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Chris G at 09:14 AM on 20 February 2010Visual depictions of CO2 levels and CO2 emissions
@ RSVP at 06:27 AM on 20 February, 2010 I understood that you were referring to the interaction between theendisfar and Alexandre. You were setting up a straw man that was a) beyond any reasonable inference from what Alexandre said, and b) pretending that the people who study the atmosphere and climate are unaware that there is such a thing as convection. I used the term "rattle around" because there are two models for EM radiation, as waves and as particles, I was thinking in terms of individual quanta, and I decided that it the context of a blog, I was not subject to the same precision of language requirements as would be required in a journal article, as long as the meaning was clear. -
Squidley at 09:07 AM on 20 February 2010Skeptical Science now an iPhone app
Android! Oh, please, oh, please, oh, please! -
johnd at 09:07 AM on 20 February 2010Is CO2 a pollutant?
When it is claimed that the increased CO2 has upset the balance, what exactly is the critical balance between CO2 and water vapour, because that is the balance that is most relevant if CO2 is a forcing agent. The graph shows how the CO2 has increased over the last 10,000 years, but given the planet has warmed over that period, the amount of water vapour would have increased faster than the CO2 has thereby gradually decreasing the amount of CO2 per unit of water vapour for much of that time span. -
Doug Bostrom at 07:37 AM on 20 February 2010Is CO2 a pollutant?
Suibhne, I suspected it was a mistake to extend my model by including lightbulb dwellers. Just to be sure you understand the model, would the lightbulb be warmer if it was concentric to the reflective sphere? If you think not, how would that be so? -
suibhne at 07:29 AM on 20 February 2010Is CO2 a pollutant?
doug_bostrom ........... if you were a strange being living on the surface of the lightbulb...... Which surface,inner or outer? Philippe Chantreau .... the way you interpret Trenberth diagram does not seem to make any sense at all. Even on one side it does not add up 342 solar from Sun On Earth surface 168 solar + 324 back radiation Your right it does not make any sense at all. -
Alexandre at 07:29 AM on 20 February 2010Visual depictions of CO2 levels and CO2 emissions
RVSP, Please correct: closer to the *former* (not the latter) And also: The saturation argument and the "atmosphere has so little CO2 that it doesn't have any effect" argument are pretty much mutually exclusive. -
Alexandre at 07:26 AM on 20 February 2010Visual depictions of CO2 levels and CO2 emissions
RSVP, I assume you're using the saturation argument. Following the question you stated: does it simply raise the radiative source or does the energy hover somewhere forever? Well, if we had to pick one, the answer would be closer to the latter. The correction I'd point is not that it "simply" raises the source. This has consequences. You must keep in mind that it's not exactly "absorption", but attenuation by scattering. So the energy caught by CO2 at some point of the atmosphere is reemited to random directions, including upwards. The upper layers get somewhat less energy than the lower ones, and so the warming goes on even if these lower layers are already at their saturation. This webpage does a nice illustrative mathematical model of this. There's also the RealClimate post on this. -
Philippe Chantreau at 06:53 AM on 20 February 2010Is CO2 a pollutant?
Suibhne, the way you interpret Trenberth diagram does not seem to make any sense at all. The energy leaving the surface as IR radiation is the same energy that was previously received as mostly SW radiation (sunlight). The surface "converts" the SW energy into IR. The surface is not an energy source, neither is the atmosphere. If you are attentive to laws of thermodynamics, the energy coming from the Sun has to go somewhere, less the surface increase indefinitely in temperature until it reaches equilibrium with the Sun itself. Why are you shocked to see energy leaving the system? Where do you think it should be going? Thye panel example is inappropriate since these are average, global flows but let's look at it anyway. If you interpose a solar panel between the down going radiation and the surface, the diagram will obviously be radically altered. Your panel will get only 198 watts from above and, after a relatively short time for the surface to reach equilibrium, nothing from the bottom. The energy that was heating the surface is now received by the panel, the surface is not going to radiate IR as it was. If you think it could be otherwise, explain how. As for G&T, it is all about semantics indeed. Understood in the frame of thermodynamics, there is no heat transfer between the atmosphere and the surface, insofar as this would refer to a net heat transfer. G&T base the confusion on equating the simplification "the atmosphere makes the surface warmer" with "there is heat transfer between the atmosphere and the surface", implying it is a neat heat transfer. That's not what happens at all. The atmosphere just makes the equilibrium temperature of the surface higher than it would otherwise be without it. A radiant barrier makes the inside of a spacecraft warmer but there is no net heat transfer between the barrier and the craft. G&T is nothing but a multi page erudite obfuscation. -
RSVP at 06:27 AM on 20 February 2010Visual depictions of CO2 levels and CO2 emissions
Chris G "Near the surface, the GHGs may be relatively opaque and energy would rattle around for some time before gradually making progress outward; " When I made that remark #18, I was attempting to let Alexandre consider what he told theendisfar, taking his remark it to its logical conclusion, and so point out an untruth. In doing so, you use the term "rattle around". Why not diffuse or disperse? -
Chris G at 06:20 AM on 20 February 2010Visual depictions of CO2 levels and CO2 emissions
...but that doesn't mean that evaporation+convection somehow anticipate a change in energy flux and prevent it from having an effect. Otherwise, there would not be the wide range of climate conditions seen in the geologic record. Those same changes in climate that are often cited as evidence that humans are not altering the climate now somewhat preclude the idea that convection has a strong buffering effect. -
Tony Noerpel at 06:02 AM on 20 February 2010What would happen if the sun fell to Maunder Minimum levels?
Hello HumanityRules Given the information provided by Jesus Rosino, we see that the solar forcing during the little ice age was between .14 and .23 W/m2. maybe that sounds small but that is over every single square meter of the Earth surface. So if we multiply by 4 X pi X (6371000) X (6371000) we get total power in joules/second. then by multiplying by 60 X 60 X 24 X 365 we can compute how many joules in each year of the MM that there was an energy imbalance. we get 3 X 10^21 joules each year. So that would explain the cold weather. but the interesting thing is that the energy imbalance today is about 1.8 W/m2 or about 6 times more intense. And that would be the problem. If I've made a math mistake, my appologies in advance. Tony -
Chris G at 05:53 AM on 20 February 2010Visual depictions of CO2 levels and CO2 emissions
theendisfar at 01:38 AM on 19 February, 2010 RSVP, "The GHE is a misnomer and has been grossly overestimated as to its ability to 'trap' heat, especially when taking into account the massive cooling effects of Convection and Evaporation. " Not sure what you mean by the cooling effect of evaporation. The gas media becomes a little warmer and the liquid media becomes a little cooler. Conservation of energy dictates that the net effect is zero. Of course, if the gas media becomes warmer, then convection becomes stronger, but that doesn't mean that evaporation+convection somehow anticipate a change in energy flux and prevent it from having an effect. As far as the size of the effect goes, the best estimates so far of a doubling of CO2 concentration are a base effect of, in round numbers, 1 K, and a fast-feedback of around 3 K. That's roughly a change of 0.5% and 1% in temperature, respectively. Granted, that's not much of a change on an absolute, physics scale, but it's quite a change within the band of what we think of as a temperate climate. -
Chris G at 05:24 AM on 20 February 2010Visual depictions of CO2 levels and CO2 emissions
@ RSVP at 03:45 AM on 20 February, 2010 Not 100% sure if you are making this mistake, but be sure you are not thinking of the atmosphere as being of a uniform density. It gets less dense with altitude quickly. Near the surface, the GHGs may be relatively opaque and energy would rattle around for some time before gradually making progress outward; as energy moves outward, the lower density of the GHGs makes it more likely for it to travel a further distance before being captured by a GHG molecule. At higher altitudes, any bits emitted outward are more likely to continue outward. Increasing CO2 concentration effectively raises the altitude at which it becomes more likely for the energy to escape than not. That aside, convection plays a large role in the process of transporting energy up from the surface as well; so, no matter how thick the atmosphere is with GHGs, the energy will not 'just stay there'. -
Doug Bostrom at 05:01 AM on 20 February 2010Is CO2 a pollutant?
suibhne at 04:19 AM on 20 February, 2010 Imagine a lightbulb illuminated in an evacuated void, radiating. Now wish a silvered sphere into being, with the lightbulb concentric to the sphere. What happens to the temperature of the lightbulb? Is the sphere heating the lightbulb? Perhaps more to the ultimate point of the discussion here, would it matter to you whether the sphere was heating the lightbulb, if you were a strange being living on the surface of the lightbulb and you liked the temperature the way it was without the sphere? -
johnd at 04:43 AM on 20 February 2010Visual depictions of CO2 levels and CO2 emissions
I would be interested in an animation of how CO2 moves to the surface in order to exchange with the vegetation and waters as this is where the greatest interaction occurs and ultimately all CO2 will be cycled through there, at least statistically. -
Riccardo at 04:29 AM on 20 February 2010It's the sun
Cliff Oates, indeed no one ignores it and we are grateful to the sun for pulling us out of the LIA. And we are also grateful for not increasing activity from the '50s at least up to now, it could have been worse. -
suibhne at 04:19 AM on 20 February 2010Is CO2 a pollutant?
CBDunkerson Some of the back radiation from the Earth must reach the SUN eventually. Would it make any sense at all to say the Earth heats the Sun? -
Cliff Oates at 04:11 AM on 20 February 2010It's the sun
Sunspot numbers averaged 45.8 from 1749 to 1920. they averaged 72.7 from 1920 to October 2009. This is an increase of 59 percent. If the Maunder Minimum from 1640 to 1710 was somewhat responsible for the Little Ice Age, this increase cannot be ignored. -
RSVP at 03:45 AM on 20 February 2010Visual depictions of CO2 levels and CO2 emissions
Theendisfar, "I suggest you research and calculate how much our "very transparent to IR" atmosphere can attenuate an IR beam in just a few meters - particularly at the 15um range." Let's suppose (in the worst case) every ounce of IR energy were absorbed within a few meters. This would simply raise the radiative heat source a few meters off the ground... or is the energy just going to stay there forever hovering over the ground? -
Dikran Marsupial at 03:37 AM on 20 February 2010What would happen if the sun fell to Maunder Minimum levels?
HumanityRules @ 15 IIRC (it is always possible I don't ;o), the models tell you of the effects of an increase in radiative forcing, whether the increase in radiative forcing is due to changes in solar activity or due to a rise in atmospheric CO2 concentrations doesn't make any difference. The change in radiative forcing due to increasing carbon and solar activity are relatively well understood, it is how the climate responds to the change in forcing that is uncertain. In other words the models don't assume a weak effect from solar radiative forcing, it is weak because the solar forcing is weak. However, I am no climate modeler, just MHO, ask an expert like Gavin Schmidt @ RealClimate -
Alexandre at 03:37 AM on 20 February 2010What would happen if the sun fell to Maunder Minimum levels?
Thanks Tony and Jesús. One of my mistakes was to neglect the cicles - hence my 2 W/m2 amplitude. -
SNRatio at 03:01 AM on 20 February 2010What would happen if the sun fell to Maunder Minimum levels?
@15, HumanityRules It is not about having "developed theories" here. It's about looking at the actual data. And the _very_ interesting thing is that the temperature variations in the not so distant past to a large degree seem to come from such _relatively small_ fluctuations in solar irradiation. The models do _not_ assume a very weak effect from solar changes, but they try to take all forcings into account, adequately quantified. And even if you can't simply equate solar and GHG forcings, their effects seem to be comparable. -
HumanityRules at 02:55 AM on 20 February 2010What would happen if the sun fell to Maunder Minimum levels?
The question I have is that if a grand minimum has an affect of between 0.09-0.3oC how was it possible to recognise the previous MM cold period. Would these be sufficient for people to recognise 1700 as a particularly cold period in history. Would this be sufficient to see the Thames freeze up and the other effects seen through Europe? As well as throwing away any significant cooling effect in the 21st C you also have to throw away the cooling effect around the MM. -
HumanityRules at 02:39 AM on 20 February 2010What would happen if the sun fell to Maunder Minimum levels?
What's the point of this? If you have models that assume a very weak effect from changes in solar radiative forcing then you are going to get a result that suggests a MM will have a minor effect on the temp over the next century. Having developed theories that have minimised the LIA and MWP whats the point of doing this experiment? -
Riccardo at 02:35 AM on 20 February 2010What would happen if the sun fell to Maunder Minimum levels?
Spencer Weart, it's always invaluable to have it put in the correct perspective. Thank you a lot. -
ProfMandia at 02:20 AM on 20 February 2010What would happen if the sun fell to Maunder Minimum levels?
John, Thanks for this gem. I will adding it to my site today. -
ProfMandia at 02:00 AM on 20 February 2010The Dunning-Kruger effect and the climate debate
How timely! I just linked to this thread because it does a great job (as usual) of illustrating the point I am making in my latest blog post titled: A Conversation at a Poker Game -
CBDunkerson at 01:52 AM on 20 February 2010Is CO2 a pollutant?
Suibhne, so... what? The entire G&T argument is some kind of semantic game? 'Greenhouse gas absorption and re-emission doesn't transfer HEAT to the surface of the Earth... just energy... which generates heat.' -
suibhne at 01:37 AM on 20 February 2010Is CO2 a pollutant?
carrot eater Philippe Chantreau If we space two lamps one irradiating from the top(492w) and one from the bottom (390w)of a double sided solar device then this light energy can be utilised in some way. Now instead of lamps look at your diagram to see the absurd situation. The energy all must ultimately come from the Sun which is only supplying 342w/m2 CBDunkerson The atmosphere does not transfer heat to the surface of the Earth. Look up the definition of heat in a thermodynamics book. Heat is sometimes mixed up with energy when people talk loosely and for a lot of situations the confusion wont matter much. A bit like some people use interchangeably the mass and weight of an object. However there are situations where such woolly thinking will lead you astray. -
Spencer Weart at 00:59 AM on 20 February 2010What would happen if the sun fell to Maunder Minimum levels?
Like so much in climate science, this just confirms things well known. A U.S. National Academy of Sciences panel estimated in 1994 that if solar radiation were to weaken as much as it had during the Maunder Minimum, the entire effect would be offset by another two decades of accumulation of greenhouse gases. That was at 1994 emission rates, of course; we now find, surprise, that at late 21st century emission rates the delay would be less than one decade. ref.: combining pp. 3 and 4 of National Research Council, Board on Global Change (1994). Solar Influences on Global Change. Washington, DC: National Academy Press (online at http://books.nap.edu/openbook.php?isbn=0309051487) -
Alexandre at 00:42 AM on 20 February 2010Visual depictions of CO2 levels and CO2 emissions
Theendisfar, I suggest you research and calculate how much our "very transparent to IR" atmosphere can attenuate an IR beam in just a few meters - particularly at the 15um range. I can help providing the coefficients and formulas if you want, but I think it would be much more convincing if you figured it out by yourself. -
Jesús Rosino at 00:39 AM on 20 February 2010What would happen if the sun fell to Maunder Minimum levels?
#7 Alexandre, Wang 2005: "The increase in cycle-averaged TSI since the Maunder minimum is estimated to be ~1 W m-2." *Then we do what Tony Noerpel says: divide by 4 for the shape of a sphere and multiply by 0.7 to substract the 30 % albedo: 0.17 W/m2. Krivova 2007: "The model predicts an increase in the solar total irradiance since the Maunder minimum of 1.3^+0.2_-0.4 Wm-2" 1.3 / 4 * 0.7 = 0.23 Balmaceda (Max Plank Institute): "This first physics-based reconstruction of TSI back to the Maunder Minimum suggests an increase of about 0.80 W/m2 since 1700" 0.8/4*0.7 = 0.14 W/m2 (documents hyperlinked in the author's name) -
70rn at 00:04 AM on 20 February 2010What would happen if the sun fell to Maunder Minimum levels?
@5 Yes but periods like the Dryas appear to have other influences, such as large influxes of melt water, the MWP is linked to North Atlantic oceanic circulation..... point is that these causes do not appear to be drivers of the current warming trend, nor do TSI levels, but anthropogenic co2 does appear to be correlated with it. Variation has occurred in the past from a number of different causes but unless one can be directly attributed to current observations raising seems somewhat immaterial. -
carrot eater at 00:03 AM on 20 February 2010Is CO2 a pollutant?
I still cannot grasp what point suibhne is trying to make with the double-solar panel. But he'd have to recalculate all the energy flows around the system, if he added something to the system. -
Tony Noerpel at 23:17 PM on 19 February 2010What would happen if the sun fell to Maunder Minimum levels?
Hi Alexandre The 2 W/m2 is the solar constant measured at the top of the atmosphere. This flux is through a circle of radius 6,371 km and an area of pi x r2 but the forcing is measured at the Earth's surface which has a surface area of 4 x pi x r2 so 2/4 = 0.5 W/m2. Then we further must take into account the solar energy which is reflected back into space without warming the planet or about 30%. That leaves 0.35 W/m2. How we get down to 0.17 to 0.23, I don't know but at least you see we are in the ballpark. Tony -
Philippe Chantreau at 22:59 PM on 19 February 2010Is CO2 a pollutant?
The bottom panel can not get anything if the top panel intercepts the energy flux going downward. The surface is heated by energy coming from above, once heated it radiates up in the IR spectrum (btw, that gives you the task of devising a solar panel using IR). If it's not heated from above it's not going to radiate anything. Why would you expect otherwise? I did not look at the diagram but I doubt that it could be interpreted such as making a shaded surface radiate heat up as a sunny one would. As for G&T, the quote above contains the essence of the problem. The atmosphere and its entire environement are a system. Not just the atmosphere and the surface, or the atmosphere and stratosphere. G&T consider only a subsystem then say it can't exist. -
carrot eater at 22:57 PM on 19 February 2010Is CO2 a pollutant?
It's odd that their figure and caption are mismatched stratosphere/atmosphere (?) and atmosphere/surface. But either way, yes, it is an argument of principle, not degree. suibhne: Why don't you like the magnitudes of the flows, anyway? You can scale them down if you really like (while keeping balances everywhere), and you'll still get an Earth surface which is warmer than it would be otherwise without an atmosphere, and so G&T would still imagine a Second Law violation. -
Alexandre at 22:47 PM on 19 February 2010What would happen if the sun fell to Maunder Minimum levels?
Jesus, you cite a difference in solar forcing ranging from 0.17 to 0.23 W/m2. The TSI itself is estimated to have been some full 2 W/m2 lower in the Maunder Minimum(according to the Max Planck Institute). I'm sure I'm comparing apples to oranges here. Can you help me understand it? -
Arkadiusz Semczyszak at 22:33 PM on 19 February 2010What would happen if the sun fell to Maunder Minimum levels?
Moreover, in small changes in TSI can not be explained by such rapid temperature changes in the past - such as Dryas, LIA, MWA, etc. ... -
Arkadiusz Semczyszak at 22:28 PM on 19 February 2010What would happen if the sun fell to Maunder Minimum levels?
sory: not Mounder - of course Maunder -
Arkadiusz Semczyszak at 22:26 PM on 19 February 2010What would happen if the sun fell to Maunder Minimum levels?
Beginning - the end of the max. LIA - not equal: the beginning - the end of Mounder minimum. It was NEVER ("NONLINEAR DYNAMICS") a simple connection: TSI - global temperature. 1.66 W / m 2 - right, but the valuation of "CO2 feedbacks" in the IPCC AR4 - no (eg, Lindzen - I recall). -
CBDunkerson at 21:56 PM on 19 February 2010Is CO2 a pollutant?
Suibhne, see section 3.9.3. Specifically, the comment on figure 32; "A machine which transfers heat from a low temperature reservoir (e.g. stratosphere) to a high temperature reservoir (e.g. atmosphere) without external work applied, cannot exist - even if it is radiatively coupled to an environment, to which it is radiatively balanced. A modern climate model is supposed to be such a variant of a perpetuum mobile of the second kind." Also, later in the same section; "Since this system is assumed to be in radiative balance with its environment, and any other forms of energy and mass exchange with its environment are strictly prohibited, it de fines a system in the sense of thermodynamics for which the second law holds strictly." Ergo, the argument is NOT, as you say, that the amount of energy is trivial (which is also untrue), but that it is absolutely impossible for ANY energy to flow from cold to hot. Which, amongst other things, would make SUNLIGHT impossible. -
Jesús Rosino at 21:47 PM on 19 February 2010What would happen if the sun fell to Maunder Minimum levels?
I was missing a paper like this, thanks for the summary! Fortunately it was already highlighted in this site that "The difference in solar radiative forcing between Maunder Minimum levels and current solar activity is estimated between 0.17 W/m2 (Wang 2005) to 0.23 W/m2 (Krivova 2007)", whereas "the radiative forcing of CO2 since pre-industrial times is 1.66 W/m2 (IPCC AR4), far outstripping solar influence." -
Hoskibui at 21:41 PM on 19 February 2010Skeptical Science now an iPhone app
Where can I find this new App? Didn't find it using this link: http://itunes.com/apps/skepticalscienceResponse: If going to http://itunes.com/apps/skepticalscience did nothing, the most likely explanation is you don't have iTunes installed. If you do have iTunes installed, go to the app store and search for skeptical science. -
suibhne at 21:09 PM on 19 February 2010Is CO2 a pollutant?
Philippe Chantreau The top panel gets 168 +324 The bottom panel gets 390 All units w/m2 That is if you really believe the diagram in the first place. ....... it is exactly G&T's position that not only no radiation flows from the atmosphere to the surface but that this is altogether impossible. Could you give a page number for your quote? -
70rn at 20:47 PM on 19 February 2010What would happen if the sun fell to Maunder Minimum levels?
"The IPCC claims the radiative forcing due to changes in the solar output since 1750 is +0.12 Wm-2, an order of magnitude smaller than its estimated net anthropogenic forcing of +1.66 Wm-2. A large body of research suggests that the IPCC has got it backwards, that it is the sun's influence that is responsible for the lion's share of climate change during the past century and beyond." Given that the sun has been steady or in decline over the period of 1950 - 2010 - this surely indicates that temperature increases since then cannot be attributed to it. Given the substantial change in temperature currently do not correspond to changes in solar output I fail to see how such a conclusion can be drawn. -
Arkadiusz Semczyszak at 20:33 PM on 19 February 2010What would happen if the sun fell to Maunder Minimum levels?
1. Analysis of solar activity in the Holocene (e.g. Solanki 2004, Usosskin 2007) shows that there is possible another scenario. Just as 5000 BCE to 4900 BCE (Older Peron) may wait for us being 2-3 thousand. years - warm period of with several small minima. 2. Changes in solar activity is not only the TSI, but gravity changes (LNO-LNC - effects on THC - it is really only a "ridiculous theories"?), and a system of climate feedbacks. Rahmstorf, Ganopolski, 2005: "We attribute the robust 1,470-year response time to the superposition of the two shorter cycles [87; 210 years], together with strongly NONLINEAR DYNAMICS and the long characteristic timescale of the thermohaline circulation." http://www.nipccreport.org/chapter5.html - "Solar Variability and Climate Cycles." - "The IPCC claims the radiative forcing due to changes in the solar output since 1750 is +0.12 Wm-2, an order of magnitude smaller than its estimated net anthropogenic forcing of +1.66 Wm-2. A large body of research suggests that the IPCC has got it backwards, that it is the sun's influence that is responsible for the lion's share of climate change during the past century and beyond." - "The role of solar activity in causing climate change is so complex that most theories of solar forcing must be considered to be as yet unproven." [...] We say: that without a proper assessment of the significance Millennium cycles, each evaluation of the impact of natural factors is incorrect. Claiming: that the Millennium cycles: How warms up to N - cooled on the S, is vague - "de facto" - false. 3. If current warming is (mostly) natural and we will have a transgression of the sea as the Older Peron (Australia - 2.5 to 4 meters - 8 to 13 feet) - whether it is worth spending money on CCS? -
Philippe Chantreau at 20:11 PM on 19 February 2010Is CO2 a pollutant?
As I recall, it is exactly G&T's position that not only no radiation flows from the atmosphere to the surface but that this is altogether impossible. I believe they state it quite clearly. -
Philippe Chantreau at 20:05 PM on 19 February 2010Is CO2 a pollutant?
Suibhne, if you put a solar panel between the surface and the sun, that part of the surface below the panel does not receive the solar 342 joules/s any more. I'm not sure I see how that idea of a 2 sided panel applies to anything. -
suibhne at 20:00 PM on 19 February 2010Is CO2 a pollutant?
carrot eater ...........I've seen all that. The basic point remains. In the end, G&T have a problem with radiative exchange between bodies of different temperature...... I cant believe that you think that the G&T position is that no re radiation whatsoever from the atmosphere arrives back on Earth. In Physics it is quite common to disregard trivial quantities. An electric kettle contains 1kg of water say. Before (and after) the kettle is switched on the water and the kettles element radiate to one another. When the kettle is switched on heat energy from the element is transferred to the water. The electrical energy input is precisely known as is the internal energy gained by the water by independently derived equations. If the kettle is well insulated the input energy and the internal energy gained by the water are almost exactly equal. I have never heard of anyone including the back radiation from the water to the element in such a calculation
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