  The difference between max and min insolation averages around 29Wm-2 and 5C which should be close to the change in SST from glacial to interglacial, "all else remaining equal" which is never the case. You have to remember though that while one region has one extreme, the opposite end of the world has the other except for the equatorial peak/valley.  At the equator things would be less variable but you would have peaks every half precessional cycle.  That would limit the range of temperature to about half of the maximum range or about 2.5 C degrees.  

  This Lake Tanganyika reconstruction by Tierney actually shows the changes better than ocean reconstructions because it doesn't have the complex thermohalide circulation to deal with.  When there is lots of glacial mass you don't "see" the precessional cycle ocean influence, but when the oceans are warm, the oscillations stand out fairly often.  Another issue is that when the oceans are warm the cloud cover increases.  Lake Tang thought is very close to the TSI/pi() estimated temperature and clouds generated by Lake Tang would tend to have less impact on the lake itself because it is relatively small and isolated.  

So does TSI/pi() and precessional impact on ocean area "solve" climate modeling issues?  No way.  It does provide  different direction to attack the problem though.


Update.

I was looking for a spread sheet I have for estimating precessional cycle solar variation, but it is locked up tighter than Dick's hat band.  So I opted for a NOAA data set that includes all orbital variations pretty Much, but it is Langleys/day.  The plot above is for the equator peak annual insolation.  It is not an annual average but the peak value for any month of the year.  Most of the time you would see a June value and a nice oscillating curve.  Using TSI/pi() though this is the curve you want to use.  Notice how this looks more like ice core temperature reconstructions that fiddle fart matching varying oscillations with occasional peaks and valleys.  If we lived on a water only world, the temperature record would look a lot more like this.  We don't though we live on a mainly water world that tanks to land mass distribution would like to become an ice world from time to time.  The average variation is around 40 Langleys per day which would be roughly 20 Wm-2 variation or about 3 C at the equator.

To do this right I would need to do all the conversions and get the peaks by latitude band etc. etc., but since there is latent and clouds to consider it would be pretty much a waste of time without a more serious model.  For now this is all I need and should show you why a precessional cycle should be "seen" in tropical Holocene reconstructions.

Since I started this Willis has a post on WUWT so you can pop over and compare a nail driver's approach to an HVAC guys approach :)


Why not 65S?

Since that question was asked here is an update.  There is more ice variation in the high northern latitudes.  Antarctica is thermally isolate and there isn't much other land area down there to grow glaciers on.  You would use the solar intensity that is most likely to trigger abrupt change in the Glacial/interglacial situation.  As I said the right way to be using each latitude band but since I am focusing on Ocean Heat Uptake due to precessional cycle changes I am going to concentrate on the bands most likely to influence ocean heat uptake.

This compares Equator, 60N and 60S peak insolation.  If I pick a ocean temperature reconstruction from any of those bands I would expect to see some sign of the precessional cycle.  The high latitudes can trigger ice sheet collapse, mainly in the NH but once in a great while in the SH which impact ocean circulation and sea level, but most of the energy absorbed by the ocean still comes from the tropics.  These curves include all orbital variations, but I am concerned with the Precessional change.



Precessional produces the higher frequency, ~20ka full cycle and ~10ka equatorial half wave.  Axial tilt would vary the intensity of the precessional insolation making in more likely for a glacial to interglacial transistion, but that only happens every 2 to 3 tilt cycles and isn't very consistent.  That is because ice sheet stability involves more factors than just solar intensity.

Since you are not going to get a perfect correlation because of differences in internal and solar dynamics, my approach is to start with the simple cycle impact on the primary atmospheric heat source, the oceans and work out from there.

So "doing it righter", orbital impact on ocean energy would look something like that ex-cloud albedo of course.  In any case, orbital influence should be a sanity check for paleo-climatologists so they don't smooth out the real signals.

Update:  Since it is windy and a bit chilly for me today I bit the bullet and played with the Berger et al, solar data for the whole million years.  This comparison of a million years of Arabian Sea SST produced by Herbert et al. in 2010, or at least the data was archived in 2010 at NCDC with the Peak equatorial insolation as determined by Berger et al. show just what should be expected.

We have a "fair" correlation.  So I would give Herbert, T.D., L.C. Peterson, K.T. Lawrence, and Z. Liu. 2010 a high five for high quality work.  Though I would mention to K. T. Lawrence that more stuff on the seesaw would nice to see :)

Since the Vostok Composite CO2 record was pretty easy to bin, here that is with Equatorial Solar.  The correlation as noted on the chart was 25%.  Interestingly there is the same 400ka weirdness.