Reflections from surface and clouds - is there an albedo expert in the house?

Wondering Willis Eschenbach is a mite upset (archived here, latest here) because scientists aren't telling him he's right. In fact, they aren't telling him anything at all. And few of the readers at WUWT are helping him out, though a number are encouraging him with "scientists don't know nuffin'" comments.

Warnings - This article is long and meanders a bit - I have to call a halt at some point. This is just a blog article after all :) If you are looking for definitive answers about albedo, you won't find them. What you will get are some of the interesting bits and pieces I discovered as I went looking. There's no guarantee I've got it all right, either. This is something I've not explored in depth before now. So feel free to quibble in the comments.

Back to Willis Eschenbach. He thinks he's found a problem with a chart in a paper by Graeme Stephens of NASA's Jet Propulsion Laboratory in Pasadena (and elsewhere), and colleagues. The paper is about planetary albedo, which is the the fraction of the incoming solar energy scattered by Earth back to space. It's not a bad introduction to the subject, with some caveats as you'll see. The authors make two main points, as described in the abstract:

1. the Northern and Southern Hemispheres (NH, SH) reflect the same amount of sunlight within ~ 0.2Wm 2. This symmetry is achieved by increased reflection from SH clouds offsetting precisely the greater reflection from the NH land masses. 
2. The albedo of Earth appears to be highly buffered on hemispheric and global scales as highlighted by both the hemispheric symmetry and a remarkably small interannual variability of reflected solar flux (~0.2% of the annual mean flux).

As I discovered, the first point has already been remarked upon in earlier papers by others. The second point about small interannual variability arguably follows from the first given the opposite seasons in the two hemispheres. I don't know if the buffering argument will hold as more ice melts, or whether there'll end up a hemispherical imbalance over time. (There are papers looking at what happens as CO2 increases, which I haven't covered here. Also, see the section on the southern hemisphere below).

The particular beef Willis has with the paper isn't about either of those points. He is complaining about a chart showing the fluctuation in albedo over the year, as Figure 5 below (click to enlarge it).

Figure 5. Annual cycles of (a) the globally averaged albedo, (b) the atmospheric, and (c) surface contributions to this cycle. The solid curves are for all-sky fluxes, and the dashed curves are the clear-sky fluxes. The error bars represent the interannual variability. Source: Stephens15

Look at the vertical axis. Although it's labeled "Albedo", these charts aren't total albedo, which is around 0.29 on average. As the caption says, it's the flux. The change in albedo from month to month. The text states the seasonal cycle hits a peak in the northern hemisphere spring from snow cover and a lesser peak in the southern hemisphere spring from cloud cover:

This seasonal cycle behavior is set in part by the seasonal cycle of surface albedo which has a boreal spring-time maximum resulting from the reflection off the brighter snow-covered land surfaces between 30°N and 60°N (Figure 5c). The second weaker maximum in the boreal fall season is influenced by reflection from midlatitude clouds of the SH (Figure 5b).

The paper is a fair coverage of the topic of albedo, if you are interested in the subject, as Willis is.

Willis' peak albedo complaint

Willis thinks that Graeme and his colleagues are wrong, and that the peak albedo should be on the solstice. He wrote:

The maximum albedo occurs on the summer and winter solstices in December and June, when one of the poles are maximally pointed at the sun. At that point, the most ice-covered area is exposed, which makes for a high albedo. In addition, because the snow- and ice-covered area is much larger in the northern hemisphere than in the southern, the December albedo is higher than the June albedo.

And on the other hand, on the equinoxes the sun sees mostly ice-free zones, and so the albedo is lowest around March and September.

Even if planetary albedo were mostly from surface reflection rather than atmospheric, I can see a few problems with the reasons Willis gave for saying there should be a peak in albedo at the solstice (ie snow and ice cover). He's done this sort of thing before, you might remember:

• In December, a large part of the snow and ice in the northern hemisphere is dark. It's also the shortest day of the year.  
• In June, there's little snow and ice in the northern hemisphere. In the southern hemisphere, the sun doesn't do much - it's dark over much of the Antarctic ice.
• The maximum snow and ice coverage in the northern hemisphere is late winter, early spring - late January to early March.
• The maximum southern sea ice coverage in the southern hemisphere is in September (~17 million sq km), the minimum in February. In December it's around 7 million sq km. 
• The maximum Arctic sea ice extent is in March.
• At the solstice - when there is a lot of snow and ice extent at the poles (opposite seasons), the sun is lowest at the one where it's winter - so there's little if any reflected. (One paper disregarded winter altogether for the northern hemisphere polar albedo.)

Here's a chart of snow cover in the northern hemisphere using data from Rutgers University Global Snow Lab:

Source: Rutgers

And a chart showing Antarctic sea ice, from Cryosphere Today, showing the maximum extent in September and the minimum in February:

Source: Crysosphere Today

More on that further down.

Interannual variability is remarkably small

Given that most of the papers I looked at discussed the difficulty of getting precise readings at the polar extremes, and given the small range in variability over the year, Willis' complaint could be a bit of a storm in a teacup. One of the papers that Stephens15 referred to was a 2009 paper by Seiji Kato, which began with:

The interannual variability of top-of-atmosphere (TOA) irradiances observed by Clouds and the Earth’s Radiant Energy System (CERES; Wielicki et al. 1996) instruments is remarkably small. Four years of CERES data from March 2000 through February 2004 indicate that the annual and global mean TOA reflected shortwave irradiance is 97.0 W m22, with maximum and minimum values of 97.2 and 96.8 W m22, respectively. The difference between the maximum and minimum values is 0.4% of the mean value.

Max to min of 0.4% over the year isn't a huge variation. It must be quite a challenge to detect. (Dr Kato puts most of the difference down to clouds.)

Different types of albedo - global, surface, effective surface, climatological

It could appear that Willis' notion is supported by Loeb et al (2007), which says the following about surface albedo (not top of atmosphere) (my emphasis):

Global albedo has a distinct and repeatable seasonal cycle. Because of the tilt of the Earth’s axis and the large surface albedo of snow at high latitudes, it reaches maximum values during the solstice months and minimum values during the equinox months. Changes in cloud and surface properties from year to year introduce slight variations in the seasonal cycle of albedo, but these perturbations are much smaller than the basic seasonal cycle of albedo. As a minimum, therefore, any approach that attempts to measure subtle changes in the Earth’s albedo must be able to characterize the broad features of global albedo changes with season. 

Below is a double chart from Loeb07, again showing the month to month change in albedo but this time it's global albedo, not just at the surface. The charts are estimates from Earthshine (left) and CERES (right), with the maximum in November/December. another peak between March and May, and a minimum around August. It's as if Stevens shoved the Loeb07 chart back a couple of months (click to enlarge):

Figure 1. Seasonal variation in (a) simulated Earthshine reflectance and (b) CERES global albedo expressed as the deviation from the 3-year mean value. Earthshine reflectances are adjusted to a common lunar phase angle of 95 Source: Loeb07

That's interesting that it shows a maximum in November-December, because Stephens15 cites Loeb07 as one of its sources for albedo. Yet Stephens15 shows the all-sky maximum in March. Loeb07 looked at top of atmosphere albedo as measured by Earthshine (reflectance as it would be observed from the moon) and direct measures from CERES (as in the figure above) and from MODIS, while Stephens15 is talking about "globally averaged albedo" as measured from the top of the atmosphere. I don't know if they are different things or the same thing. (Loeb07 also plotted monthly anomalies to compare the three sources.)

In Loeb07, the authors talked about the difficulties in all methods:

Monitoring changes in the Earth’s SW TOA radiation is critical for understanding climate. However, because of the spatial and temporal scales involved and the need to account for radiant energy across the entire solar spectrum, it presents a significant observational challenge: all methods that attempt to measure the Earth’s TOA radiation suffer from sampling errors due to inadequate spatial, temporal or spectral coverage. ...Simulations of lunar Earthshine measurements show far less variability than those observed from the ground by Palle´ et al. [2004], but still show 4–5 times the variability observed from CERES global data. Furthermore, while CERES global albedos exhibit a well-defined seasonal cycle with albedo maxima and minima occurring at the same time each year, the seasonal cycle in lunar Earthshine reflectance simulations is highly variable and out-of-phase from one year to the next. Radiative transfer model (RTM) approaches that use imager cloud and aerosol retrievals reproduce most of the change in SW TOA radiation observed in broadband CERES data, but the assumptions used to represent the spectral properties of the atmosphere, clouds, aerosols and surface in the RTM calculations can introduce significant uncertainties in annual mean changes in regional and global SW TOA flux. Such uncertainties can cause interannual anomaly errors ranging from 1% for global ocean to 2% for global land, much too large for climate change decadal signals. 

Let me point out that in the acknowledgements, Stephens15 makes it clear that Norman Loeb (of Loeb07) provided input into the paper. So there might not be any discrepancy between the two papers. However he wasn't one of the authors so he can't be held responsible for the content.


Then there is this 2005 paper from J Climate by Xin Qu and Alex Hall, in which they write about effective surface albedo in sea ice zones (which takes into account transmissivity of reflections from the surface through the atmosphere) - my emphasis:

Effective surface albedo undergoes a small seasonal variation in both sea ice zones. It is similar in both hemispheres, being largest during the springtime of each hemisphere, smallest during fall, and in between during summer. This is also largely consistent with seasonal variations in surface albedo—largest during spring, smallest during fall, and in between during summer (black bars in Figs. 5b,c, and also see Fig. 1a)....

...atmospheric albedo also shows a small seasonal variation over all regions. It is smaller during spring and summer than winter and fall. For example, atmospheric albedo in NH snow-covered land areas is larger in DJF and SON than MAM and JJA. This difference is almost certainly associated with seasonal variations in the position of the earth to the sun, represented by solar zenith angle. Larger zenith angles during winter and fall in high latitudes increase the optical path of incoming solar photons, thus enhancing the albedo of the atmosphere.

In addition to looking at transmissivity of surface albedo (how much SW gets out to space through the atmosphere), Qu and Hall found that surface variability over the annual seasonal cycle is different to planetary variability and attribute the difference to cloud cover (ie clouds themselves reflecting the sun back out). Here is a chart showing the contribution to seasonal change in planetary albedo of surface and atmospheric albedo in the polar regions.

FIG. 6. Surface (black bars) and atmospheric (gray bars) contributions to the change in planetary albedo within seasons with similar zenith angles (refer text for equations). Source: Qu and Hall 2005

What Qu and Hall discuss is the interplay between the atmosphere and the surface in the cryosphere, and the impact this has on planet-wide albedo. They agree that in the northern hemisphere, snow albedo is strongest in springtime:

Although not strong enough to prevent the surface from dominating planetary albedo variability, the damping effect of the atmosphere significantly attenuates planetary albedo variability generated by surface fluctuations. For example, the magnitude of interannual planetary albedo variability in the cryosphere regions is about 10 times smaller than the magnitude of interannual surface albedo variability. This damping effect therefore partly constrains the strength of surface albedo feedback. Moreover, because this effect tends to vary seasonally, it may also contribute to seasonal variations in the strength of surface albedo feedback. For example, effective transmissivity is greater during spring than fall in NH extratropical land areas, implying that a snow albedo anomaly in NH extratropical land areas results in a larger planetary albedo anomaly in spring than fall. This is probably another reason why snow albedo feedback is stronger in spring, together with two other well-established reasons: extensive snow extent and relatively large solar radiation (e.g., Robock 1980; Hall 2004). 

Looking at different papers can be quite confusing when it comes to albedo. Albedo comes in several flavours - surface, atmosphere, surface through the atmosphere and top of atmosphere. It also comes from a range of different sources. There are papers describing site-specific albedo (eg from specific locations in the Arctic and Antarctica). Papers examining albedo at the poles. And other papers that take a view across the whole of earth.

This new paper by Chad W. Thackeray, Christopher G. Fletcher, and Chris Derksen talks about climatological albedo, and how it increases to a peak in March in the northern hemisphere:

The observed seasonal evolution of albedo has been shown to increase throughout the winter, peaking in March on average in the Northern Hemisphere (NH) [Fang et al., 2007; He et al., 2014]. He et al. [2014] suggested that this late winter maximum albedo is due to weak insolation during winter and the increasing influence of snow and ice-covered surfaces on the shortwave radiation budget during the winter-to-spring transition. This peak albedo is strongly tied to land cover, with forested regions being the least reflective, even with high snow cover, because the forest canopy masks the surface [Jin et al., 2002; Barlage et al., 2005; Fang et al., 2007]. 

He et al (2014), cited by Thackeray15, is another interesting and comprehensive paper on the subject of albedo.  This is what they say about surface albedo (not top of atmosphere (TOA):

It is interesting to find that the mean surface albedo for the Northern Hemisphere peaks in March (Figure 2b). This can be explained by the fact that high-latitude regions on the Northern Hemisphere receive little amount of downward solar radiation(<5Wm-2) in winter. Consequently, strongly reflective surfaces common to these latitudes, such as snow and ice, do not actively contribute to the shortwave radiation budget. From winter to spring, increasingly high surface albedos are observed, because snow and ice contribute to the radiation budget more and more as a result of increasing exposure to sunlight. 

Differences between the albedo data sets range from approximately 3% to 5% (not considering the ISCCP data) depending on the season and location. In the Northern Hemisphere, surface albedo peaks in March and April,when the amount of snow cover exposed to sunlight reaches its maximum. Not surprisingly, differences in albedo also peak for the same season with SD > 0.02 (Figure 2b). For the Southern Hemisphere, these data sets were not in good agreement from October to January with SD > 0.015 (not considering the ISCCP data), which likely resulted from the large differences in albedo over the Antarctic region (Figure 3) 

Below is the surface albedo from He14:

Figure 2. Monthly climatological surface shortwave albedo derived from satellite-based albedo data sets for (a) the globe, (b) the Northern Hemisphere, and (c) the Southern Hemisphere. The “mean” and “SD” are calculated from all the data sets except the ISCCP. Source: He14 

Globally, it shows the highest surface albedo is in December and the lowest from June to December. The highest surface albedo in the northern hemisphere is in March. In the southern hemisphere it's highest in December, which is the time when there is most sunlight. So despite the fact that the southern hemisphere has a lot more open ocean (therefore low albedo), I can only guess that it's down to reflections from Antarctica. I would have added the southern monsoon clouds except that this is just surface albedo that's being talked about.

Melting Arctic reduces albedo

Then in light of Stephens15, which suggests that cloud albedo might be a balancing factor over the two hemispheres, it doesn't mean that total albedo won't decline. Kristina Pistone, Ian Eisenman, and V. Ramanathan reported in PNAS in 2014 (my emphasis):

We find that the Arctic planetary albedo has decreased from 0.52 to 0.48 between 1979 and 2011, corresponding to an additional 6.4 ± 0.9 W/m2 of solar energy input into the Arctic Ocean region since 1979. Averaged over the globe, this albedo decrease corresponds to a forcing that is 25% as large as that due to the change in CO2 during this period, considerably larger than expectations from models and other less direct recent estimates. Changes in cloudiness appear to play a negligible role in observed Arctic darkening, thus reducing the possibility of Arctic cloud albedo feedbacks mitigating future Arctic warming. 

Southern hemisphere albedo

Finally (because I've read more than my normal quota of papers for the day), in a paper by Georg Feulner et al (2014) in J Climate, about the southern hemisphere, which was published last year, the authors discuss the differences in albedo between the two hemispheres. They raise some of the points I made above - which is nice to know. They also make the point that there's very little difference between the reflected energy from both hemispheres. (My paras and emphasis.)

As explained above, based on astronomical calculations Earth’s two hemispheres receive equal amounts of 87.4 PW of energy from the sun. Part of this radiation is reflected back to space by clouds in the atmosphere and by the surface itself, quantified by the planet’s albedo of about 30%. According to the CERES-FT08 dataset, the reflected energy flows are 26.0 and 26.1 PW for the Northern and Southern Hemisphere, respectively (see Table 2).

The slightly larger total albedo of the Southern Hemisphere is caused by several factors. To begin with, the Southern Hemisphere reflects more radiation back to space due to a larger annual fraction of low clouds, which dominate the cloud–albedo effect (Hartmann et al. 1992). Indeed, for the time period 1961–90, the ERA-40 (Uppala et al. 2005) reanalysis dataset yields annually averaged low cloud cover fractions of 0.31 and 0.38 for the Northern and Southern Hemisphere, respectively, and the CERES-FT08 data show that the amount of radiation reflected by the Southern Hemisphere is larger by about 1.7 PW due to this.

This higher atmospheric albedo in the SH is almost balanced by the lower surface albedo due to the larger area covered by oceans in the Southern Hemisphere, however. In the CERES-FT08 data, the surface in the Northern Hemisphere reflects roughly 1.6 PW more radiation than in the Southern Hemisphere due to this effect. The higher average albedo of the Antarctic, which is often mentioned as one potential reason for the hemispheric temperature difference, plays a role here but obviously cannot compensate for the larger and comparatively dark areas of ocean in the SH. 

And for a bonus, since you've made it this far, the Fuelner paper is about the temperature difference between the southern and northern hemispheres. It suggests that it's mostly down to meridional heat transport in the ocean from the south to the north, with around 10% because of albedo differences:

The combined effect of meridional transport of heat in the oceans and albedo differences between the Antarctic and the Arctic therefore is the main cause of the warmer Northern Hemisphere, but the discussion also highlights that much remains to be done to improve our understanding of Earth’s energy budget, a task appearing even more important in today’s changing climate. 

How Willis Eschenbach got it wrong

At this point I'll repeat what Willis wrote because if he was talking about surface albedo (not top of atmosphere), then he got part of it right, according the He14, but for the wrong reasons. Remember that the chart in Figure 5 in Stephens15 (above) put the global all sky peaks in albedo in Feb-March and late September. And there are other papers that show that the in the northern hemisphere, the peak albedo is in Feb-March. Whereas Willis disagreed and wrote:

The maximum albedo occurs on the summer and winter solstices in December and June, when one of the poles are maximally pointed at the sun. At that point, the most ice-covered area is exposed, which makes for a high albedo. In addition, because the snow- and ice-covered area is much larger in the northern hemisphere than in the southern, the December albedo is higher than the June albedo.

And on the other hand, on the equinoxes the sun sees mostly ice-free zones, and so the albedo is lowest around March and September.

Even if he was talking about the surface, in the northern hemisphere, Willis has it wrong. It's March when the surface albedo is the highest, not December. At least according to much of the literature. He's also wrong about "mostly ice free zones" in March and September. There is lots of snow and ice at the equinoxes. In March the Arctic sea ice is at its maximum, and the extent of snow cover in the northern hemisphere is about the same at the beginning of March as it is at the December solstice. In September Antarctic sea ice is at its maximum.

Willis also has it wrong for why the December albedo is higher than in June. If you go by the charts in Hu14 above, it's not because of the northern hemisphere, it's all down to the southern hemisphere. (That's just talking surface albedo, which as I understand it is the reflection from the surface, not counting the atmosphere. And I don't know if it's "effective surface" or just plain surface. That is, whether it takes transmissivity into account.)

Peter Webster's response to Willis and Judith's "profound"

The Stephens et al paper came out a while ago (in March this year). Judith Curry wrote about it saying: "The implications of this paper strike me as profound." She seemed to think the paper implied "the presence of a stabilizing feedback between atmosphere/ocean circulations, clouds and radiation".  I don't think it implied that there is any more stabilising feedback than was known before this paper was published. As far as I could tell, it was about the relative even spread at the present time. I don't thing it made predictions about the future. The authors did state: "Whether the symmetry referred to above and the regulation of Earth’s albedo relevant to it is a fundamental property of the Earth’s climate system is not yet known." In any case, it wasn't the first paper to remark on the almost (but not quite) symmetrical albedo. (Willis didn't jump into the discussion at Curry's place.)

ATTP had an article about it too. He thought it a solid paper, but wasn't so impressed as to call it profound.

I haven't read all the comments at either place but I didn't see any discussion about whether the interannual albedo representation is right or wrong. Anyway, I decided to do some investigating of my own.

One thing I found interesting is that Willis goes to great lengths to excuse one of the co-authors, Peter Webster (of Curry and Webster) from any responsibility for the paper. I've no idea what contribution Peter made, but he didn't seem to have an answer to Willis' concern. Yet I'd say that Willis' concern was fundamental to the paper. Willis approached Peter Webster, who passed the buck to the lead author, Graham Stephens. Then when there was no response from Dr Stephens, Peter suggested Willis go ahead an publish. Willis didn't want to go to the bother of doing that. Instead he wrote about his concern at WUWT (and complained long and loud that he didn't get a response from Dr Stephens - implying his WUWT article was payback.) Willis' self-righteous rant starts about here.

From the WUWT comments

Do you want these? This article is quite long as it is. One person picked up Willis on the March snow cover in the northern hemisphere:


It looks to me that it was Pat Frank who got it wrong, not Graeme Stephens.

July 10, 2015 at 7:29 pm
A couple of years ago, I discovered a decimal mistake in the RMS uncertainty in the TOA budget in Figure 1 of Graeme Stephens’ 2012 paper, “An update on Earth’s energy balance in light of the latest global observations” Nature Geosci. 5, 691.
It’s written as ±0.4 Wm^-2, but should be 4 Wm^-2 (making the TOA imbalance a very definitive 0.6±4 Wm^-2).
I wrote two polite emails to Dr. Stephens asking him about this, but he never replied. So, don’t take his silence personally, Willis. It may be his policy to not reply to polite critical emails.

The paper itself pointed out the difference between calibration uncertainty of ±4 Wm–2 and uncertainty in inferred ocean heat content information of ±0.4 Wm–2 (from Argo measurements):

The solar flux entering Earth is the most-accurately monitored of all fluxes through the system and varies least over time. Fluxes leaving Earth at the TOA are also well documented, although inherently less accurate with an uncertainty of ±4 Wm–2 on the net TOA flux that mostly stems from calibration errors on measurements of the outgoing fluxes. This uncertainty is almost an order of magnitude larger than the imbalance of 0.58 ±0.4 Wm–2 inferred from OHC information. The outgoing TOA fluxes presented in Fig. B1 are the TOA CERES fluxes adjusted within the measurement uncertainty to match this OHC inferred imbalance. 

Willis Eschenbach backtracks from his claim of the most ice-covered area being exposed, when challenged by Richard Verney:

July 11, 2015 at 3:19 am (extract - minus quote)
Thanks for an interesting question, richard. The albedo peaks represent some kind of mix of winter snow, winter ice, winter clouds, and solar angle. We know when it peaks, so I fear that theories about when it should peak are only as good as their ability to match observations. I fear that your theory doesn’t do that well given that it predicts a peak in late January. I’ve never seen any estimate of the albedo that peaked in late January, regardless of the source. I couldn’t say why that is … I can only report the observations.
Regards,
w.

References and further reading

From the HotWhopper archives: Wondering Willis Eschenbach looks for sunlight in the Arctic winter - yeah, really!

Below are the references I used in this article. I looked at others as well. If it's not listed below it doesn't mean it wasn't any good. Quite the contrary. I've started to compile a longer list of references that I looked at, which you can see in a new page on the static HotWhopper site here. (I'll be adding more during the day.) Then of course there's the citations at the end of every paper. If you haven't thought much about albedo, rest assured, the scientists have.

Stephens, Graeme L., Denis O'Brien, Peter J. Webster, Peter Pilewski, Seiji Kato, and Jui‐lin Li. "The albedo of Earth." Reviews of Geophysics 53, no. 1 (2015): 141-163. DOI: 10.1002/2014RG000449 (pdf here)

Kato, Seiji. "Interannual variability of the global radiation budget." Journal of Climate 22, no. 18 (2009): 4893-4907. http://dx.doi.org/10.1175/2009JCLI2795.1 (open access)

Loeb, Norman G., Bruce A. Wielicki, Fred G. Rose, and David R. Doelling. "Variability in global top‐of‐atmosphere shortwave radiation between 2000 and 2005." Geophysical Research Letters 34, no. 3 (2007). DOI: 10.1029/2006GL028196 (pdf here)

Qu, Xin, and Alex Hall. "Surface contribution to planetary albedo variability in cryosphere regions." Journal of Climate 18, no. 24 (2005): 5239-5252. doi: http://dx.doi.org/10.1175/JCLI3555.1 (open access)

Thackeray, C. W., C. G. Fletcher, and C. Derksen (2015), Quantifying the skill of CMIP5 models in simulating seasonal albedo and snow cover evolution, J. Geophys. Res. Atmos., 120, doi:10.1002/2015JD023325

He, Tao, Shunlin Liang, and Dan‐Xia Song. "Analysis of global land surface albedo climatology and spatial‐temporal variation during 1981–2010 from multiple satellite products." Journal of Geophysical Research: Atmospheres 119, no. 17 (2014): 10-281. DOI: 10.1002/2014JD021667 (pdf here) - Note: This paper gives a description of the various satellites used to calculate measures of albedo.

Pistone, Kristina, Ian Eisenman, and V. Ramanathan. "Observational determination of albedo decrease caused by vanishing Arctic sea ice." Proceedings of the National Academy of Sciences 111, no. 9 (2014): 3322-3326. doi: 10.1073/pnas.1318201111 (open access)

Feulner, Georg, Stefan Rahmstorf, Anders Levermann, and Silvia Volkwardt. "On the origin of the surface air temperature difference between the hemispheres in earth's present-day climate." Journal of Climate 26, no. 18 (2013): 7136-7150. DOI: 10.1175/JCLI-D-12-00636.1 (pdf here)