From the “settled science” department comes this new revision of Earth’s entire radiation budget. Many WUWT readers can recall seeing this radiation budget graphic from Kenneth Trenberth in 2009:
![erb[1]](http://wattsupwiththat.files.wordpress.com/2014/01/erb1.jpg?quality=83)
That figure in a slightly different form also appeared in the 2007 IPCC AR4 WG1 report with different numbers:
![faq-1-1-figure-1-l[1]](http://wattsupwiththat.files.wordpress.com/2014/01/faq-1-1-figure-1-l1.png?quality=75)
Source: http://www.ipcc.ch/publications_and_data/ar4/wg1/en/fig/faq-1-1-figure-1-l.png
Note that in Trenberth’s 2009 paper, the energy from “back radiation” (from GHG action) value went up from 324 w/square meter cited by the IPCC in 2007 to 333 w/square meter. The net effect of that is increased energy back to Earth’s surface, making it warmer.
It seems odd that would increase so much, so quickly in two years. Even more surprising, is that now, the value has been revised even higher, to 340.3 w/square meter, while at the same time, the “Net Absorbed” value, that extra bit of energy that we get to keep from the sun on Earth, thanks to increased GHG action, has gone DOWN.
I know, it doesn’t make much sense, read on.
Alan Siddons writes in an email:
Reviewing NASA’s Earth Radiation Budget (ERB) program this week, I noticed a graphic depiction I hadn’t seen before, at
http://science-edu.larc.nasa.gov/energy_budget/pdf/Energy_Budget_Litho_10year.pdf .
It was drafted with the assistance of Kevin Trenberth and contains some notable differences from the last effort of his that I’d seen, so I’ve inserted NASA’s new values over it.
Cooler sun than before but a warmer surface. Less albedo and air absorption. Non-radiative cooling is higher than before but surface emission is higher too. “Net absorbed” refers to radiant energy going in but not yet being radiated – a ticking time bomb.
==============================================================
Note that somehow, between 2009 and the present, it was decided (presumably based on CERES measurements) that the Net Absorbed value (which is the extra energy absorbed that would result from increased GHG’s) would go DOWN from 0.9 w/square meter to 0.6w/square meter – an decrease of one third of the 2009 value.
This isn’t a typo, since many of the other numbers have changed as well.
With all the talk of the “settled science” that is certain about increases in Greenhouse gases, it seems that with such a revision, there’s still some very unsettled revisionist work afoot to get a handle on what the “real” energy budget of the Earth is. Perhaps the recent published works on climate sensitivity, coupled with observations of “the pause” have had some affect on these numbers as well. Meanwhile, according to the Mauna Loa data, CO2 concentration has risen from 388.16ppm in November 2009 when we had the big Copenhagen COP15 meeting that was supposed to change everything, to 397.31ppm in November 2013.
So with GHG’s on the increase, their effect has been reduced by a third in the NASA planetary energy budget. That’s quite remarkable.
So was Trenberth’s 2009 energy budget wrong, running too hot? It sure seems so. This is what NASA writes about that diagram:
The energy budget diagram on the front shows our best understanding of energy flows into and away from the Earth. It is based on the work of many scientists over more than 100 years, with the most recent measurements from the Clouds and the Earth’s Radiant Energy System (CERES; http://ceres.larc.nasa.gov) satellite instrument providing high accuracy data of the radiation components (reflected solar and emitted infrared radiation fluxes).
This energy balance determines the climate of the Earth. Our understanding of these energy flows will continue to evolve as scientists obtain a longer and longer record using new and better instruments (http://clarreo.larc.nasa.gov).
Source: http://science-edu.larc.nasa.gov/energy_budget/
It seems to be a clear case of observations trumping Trenberth.
So with the retained energy (the net absorbed figure) resulting from GHG’s like CO2 dropping by one third since 2009, can we now call off some of the most alarming aspects of global warming theory?
Related posts:
CERES Satellite Data and Climate Sensitivity
==============================================================
UPDATE:
Alan Siddons writes in with some further research. Commenter John West also noted this in comments. Siddons writes:
Well, let me tell you what I found while tracking down that IPCC illustration. I did find it on an IPCC document, Regional Changes of Climate and some basic concepts , but it looked shabby there too, so I surmised that it was a careless copy-paste of somebody else’s work, not a product of the IPCC itself. On that basis I searched for “radiation budget” or “energy budget” and added the illustration’s particular figures to my search demand.
Bingo. The illustration actually came from a May 2013 American Institute of Physics paper, A new diagram of the global energy balance , by Martin Wild, et al.
Here’s a small version for your records.
Other notes by Wild, Decadal changes in surface radiative fluxes – overview and update , yield some insight into his perspective — for instance, this panel,
which seems to indicate that less sunlight creates more compensatory back-radiation but a weaker terrestrial emission, while more sunlight “unmasks” the greenhouse effect. Wild’s conclusions are also notable.
- Still considerable uncertainties in global mean radiation budget at the surface.
- Models still tend to overestimate downward solar and underestimate downward thermal radiation
- Strong decadal changes observed in both surface solar and thermal fluxes.
This last point seems to imply that changes to the Radiation Budget are not merely a result of improved measurements but reflect rather sudden changes in our thermal environment.
================================================================
This leads me to wonder, why did NASA choose the values from Wild et al as opposed to Trenberth from the National Center For Atmosphereic Research?
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Gail Combs says:
January 17, 2014 at 9:47 am
Michael Moon says: @ur momisugly January 17, 2014 at 8:48 am
“Back Radiation!”
This is a figment of the imagination….
>>>>>>>>>>>>>>>>>>>>>
That depends on whether you are talking on the molecular level or macro level. Net there is no “Back Radiation” because it violates the 2nd Law. However thanks to the 400 ppm of CO2 you can get a retarding in the time it takes for the radiation to exit TOA…. nanoseconds?
As I said I am a chemist so do not have the maths to figure it out but that photon of the correct wavelength to interact with the very scarce amount of CO2 is not going to be hanging around very long while on its way out even if it does manage to find a CO2 molecule to interrupt it in its journey.
I have never seen the amount of outgoing energy for the CO2 bands which is why I like this graph Outgoing seems to be down around tenths. Digging around just now I found this graph Which if I am reading it correctly says the energy is down in the 0.08 Wm2 or less range. So yes in the tenths or less.
I’m afraid you’re not reading it correctly Gail. The units are W/(m^2.sr.cm-1) so if considering emission from a surface you’d first have to multiply by 2pi (~6) then the width of the band in wave numbers (say ~100). So approximately in the 15micron band, 50W/m^2.
bobl 2:03pm: “@AlecM The Meteorologists imagine the clouds heat the surface, but in reality, they reduce its IR cooling rate! …Yes, this is how I look at it, however you can look at the radiation flows and describe the reduced radiation loss…reflected IR is also broadbanded as it thermalises at the surface…”
******
Be very careful discussing clouds. Pretty sure true meteorologists don’t think clouds “heat” the surface since they are at a cooler height; the sun alone increases surface T. Clouds do increase the entropy and enthalpy of the solid and liquid surface, clouds don’t have energy source to use up so do not increase the surface temperature even by reflection.
All else being equal, less radiation is emitted from a clear sky than from a cloudy sky, not, as has been stated hundreds of times until it has become an immutable truth, because clouds reflect ground radiation but because emission by clouds is greater than by air at the same temperature. ~Bohren 1998 p. 358.
Also, you got tripped up here 2:41pm: “..50% chance that photon will be aimed toward the ground, when that photon strikes the ground it can add to the incident energy and make the ground warmer.”
Again, the sun uses up an energy source and increases ground temperature. Drill that in. Since the 50% chance photon aimed toward the ground comes from a cooler level than the surface on avg., the photon on avg. can’t increase the temperature of the ground. That photon will increase the entropy and the enthalpy of the solid and liquid ground when it gets annihilated.
If not careful with these statements, whole websites spring up, books get written and threads go to 1,000 posts pointing out the resultant issues.
Has anybody thought about this? Possibly CO2 helps cooling instead of warming:
So, what would happen, if we had no Greenhouse Gases?
Remember, Greenhouse Gases can absorb longwave IR radiation and get heated up. They can also be heated up though contact with the O and N molecules of the air, which are first heated up by the surface, convection and incoming sunrays. The hotter they are, the more they are radiating and as there nothing comes back from the outer space, they will cool the atmosphere.
In the contrary, O and N molecules cannot absorb nor radiate heat. But they can collect heat from other molecules and the earth surface through contact. This is why the air is a such a good insulator. Bu the heat, once trapped, cannot radiate, and the molecules stay hot. To cool down, they need the help from greenhouse gases.
Now we look at our Earth Surface, heated up with 160 w/m² (as you see in the graphic). About 80 we get into the atmosphere trough radiation, 20 through thermal convection. No greenhouse gases in the air, except water vapour. 40 will vanish through the Atmospheric window, and 20 don’t go into the atmosphere but straight into space, not disturbed by GG.
Now we have a problem: There are remaining 100 w/m² in the atmosphere, and they can’t escape. No help from the GG. So the air temperature will climb up to the hottest tempeartures on Earth, about 60°. The poles will melt, and we will be boiled. Thank God, we have the greenhouse gases! They don’t heat up, they mostly cool.
Okay, there is something wrong with my model, as water vapour is also a greenhouse gas, and it can help in cooling a bit. But it will not help with all the 100w/m². Even some Watts are dangerous. Why? look at the graphic: There is mentioned a 0.6 or 0.9 w/m² net absorbed energy, which is’t released from the surface. Which means even this small amount is considered as dangerous as it will remain in the atmosphere and heat it up. But we have to handle 100 w/m²!
Steve Case
Not sure why you would get banned?
your point is valid but some of the gases does hold heat such as water vapor. All data they have to show how much heat actually is held is all done with models.
There is a very easy peasy experiment. The experiment will give empirical evidence to show how much heat is held by the atmosphere. I don’t have the equipment myself to do it but it can be done.
Check the drop in temperature of the moon vs the earth per hour after the initial inversion layer drops. There are some locations on the earth that has similar temperature drops of the inversion layer. The difference with a few minor differences between the earth and the moon that can be calculated will give you how much the Earths atmosphere holds heat.
I would like to know why this experiment hasn’t been done yet.
Thank you.
Something to add to my previous Post on cooling CO2:
One supporter of the Turney Journey (Shock-al-sky, you remember?) was (possibly, now some supporters are denying) the University of Exeter , which startet now a online course on Climate Change and Solutions, which I joined this week. As the have recommended to start a blog, I did it. No tmuch to write there in, as the course is low-level. So I use it to write further ideas about Global Warming, The text above is just a small part of the whole, so I invite you to get there further enlightment about CO2 and the comming doom.
http://klimawandler.blogspot.de/
How much of the Sun’s energy is expended in rotating the earth? Willis appears to looking for missing energy and I understand the earth heats as the day progresses. Is it possible that earth operates like a version of Crooke’s Radiometer with the evening side warmer than the morning side?
J.Herbst 4:45: “..O and N molecules cannot absorb nor radiate…”
Yes. They can. All matter > 0K radiates and absorbs; N and O are matter in gaseous state at earth temp.s.
Now we have a problem: There are remaining 100 w/m² in the atmosphere, and they can’t escape.
Neither can the 100 W/m^2 ever get in to need an escape because if earth atm gas can’t radiate in your model then neither can the gas in the sun radiate. No energy arrives then from the sun (or stars) thru outer space.
bulsit says:
January 17, 2014 at 2:34 pm
“I have never seen that atmospheric gases are source of energy to some warmer. Nor gases can’t be blankets, in free flowing environment. They could be blankets only when they don’t move…between glasses. How long this totally crap can continue!”……….
I agree. They keep talking about a gas as if it was a solid, just laying there like a piece of insulation.
Insulation in my attic slows down heat tranfer; CO2 is a blanket; your sweater keeps you warm.. Yes they are solids that slow down heat transfer.
Guess what… I took the insulation out of my attic and poured in dry ice [solid CO2]
Wow, I thought, 100% CO2 should really give me lots of back-radiation, and my furnace would hardly ever be on.
The CO2 sublimated and rose up through my roof vents. My heating bill rose drastically. ;^)
Why is it that no one ever mentions that CO2, being a gas, expands, and rises, when heated?
If it expands and rises when heated then the temperature does not go up, does it?
All matter will radiate, and absorb/scatter photons, however when the photon energy is equal to the band gap, a substance can absorb. It is wrong to say that diatomic gasses can’t affect received radiation, they do, but its not much. Greenhouse gasses can radiate much more.
Also the way I see it, absent of energy transport the total energy of the gas must be the same throughout the atmosphere. Thus the Ke + Pe of a gas must be a constant, and as the potential energy rises the kinetic energy (temperature must fall). Absent any inputs there must be a gradient from warm to cold, dependent only on the depth of atmosphere and gravity. Without this gradient convection doesn’t work. So those that suggest that the entire difference between the blackbody description (-18C) and the situation with atmosphere (15C) are due to GHGs miss an important point.
richardscourtney says, January 17, 2014 at 12:43 pm:
“As you say
On a warm muggy overcast night, it may stay that way nearly all night long, but it won’t get any warmer.
You do not add that
on a clear night the temperature drops often rapidly.
And, of course, the difference is that radiation from the surface can reach space more easily on a night which is not overcast.
And when the Sun comes up the surface is also heated from the Sun but the effect you report does not cease.
So, you have provided an excellent example of the radiative greenhouse effect and how it can vary at a locality. Thankyou.”
Richard, if the clouds are still there when the Sun rises, they cause the surface temperature to rise more slowly than if they weren’t there. Opposite effect.
It is indeed true, when the surface cools (is no longer heated by the sun), then a cloud cover (and/or humid air) would reduce its cooling rate compared to no cloud cover (and/or dry air). But when the day breaks and the sunbeams come in from above, then that cloud cover and high atmospheric humidity will have the opposite effect. And at least in the tropics, where most of the energy from the Sun is absorbed by the Earth system, this cooling effect is distinctly stronger than the nightly warming effect.
So if that’s your GHE, then it would be hard to call it a ‘warming’ effect.
Notice how all the arrows in the diagrams above represent ‘heat’ flows, EXCEPT the two thick IR ones moving up from and down to the surface. And yet everyone seems to take for granted that the energy flows they represent is somehow equal to all the other ones. They expect them to ‘work’ like the others, to give the same results or effects as the others. AS IF they were ‘heat’ flows.
That’s where the deception lies hidden. Because no one tells us about this. No one notifies us about it.
If anything, the real radiative heat flux between surface and atmosphere is the UP-arrow minus the DOWN-arrow. Only that can heat anything. Because it’s … heat.
bobl saaid at 2:41 pm
Incoming energy heats the surface, the surface raises to a temperature and radiates that heat away as IR, the photon leaves the surface and interacts with a CO2 molecule raising it’s excitation state, nanoseconds later the photon is re-emitted as emission but there is an almost 50% chance that photon will be aimed toward the ground, when that photon strikes the ground it can add to the incident energy and make the ground warmer.
No it won’t make the ground warmer. For one thing it’s the same photon that just left.
Gail Combs said 2:41 pm
Actually I have seen it get warmer over night but that is from hot air moving into the area from the southwest.
I knew someone would say that, I dithered on putting in a caveat stipulating a CALM muggy & overcast night, but I din’t want to make it messy.
I’m just surprised that you took that bait, and didn’t use a smiley face (-:
Ox AO said at 5:13 pm
Not sure why you would get banned?
Because the “Waiting for Moderation” sign popped up on my post (-:
Alberta Slim says:
January 17, 2014 at 5:43 pm
The CO2 sublimated and rose up through my roof vents. My heating bill rose drastically. ;^)
Why is it that no one ever mentions that CO2, being a gas, expands, and rises, when heated?
If it expands and rises when heated then the temperature does not go up, does it?
AGW gases don’t expand when heated nor condense when cooled. Climate scientists are not meteorologists..
Puts me most in mind of “Hidden Variable Fraud”, assigning all loose scraps of unattributed causality to one’s preferred “forcing”.
btw – all figures in all Trenberths plots. No emissivity. Power and amount emitted / received are all wrong. AND, power of grey body emission is not amount of grey body emission. If it were, it would be a black body, and we all know nothing is a black body. All of all of the plots is in black body, because there is no emissivity. We live in (complex) grey body reality.
Mind you we all know P/4 does not apply at earth’s surface either, as shown by day and night at earth’s surface. Yet all the plots start with P/4. The earth is not flat.
AND, no one has observed atmospheric “back radiation” warming earth’s surface.
Alan Siddons used the term “greenhouse land physics” many years back, and above are the requirements for such an imaginary “landscape”, “paradigm”, or rather failed pseudo science.
This new graphic contains the the same fundamental problem as the old graphic; it is the “global mean” of these various readings. Producing a “global average” of downwelling IR radiation obscures the reality that hotter, drier climates have a lower level of downwelling IR radiation than do cooler, more humid climates that lie along the same latitude.
.
In 2011, for example the average 24/7/52 downwelling IR radiation measured at the SURFRAD site at Desert Rock, Nevada was 299 W/m^2, while at Goodwin Creek, Mississippi it was measured to be 350 W/m^2. This extra 51 W/m^2 of downwelling IR radiation in Mississippi was due to the fact that the absolute humidity in Mississippi was 250% higher than in Nevada, which increased the emissivity of the ground level air. Never the less the yearly mean ground level air temperature at the Mississippi site was cooler than the Nevada site. To put a fine point on it, even though a 250% increase in humidity caused a 51 W/m^2 increase in downwelling IR radiation at the Mississippi site no “heat-amplifying” affect was observed.
.
As mentioned in a previous post “Andrew Dessler and colleagues from Texas A&M University in College Station confirmed that the heat-amplifying effect of water vapor is potent enough to double the climate warming caused by increased levels of carbon dioxide in the atmosphere….”
.
What “heat-amplifying effect”? The “heat-amplifying effect” of which they speak does not exist within the actual atmosphere and it can only exists in theory if one obscures physical reality by working with global averages instead of regional comparisons. It is an easily observable phenomenon that wetter climates along the same latitude are the cooler climates; take Saudi Arabia vs. Bangladesh for example or Phoenix, Arizona vs. Dallas, Texas or the Congo vs. Nairobi.
.
You see, if one takes the above mentioned readings and says that the average 24/7/52 downwelling IR radiation was 324.5 W/m^2, the average temperature was 17.2C and the average absolute humidity was 6.65 g/kg, the fact that the higher humidity in Mississippi caused a drop in its temperature is completely obscured and one can assert that the 6.65 g/km of water vapor raised the temperature up to 17.2 C from whatever imaginary number that you claim it might have been had the water vapor been absent. The “greenhouse effect” hypothesis asserts that without “greenhouse gases” in the atmosphere the global mean temperature would be 33 C cooler; yet when nature takes the “most powerful greenhouse gas” out of the air such as in a desert or during a drought the temperature goes up and heat-waves ensue.
Carl
Informative post again! I ask permission to use picture
http://wattsupwiththat.files.wordpress.com/2014/01/nasa-_rad_budget-old-new.png?w=640&h=464
in my own blog article:
http://roskasaitti.wordpress.com/2014/01/18/kadonneesta-lammosta-loytyi-33-arviontivirheena/
If not OK I remove the image.
@ur momisugly ristoi These are public domain images, so you are most certainly welcome to use them.
Kristian:
Thankyou for your reply (at January 17, 2014 at 6:40 pm) to my post (at January 17, 2014 at 12:43 pm).
It seems there is a confusion.
The reality of the radiative greenhouse effect is a different issue from the validity of global energy budgets.
My post you have answered refuted a mistaken assertion that radiative effects don’t increase global average surface temperature (GAST). It pointed out that the person making the assertion had provided an example which demonstrated the opposite of his assertion. And what I said is true. You have replied by attempting to discuss irrelevant details related to that example, and I am not willing to engage in such an ‘Angels On A Pin’ discussion.
Importantly, it seems you think I accept energy budget determinations because you confuse that issue with what I said about the example. I do NOT agree any such determinations of average energy flows in and through the climate system because they only represent the assumptions of their compilers: this is stated in my above post at
http://wattsupwiththat.com/2014/01/17/nasa-revises-earths-radiation-budget-diminishing-some-of-trenberths-claims-in-the-process/#comment-1538857
Richard
1. Why is radiation from a cold Earth claimed to be over 4 times as great as losses from convection and latent heat losses ? Wind chill seems more common than radiation chill and Willis’ tropical thunderclouds would appear to have a huge influence on climate.
2. If clouds cover 70% of the Earth’s surface, why is it claimed they only reflect 25% of solar radiation ?
@Anthony Watts January 18, 2014 at 2:47 am
Thank You.
May I tell that WUWT is quite high ranked also in Finland. Even professor of climate/environment change Korhola tell that he likes.
@ristoi
“kiitos”
If we take plant live out of the system would there be any difference ?
Steve Case says:
January 17, 2014 at 7:08 pm
No it won’t make the ground warmer. For one thing it’s the same photon that just left.
Without the reflected energy
Over an interval – during heating (IE As the surface is warming) 100 Photons come in – 50 Photons leave (50 photons cause warming) , with insulation 100 Photons come in, 50 leave, 25 return 75 photons cause warming.
Now traditionally we would set a boundary at the limits of the system and Say without our reflective insulation, 100 photons in – 50 photons out, 50 photons worth (units) of warming, vs with insulation 100 photons in, 25 photons out, 75 units of warming. The Temperature of an object depends on the Nett rate of energy in vs the Nett rate of energy out. These two descriptions are equivalent.
The Greenhouse effect works only because there is a frequency change between inbound and outbound energy, so our outbound longwave energy can be reduced by CO2 while the inbound shortwave is not, this is logical.
Note here I am NOT saying that we get 125 Photons in and 25 photons out, the 25 photons returning are part of the initial 100 photons that entered, I have not created any photons, But I have retained a larger portion of the incident energy by insulating the object – I have lowered its losses and thus I increase the objects temperature relative to the uninsulated state. However, there’s a catch.
If my object was perfectly black, and absorbed all the energy incident, no amount of insulation would make it any warmer.
In the example given, the insulated object warms until the losses equal the input, IE 100 photons in Vs 100 Photons out.
These kind of diagrams are yet another example of the pseudo-science that infests climatology, they are meaningless garbage. GHGs have little effect on the global climate, and this is easy to demonstrate.
Take a hot dry area, say the Sahara Desert. The daily temperature can vary by up to 40C – baking hot in the day and freezing overnight! All one can say about GHGs is that they may make the hottest part of the day slightly hotter, but the effect will soon disappear once the sun is lower in the sky.
Now take a hot place with a lot of water – say the Brazilian rain forest. Here the daily temperature range is 2C to 5C, with an average temperature of 25C. The effect of water has a dramatic effect on the climate. Note that the water causes cooling during the day and warming during the night. By definition this means it is not a GHG. It acts more like an insulator – call it ‘the Thermos Effect’!
The amount of GHGs will be similar in both areas so this demonstrates that water, which is not a GHG, has a massive effect compared to any possible effect of CO2. The effect of GHGs can only be seen in dry regions as water masks them elsewhere.
This is further demonstrated by looking at the annual change in temperature. The rain forest varies by only 2C over the year but the Sahara goes from daily maximums of 40C to 15C, further showing the lack of effect of GHGs.
Another issue I have with GHGs is that their effect will be consistent – they only vary slowly. So if any area is suddenly hotter/colder/wetter/drier it can not be due to GHGs as this would mean the effect would be the same day after day, year after year. It is something else.
The only climate science that is consistent revolves round the idea that the Sun [in various ways] interacts with water [in all its’ forms] to create the climate. For example the 60 year cycle of warming and cooling caused by interaction between the solar cycle and the oceans forecast that the global temperature rise would drop off around the year 2000, which it did.
Under normal conditions this would mean the ‘pause’ will last to around 2030. Unfortunately the Sun is currently behaving much like it did during the ‘little ice age’ so the cooling could last much longer and become quite severe. All the warming we have had since 1800 could be reversed – possibly quite quickly. This could cause many of the calamities claimed by CAGW, such as reduced crops and climate refugees.
I would say that the Sun and water on Earth controls almost all the climate and global temperatures of Earth. There may be some other minor effects, but with negligible impact.
See these 71 papers showing the Sun controls climate and not CO2 :
http://hockeyschtick.blogspot.co.uk/2014/01/71-new-papers-reported-in-2013.html
In this post and commentary, there is an extraordinary amount of common sense on display. I’m really proud of most of you, in particular, Gail, Carl Brehmer, Alan Siddons, Derek Alker and others, you know who you are. If you want to solve a thermodynamic problem, turn to the engineers and chemists. For the love of God, don’t seek thermodynamic wisdom from a climatologist or bureaucrat.
On latent heat.
In the cartoons this evolved from 78 W/m2 (IPCC 2007) to 80 W/m2 (Mr. T 2009) to 86.4 W/m2 (Wild 2013). Meanwhile global average precipitation doesn’t seem to change much around 2.6 mm/day:
http://bobtisdale.files.wordpress.com/2013/07/figure-x.png
Evaporative heat can be calculated straight forward from the precipitation:
2.6 mm/day = 2.6 liters (kg) per m2 per day = 2.6 / (24*3600) kg/s per m2 = 3*10^-5 kg/(s*m2)
Specific evaporative heat of water amounts 2.26*10^6 J/kg
3*10^-5 * 2.26*10^6 = 68 W/m2
I can’t explain the big difference with the cartoons. Sublimation and return of relatively cold precipitation will account for more heat extraction from the surface, however this must largely be guesswork. The same goes for heat transfer by conduction. It seems impossible do all this with an accuracy to justify an imbalance of 0.6 or 0.9 W/m2.