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## Climate time lag

#### Posted on 8 July 2009 by John Cook

The previous post on CO2/Temperature correlation sparked some interesting comments on climate time lag. Unfortunately, the discussion went pear shaped with some ideological anti-intellectualism and things got a little bitchy after that. Nevertheless, climate time lag is an important subject that deserves more attention. Several metaphors were invoked in an effort to explain the phenomenon including stove hot plates and warming baths. However, I find the best way to understand climate time lag is a direct look at the science.

Our climate receives its energy from the sun. The amount of energy the planet absorbs from the sun is calculated from this equation:

### Incoming Energy Flux= πR2S(1-A)

R is the radius of the earth, S (the solar constant) is the energy flux from the sun and A is the Earth's albedo - around 30% of sunlight is reflected back to space. The earth also radiates energy into space. The amount of energy emitted is a function of its temperature:

### Outgoing Energy Flux = 4πR2εσT4

σ is Boltzmann's constant, T is the absolute temperature in degrees Kelvin and ε is the average emissivity of the earth. Emissivity is a measure of how efficiently the earth radiates energy, between 0 and 1. A blackbody has an emissivity of 1. Greenhouse gases lower the earth's emissivity. When the climate is in equilibrium, energy in equals the energy out.

### S(1-A) = 4εσT4

What happens if the sun warms (solar constant S increases) then maintains a sustained peak? This is what occured in the early 20th century when solar levels rose then plateaued at a hotter state in the 1950's. The radiative forcing from the warming sun is not particularly large - between 0.17 W/m2 (Wang 2005) to 0.23 W/m2 (Krivova 2007) since the Maunder Minimum. Nevertheless, let's assume for the sake of argument that there is some amplifying effect (perhaps the cosmic ray effect on clouds) so that the warming sun has a substantial effect on global temperature.

When the sun warms, initially more solar energy is coming in than is radiating back out. The earth accumulates heat and it's temperature rises. As the earth warms, the amount of energy radiating back out to space increases. Eventually, the energy out matches the incoming solar energy and the planet is in equilibrium again. The time lag is how long it takes climate to return to equilibrium.

How long does the climate take to return to equilibrium? The lag is a function of climate sensitivity. The more sensitive climate is, the longer the lag. Hansen 2005 estimates the climate lag time is between 25 to 50 years.

How would climate have responded to the solar levels maxing out in the 50's? For the next few decades after the 50's, the radiative imbalance would've gradually decreased until the climate reached radiative equilibrium around the late 80's (give or take a decade). So how has our planet's radiative imbalance evolved over the latter 20th century?

Figure 1: net radiation flux at the top of the atmosphere (Hansen 2005).

Hansen 2005 finds that the net radiative imbalance has steadily increased over the 20th century. There is no indication that the climate is heading towards equilibrium - quite the contrary. This is confirmed by satellite measurements of energy flux at the top of the atmosphere:

Figure 2: Global ocean heat storage (blue) against global net flux anomalies (Wong 2005).

The climate is not heading towards equilibrium. Rather, the radiative imbalance is increasing with the climate steadily receiving more energy than it is radiating back out into space. And this is where the true significance of climate time lag lies. Even if the radiative imbalance were to level off at its current rate of around 0.85W/m2, it would take several decades for the climate to return to radiative equilibrium. Based on this climate lag, Hansen 2005 calculates there is still 0.6°C warming still "in the pipeline".

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Comments 301 to 347 out of 347:

1. Falkenherz, you make a typical error in assuming that forcing (the Watt per square meter value, aka the extra energy per time and area input to the system) has something to do with climate sensitivity (roughly: the expected warming, aka temperature, for a doubling of CO2 in the atmosphere). "Serious" skeptics like Lindzen, whom you seemingly refer to, claim that climate sensitivity is low and that we should already have observed more warming. However, as you can explore by follwing the link to "Lindzen Illusions" up left, he (and others) has failed to provide conclusive evidence for his hypothesis. Instead, there are multiple lines of evidence that climate sensitivity is roughly 3+-1 K, and you can explore that here . If other "serious skeptics" claim that solar forcing has a huge time lag while CO2 forcing has not, they should present that evidence. Remember: Extraordinary claims require extraordinary evidence. To demand more knowledge is just another moving the goalpost move to prevent addressing the issue in the first place.
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2. Falkenherz, Just to make sure I understand you correctly: Suppose we ignore GHG for now. Let's say 20 years ago the earth is in equilibrium with solar radiation. TSI starts increasing, and the earth warms. Now if TSI drops back to to its original value today, are you suggesting that it will continue to warm for several decades due to the lag?
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3. Falkenhurst, Who are these mythical "serious skeptics" you refer to? Please name names. If they have posted on the web we will be familiar with their arguments and you will no longer have to interpret for them. Without specific names it appears that you are raising red herrings with your speculations about "serious skeptics". You appear to be hiding your own notions behind a smoke of "someone else serious said this".
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4. Argh, don't spell my name like that, it hurts! By all means, if you can read German, look up some things below. This is about overestimating climate sensitivity: http://www.eike-klima-energie.eu/klima-anzeige/der-anthropogene-treibhauseffekt-eine-spektroskopische-geringfuegigkeit/ This is about the sun: http://www.eike-klima-energie.eu/klima-anzeige/fanatiker-der-globalen-erwaermung-nehmen-zur-kenntnis-sonnenflecken-beeinflussen-in-der-tat-das-klima/ (just a repition of the article from the Washinton Times) and here, comments #64 and #85: http://www.eike-klima-energie.eu/climategate-anzeige/der-anthropogene-treibhauseffekt-eine-spektroskopische-geringfuegigkeit/#comment_306 Disclaimer; I am aware that this website is posting 99,9%horrible sonsense. So don't read it. (It took me some time to nail them down to a few more serious points from some few 1 or 2 commenters out of thousands there. I am doing this exercise because I have to deal with similar people like this in my job from time to time. So I have to fetch them where they start from.) Just to summarize their "more serious" points to a coherent conclusion (which goes a bit beyond the "lag-topic" of this article): 1. Water vapor forcing is the main reason why a high cliamte sensitivity is assumed. This is horribly overestimated, as there is also a substantial negative forcing which comes from the increased vapourising process at higher temperature. 2. TSI forcing is vastly underestimated, because the short term observations don't tell anything about long-term TSI nor its long term effects on the climate system.
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5. Falkenherz you write "2. TSI forcing is vastly underestimated, because the short term observations don't tell anything about long-term TSI nor its long term effects on the climate system. Is there any physical reason to expect the long term effect of TSI to be anything more than the integral of short term TSI? Can you tell me the physical mechansism that you think is involved?
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6. Falkenherz , I read through your first link via google translate, and it contains numerous errors that it can't really be taken seriously. Pt 1: CO2 effect is saturated. Nonsense. See article here on SkS and a detailed series on CO2 at Science of Doom , particularly on saturation . Pt 2: I don't understand what they are getting at (perhaps due to google translate). (BTW there is no such thing as an "IPCC computer model". IPCC summarizes the current scientific understanding. They don't write their own codes) Pt 3: A laboratory measurement of CO2 absorption is fine and dandy, but to really understand its effect you have to consider its cumulative effect in an atmosphere column, not just the absorption over a 10cm. Pt 4+5: They basically argue that a CO2 forcing of 3.7W/m^2 is small compared to the existing greenhouse effect, which is of course nonsense because the effect is entirely determined by climate sensitivity. Pt 6: Here's where I stopped reading, and this is why: The author proceeds to argue that water vapour feed back does not exist based on this graph: This is the water vapour content over atlantic ocean from 1950-1972. Even if you consider this data alone it doesn't mean anything, because between 1950-1970 the global temperature was flat, and SST over tropical atlantic decreased , so even if the data shows a statically significant trend it actually shows support for water vapour being determined by temperature and strengthening the case for water vapour feedback. The water vapour feedback argument is based on temperature not CO2, so plotting CO2 against water vapour to "disprove" water vapour feedback is misleading at best. In addition it is now 2012, so there is no excuse for not including modern data and global coverage.
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7. It must be the google translator. Otherwise the first link posted by Falkenherz would only show the ignorance of the author on atmospheric radiation physics, at least up to where I could stomach to read. A very basic course on atmospheric physics is kindly suggested. When a self-styled skeptic argue on such a foundamental physics knowledge you know for sure that he's not a serious skeptic.
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8. Falkenherz I am German too, and it herz ;-) to see that page. Next time, just name "Eike" and we know what is going on. My suggestion is to not try to counter these people on that page with scientific arguments unless you are a scientist and you know what you are talking about. They belong to a group that suffers what some have called the "smart idiot effect". Because they are smart, they will always come up with a clever fallacy that convinces them that they are right. Most of what they write sounds very scientific, and is at first glance hard to debunk. It takes time and energy to do so carefully, which we do not have. The goal of these pages is usually not to show good science. That happens in the scientific literature, where he could not get this published. Instead, the goal is to sow doubt and convince the unskeptical and the gullible to oppose action on climate change. The fact that some CO2 absorptions are in saturation has been made for a long time, including by one organic chemistry professor at my own university in the mid nineties. It comes natural to chemists with spectroscopy experience to make this assumption, and confirmation bias does the rest. We can be glad that this saturation effect is actually in place, because the greenhouse effect would otherwise be much stronger, because Lambert-Beer's Law is an exponential function! (GHGs that absorb in the atmospheric window, like CFCs, are having a much stronger per molecule effect than CO2!) Climate scientists have long been aware of this, and you can read in textbooks about how this is solved. The CO2 greenhouse absorption is logarithmic, i.e. the more you pump into the atmosphere, the less effect you get. A few years ago, there was an oil industry engineer at our university who gave a talk outlining all the details, including the conclusion that greenhouse warming from a doubling of CO2 would be 1.2 K on average. He can hardly be called a biased scientist (he just failed to mention that positive feedbacks raise this result to 2-3 K actual T rise). I will try to get my hands on the talk, and can ping you then here.
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9. Forget the oil industry guy ... go here: http://atmo.tamu.edu/profile/GNorth and click on the two lowest links on the right-hand side.
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10. IanC, Riccardo and I said, don't read it... ;) Problem about EIKE is, that the call themselves an "european institute", and this classification does not seem to be legally protected. That's why I think posting there, pointing out logical fallacies in those articles which actually try to show some scientific arguments, is important. Most of that work, they already do by themselves, as there are at least four lines of sceptics who collode with each other. :D It is also a challenge for me as a non-scientist, to unveil pseudoscientific blabla with simple logic. And when I fail, I come here. :) gws, thanks for the link to the presentation, very clear, very helpful! And some subtle support at EIKE would not harm. You should be able to recognize my other nick there (hopefully).
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12. Falkenherz, I wasn't just mirroring the question back to you, it is the key question. If some one suggests some climate phenoemenon, such as a lag, ask them for a physically plausible mechanism that can explain the strength of effect as well as the correlation. If they refuse to do so, it is an indication that they are trolling. Be a skeptic, if there isn't a plausible physical explanation, don't pay much attention to the hypothesis.
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13. Falkenherz Well, that comment lacks all logic, as I expected ... "Dr.Paul" uses no physical argument whatsoever but only logical fallacies, particularly the "argument from authority" ("I said it is so, why don't you want to learn!"). Avoid addressing his ad hominems, just ask questions about science. Some facts to consider / questions to ask: - If warming drove CO2 out of the ocean, why does ocean pH keep dropping? Ask him if he understands and could explain the ocean water CO2 equilibrium (read the "OA not OK" paper on SkS). - ask him to explain why water vapour cools (the atmosphere) seeing that latent heat of evaporation is taking from the surface during evapotranspiratin, and redeposited into the atmosphere during condensation (this is found in most geography textbooks and ALL meteorology textbooks; are meteorologists all dumb?) - ask him if he recognizes the temperature-CO2 correlation during the glaciations and during recent times, if he understands that CO2 is not the only driver of climate, and if he understands the terms forcing and feedback (sorry, do not know the German terms, but you can probably check on Rahmsdorf's blog) - ask if he understands the difference between correlation and causation You see, these are all very trivial things. I am sorry but I will not go there myself, as I do not want to waste my time with somebody who is so obviously delusional. EIKE is far from what you called "serious" before, and I hope you recognize that too. The name is a typical PR strategy used to impress ... good sounding, but empty. -
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14. gws, the comment number only appeared because it was the current one when i copied the website; acutally, that on is one of the most unfounded commenters from over there. But look a bit for Dietze, Ebel, NicoBaecker, Innerhofer, Kramm, Hader, Mayer... they seem to put a bit more effort into their comments. In the beginning I wasn't even sure if they are sceptics or realists, but they all seem to be sceptics with some very specific arguments (and some very specific fallacies)...
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15. Falkenherz it would be helpfull, more constructive and less time consuming if you stop pointing us to (several) unspecified comments and claims in german. Ask a question (in the appropriate thread) about something you read and you may open a usefull discussion.
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17. Falkenherz - Regarding time lags, please keep in mind that while thermal inertial means the climate takes time to respond to an energy imbalance (warming until that imbalance is cancelled out), there is no such time lag in the imbalance, the forcing itself. Volcanic activity drops insolation via aerosols, and that imbalance change takes only a few months, for example. Solar changes are a changes in the energy imbalance, and therefore occur quickly - changing the rate of climate change. There is no proposed mechanism for solar imbalances to be "banked away" long enough for them to still apply decades later. The "climate lag" discussed in this thread is a response lag, not a forcing lag. I suspect that is where the confusion has arisen.
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18. Yes, it is important to keep the forcing and the response distinct. The forcing takes effect immediately. The response starts immediately, too. The time lag is related to how long it takes for the response to restore equilibrium - i.e., how long it takes for the response to counteract the forcing. Take the volcanic eruption example: immediate changes to radiation, which upset the local energy balance of the earth-atmosphere system. Over time, as the aerosols spread and the radiative imbalance alters temperature, there is a relatively rapid drop in temperature. Over time, as the system responds (aerosols are removed), the system slowly returns to the pre-eruption radiative conditions and temperatures return to normal. For a more permanent disruption (e,g, IR changes due to increasing CO2) the radiative change is immediate, so temperature begins to change almost immediately, but the restoration to radiative equilibrium takes time, so there is a lag until temperatures stabilize again. (Temperatures go up, to increase IR emission.) In this case "time lag" is because the temperature rises slowly, due to the amount of land and ocean that needs to be heated. If it were just the atmosphere, a few months would do. The ocean mixed layer takes years to decades. The deep ocean takes centuries. "Time lag" does not mean "nothing happens for a while", it means "things keep changing for a while". Most of the "skeptic" arguments that use "time lag" seem to rely on a physically-impossible variation of "nothing happens for a while". Trying to claim that current warming is the result of some (any) arbitrary past solar change is just wishful thinking. You don't get to say "I'll wish away this warming by pretending that it is caused by any past solar increase I can find in the record". Such "time lags" usually disappear from the "explanation" as soon as the "skeptic" needs to explain a temperature change that actually matches a solar change at the same point in time. If you see someone talking about time lags that mysteriously come and go (or change in duration) depending on whether they are "needed"or not, then chances are that the "time lag" doesn't have any physics behind it - just rhetoric.
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20. An analogy for forcings versus responses: Think of a system with an elephant in a cart with a long springy lever attached. Multiple hands are on the lever, pushing and pulling the end to various locations (climate forcings), while the cart with the elephant slowly moves in response (climate lag). Keep in mind that the elephant may shift back and forth on its own (ENSO, for example). Changes in TSI change how many hands are on the lever, where the end of it is - but not, at that moment, the position of the elephant. That position changes only with the time integral of the forcing. And as Sphaerica notes, the climate elephant is in motion, and even if we stopped moving the lever now it has quite a way to travel before the bend in the lever (the imbalance) gets straightened out.
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21. I am not sure I understand your point or if you misunderstood my point; I understand your point as follows: Assume a solar flare that adds +8 W/m2 and it takes x years to get to the corresponding end-temperature of, say +4 Degrees. Assume now temperature is halfway through the process at x/2 with currently +2 Degrees, and the solar flare is now switched off; accordingly, temperature rise should stop at +2 and will slowly drop back to 0, the value from before. So far, so good. (But the chaotic climate system might as well let us see that "immediate no-more-warming response" with an additional delay, right?) Now, my point is: Assume TSI increased over the last 300 years in slow and little steps, then it halts at +2 W/m2 in 1960, compared to 300 years ago. Shouldn't temperature still rise until the corresponding balance of temperature is achieved (again, modified by climate chaotics)? And this lag I understood from the article can take between 25-50 years. That should be the TSI lag I meant. Now, assume also that CO2 increases since 1960 and adds +4 W/m2 in 2020. Assume also, that +1 W/m2 of that is part of the increased CO2 following temperature raise caused by TSI. So, we have a +3 W/m2 "extra" forcing from CO2 in 2020 (which represents the anthropomorphic part). If we have to assume the same lag times as above, it could take another 25-50 years to see the effect of that extra forcing. But right now, we probably only see the effects from the (ending) TSI-lag and maybe a little bit already of the "extra" CO2. I mean, we cannot even know what the last 50 years of CO2 forcing caused was part of the global warming, right? Correspondinly, the point of yours which I was doubting is, that you assume that the *entire* GW since 1960 is caused by CO2, as if a TSI lag was suddenly not there anymore. My point was, the GW since 1960 could still be caused by the earth going into equilibrium with the current level of TSI, and we might see only later the real effects of the extra CO2. (And from here on, I added a speculation on the arctic ice core which I omit now, because we should be first clear about this basic point). Where am I wrong?
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...you assume that the *entire* GW since 1960 is caused by CO2, as if a TSI lag was suddenly not there anymore...
It's not there any more, if the increase in TSI is gone (the forcing is gone).
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23. Falkenherz: First, I'll assume that at least part of what you are saying is a "thought experiment" scenario, rather than a thorough analysis of recent temperature changes and forcing factors. Thus, what I say will be simplistic if applied to the "real world" case. If we imagine a world were TSI increased until 1960, and then remained constant, the question is whether we can attribute a rapid rise in temperature in the (say) 1980-2010 period to that earlier (pre-1960) TSI increase. As you state, will the temperature continue to rise post 1960? The answer is yes, the temperatures will continue to rise post-1960, until a new equilibrium will be reached (25-50 years is not unreasonable), but we have to think about what that pattern of continuing temperature rise will be. - the rate of rise after 1960 should be expected to slow. After all, the 1960 rate of rise is based not only on the 1959-60 increase in TSI, but all the earlier TSI increases that have a lagged response. In addition, the rise in T due to the 1960 rise in TSI will be expected (as a first approximation) to follow an exponential decay sort of pattern: a larger immediate rise, followed by gradually decreasing rate of T rise as the system approaches its new equilibrium. So we've got two factors that say the rate of increase should slow: the ever-decreasing time-lagged "old" increase in TSI, and the nature of an exponential-decay-type response to the "current" or final step to the new TSI. - what will be very unlikely is a response post-1960 that will see little change, or a cooling, followed much later by a rapid rise in temperatures. Sphaerica has already commented on the chaotic nature and spatial variability of the response. To get a situation where the atmosphere fails to show a response to the up-to-1960 TSI increase for 10-30 years, and then suddenly starts to increase, you need to argue a reasonable mechanism. To accomplish this would require that a large amount of heat be stored somewhere else for several decades, and then be allowed to start working into the atmosphere and appearing as increased air temperatures. On the short term (a few years) El Nina/La Nina does just this sort of thing -shifting heat storage between the oceans and the atmosphere - which is a major reason why air temperature rise is not perfectly steady in response to the relatively smooth rise in CO2 forcing. We can see the result in ocean heat storage, however. For longer periods of time, there is no known physical mechanism that can do this. For El Nino/La Nina, the physical mechanism are fairly well-understood. For "skeptics" correlations with arbitrary cycles such as AMDO, no such physical mechanism has been proposed, let alone accepted. And if the mechanism exists for TSI, then it should also exist for things like volcanic activity, where we see pretty rapid response. It's back to the magic "now you see it, now you don't" disappearing/reappearing unnamed "possible mechanism" that purveyors of doubt want to believe will be under their Christmas tree next December.
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24. Maybe it's easier to see these things graphically for the simplified energy balance model with a step-like forcing (thin red dashed line) applied at t=0. The red line is the energy imbalance and the black line is the temperature response. The time constant is 50 years. In this simple model the lag time is just the time taken to get about 63% of the effect. The response stats immediately and proressively slows down due to the decreasing energy imbalance, as expected.
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Moderator Response: This would be a great addition to the original post....
25. Thanks, Riccardo. I had been trying to verbally describe what I would see in a graph, but I'm away from home at the moment so I couldn't easily do a graph myself. It helps a lot, I think.
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26. Thanks again, expecially Bob's comment (and Sphaerica's comment on the 1 W/m2->0,25 W/m2) clarify a lot for me. What I understand now is, my "thought experiment" is correct, but the figures I assumed in my example do not match to what we observe. So let's clarify what we observe now. See the graph "historical TSI re contruction" in the following link; http://lasp.colorado.edu/sorce/data/tsi_data.htm If I eyeball this, there has been an increase of TSI between 1700 to 2000 from roughly 1360,3 to 1361,3. This is the 1 W/m2 you are talking about, which translates into a "spherical" impact of 0,25 W/m2 (I don't know if that last step is challenged by sceptics, since we should talk about the sun energy which is overal captured from space on earth?). This also is Spaerica's point. So, reality tells us that an increase of TSI is 0,25 W/m2, and the lag to global temperature should be about 25-50 years, maybe even 150 years when the increment is small like this. Now, Bob, I understand that temperature rise should level off, if it would be just a lag. But you state "To get a situation where the atmosphere fails to show a response to the up-to-1960 TSI increase for 10-30 years, and then suddenly starts to increase, you need to argue a reasonable mechanism." I don't understand the part about "fails to show a response", but overall I believe this statement refers to the "hockeystick", right? So what you mean to say is, temp rises much higher/faster since roughly 1990 than ever before since 1850, and this cannot match to a TSI "lag pattern" from 1960 onwards? Turning to global temperature, I eyeball from this graph SPM.3 (http://www.ipcc.ch/publications_and_data/ar4/wg1/en/spmsspm-direct-observations.html) an increase since 1960 from roughly 13,9 to 14,5 Degrees. My problem here is, that the global temperature is only shown since 1850, not since 1700. Maybe you could put this into this long-term perspective? How much raise has happened since 1700, and how much since 1960? If the relations do not match, as you imply, then indeed we cannot assume a TSI lag. If it was a TSI lag, then we should see a leveling off, which means the raise of global temperature since 1960 to 2000 must be overall much less than the raise between 1700 and 1960, right? What I am basically trying to do, is finding the long-term perspective, because I suspect that everything happening in under 50 years could also have causes which we could attribute to "climate chaotics" besides the known GHG effects. (This of course not if we don't have an alternative possible explanation, one of which could be the here discussed lag.)
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27. Falkenherz, On 1/4 TSI... Imagine drawing a circle on the wall -- the earth. In the middle of the room is a lightbulb -- the sun. The light that falls in the circle is the light received by the earth from the sun... it's in the shape of a disk. But the earth isn't a circle, it's a sphere. That light isn't falling on a disk but on the surface of that sphere. Since the surface is curved, it has a larger surface area than the disk. This means two things. First, that the same amount of light is falling on a larger area at the edges of there sphere: And second (because the sphere is rotating) that the light is falling on both the front and the back of the sphere. In the end, the computation is very straightforward. The light being delivered covers the area of a circle (πr^2) while the light being received is spread out over the area of a sphere (4πr^2). So the amount of energy received per unit area on the earth is energy-delivered-per-unit-area times area-of-delivery divided by area-of-receipt, or: energy * πr^2 / 4πr^2 = energy / 4 1361 * πr^2 / 4πr^2 = 1361 / 4 = 340.25 W/m^2 Interestingly, the only denier I've seen that has been foolish enough to dispute this is Postma, but even he comes up with the same answer... he just claims the logic of the geometry is wrong.
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28. Another good image:
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29. Falkenherz: Sphaerica has given you a couple of good diagrams. You can also see the effects of the 1:4 ratio in the equations in the text of the OP. Look at the one that has: S(1-A) = 4εσT4 ...and divide both sides by 4. The 4 disappears on the right, and we have S/4 on the left. ...now, you were asking about the "fails to appear" comment of mine, and said "So what you mean to say is, temp rises much higher/faster since roughly 1990 than ever before since 1850, and this cannot match to a TSI "lag pattern" from 1960 onwards? That is basically it, but we don't even need to look back to the 1800s, just look at T through the mid-1900s to now. Look at Riccardo's graph, and let's assume that his 0 time value represents 1960, when TSI stopped rising. What we would expect is to see temperature rising like it does in Riccardo's graph - most rapidly in the first few years, followed by a tapering off and eventual equilibrium. What you would not expect is to see temperatures steady for a couple of decades, then see a sharp rise like Riccardo's graph - but delayed to start around 1980 or so. From Riccardo's graph, we see that the flux imbalance starts at time 0, and gradually drops as T rises (due to extra IR loss to space as T rises). If the atmosphere did not warm for 20 years, the flux imbalance (delta-F) would remain at 1.0 for 20 years, and that energy has to go somewhere. Since it is not appearing in the atmosphere, where would it be hiding? (You won't get an answer from "skeptics".) That's where you would have to provide a plausible physical explanation to explain the "missing" energy and why it doesn't start to affect the atmosphere until many years later. That's the difficulty in the argument that the 1980s-onwards warming is delayed from earlier TSI increases. It ignores physics. As for pre-1850: we don't show measured temperatures for earlier times because the direct measurements don't exist. Think about when the thermometer and the concept of temperature were invented, and then think about how long it might take to get decent global coverage, and you'll see the problem. Before 1850, proxies are required - things that we can measure now, like tree rings, sediments, ice cores, etc. that have a record from the past that responds to temperature (but isn't a direct measurement of temperature). That's how we fill in the gaps from the past, and that the sort of data that goes into Mann's work (and other similar studies) and shows the Hockey Stick.
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30. Bob, I'm not sure I entirely agree with you, because the same applies to CO2 forcing. Why the hiatus in warming from 1945 to 1980? The usual answer (one I accept) is the increase in dimming aerosols due to pollution/smog in that period, and that applies equally to any forcing (TSI or CO2). But I would still question how a 0.25 W/m2 forcing amounts to anything notable, particularly given the quiet sun for the past 15 years or so. That's why the deniers had to introduce the idea of cosmic rays and cloud nucleation, because the TSI alone wasn't anywhere near strong enough.
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31. Sphaerica - It should also be noted that some of the 1940's drop is due to (a) limited ocean coverage during WWII and (b) changing techniques for ocean sampling. HadCRUT4 (with corrections for those issues) shows a hiatus until the mid-1970's, but much less of one than HadCRUT3, for example. I completely agree that a 0.25 W/m^2 forcing difference is minor compared to observed changes - that translates to a 0.075°C direct temperature change, or something like < 0.25°C with fully realized feedbacks. Insolation changes are simply too small to explain the last 50 years of climate change - not to mention being of the wrong sign. Falkenherz - There is no mechanism whatsoever that would allow past TSI changes to "come out of the woodwork" 50 years later. Temperature change due to any initial forcing shift taper off over time as the imbalance is reduced, but the ongoing rate of change in global mean temperature shows that the forcings are continuing to increase. The ongoing rate of change (close to linear over the last 40 years) is chasing an ongoing forcing change. Insolation has in fact been decreasing over that time, and if anything is reducing the rate of warming. Many 'skeptic' arguments to claim "it's the sun", but when you examine such claims you see almost no climate lag before the middle of the 20th century - and the invocation of a 50+ year lag suddenly kicking in once insolation starts to decrease. In other words, such arguments are purest fantasy, unsupportable in the real world.
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32. KR, There's an important point in your comment... that the time-lag results are non-linear. They will taper off as you get closer and closer to equilibrium. The fact that warming is relatively constant is actually a good argument that whatever the forcing is, it must be increasing continually in order for warming to remain linear. And the only forcing that is continually increasing is CO2. This by itself is one more strong argument that CO2 must be the cause, because the time-lag argument, rather than pointing to some past forcing (TSI) as a cause of current temperature increases, actually does the exact opposite, and points against any forcing that is not only currently active but still increasing -- of which CO2 is the only candidate.
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33. Sphaerica - Yes, that's exactly my point. The only other forcings with significant ongoing change are aerosols, which are concomitant with emissions - reducing the CO2 forcing considerably, but summing to approximately linear in increase. [Source] Temperature response to a 'step' forcing would be an exponential decay towards equilibrium - but with an ongoing change in forcings, temperature will follow along (somewhere behind the curve, so to speak). Linear temperature increase (observed) is very strong evidence for ongoing increases in climate forcings - and again, that eliminates insolation as a cause.
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34. Sphaerica @ 330: No, we're not in disagreement. I'm still focusing on the thought experiment where TSI is the only forcing in play, and we're exploring how the system would react when TSI stops increasing. It's the counterargument to the "it's all solar, there is just a time lag" skeptic position. After all, a skeptic isn't going to try to convince me that the lag in the solar response is the result of a strong CO2 effect, will they? :-) You are correct in saying that in the real world (rather than skeptic-world) you do have to consider all the forcings, and the changes in forcings over time are rarely simple or step changes. Aerosols are a significant factor in the 1940-1970 period, and TSI plays a supporting role, too. Throw in a few volcanic eruptions, some El Nino for noise, and nothing looks as simple as Riccardo's graph.
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35. Sphaerica comment 330 "[...] the increase in dimming aerosols due to pollution/smog in that period, and that applies equally to any forcing (TSI or CO2)." The direct aerosol effect depends strongly on wavelength, being much larger at short wavelengths. It is often negleted in the infrared. KR and Spherica again in the simple zero-dimensional energy balance model, a linear temperature increase means a linearly increasing forcing and a constant energy imbalance, whatever the response time might be. Current linearly increasing temperature rules out a lagged response to the TSI forcing of the first half of the XX century. It also tells us that the response time can not be larger than belived (a few decades). A stronger evidence, though, is the increasing ocean heat content. A even stronger one would be a robust estimate of the radiatiative imbalance, which unfortunately we don't have and won't have in any foreseeable future.
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36. Riccardo: yes, size distribution of aerosols is important. Aerosols can have two effects on radiation: absorption, or scattering. Absorption depends roughly on colour: something like dust doesn't absorb as much as something like soot. Scattering is according to Mie theory, and the wavelengths that are scattered most strongly are roughly the same as the size of the particles. Small particles = small wavelength, and the typical particle size in the atmosphere matches visible light. To scatter IR, you'd need larger particles, and they just tend to fall out of the air too fast. The smaller the particle, the longer they tend to stay - especially if they are injected into the stratosphere (e.g., volcanic eruptions) and can avoid getting rained out. Air molecules are much smaller, and follow Rayleigh scattering (see the Mie link above). This is strongly wavelength-dependent, and is the "blue sky" effect. Lots of aerosols of varying sizes tends to cause scattering across many wavelengths, and the "white" washes out the blue. Sun photometers are capable of taking direct sunlight readings and "backing out" the aerosol properties. AERONET is a world-wide monitoring effort.
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37. Just a note on dimming aerosols... even if they operated exclusively on visible light (as a simplification for consideration)... In the TSI scenario, the sun gets brighter but the dimming aerosols counteract that. In the CO2 scenario, the sun gets dimmer on average (due to the aerosols) but CO2 counteracts that (less inbound radiation, but also less outbound due to the GHE). In any event, dimming aerosols are a negative forcing, regardless of what other mechanisms are taking place. Admittedly, this is a simplification. The exact details won't be exactly the same, but... I still don't buy dimming aerosols as an argument against a TSI cause but not equally so against CO2. The linearly increasing temperatures, however, are another story. That kills TSI dead on the spot.
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38. KR and Spherica 331 - 333: Thank you for this exchange of ideas. The almost linear rising trend in temps must be due to an on-going increase in positive forcing and CO2 is the only reasonable culprit. The penny has dropped in my mind. I find small nuggets like this easy to understand, unlike some of the more esoteric discussions where I struggle to keep up.
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41. KR, the difficulty of non-scientist people like me is to understand the arguments I read about, and clarification is the tool. That's why it is great of you guys to offer a comment function and take the time to answer. Truth will answer to any question, and, in fact, it is only fully revealed by questions. I understand that I misunderstood the paragraph I quoted, and the uncertainity expressed cannot exceed the range of TSI given there. In that case, I was mislead by "...incomplete understanding of solar variability mechanisms over long time scales..." The key issue I was trying to clarify for me is in your No (5). And there, we seem not to understand each other's points, or my understanding is simply too limited. Maybe one last try: I am not talking about anything "hidden", concerning a temperature lag from long-term TSI. I simply believe that the matter of observing a decreasing temperature trend could be a matter of which timescale you are looking at. If you compare 1850 to 2010, and take 1960 as a "breakpoint" (and assuming that the data showing a declining TSI is indeed correct), imo no one can rally dispute your conclusion. But, would that counclusion be so clear if you looked at 1700 to 2010, with the same "breakpoint" at 1960? Relations might be different then, and what we perceive as "linear" (btw, I did not introduce this word and I don't see the relevance of it in our discussion, in fact, the "hockeystick" is far from linear) over the last 50 years might as well be read a slow trailing off if we wait a bit into the future. And CO2 on top might only be able to prolong ("hide"?) the process of trailing off, but not increase much beyond what TSI did on the long term. behold, a core argument of some sceptics.
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42. Maybe even simpler: Just displace the blue curve in your graph 40 years to the right in order to represent a 40-year lag of global temperature following TSI (i.e. adapting to the new energy equilibrum, ceteri paribus). Does this illuminate what I mean with my speculative point a bit better? Again, all the arguments seem to be there, but for me it does not come together, yet.
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43. Falkenherz please can you specify a physically plausible mechanism that explains why there should be a 40 year lag of global temperature following TSI. The human eye is very good at detecting patterns in data that are not actually there and are merely artefacts of random/chaotic variability (which is why we have statistics). Requiring a plausible physical mechanism guards against jumping to conclusions based on spurious correlations.
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44. Agree, KR -- Falkenherz, why not a 140-year lag, or a 260-year lag. There are other similar periods of solar increase. Working back to physical principles from a graph of temperature is a bad idea. Surface temp is a very complex process. You've read Foster & Rahmstorf (2011), yes?
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45. Excuse me, DK, I meant "DK" and not "KR."
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46. Falkenherz: That would be moving the blue curve to the left, not right ... where does the presumption of a 40something TSI-climate time lag come from anyway?
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47. Dikran... now I give up, really. :( Can someone please point me towards a graph showing TSI (estimations) since 1700, and another graph showing global temperature (estimations) since 1700? Proxies, reconstructions, I don't care, I just want to know what we have for these two data since 1700 and I want to see how they correlate since the end of the maunder minimum around 1700. Then I can come back to you about "climate" lags.
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48. It appears to me, Falkenherz, you still have not understood the graph posted by Riccardo @324, and its implications verbally explained to you in detail, have you?
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49. Falkenherz, rather than getting sucked into climastrology & curve-fitting, why not examine physical mechanisms potentially involved in lags between causes and effects? Try reading Climate Change: The 40 Year Delay Between Cause and Effect. As always, should you have any questions on that thread, please place them there. The regulars here will see them.
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50. Falkenherz, my research interests lie in statistics, so I know from experience how dangerous it is to look for correllations first and explanations second. At the end of the day, if the correllation is real it is because of a physical reason, so if there is a correlation, but no physical explanation, assume that the correlation is spurious.
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