Three Clocks

Hmmmn.
To focus on specific questions:
1.

First, the solar input. Although a lot of folks talk about the “solar constant”, over the course of the year the sun is anything but constant. Because the Earth’s orbit is not circular, annually the Earth moves closer and further from the sun. This gives an annual change of about 22 W/m2, with a high point in early January and a low point exactly six months later in early July. So that’s one clock—peaks in January, bottoms out in July, six months rise, six months fall.

I am very willing to be corrected, but I have long understood that the true solar TOA value is
TOA (day-of-year) =TSI*(1+0.0342*(COS(2*3.141*((DOY-3)/365))))
Where TSI = 1361 Watts/m^2 per Lief’s latest note to us here at WUWT) and
the 2*pi/365 formats the cosine curve into Excel’s radian format.
Maximum is 3 January at 1410 watts/m^2
Minimum is 5 July at 1314 watts/m^2.
Given that both the maximum and minimum are rather “slow” changes, obviously January is “high” over a period of a slowly changing peak of about 4 weeks, and July is the minimum at the same slowly changing 4 week “low point.”
1A. Earth’s albedo: Almost all of the earth’s land surface is in the northern hemisphere, which is being irradiated according to the solstices’ variation points: “Zero” on March 22 and Sept 22 (or thereabouts) and maximum southern tilt on Dec 22 (southern end exposed to the sun) and June 22 (northern end exposed to the sun.) Note that these dates “ALMOST” – but not quite! – mimic the minimum and maximum solar exposures! (The change from peak northern and southern hemisphere exposure and peak TOA values is said to be an important part of the overall cycle changes that cause Ice Age buildups.)
2. Although sunlight at TOA is a geometric function of declination angle and the earth’s tilt and year-long rotation period, the “heat absorbed” and the final earth temperature (proportional to the re-radiated long-wave radiation measured at CERES) is going to be more like the daily earth temperature record.
And, each day, the earth’s actual hourly temperature repeats that same cycle: Maximum NOT at maximum solar exposure (12:00 noon) and minimum at least solar exposure (24:00 or 0:00 hours) but maximum slightly afternoon (14:00 hours) and minimum just before dawn at 4:00 – 5:00 AM). The hourly temperature change is most definitely NOT a simple sine or cosine wave differential from the easy solar cycle!
Now, “translate” each of 24 hours into a 12 month cycle.
For the north, final temperatures will be most like the “land” temperatures we recognize above. Maximum solar exposure in late June at latitude +23.5 degrees, and, naturally, one “hour” later (or 2/24 months later) would be Mid-July to early August for maximum temperatures in the north, right? Maximum land temperatures => maximum long-wave radiation outbound, right?
Now, for the soutehrn end.
The maximum solar exposure is 22 December, but maximum solar oputput – the +1.5% increase above in TOA value above – occurs slightly later on 3 Janury.
But, of all the land area down south, South America and Africa are themselves in the northern hemisphere for a good part of their land mass. (Africa in particular – the Equator cuts under the Sahara; India is all northern hemisphere, and as much as I hold the OZZIES and NEZZIES in high regard, neither is very large. And almost NO southern land mass has any ice caps except the few Andes peaks.) Thus, Antarctic’s total ice area (at sea ice maximum) is 14.0 (land area) + 3.5 (ice shelves) + 19.5 (sea ice) = 37.0 Mkm^2 of reflective surface. At minimum sea ice, 14.0 Mkm^2 + 3.5 + 3.5 Mkm^2 = 21.0 Mkm^2 of sea ice down south.
Larger than all of the rest of the southern land areas combined.
To compare, up north, at minimum, sea ice is about 3.0 Mkm^2 (all above 78-80 north latitude) and 14.0 Mkm^2 at maximum, all above 72 north latitude. (At maximum, there is a bunch of land ice as well.) The Great Lakes, Baltic Ocean, Bering Straits, etc. But much, much less northern ice in all.
So, total land area in the southern hemisphere = 35 Mkm^2 of “land” albedo at 0.30 and 37.0 Mkm^2 of “ice albedo” at 0.83 (at maximum sea ice) and about 21.0 “ice” albedo (at minimum sea ice). Total southern hemisphere area = 514 Mkm^2.
Thus, would you not “expect” the southern hemisphere to “reflect” this tremendous mismatch in solar heat storage? That 475 difference in ocean albedo od 0.065 plus its thermal inertia would keep the southern land hemisphere very, very slow to respond to solar exposure changes.
Thus, I would almost question the CERES results if they did not have different cycles at different peak times.

John A says:
March 9, 2014 at 9:25 am (replying to)
Willis,
Can you explain why the reflected solar peaks before the incoming solar and bottoms out after the incoming solar (figure 1). It’s a bit of a head-scratcher for me…

The rotating sphere but slowly titling-back-and-forth-3D geometry under a slowly changing solar exposure at TOA is a bit complex, but there is no particular reason why the reflected energy should ever peak near the yearly radiation TOA dates.
Let’s look at the 22nd of each month, starting on Dec 22.
Dec 22, day-of-year = 357. Radiation at TOA high at 1406 watts/m^2, but NOT yet at its maximum. Earth’s tilt at a maximum towards the south pole, but southern sea ice at 10.4 Mkm^2 is not yet at its minimum. (Total southern ice about 28.0 Mkm^2, edge of southern sea ice in 2013 about -62.9 degrees south.) Northern sea ice and much of its northern land ice is still in the dark nearly all of every 24 hours.
Jan 22, day-of-year =22. Radiation past its peak at 1405 watts/M^2 -> still very high. Earth’s tilt reducing towards zero, but still strongly to the south pole. Northern sea ice all in the dark, northern land ice about 50-50 in the dark all the time. Southern sea ice not yet at its minimum in 2013 at 4.6 Mkm^2, total southern ice = 22.1 Mkm^2; edge is at latitude -65.9.
Feb 22, day-of-year = 53. Radiation at TOA decreasing from its peak at 1391 watts/m^2 but still above the yearly average value of 1361. Northern sea ice is just beginning to see some daylight once each day at noon. Northern sea ice still increasing (land ice area about the same as before) at 15.3 Mkkm^2 (2012 data). Southern sea ice near its minimum for the year at 3.9 Mkm^2, total southern sea ice also near minimum (obviously) at 21.4 Mkm^2, edge of southern sea ice about -66.4 latitude.
Mar 22, day-of-year = 82. Radiation down to near “yearly average” at 1371 watts/m^2. Earth’s tilt = 0, Northern and southern hemispheres getting equal hours of sunlight at last. Northern sea ice nearing its maximum now (much later than southern sea ice’s minimum date!) at 15.1 Mkm^2 at latitude 70.5 north. Northern land ice melting in temperature latitudes, still strong further north across Canada and Siberia and Alaska. Further south, northern land areas beginning to green up and grow darker. Southern sea ice growing now 5.5 Mkm^2, total southern ice = 23.0 Mkm*2, edge of southern sea ice at – 65.5 latitude.
April 22, day-of-year = 113. Radiation continues to decrease towards mid-summer minimum at 1347 watts/m^2. Tilt going towards the north pole. Northern sea ice just past its maximum, now at 14.1 Mkm^2, with a southern edge at 70.9 latitude. Most of the northern land ice is melted, some remains in the Arctic shores. Southern sea ice is increasing, now 8.3 Mkm^2, total southern ice = 25.8 Mkm^2, edge = -64.0 south latitude but it is still getting considerable solar exposure every day.
May 22, day of year = 143. Radiation at TOA now down to 1326 watts/m^2. Northern sea ice decreasing from 12.6 Mkm^2, northern edge = 71/9 latitude, almost no land ice at all across Siberia and Canada. Southern sea ice increasing, now at 11.66 Mkm^2, total southern ice now 29.2 Mkm^2, but much of the southern ice is not exposed to the sun most of the day. Maximum sun elevation at the edge of southern sea ice at latitude -62.3 is only 7.2 degrees at noon.
June 22, day-of-year = 174. Radiation still decreasing, but near its low point at 1315 watts/m^2. Northern sea ice decreasing at 10.2 Mkm^2, edge at latitude 73.7 degrees north, but it is exposed all day. No northern land ice to speak of. Southern sea ice increasing, now at 14.8 Mkm^2, total southern ice = 32.3 Mkm^2. Maximum earth tilt AWAY from the southern sea ice, but the edge of that southern sea ice = -60.8 latitude and the solar elevation at noon = 5.7 degrees, so some energy is still being reflected in the southern hemisphere.
July 22, day-of-year = 204. Radiation at TOA is past its lowest point, but just barely at 1317 watts/m^2. More importantly, northern sea ice albedo is now near its yearly low due to melt ponds, acculumated dirt and soot, and the lack of much fresh snow since May. Judith Curry’s measurements show mid-summer northern sea ice albedo at only 0.46 over June-July, far down from the mid-winter maximum of 0.83 albedo. Thus, both northern sea ice and northern ocean water at low solar elevation angles are nearly the same this timeof year! Northern sea ice is still exposed to 24 hours of sun, but its edge is at 76.3 latitude and is headed north rapidly as area decreases, at noon the sun is now only 33.2 solar elevation angle, northern sea ice area = only 7.4 Mkm^2. Southern sea ice increasing, and sun’s tilt is coming back towards the south pole, but is still to the northern hemisphere. Southern sea ice = 17.3 Mkm^2, total southern ice = 34.8 Mkm^2 with an edge at -59.7 degrees latitude. SEA at noon is now 10.0 above the horizon, and that angle will continue to increase.
22 Aug, day-of-year = 235. TOA radiation up to 1330 watts/m^2 but it is still below the yearly average. Northern sea ice now down to only 5.2 Mkm^2 in 2012, edge at latitude 78.5. Highest SEA now only 21.7 degrees at noon. Southern sea ice now up to 19.03 Mkm^2, total southern ice = 36.5 Mkm^2 at latitude -59.0 latitude, so both are nearing their maximum for the year, but are not yet at it. Southern sea ice at the edge is now getting 19.3 SEA degrees above the horizon.
Sept 22, day-of-year = 266 – the most intersting day of the year! Radiaiton at TOA is now close to the yearly average: 1352 watts/m^2. Northern sea ice at its yearly minimum – in 2012 that was 4.0 Mkm^2 ice extents. Maybe a little bit of northern land ice, but very, very little. Earth’s tilt back to 0.0, both poles exposed to 12 hours of sun, both get 12 hours of darkness. Southern sea ice approaching its maximum at 19.6 Mkm^2, total area = 37.1 Mkm^2, edge of the southern sea ice = -58.7 latitude in 2013. Southern sea ice is has 30.7 solar SEA at noon, Arctic sea ice now only has 10.7 SEA at noon. Thus, at noon, the “newly melted” Arctic ocean surface is exposed to only 108 Watts/m^2 at sea level; but every meter of that 1.9 million “excess” Antarctic sea ice (excess over the yearly “normal” in September) is exposed to 501 Watts/m^! A 5 to 1 ratio of Antarctic to Arctic exposure per square meter on the same day of year!
Oct 22, day-of-year = 296. The earth’s tilt is to the south, moving more towards the south pole every day. Northern land ice is increasing, but northern sea ice is in darkness even at noon at latitude 76.2 at a total of 7.4 Mkm^2. Southern sea ice is still near maximum (at maximum on some years) at 18.7 Mkm^2 sea ice, 36.2 total ice, with a sea ice edge at latitude -59.1. At noon, even though the Arctic sea ice is in the dark, the southern sea ice is sees 42.0 degrees SEA, and received a total 723 watts/m^2 at noon. At that SEA, 128 watts are absorbed by the sea ice, and 595 watts are reflected back into space to cool the planet. Regardless of how much (or how little) Arctic ocean water is exposed by melting sea ice from the “normal” there is no sunlight to heat the ocean water, and cooling increases because of greater open ocean evaporation, convection losses, and radiation losses.