## A Flanner in the Works for Snow and Ice

#### Posted on 23 January 2011 by MarkR

A new paper by Flanner *et al* in *Nature Geosciences* tries to estimate the so called ‘cryosphere albedo feedback’ since 1979. As Earth warms, ice and snow melt and the loss of their shiny, reflective surfaces means more sunlight is absorbed and global warming receives a boost.

The strength of a feedback can be calculated from how much extra heating it adds as temperatures increase; the equations are here. Climate models expect that changes in Northern Hemisphere snow and ice since 1979 should have been a positive feedback of about 0.25 W m^{-2} K^{-1} - i.e. for each degree of global warming, the loss of snow and ice means that another 0.25 W of sunlight is absorbed per square metre of the Northern Hemisphere. Globally, and in the long run it’s expected to be 0.2 because there’s less snow in the south and you eventually run out of summer snow to melt.

Flanner *et al* use satellites to measure the change in shortwave (i.e. sunlight) reflectivity across the Northern Hemisphere from 1979 to 2008.

They find the total amount of cooling that ice & snow provide to the Northern Hemisphere month by month split between sea ice and snow:

**Figure 1** – *a) is the total cooling effect by month of snow, ice and snow+ice. b) is the change in cooling effect for each month since 1979 split into snow, ice and snow+ice. Positive means melting has led to more warming, negative means it’s added to cooling.*

Even though there is much more ice in the winter, the days are shorter and the sunlight weaker so the total cooling effect is smaller. May to June ice & snow is much more important even though there is less of it. Next they made annual averages and mapped these over the hemisphere:

**Figure 2** – *a) total cooling effect and b) change in cooling effect since 1979 in snow and ice of the Northern Hemisphere.*

The authors find that the total effect is 0.33-1.07 W m^{-2} K^{-1} with a best estimate of 0.62 W m^{-2} K^{-1}, significantly higher than climate models’ 0.25 W m^{-2} K^{-1}. Models have underestimated the darkening of the Northern Hemisphere and therefore how much global warming we’re ultimately in for.

Perhaps the first snow and ice melted more quickly than expected and eventually we’ll run out of the easy to melt bits, or maybe the decline in Arctic sea ice will halt for ~30 years to bring it back in line with models. However, if the current pattern holds then this would boost the best estimate of global warming temperature rises by about 20% - here’s hoping it’s just a blip!

Bob Lacatenaat 00:03 AM on 10 April, 2011Bob Lacatenaat 00:09 AM on 10 April, 2011withinthe Arctic Circle at 75˚ (which is where the edge of the ice generally is in March/April, and is right now, and so is the primary area of concern). Your constant efforts to nitpick people's words and then pedantically carry on about it are neither helpful to debate nor appreciated, and I personally think they reflect rather poorly on you yourself rather than the people whom you are criticizing. [Moderators: Yes, I'm in a very bad mood this morning, and so have little patience for some things.]Bob Lacatenaat 03:04 AM on 10 April, 2011Tom Curtisat 14:18 PM on 10 April, 2011changein forcing is known to be stronger at higher latitudes, even though the total forcing is greater in the tropics, so his argument, if you distinguish between these two things is absurd. Likewise he insists that because Trenberth determined the total energy used in additional ice melt in the arctic is about 1*10^20 Joules per annum, that this sets an effective limit on the total change in flux, and change in forcing in the arctic. The non-sequitur is evident. Energy gained need not be retained, and if retained need not all go into one usage. In fact it is known that arctic water is carried to the ocean depths, carrying substantial heat with it. It is also quite probable that increased forcing in the arctic will result in less energy transfer from the tropics, resulting in a net heat gain outside the arctic. Without a full accounting of heat flows into and out of the arctic over the period of interest, which Lambert neither attempts nor cites, his argument is missing crucial premises. It is as though he believes that if he does not know what the energy flows are, they must not exist.It is only necessary to keep these various concepts distinct to see the absurdity of Lambert's arguments on these points- so no further rebuttal is necessary. Finally, Lambert persists in his arguments regarding the size of the area effected, and the low angle of incidence, as proof that change in forcing in the arctic cannot be significant. These factors are significant,and are fully accounted for in studies such as those by Flanner. Therefore, his argument is ungrounded. If he wished to pursue this argument honestly, he would analyse the method used by Flanner to account for these factors, and show the flaws, if any. For whatever reason, he wants to avoid that work, and declare Flanner void based on his own unquantified estimates of the effects involved, together with his misuse of a number from Trenberth. The easiest way to rebut him is to give him all he asks for. I previously worked out a rough estimate of the total increase of energy flux absorbed in the Arctic due to loss of sea ice over the last thirty years. That number is not to be confused with the increase in forcing as it does not account for the increase in outward flux. It was sufficiently large, however, that it was evident that even after allowing for any reasonable increase in outward flux, the forcings claimed by Flanner are reasonable. It is not possible to refute them in other words, by back of the envelope calculations. Lambert, of course, considers by number too large. He thinks it should be 2 orders of magnitude smaller. So I recalculated the figure making conservative assumptions, and allowing for every factor he has identified as significant. (I also did not allow for the other factors he did not bother identifying that tend to work the other way.) The result? The minimum change of inward flux with the most conservative estimate is just a third of my initial estimate (after correction for an error in calculation). Where, for his argument to fly, Lambert needs it to be 150 times smaller, it is just 3 times smaller.No wonder Lambert never quantified his argument, for once you do it is transparent it will not carry the weight he puts on it.The new calculation follows: Courtesy of Daniel Bailey, we know that the average latitude of the edge of summer sea ice in the arctic is 75 degrees. Over the summer months, at 75 degrees North, the average Zenith angle is about 57 degrees, with the sun varying from 57 degrees to 3 degrees above the horizon during the 24 hour day. I will treat the sun as having an angle above the horizon of 55 degrees for 3 hours (around noon), 45 degrees for 6 hours (around 9 am and 3 pm), 30 degrees for 6 hours (around 6 am and 6 pm, 15 degrees for six hours (around 3 am and 9 pm), and 0 degrees for 3 hours (around 'midnight'). These are, of course, approximations, but by my estimate they underestimate the values, which will lead to an overstating of the albedo of water at that latitude in the NH summer. They are more conservative than simple geometry indicates, of course, because refraction in the atmosphere means that light curves towards the surface, thus striking the surface at a higher angle of incidence than indicated by simple geometry. I would not normally consider this worth mentioning, but Ken Lambert wants to mention every factor that operates on the other side of the equation, not matter how slight. We should therefore keep track of all the factors that he does not want to mention. To actually determine the albedo, we consult the following chart from wikipedia: From that we can determine the ocean at that latitude will have an albedo of 0.05 for 15 hours of the day, ie, for any time when the sun is more than 20 degrees above the horizon. It has an albedo of 0.15 for six hours of the day (when the sun is about 15 degrees above the horizon), and an albedo of 1 for 3 hours of the day. Again, you will notice these are conservative estimates based on the charts. Therefore the average albedo is 0.2 My original estimate of ocean albedo was 0.1 The difference means that the change in albedo when sea ice melts is 0.7 rather than the 0.8 of my original estimate, meaning my original estimate was 1/7th too high. Those who have followed KL's posts in this debate will wonder why he has made such a big thing of the increase in albedo because of the high angle of incidence. Those of a more cynical nature will wonder why he always mentioned it, but never quantified it. I need to make some further adjustment based on data in Trenberth's energy balance diagram: The first thing to notice is the cloud albedo, which is 0.23 This is a significant over estimate for the arctic as there is a much higher amount of cloud in the tropics. I will use the figure unadjusted. The second thing to notice solar radiation absorbed by the atmosphere, which is again about 23%. Adjusting that for the average increase in path length over the day at 75 North over the summer months leads to a calculated absorption of 46%. Again, this is a significant over estimate of the effect. Much of the absorbed energy is UV radiation absorbed in the mesosphere and stratosphere. Because it is almost entirely absorbed, even in the tropics, the additional path length cannot lead to a doubling of the energy absorbed. In fact, in those portions of the spectrum where the radiation is entirely absorbed, increasing the path length results in no increase in absorption. Even where only part of the energy is absorbed, the correct treatment would be based on the Beers Lambert law, which applied to the total absorption would lead to an estimate of 40% absorption from doubling path length (rather than the 46% I will use), and is still an overestimate as it still does not allow for those significant areas of total absorption, particularly in the UV spectrum. Finally, it is also an overestimate because Trenberth's figure already includes the increased absorption due to path length in polar regions in the average, inflating the base figure before my calculation. Allowing for all these factors, a more accurate estimate is likely to be around 32% absorption, but I intend to give Lambert's objections absolutely everything that they could be conceivably by permitted, so I will use the 46% value. So, given these figures, and given that the top of atmosphere summer insolation at 75 degrees North averages 500 w/m^2, we can then determine that the average absorption byopen ocean surfaceat 75 degrees North in the summer is 500*0.54*0.77*0.8 = 166.32 w/m^2. We can also determine that the average absorption by sea ice at the same latitude and time is 500*0.54*0.77*0.1 = 20.78 w/m^2. The difference, 145.53 w/m^2 is theadditionalpower absorbed in the arctic for each square meter of sea ice that melts. Over the summer season, that means for each additional square meter of sea ice melted, and additional 1.1 billion Joules of energy is absorbed. The average change insea ice areasince 1978 during the summer is a reduction of 2 million square kilometers, or 2*10^12 square meters. That means the average additional energy received in the arctic summer due to global warming induce melt back is 2.2*10^21 Joules, or about a third of my rough estimate. Please note, because I have estimated conservatively at every step, this is definitely and underestimate of the real value. Also note, this estimate takes into account every single one of the factors Ken Lambert considers important. To put this into perspective (and bring it back on topic), Flanner estimates achangeNH average forcing from melted sea ice of 0.47 w/m^2 over the three months with greatest increased forcing, which works out at 9.25*10^20 Joules over that period. That is less than half of the minimum value for the increase of incoming energy. Consequently, Lambert's claim that "Flanner's number is simply impossible" shows only that he is unwilling to address the evidence. Just briefly, and because Ken Lambert insists the comparison is significant, we might compare that figure to the equivalent figure at 23 degrees North. The comparison is very easy. There was no sea ice at 23 degrees north, even in the little ice age. So theadditionalenergy absorbed due to sea ice melt at 23 degrees north is zero. Ken Lambert keeps on arguing that the calculations of additional incoming energy by me, and the calculations of ice albedo feedback by Flanner must be in error because of the relatively small part of the globe which is effected. What he neglects is thatit may be a small part of the globe, but it is a very large part of the ice (and snow) covered portion of the globe. Because albedo effects are much stronger, for a given percentage change in the forcing agent, than are green house effects; this means that a relatively small part of the globe can have a disproportionately large effect on the total feedback to an initial forcing.Ken Lambertat 23:34 PM on 10 April, 2011Tom Curtisat 01:04 AM on 11 April, 2011~~biased in his favour~~conservative, he can let me know and I will do the calculation for 45 days before and after the solstice. Making this adjustment reduces the additional energy absorbed over the summer according to the conservative estimate from 2.2*10^21 to 1.7*10^21 That is still nearly double the 9.25*10^20 which we can expect from the additionalforcingas calculated by Flanner over that period. It is still sufficient energy to melt 1.9 million square kilometers of 3 meter thick ice, or 25% of the remaining icecap. And it is still approximately 3 times the energy annual energy influx that Ken Lambert insists, "Therefore the Arctic must absorb less (much less) than the uniformly distributed portion of 6.4E20 Joules/yr." And it is still 17 times greater than the energy which Ken Lambert misrepresents Trenberth as indicating is the maximum absorbed in the arctic. Ken Lambert questions some of my other figures without being explicit. All are adequately explained - but if he feels my using a 90 day summer, or ignoring the effects of waves, or whatever, is insufficiently~~biased in his favour~~conservative, he again need only let me know. Ken Lambert would also do well to learn the meaning of "Gish gallop" before he makes a complete fool of himself.Ken Lambertat 22:30 PM on 11 April, 2011Bob Lacatenaat 22:36 PM on 11 April, 2011Tom Curtisat 23:32 PM on 11 April, 2011Ken Lambertat 14:16 PM on 12 April, 2011Bob Lacatenaat 16:22 PM on 12 April, 2011Tom Curtisat 17:32 PM on 12 April, 2011area, which is slightly different but exhibits similar changes over time: You will clearly sea that the 2010 sea ice area through the summer months is from two to three million square kilometers less than it was in the late 1970s. On the other hand, every year there is an approximately eight million square kilometer reduction in sea ice area from the maximum around mid March to the minimum around mid September. That eight million square kilometer annual fluctuation drives the annual reduction in sea ice, and the annual reduction in sea ice thickness of about one meter across the whole ice pack. It is the reason the sea ice minimum is in mid-September rather than closer to the peak insolation in mid-July. That effect would have been operating for as long as we have had arctic sea ice, but it cannot lead to a runaway effect because the winter months eliminate the insolation that drives it. In contrast, the 2 million square kilometer additional reduction in sea ice extent since 1979 did not exist before, and is an additional forcing of arctic melt back. As you can see, that additional reduction in sea ice is a new feature, not having been observed before 1950, and not distinguishable from background noise before 1960. You will also note that as the additional melt back is more extensive in summer than in winter, in the past the variation between summer and winter was about half what it is now, with a consequently much reduced summer feedback of the seasonal melt. If you are observant, you will also notice that the two million square kilometer figure I use is very conservative, with the actual figure being close to three million for sea ice area, and four million for sea ice extent (reduction from 1979 only). That is, of course, in keeping with my intention to give you everything you could desire to sustain your theory (which collapses for all that generosity).Ken Lambertat 23:47 PM on 12 April, 2011Moderator Response:Later in the same comment (from which you quote) Tom says this:"Emphasis added. Details of calculation in my 56 and my 54."Ken Lambertat 08:05 AM on 15 April, 2011Ken Lambertat 11:29 AM on 15 April, 2011Ken Lambertat 00:25 AM on 16 April, 2011Tom Curtisat 10:43 AM on 16 April, 2011Once you have factored in all these factors, perhaps then you can make a sensible comparison to Flanner's estimated increase in forcing due to loss of sea ice.Ken Lambertat 11:43 AM on 16 April, 2011Tom Curtisat 11:49 AM on 16 April, 2011reiterate what I have already clearly stated in 54 and 56 above.Daniel Baileyat 12:06 PM on 16 April, 2011Ken Lambertat 12:15 PM on 16 April, 2011Tom Curtisat 13:32 PM on 17 April, 2011Tom Curtisat 15:06 PM on 17 April, 2011over the whole yearincluding six months of darkness, is nearly 100 w/m^2, so my estimate for the summer months of 127 W/m^2 is certainly conservative. 4) From the half hourly values obtained in (3), I calculated theadditionalenergy absorbed by ocean surface exposed by melting sea ice as the difference between the albedo (0.9) of the sea ice and the albedo of the ocean given the angle of incidence, multiplied by the effective surface radiation (as calculated in 3). Taking the mean of that value, the average additional power absorbed by the ocean is 97 W/m^2. 5) Using that value, I calculate the total additional energy absorbed as 7.57 x 10^8 Joules per meter squared over a notional 90 day summer, or 1.51 x 10^21 Joules over the whole 2 million square km of additional ice cap melted over the period 1979-2011. This is a reduction from my 1.7*10^21 estimate in 56, but is now (at last) error free so far as I can determine, and still a very conservative estimate. So conservative, in fact, that it assumeszeroinsolation for 9.5 hours of the day in the arctic summer. But it is still a sufficiently large figure to show that you are significantly underestimating the forcing effect of arctic melt back, and that there is no basis from considerations of incoming energy to think Flanner is incorrect about overall forcing.Ken Lambertat 23:15 PM on 17 April, 2011Tom Curtisat 00:15 AM on 18 April, 2011each summerthat would not have been absorbed except for the reduced sea ice area.Ken Lambertat 08:21 AM on 18 April, 2011Tom Curtisat 09:41 AM on 18 April, 2011Tom Curtisat 09:43 AM on 18 April, 2011Ken Lambertat 12:11 PM on 18 April, 2011Tom Curtisat 12:24 PM on 18 April, 2011Ken Lambertat 13:16 PM on 18 April, 2011Tom Curtisat 14:11 PM on 18 April, 2011since 1979." (My emphasis.) It's right there in the first sentence. Therefore if we want to do a plausibility check on Flanner (which is technically what this exercise is), we need to compare the change in summer incoming energy flux from 1979 to 2008. That is, by a very conservative approximation, 1.35*10^21 Joules. If we extent the comparison period to 2010, the change is 1.51*10^21 Joules, again very conservatively estimated. What is more, even the original post by Sphaerica from which this debate sprung is clearly considering the change in arctic forcing between the 1978-2000 average and the present, ie, effectively 2010. So why you should suddenly be interested in the mean annualchange in the changein the ice albedo forcing during the Arctic summer rather than, as we have been discussing, the mean annual change in the ice albedo forcing during the arctic summer is almost entirely mystifying. It does not even make much sense as mere passing curiousity. After all, as revealed by Piomas, the total ice volume has not been recovering each winter. The Ice does not need to melt back from the March of 1979 position each year. Therefore the change of the change is not a predictor of how extensive the ice melt will be each summer. This is a genuine feedback situation, with each summers melt making each successive summer's melt easier, and likely to be more extensive. (Note, likely, not guaranteed - there are other factors here.)Ken Lambertat 00:03 AM on 19 April, 2011Tom Curtisat 00:38 AM on 19 April, 2011it is not mathematically possible that what you have calculated is the cumulative energy flux over thirty years. And lest there be any doubt over what time period the incoming energy has been calculated, here is the relevant formula from my spread sheet, which calculates the energy input per meter squared from effective change in radiance absorbed by the surface as a result of sea ice melt:=I105*60*60*24*90Put in the simplest terms, 60*60*24*90 =/= 60*60*24*365.25*32; 11688 does not equal 90. Nor is it a possible mathematical confusion that they are the same. I perfectly understand that you are getting desperate, defending as you are, the in defensible. But resorting to such ridiculous tactics as pretending to the confusion you apparently espouse only succeeds in making you look the complete fool. At this stage I cannot be any clearer about my method. As this is already a repeat of this information,there can be no basis for your confusion other than a pointless rhetorical strategy. Should you persist in this ( -snip- ) strategy, I will request that the moderators take notice of your obvious trolling.Moderator Response:[Dikran Marsupial] Bold tags (hopefully) fixed.

[DB] Inflammatory term snipped.

Ken Lambertat 22:51 PM on 19 April, 2011Moderator Response:[DB] Personal remarks snipped.Tom Curtisat 23:28 PM on 19 April, 2011Ken Lambertat 09:25 AM on 20 April, 2011Tom Curtisat 10:49 AM on 20 April, 2011Mean difference between 1979 and target year: 0.445 million km^2Mean additional energy flux compared to 1979: 3.37*10^20 Joulescumulative additional energy flux compared to 1979: 1.01*10^22 JoulesMean additional energy flux for the 2004-2008 mean compared to to 1979:1.39*10^21 Joulescumulative additional energy flux for the 2004-2008 mean compared to 1979: 6.97*10^21 Joules. Very clearly from your calculation, the value you determine in the quoted section of 87 is thecumulative additional energy in ice melt over the period 1979-2010. That is comparable to thecumulative additional energy flux compared to 1979, or 1.01*10^22 Joules. In contrast, the 1.51*10^21 Joule figure I calculated is comparable to theMean additional energy flux for the 2004-2008 mean compared to to 1979, or1.39*10^21 Joules. It differs slightly because it is calculated for an approximate average of the years 2006-2010 rather than 2004-2010, and also because it is compared to an approximate average of 1979-2003 (which has slightly more ice than 1979 itself). I do not know how I could possibly be clearer than I have been in this post. Therefore if you persist with the absurdity that the difference in energy flux over a season is the difference in energy flux over 32 years, there is no further basis for debate between us.Ken Lambertat 23:29 PM on 20 April, 2011Tom Curtisat 01:12 AM on 21 April, 2011is not the only form in which energy has accumulated in the Arctic. Your persistence in treating it as though it were only underlines how desperate you are to deflate the figures beyond all reason. Second, the appropriate comparison for determining the significance of arctic sea ice melt as a forcing mechanism is between Flanner's calculated forcing which, adjusted for the relevant temperature increase, is NH forcing * temperature increase since 1979-1983 *0.5 (to average globally, or 0.63*0.43*0.5 = 0.135 W/m^2. Of that, just over half is due to snow melt, and just under half, say 0.06 W/m^2 is due to sea ice melt, or 6.7% of the total globally averaged forcing.Note, that is not the total arctic forcing, but only that due to sea ice melt. This comparison is particularly appropriate as both studies consider the same time frame. Third, even more informative is if you consider the rate at which the sea ice albedo is increasing. Over the 30 years from 1979 to 2008, the increase in incoming flux absorbed by the Arctic ocean due to additional sea melt has been increasing by 15% per year. If this continues, as seems likely, in ten years the arctic ice albedo feedback will add an additional 0.18 Watts/meter^2 or 20% to globally averaged energy imbalance. It is not likely to get much larger than that because it will run out of pole to melt. (Snow albedo will continue to drive increases in feedbacks for sometime, however.) However, that is a substantial effect and represents a substantial increase in warming rates above model predictions.Ken Lambertat 12:11 PM on 23 April, 2011adeladyat 13:43 PM on 23 April, 2011Bob Lacatenaat 13:57 PM on 23 April, 2011^{2}. For 4.4% of the earth's surface, this equates to 184 * .044 = 8.096 W/m^{2}. If the albedo change is from ice (.9 albedo) to open water (.1 albedo), or a change in absorption of 0.8, then 8.096 W/m^{2}* 0.8 = 6.4768 W/m^{2}. If this change only applies to 3 months out of the year (1/4), that's 6.4768 W/m^{2}/ 4 = 1.6192 W/m^{2}. This does not multiply the number by any factor to account for the fact that the area is under 20-24 hours of high-incidence insolation per day. A forcing of 1.6192 W/m^{2}is close to one half of the 3.7 W/m^{2}forcing caused directly by CO_{2}, which would itself cause 1˚C of climate change, and a total of 3˚C with feedbacks. Since those same feedbacks operate regardless of the forcing, we can assume a warming rate of 3˚C / 3.7 W/m^{2}. For our high conservative estimate of 1.6192 W/m^{2}, this translates toan additional warming of 1.3˚C. One could argue that the change in albedo from sea ice (.7 albedo) to open water would be only 0.6, and that the entire Arctic will never (?) melt for an entire 3 month span, so let's make another estimate of only 3% of the earth's surface, and an albedo change of only 0.6, giving 184 W/m^{2}* 0.03 (%surface) * 0.6 albedo * (1/4 yr) * 3˚C / 3.7 W/m^{2}= 0.67˚C So with a very conservative estimate, 0.67˚C is still very far from inconsequential when it is being added to other warming that is already at dangerous levels. [Admittedly, this is sort of double counting, since this feedback is already included in the estimated 3˚C of warming from the original 3.7 W/m^{2}of doubled CO_{2}forcing. But the point is still the same. This value isinsignificant.] Oh, and please certainly check my math, and my logic. I certainly could have made an error in there.notKen Lambertat 22:23 PM on 23 April, 2011Ken Lambertat 22:46 PM on 23 April, 2011Tom Curtisat 23:22 PM on 23 April, 2011annualaverage for the arctic is indeed just over 50 w/m^2, so Sphaerica ought indeed to divide by three. But thenhe ought also to multiply by four to eliminate the seasonal parameter he introduced, seeing as how he would be using an annual average. Why is it, I wonder, that you never notice errors or adjustments that favour your argument, but always notice any regardless of their merit, that are not favourable to your argument?Tom Curtisat 00:28 AM on 24 April, 2011relative to 1979for successive five year periods from 1979 to 2008: 1979-1983: -7.40E+020 Joules 1984-1988: -4.18E+020 Joules 1989-1993: 8.24E+020 Joules 1994-1998: 1.41E+021 Joules 1999-2003: 2.06E+021 Joules 2004-2008: 6.97E+021 Joules If you pay attention you will notice that for the first 10 years, the value is negative. In fact, for eleven of the first eighteen years between 1979 and 2008, the ice albedo effect was a negative feedback relative to 1979 levels (though a positive feedback if compared to 1950 levels). The reason for this is that 1979 set a new record for summer minimum ice extent, so natural variation took the ice extent above that record in a significant number of the following years. The most important consequence of thatfor this debateis that the cumulative increase in incoming flux relative to 1979 levels (ie, your chosen comparison period) does not become positive until 1995. In other words, the doubled figure which will only be "...2.8% of accumulated heat from 4.4% of the Earths surface area over the last 31 years of official AGW" will in fact only be accumulated energy over something less than 16 years. Further more, for most of those 16 years, the change in the summer accumulated energy flux was only small, with a 6*10^20 Joule increase in the 5 year accumulation. But the last five year period shows a 4.91*10^21 increase over the preceding years.That is nearly half the accumulated value for the thirty years in just the last five years!In fact 2007 alone accumulated more energy (2.54E+021 Joules) than any five year interval ending prior to 2005, and indeed, more than the 10 years from 1989-1998. 2008 (2.05E+021 Joules) is not far behind, and accumulated just 0.5% less energy than the five years from 1999-2003. Clearly the ice albedo effect was not such a big deal 20 odd years ago, but then again, nobody said it was.It is a big deal now. Thirty years accumulation at the average rate of the five years from 2004-2008 would accumulate 4.182*10^22 Joules. By your calculation that you say I don't get, that means it would constitute 5.6% of the Earth's accumulated energy. And that is with a figure very conservatively estimated, which ignores the additional energy gain in any season outside of summer, and in which three years of the five year average come from before the drastic 2007 reduction in summer sea ice. So what I get, but you plainly do not is that the ice albedo effect has gone from "ho hum" 15 years ago to a game breaker today. No matter what contortions you try, and no matter how much you want to include the low values of 30 years ago in your comparisons to mask the high values today, I will not forget this fact. And as clearly indicated in my point three @90 above, all indications indicate that it is going to get worse. In ten years time the ice albedo effect is likely to add 0.18 Watts/meter squared to the global energy imbalance (bringing its total effect relative to 1979 up to 0.24 Watts/meter squared. At that point, the 4.4% of the Earth you think is so trivial will be causing 22% of the total global warming. And that is significant.Bob Lacatenaat 01:26 AM on 24 April, 20110.67˚C to 1.3˚C. All other arguments are moot unless I've made a (real) mistake in my calculations. The question at hand has been whether or not the melting of summer ice in the Arctic will have any impact on climate. The proposal was that the increased positive albedo feedback would be significant. The argument was that the Arctic only covers 4.4% of the globe, so the feedback cannot be significant. The numbers show thatthe positive feedback is more than merely significant, but downright scary. Case closed.Alec Cowanat 06:59 AM on 24 April, 2011"I am glad your calculation agrees with mine that the effect of arctic ice melt is trivial (2.8% increase in arctic forcings since 1978)".A"What about the effects on the other 95.6% of the Earth's surface, like the 70% occupied by the oceans where we still can't find the absorbed heat".B From here:"What is your point in calculating the incoming and ignoring the outgoing?"C"Surely the whole discussion of AGW is about the *net* warming effects. One might as well suggest that we only look at possible changes incoming flux on *any* part of the Earth, while ignoring the changes in outgoing flux".D ("outgoing flux" and "cellar door", don't they sound charming?) From here:"Tom, wilfully leaving out relevant information of which you are aware simply is a distortion of the case to suit a particular bias".EBob Lacatenaat 08:33 AM on 24 April, 2011