Past the tipping point

By Steve Goddard

In 2007, Dr. Hansen boldly declared

“…defying government gag orders. Hansen told Reuters, quote, “The reason so much (of the Arctic ice) went suddenly is that it is hitting a tipping point that we have been warning about for the past few years.”

and Mark Serreze placed the blame squarely on CO2.

“…the effects of greenhouse warming are now coming through loud and clear.”

So let’s see how the greenhouse gas induced tipping point is working out. By this date in 1990, there was already a large hole in the ice in the Laptev Sea (upper right, near Siberia.) Watch the video:

Generated from UIUC maps.

Solar radiation in the Arctic is very close to it’s peak by May 25, so there was a lot of solar energy being absorbed through the ice in the Arctic ocean by this date in 1990.

http://earthobservatory.nasa.gov/Features/EnergyBalance/images/annual_solar_insolation.png

Sea ice concentration is considerably higher now than it was on this date 20 years ago.

Generated from UIUC maps.

This means higher albedo (reflectance) and less absorption of solar energy. Note in the insolation graph above, that by the end of July the amount of sunshine in the Arctic begins to drop off very quickly.

You can see in the JAXA graph above that the 2007 divergence occurred in late July after Arctic insolation was already shutting down, essentially nullifying the Arctic albedo feedback argument. The Arctic minimum comes too late in the summer to have  a significant impact on the radiation budget, due to the very low angle sun at that time. In fact, CERES has measured that during September 2008, the Arctic net radiation balance was strongly negative. The open water loses heat to the atmosphere (because it is not insulated by ice)  meaning that declining ice cover is probably a negative feedback, not a positive one. NASA’s Earth Observatory explains:

This map (below) of net radiation (incoming sunlight minus reflected light and outgoing heat) shows global energy imbalances in September 2008, the month of an equinox. Areas around the equator absorbed about 200 watts per square meter more on average (orange and red) than they reflected or radiated. Areas near the poles reflected and/or radiated about 200 more watts per square meter (green and blue) than they absorbed. Mid-latitudes were roughly in balance. (NASA map by Robert Simmon, based on CERES data.)

http://earthobservatory.nasa.gov/Features/EnergyBalance/images/ceres_net_radiation_200809.jpg

Looks like the Arctic is less tipped than it was 20 years ago. It is a shame that Dr. Hansen feels like he is gagged, when he has such important information needed to save the planet.

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rbateman
May 26, 2010 7:04 pm

Ulric Lyons says:
May 26, 2010 at 6:35 pm
Not a whole lot different from the Vikings sailing as far as 79 deg. N Latitude.
Though, with the Vikings, cairns have been found.

rbateman
May 26, 2010 7:09 pm

So, this tipping point business is decidedly concurrent.
As the Arctic hits -1.0M km2 anomaly, the Antarctic is not far behind at +.8M km2 anomaly.
Why? What’s up with the Antarctic going positively berserk making ice?

May 26, 2010 7:26 pm

@stevengoddard says:
“REPLY: And clear windy days in the Arctic are likely to be the exception, not the norm”
Days when the Arctic sea is flat as a mirror would be the rarest. Even little waves will vary the angle of incidence considerably. Try it out with a torch on a swimming pool in the dark!
Arctic ice melt carries on for as long as the sun is shining on it, and low Sun angles will reflect more light off the water onto the ice edges accelerating loss of margins. Loss by sulblimation and ablation will happen a very low temperatures under direct sunlight, so it is not just the water that is causing seasonal ice loss, as it is clear that when the Sun remains below the horizon from early October, is when the ice starts to re-form.

Richard M
May 26, 2010 7:30 pm

stevengoddard says:
May 26, 2010 at 3:53 pm
Richard M
NSIDC reports that warm autumn air temperatures in the Arctic are often due to heat released from seawater as it freezes.

I realize that, I’m looking at it longer term. What proof do we have that the sea ice isn’t melting due to other conditions (like EM Smith’s ocean circulation or possibly geothermal induced ocean warming, or both). The lower ice extent reflects less heat and the Arctic warms. This reduces the flow of heat from the lower latitudes and you end up with a slight warming of the globe … especially the NH.
Has anyone seriously questioned cause and effect?

jeff brown
May 26, 2010 7:44 pm

Ancient records confirm Arctic warming due to man
If Arctic warming continues at its current rate, the Arctic Ocean could have ice-free summers by 2040 or even earlier, modelling studies suggest. The last time the ocean may have had ice-free seasons was around 10,000 years ago, when the region was getting much more sunlight than today due to Earth’s orbital fluctuations. By using geological records to piece together the history of Arctic sea ice over the last 50 million years, scientists have shown that the combined magnitude and abruptness of the recent ice loss is likely higher than ever before and can’t be explained by any known natural variables.
Leonid Polyak, from the Byrd Polar Research Center of Ohio State University, US, and colleagues employed marine sediment cores and ice-core and terrestrial Arctic temperature records. Palaeoclimate proxies found in these sediments, such as ice-rafted debris, microscopic organisms, driftwood, whalebone, and plant material, indicate the presence or absence of sea ice in a particular region. Historical records and satellite data complete the picture for modern times.
The proxy records show that around 50 million years ago the Arctic was a balmy place, with summer temperatures as high as 24 °C and subtropical aquatic ferns basking in the warm waters. Then around 47 million years ago sea ice started to form, most probably encouraged by a fall in atmospheric carbon dioxide and an accompanying drop in temperatures.
Atmospheric carbon dioxide continued to decrease – caused in part by weathering of rocks as the Earth reorganised its continents – and temperatures fell. Then around 3 million years ago the carbon dioxide decline slowed and regular glacial cycles started to dominate temperature changes, driven by orbital variations which alter the amount of solar radiation reaching Earth. Since then the Earth has swung predictably from glacial to interglacial and back again, every few tens of thousands of years. Emerging data suggest that Arctic sea-ice was probably much reduced during the major interglacials.
For the last 11,000 years or so we have been enjoying a relatively warm, low-ice interglacial period, with a gentle cooling as we head towards the next glacial. “From orbital variations, we’d expect the Arctic to continue to slowly cool as it has done so for the past several thousand years, eventually slipping into a new ice age,” said Mark Serreze director of the US National Snow and Ice Data Center at the University of Colorado.
But the last 100 years have bucked the trend in a big way. “We’ve lost about 30% of the summer ice extent and as much as 85% of the multi-year ice volume since the 1970s,” Serreze told environmentalresearchweb. And this decrease can’t be explained by natural variations alone. “If you ignored our recent atmospheric carbon dioxide rise, the recent reduction in sea ice in the Arctic would look highly anomalous, because it comes at a time when orbits favour extensive sea ice,” said Richard Alley from Pennsylvania State University.
Publishing their findings in Quaternary Science Reviews, Polyak and his colleagues conclude that the recent decrease in Arctic sea ice doesn’t fit any of the natural variabilities known from existing paleoclimatic data. This conclusion implies that the most plausible trigger for this warming is rising atmospheric carbon dioxide levels coming from human activities. “Orbital variations, which are currently slowly cooling the Arctic, are still there, it’s just that climate warming due to human activities is now dominating and operating on a much shorter timescale – about 100 years – than orbital variations – [which operate over] thousands of years,” explained Serreze.
The implications of ice-free summers in the Arctic within a few decades are of great concern. Coastal erosion will likely increase and many ice-adapted species will struggle, which will inevitably affect the human inhabitants of the Arctic. Out beyond the Arctic, weather systems will alter as atmospheric circulation patterns adjust to the effect of an ice-free Arctic Ocean.
As the geological record shows, the Arctic has occasionally been ice-free in the past. However, the current speed of on-going change is exceptional. “In the past, one went from heavier ice to milder, or ice-free, conditions over the span of thousands of years,” said Serreze. “Now we are talking about doing it in 100 years, or less. Can species like polar bears adapt to such rapid change? We’ll see.”

May 26, 2010 7:47 pm

Ulric Lyons
There are other things besides reflectance which attenuate Arctic light at low angles. The long path through the atmosphere probably reduces light by 90+%, and the long projection on the surface at low angles attenuates it even more. sin(5 degrees) = 0.09. Between reflectance, long atmospheric paths, and long projections – the net effect is that sunlight entering the ocean is reduced by a couple of orders of magnitude relative to the equator.
Sounds like a good topic for an article.

jeff brown
May 26, 2010 7:55 pm

Jack Simmons says:
May 26, 2010 at 6:27 pm
Jack, really you think there would be no impact of the Arctic sea ice cover were to disappear during summers? Really? Do you understand what drives our atmospheric and oceanic circulation?

May 26, 2010 8:59 pm

jeff brown
There is approximately zero chance of Arctic ice disappearing during the summer.

R. Gates
May 26, 2010 9:08 pm

Jack Simmons says:
May 26, 2010 at 6:27 pm
I don’t really care what the arctic does.
_____________
I wonder if that is the common attitude of AGW skeptics? I would hope not, but if it is, it would explain a great deal…

May 26, 2010 9:21 pm

Arctic net radiation balance is negative from August till April.
http://earthobservatory.nasa.gov/GlobalMaps/view.php?d1=MOD_LSTAD_M&d2=CERES_NETFLUX_M
But yearly ice loss starts when the Sun first shines on it, and stops when the Sun stops shining on it. Give it colder winter and there is more ice, a warmer summer and there is less ice, generaly. I do think there has been a reduction in Arctic/N.H. atmospheric water vapour since July 2007, and the following wet summers, that could be partly responsible for declining summer ice.
http://earthobservatory.nasa.gov/GlobalMaps/view.php?d1=MYDAL2_M_SKY_WV#

R. Gates
May 26, 2010 9:24 pm

And then there was 1…
Just one year had a lower amount of arctic sea ice than 2010 for this time of year in the past 8 years…and that was 2006, and then just baresly (based on IJIS/JAXA data), and from the steep rate of decline, it looks like 2010 will soon eclipse that year as well. See:
http://www.ijis.iarc.uaf.edu/en/home/seaice_extent.htm
Of course it’s purely of interest in a statistical manner, but it shows how rapid the early melt has been when the sea ice extent can go from the highest in the past 8 years to very close to the lowest in just about 1 month. We would not expect this rapid melt to continue UNLESS, this graph:
http://psc.apl.washington.edu/ArcticSeaiceVolume/images/BPIOMASIceVolumeAnomalyCurrent.png
Is more accurate than some might think, and all that multi-year ice will also melt fast once the 1st year ice has been eaten away…

May 26, 2010 9:26 pm

To jeff brown: Ancient records do not confirm Arctic warming due to man. The present Arctic warming started at the turn of the twentieth century, after a two thousand year old cooling trend (Kaufman et al. Science 325:1236-1239). Such a sudden warming cannot be caused by carbon dioxide in the air because laws of physics require a simultaneous jump in its partial pressure and this did not happen. The only physical process capable of starting a sudden warming is a rearrangement of the North Atlantic current system that directed the Gulf Stream unto its present northerly course. There was a break in the warming from 1940 to 1960 after which it resumed. By 2003 Arctic temperature had recovered enough to reach the previous high point recorded in the thirties. In addition to the Gulf Stream a smaller amount of warm water enters through the Bering Strait in the west. Thanks to wind patterns an unusual amount of warm water entered through this strait in 2007 and cleared a large bubble of water ahead of it while the Gulf Stream side of the Arctic changed only a little. Forget the predictions you read about. These guys are working with a wrong theory of Arctic warming.

Anu
May 26, 2010 9:32 pm

tonyb says:
May 26, 2010 at 12:32 pm
As for anecdotal evidence being inferior to computer models (which even the IPCC admit are unreliable) here are a series of links demonstrating that ‘abnormality’ is the norm as far as sea ice melt is concerned

I wasn’t implying that anecdotal evidence, such as ship captain’s logs, coastal Eskimo memories, or ancient Icelandic Sagas are “inferior” to computer models.
I was implying that they are “inferior” to global climate variable measurements by satelliteS, ocean floats and other global measurements. The last 5 decades have been the best, most precise, total-planet measurements of climatology variables in the history of humanity. This level of detail is needed to figure out what is happening, now, with Earth’s climate. It is interesting to paleoclimatologists to study weird climate events in the past, but since the data is so coarse and vague, it doesn’t help much with current climate models. Yes, it has some value pointing out expected variability, but it has no explanatory value – no predictive value, other than vague expectations of “60 year ocean cycles” – or “maybe 70”. This is how ancient Egyptians did astronomy – lots of observations, notice of some patterns, and “predictions” like – “there might be an eclipse sometime this year. Or maybe next. One is due soon”.
It took the Greeks to get Science rolling, and actually try to explain why eclipses happen, or what things are made of, etc. But they were grateful for the centuries of Egyptian, and Mesopotamian, observations that got them started. Just like the scientists were grateful to the South American fishermen that told them about El Nino.
As for the current warming not being “abnormal” enough:
If a doctor is treating a patient with a temperature of 104 °F, it doesn’t matter if some amateurs standing nearby start recounting stories of how they knew someone with a temperature of 1o4.5 °F, or 105 °F, or 106 °F once – and they wound up just fine after drinking water and resting in a cool place.
The doctor must determine the exact cause of this hyperthermia, and that underlying cause must be corrected. Exertional hyperthermia is very different than Kawasaki syndrome, thyroid storm, sepsis, serotonin syndrome, neuroleptic malignant syndrome, and certain drug effects – if you don’t want hyperpyrexia and death to follow, you better let the Dr. do his job.
If the majority of climatologists are saying that this hyperthermia is being caused by CO2 buildup in the atmosphere, based on their detailed diagnosis, and it is going to get much worse, telling stories about some Vikings enjoying a warm century a thousand years ago before it got cooler for awhile, doesn’t really help.
But I realize amateurs standing nearby love to talk… as do I.
And it is interesting to read about past climate changes. I recently finished
The Long Summer: How Climate Changed Civilization by Brian Fagan:
http://www.amazon.com/Long-Summer-Climate-Changed-Civilization/dp/0465022812

Anu
May 26, 2010 10:01 pm

R. Gates says:
May 26, 2010 at 9:08 pm
Jack Simmons says:
May 26, 2010 at 6:27 pm
I don’t really care what the arctic does.
_____________
I wonder if that is the common attitude of AGW skeptics? I would hope not, but if it is, it would explain a great deal…

Yeah, some people actually think it is just a question of whether the polar bears survive or not…
but if precipitation patterns change abruptly one half decade and global crops have dismal years and the grain stores are depleted and food prices quadruple, you will hear these same people screaming at “the Government” for “not having done something”.

So what are global grain stores, what is a normal level of stores and should we be worried? According to the Energy Bulletin, “World carryover stocks of grain, the amount in the bin when the next harvest begins, are the most basic measure of food security. Whenever stocks drop below 60 days of consumption, prices begin to rise.”
What would it mean if the world ran out of grain? For those of us who live in the developed world and who are so used to being able to get whatever food we want any time we want it, this is totally unimaginable. I guess that’s why we don’t even try to imagine it. For many in the developing world, this is already a daily reality.

Regional civilizations have collapsed in the past due to regional climate change. Many people cannot even conceive of global civilization collapsing due to global climate change, much less assess what the risk is.

May 26, 2010 10:29 pm

@stevengoddard says:
May 26, 2010 at 7:47 pm
“The long path through the atmosphere probably reduces light by 90+%”
Is that just UV?, as 90% of visible sounds pretty dim.
The troposphere is 7 km deep at the poles and 17 km deep at the equator.

kwik
May 26, 2010 10:46 pm

Anu says:
May 26, 2010 at 9:32 pm
Anu, if you are as worried as it looks like here, I think you owe it to yourselves to read Dr. Spencers latest book.

tonyb
Editor
May 27, 2010 12:23 am

Anu and Ulric Lyons
Anu said
“This level of detail is needed to figure out what is happening, now, with Earth’s climate. It is interesting to paleoclimatologists to study weird climate events in the past, but since the data is so coarse and vague, it doesn’t help much with current climate models. Yes, it has some value pointing out expected variability, but it has no explanatory value – no predictive value, other than vague expectations of “60 year ocean cycles” – or “maybe 70″.
You then talked about the need to treat someone with a temperature of 104F and cite Brian Fagans work (who I have read before)
That is the point Anu, I see a perfectly normal patient -based on my very long observations of him, not just the last two minutes- who has a temperature around normal, and not someone in a severe fever who is about to die. He certainly does not need to be put into intensive care.
Al Gore also wrote an excellent book ‘Earth in the Balance’ back in 1992 in which he cited past climatic variability.
I believe our civilisation is very vulnerable due to our mono cultures and the way we rely on fragile suipply chains, a subject explored well in Peter Taylors ‘Chill’. We are geared up to combating ‘warmth’ but not to dealing with the much worse consequences of cold.
So sorry Anu, to me the patient appears normal based on all the evidence we see before us stretching back into the depths of history.
Ulric Lyons
I didn’t quote Mckenzie in the 15 links, although I have a reference I shall quote at the end. When I first read his book I was highly sceptical of his claims but eventually corresponded with him,. He does have access to some very interesting material which he is reluctant to put into the public domain as he may use it on future books.
Undoubtedly the period of which he writes had some of the hottest summers that we can trace. It is probable that a Chinese fleet could have sailed via the Arctic route as described as we now know that ice is highly variable even year to year. I doubt it was entirely ice free but certainly likely to be more ice free than in most incidents since the Vikings.
Here is the reference that I didn’t include with my 15 links sent in response to Anu earlier. There is a great deal of back up information available including web sites dedicated to pouring scorn on the authors claims.
“Contrast that with events PRIOR to the LIA like Gavin Menzies’ maps of the Chinese voyages he postulates SIX centuries ago. LinkText Here If Menzies’ postulations bear out, the successful Chinese voyages may have prompted the later searches for the Northwest Passage.”
tonyb

tonyb
Editor
May 27, 2010 12:26 am

My 12.23 post.
Sorry embedded link did not work. Here it is again
http://www.gavinmenzies.net/pages/maps/voyages.htm
tonyb

May 27, 2010 4:25 am

@Anu says:
May 26, 2010 at 9:32 pm
“paleoclimatologists to study weird climate events in the past, but since the data is so coarse and vague”
I think its analysis is coarse and vague. On CET, I have found a good number of event cycles, and SSN/temperature relationships, that seem to have been largely overlooked, and that can give, most of the time, a good idea of monthly temperature deviations from normals. Longer event cycles can be determined from written records of peak events such as major river freezings, very accurately, and from proxies for LIA and MWP type periods though the Holocene, we see the c.1157yr and 4627.33yr high and low event clusters. A one “size fits all” 60yr cycle that does not fit more than one step backwards in following real temperatures, does not cut the mustard with me one iota. Clearly the best computer models are grossly defficient, as we have witnessed by MetO seasonal forecasts, they can not tell you what the next 15 summers or winters will be like, and if you can`t do that, you can`t forecast climate.
Cold winters during the Modern Warming, have occurred just when they should have, including the last two, and the only thing we can do to take the sting out of future cold winters, is elavate CO2 levels. But some studies would suggest even this would be in vain:
http://www.rsc.org/Education/EiC/issues/2006May/endpoint.asp
{ 0.12K over the next 100 years}

May 27, 2010 5:47 am

Ulric Lyons
Sometimes at sunrise or sunset, the sun is so dim that you can look right at it. Probably closer to 99% reduction.
http://www.sercc.com/files/3/sunrise.jpg

Mike M
May 27, 2010 6:11 am

Anu says:
Regional civilizations have collapsed in the past due to regional climate change. Many people cannot even conceive of global civilization collapsing due to global climate change, much less assess what the risk is.

True. And that’s why it is imperative to STOP wasting time and money on this hoax that human fossil fuel use has any significant affect on climate so we must therefore cut back on it. The climate is going to change no matter what we do and fossil fuel has now become ESSENTIAL to feed the world.
My fear is that progressives get their way and our food supply is reduced trying to plow fields with solar cells, fertilize with animal dung and then selling the food to some bio-fuel distillery for rich countries to burn in their machines.
So after third world is already starving from that and we are patting ourselves on the back that we got CO2 back down to 350ppm.. THEN nature proves in some big way that we have nothing to do with it and gives us a huge extended drought or severe cold resulting in world starvation – and we are totally unprepared to respond to it because we wasted all of our resources on ‘green’ technology to make people like Al Gore and Maurice Strong rich.
Then it’s too late. The way to save the planet for humanity is to make everyone RICH – not poor. The richest countries are the cleanest ones with the most static populations and, most importantly, the ones BEST able to deal with any disaster including climate disasters. (Does anyone expect the Zimbabwe navy to respond to a tsunami disaster area to supply water.)

May 27, 2010 6:42 am

@stevengoddard says:
May 27, 2010 at 5:47 am
I can see 90% UV loss at higher lattitudes because of ozone distribution. Angle of incidence will make more difference at the suface contact area than depth of atmosphere travelled through, because of the shallower troposphere nearer the pole.
The troposphere is 7 km deep at the poles and 17 km deep at the equator.
At midday on the Autumn equinox, the Sun is nearly 10deg. above the horizon at 80deg. North, and 19deg above the horizon at 70deg. North.
And often the Sun is far too bright to look at, at sunset, anywhere on the planet.

Steve Keohane
May 27, 2010 7:16 am

Tommy says: May 26, 2010 at 11:35 am
Steve Keohane says: May 26, 2010 at 7:17 am
“Please explain how the Arctic area shrinks from a closer observation point.”
By “Arctic area” do you mean the boundary of ice?

No, I mean the shoreline of the arctic sea, that is the boundary.
“Here is a scale drawing of the earth and the two points of observation. The satellite is obviously too close to capture the full diameter of the earth, so it is within the area where the relative size of the features can vary in area wrt the diameter of the earth, but not in the way you describe.”
Good point. The diagram indeed explains that >50% of the surface is blocked by the horizon. In order to see the full diameter of the planet, the observation point would need to be at infinity distance, or the planet would need to be cut in half by divine intervention (preferably with me riding in a comfy cockpit of the satellite). As for the relative size of features, as an object gets closer, the nearest features should appear to enlarge at a faster rate than the farthest ones, unless the features themselves were changing in shape/size during the trip.

Since the arctic sea is the closest feature in a top down, from the north, point of observation, it should by your description, and my thinking, be larger and it is not larger, it is relatively smaller to the diameter of the earth.
http://i44.tinypic.com/2vrwuae.jpg

Steve Keohane
May 27, 2010 7:30 am

R. Gates says: May 26, 2010 at 12:16 pm
For some of you who may actually have the time and inclination to play with some atmospheric and ocean radiative transfer models yourself. Try:
http://snowdog.larc.nasa.gov/jin/rtset.html
And to play with albedo, windspeed, longitude, etc, try:
http://snowdog.larc.nasa.gov/jin/albedofind.html

Interesting, not relevant here though. Your first link only allows for SUB-arctic atmospheric modeling. The second proves there is little to no change wrt wind/waves and albedo. Results below for a 45° angle of incidence:
Wind Speed (MPH) Albedo
1 .037
2 .036
3 .036
4 .036
8 .036
16 .037
32 .037

May 27, 2010 4:46 pm

From above: Thickness of atmosphere (polar) = 7 km. NASA quotes a lower atmosphere thickness as 7 miles, or 12 km, or 39,000 feet; but many clouds are much higher than that.
Use the 100,000 foot “edge of space” where the atmosphere turns black to the naked eye. 30.48 km.
From AutoCAD, using a polar radius of 6356 km as a circle.
Tilt it 23.5 degrees from vertical to show the sun’s angles at mid-summer – June 21-22. Every point further north of the Arctic circle will receive some sunshine, and theorectically at least, heat up some.
Plot (from south to north) these points:
Canadian Arctic Circle = CAC at 66.5 degrees north,
Canadian 80 north = C80N,
North Pole (90 degrees),
Russian 80 North = R80N,
Russian Arctic Circle = RAC also at 66.5 degrees north
Distance the sunlight travels through a 30.5 km thick stmosphere at each of these points, and the incident angle of sunlight is:
CAC = 41.6 km atmosphere (absorb) at 49.1 incident deg => sin 49.1 = .756 max
C80N = 54.9 km atmosphere (absorb) at 36.5 deg incident => sin 36.5 = .594 max
NP = 75.5 km atmosphere (absorb) at 25.9 deg => sin 25.9 = .436 max
R80N = 125.5 km atmosphere (absorb) at 15.9 deg => sin 15.9 = .273 max
RAC = 623.2 km atmosphere (absorb) at 0.0 deg => sin 0.0 = .000 max
Keep in mind that virtually all of sunlight is reflected off of the surface of the water at less than 21 degrees, so only half of the light supposedly available during a “24 hour polar day” could actually be absorbed under ANY combination of ice coverage or open water.
Only that part of the Arctic receiving sunlight at an incident angle greater than 21 degrees can absorb heat, and – as the earth rotates around the north pole the incident angle is will decrease from maximum to minimum and back to maximum. As a good approximation for 80 north, once the earth has rotated 6 hours, the incident angle is less than this 21-22 degree point when all of the light (and heat) energy is reflected.
We must also address the change in seasons: this AutoCAD drawing is only correct for one day a year, every other day will further decrease absorption values.