No, David Stockwell, it’s not the Sun

A few days ago I posted a video that, in less than 4 minutes, rebutted 10 common climate myths. The most amusing was the emphatic No to the claim that it’s because the Sun is getting hotter. To a certain extent, this is all that one need say with respect to this claim. It really can’t just be the Sun. Since then, however, I’ve encountered David Stockwell’s work suggesting that it is the Sun because the rise in surface temperature correlates well with the cumulative Total Solar Irradiance (TSI).

Now, I haven’t actually read David’s papers so can’t really comment about what he’s proposed. You may think that it is somewhat unreasonable to criticise someone’s work without actually reading it. There is, however, a good reason for this. It’s because it really can’t be the Sun. Why is this? A very obvious reason relates to climate sensitivity. The surface temperature has increased by 0.85oC since pre-industrial times. There is still a 0.7 Wm-2 radiative imbalance. If you’re suggesting that this is a response to a change in solar forcing, then you’re suggesting that the change in solar forcing since pre-industrial times has resulted in an increase in equilibrium surface temperature of around 1oC.

The problem, though, is that the solar forcing today is only about 0.1 Wm-2 greater than it was in pre-industrial times. An increase in surface temperature of 1oC produces an increase in surface flux of around 5.4 Wm-2. That would imply an incredibly large amplification factor. There is no evidence to suggest that our climate is that sensitive to changes in solar forcing. Furthermore, if it were that sensitive to changes in solar forcing, it would also be very sensitive to changes in other external forcings, such as anthropogenic forcings. The climate can’t be incredibly sensitive to changes in solar forcing while having no sensitivity at all to changes in other forcings. It really doesn’t make sense.

One of the reasons I wanted to write this post, though, was that there was something I’d been meaning to work out. An alternative to the system being very sensitive to changes in solar forcing would be that, for some unknown reason, the surface temperature in the mid-1800s was 1oC below the actual equilibrium value. Since then, therefore, we’ve simply been recovering towards equilibrium. If the equilibrium temperature is To and the current surface temperature is T, then the amount of energy, dE, that the system will accrue in a time dt is
TempTime
where A is the surface area of the Earth.

However, as the Earth accrues energy the surface temperature, T, will rise and so we need some estimate of how this will change with energy. The land and atmosphere have a mass of around 1019kg and a specific heat capacity of 1000 J kg-1 K-1. This means that it would take 1022J of energy to increase the temperature of the land and atmosphere by 1oC. The oceans, however, have a heat capacity 100 times greater than that of the land and atmosphere. So, increasing the temperature by 1oC would require 1024 J. As a check of this, the ocean heat content has increased by about 2.5 x 1023 J since 1960, while surface temperatures have risen by about 0.6oC. That would imply 5 x 1023 J per degree, but 1024J per degree is close enough for what I’m trying to illustrate here. So, the other condition we need then is
dTdE
So, I wrote a short computer code that would work out how the temperature would change with time if initially T = 288 K, To = 289 K, the energy changes according to the first equation above, and the temperature changes according to the second equation. the result is shown in the figure below. Basically, if we were simply recovering towards equilibrium from being 1oC below equilibrium, it would take only 20 years for temperatures to rise by 0.85oC and within 60 years we’d be virtually at equilibrium. Also, the profile is clearly not linear. The dashed-line simply shows what would happen if we happened to end up 1oC degree above equilibrium. Bear in mind that my estimate for the relationship between energy and temperature is possibly on the high side, so it may actually be faster. Also, this is quite different to what would happen if a pulse of energy (from an ENSO event for example) were to suddenly heat the land and atmosphere. That would decay very quickly – probably only a few months.
TempTime
This post was partly just a bit of fun. I had really just wanted to check how long it would take for the temperature to rise if it just happened to start 1oC below equilibrium. Essentially, far faster than the timescale it has actually taken for surface temperatures to rise by 0.85oC, and with a temporal profile that is very different to what’s been observed. Ultimately, however, it wasn’t really necessary to do that calculation. Basically we know that it can’t be the Sun because that would imply that the climate is much more sensitive to changes in external forcings than other evidence suggests, and this would apply both to changes in solar forcings and to changes in anthropogenic forcings. You can’t suggest that it is both much more sensitive to changes in solar forcings than expected while, at the same time, being much less sensitive to anthropogenic forcings.

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42 Responses to No, David Stockwell, it’s not the Sun

  1. I was leaving this to see if anyone noticed, but I think should probably have used T = 254 K and To = 255 K, rather than T = 288 K and To = 289 K. It doesn’t, however, make much difference. Temperature increases by 0.85oC in about 30 years and is virtually at equilibrium by about 80 years.

  2. Rachel says:

    I have to confess that I tend to skim over the bits with numbers.

  3. As I suspect most do. That’s why I get away with so many mistakes 🙂

  4. OPatrick says:

    Talking of numbers could you clarify this value: “The land and atmosphere have a mass of around 1019kg” – how do you decide which part of ‘the land’ to include in the mass calculation?

  5. OPatrick, it is an approximation, but what I did there was the following. The atmosphere has a mass of 5 x 1018 kg. If you consider the land to be the top 1m, then you get a mass of about 7 x 1017kg. So, I don’t actually know how deep one should consider the land in this context but assuming that radiative heating doesn’t extend below 10m, then 1019 kg seems like a reasonable upper limit for the land and atmosphere. If someone knows better than that, feel free to point it out.

  6. In fact, this figure here suggests the continents and atmosphere absorb about as much heat as each other. Since they have roughly the same specific heat capacity that would seem to indicate a similar mass is involved, so a total of about 1019 kg seems reasonable. Of course, as I suggest in the post, my factor of 100 greater for oceans is almost certainly too high, but that would just mean that it is quite a bit faster than I estimate here.

  7. Also talking of numbers, I finally have to ask the following (perhaps rather dumb) question regarding your flux estimate (as you’ve mentioned it in several posts now). You write: “An increase in surface temperature of 1K produces an increase in surface flux of around 5.4 W/m2.”
    I was always under the impression that you are talking about the Planck response here. However, it is usually specified as -3.2 W/m2/K, which leaves me with a change in surface flux of 3.2 W/m2. Am I missing something fundamental here? Thanks for enlightening me, Wotts 🙂

  8. Ooops, italics not properly closed … always reminds me that preview option would be great 😉

    Also talking of numbers, I finally have to ask the following (perhaps rather dumb) question regarding your flux estimate (as you’ve mentioned it in several posts now). You write: “An increase in surface temperature of 1K produces an increase in surface flux of around 5.4 W/m2.
    I was always under the impression that you are talking about the Planck response here. However, it is usually specified as -3.2 W/m2/K, which leaves me with a change in surface flux of 3.2 W/m2. Am I missing something fundamental here? Thanks for enlightening me, Wotts

  9. Karsten, I was talking of the Planck response. Indeed I simply gave the magnitude and not the sign, which I should have done. I’ve also ignored the emissivity (around 0.6 I believe). So, yes, it should really be -3.2 Wm-2. However, to be fair, I did specifically say “surface flux”, but you’re correct that including the emissivity would be more appropriate (assuming that’s what you’re suggesting).

  10. OPatrick says:

    Thanks. I ask partly because I was recently involved in a conversation with someone who claimed that as the Earth has a mass of 5.98 x1024 kg we are only experiencing a temperature increase of 1.67 x 10-6 degrees per year.

    Incidentally, can I use superscript in comments? It ignored my ‘sup’ request.

  11. You should be able to use sup. I’ve fixed your comment by doing exactly that.

    The Guardian comment is quite remarkable. I think your response to it was probably all it deserved.

  12. Okay, thanks Wotts. Just double-checked, the feedback/response convention seems to be Earth’s radiating (average) temperature, which makes it -3.2W/m2/K in GCM’s. For the surface, your blackbody estimate of -5.4W/m2/K is about right. The difference determines Earth’s emissivity. So surface flux change and Planck response doesn’t seem to be the same thing after all. Guess it was me who messed things up a bit here 😉

  13. BBD says:

    Oh look. Two scientists exploring a problem admit errors, refine analysis, seek improved understanding.

    Look, “sceptics”. Look.

  14. Karsten, to be honest I’ve become a little confused about which is more appropriate for determining the amplification/feedback. I was reading Lockwood (2010) which seems to use the change in surface flux compared to the change in forcings to estimate an amplification factor (or, feedbacks I guess). Having said that, it’s been a long day and I may be just get myself more confused if I continue to think about this any longer 🙂

  15. DocMartyn says:

    “If the equilibrium temperature is To and the current surface temperature is T, then the amount of energy, dE, that the system will accrue in a time dt is………………”

    Do you think that the term ‘equilibrium temperature’ is a correct usage for the average of (Tmax + Tmin)/2, taken at points of a rotating spheres surface?

    If I were to pace a meter long steel rod into a fire, would the ‘equilibrium temperature’ be (Hot Tip + Cool Tip)/2 ?

  16. Wotts, I’ve just checked Lockwood 2010 and you’re absolutely spot on. 5.4W/m2/K is the Planck response of the surface temperature change. The confusion arises from the fact that the Planck response in GCM’s is expressed in terms of flux changes at the top of the atmosphere. Therefore, it’s a function of Earth’s total emissivity ( = 1/4*S(1-A) / (sigma*Ts^4) = 0.61 ; S=SW in ; A=albedo ; sigma=Boltzm.C. ; Ts=sfc Temperature ). With this number, we get straight to the model estimate of approx. 3.2W/m2/K. Guess that’s about it.

    A minor nit though: It should probably be sigma*T^4 twice in your first equation (rather than T^2 for the first term).

  17. DocMartyn, I wasn’t meaning the average though. I was simply meaning the temperature at which the system would be in radiative equilibrium.

    Karsten, indeed – thanks – a typo.

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  20. nuwurld says:

    andthentheresphysics, hello. You made a statement,

    “The climate can’t be incredibly sensitive to changes in solar forcing while having no sensitivity at all to changes in other forcings. It really doesn’t make sense.”

    Do you want to discuss that?

  21. nuwurld, sure, as long as it’s not related to some kind of semantic pedantry.

  22. nuwurld says:

    attps. Do you agree that in radiative energy exchange, what is exchanged in Watts is related to the “differences” in kinetic distribution? That is where the individual mean thermal velocities of the objects determines their temperatures, such that a temperature increase requires an increase in mean thermal velocity and a temperature decrease a reduction in the mean thermal velocity?

  23. nuwurld,

    individual mean thermal velocities of the objects determines their temperatures,

    Sure, that’s seem fine.

    such that a temperature increase requires an increase in mean thermal velocity and a temperature decrease a reduction in the mean thermal velocity?

    Again, seems reasonable.

    Can I ask you a favour though. If you’re trying to make a point, can you simply go ahead and make it. I’m not really interested in an exchange where you ask me a bunch of questions that I may or may not agree to and then at then end you get to say “Aha, see you’re wrong/confused”. I don’t know if you’re trying to do this, but there are hints that you have an agenda. Just make whatever point you’re trying to make and we can go from there.

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  25. I don’t yet have the AR5 links, but section 2.8.5 in the 2007 IPCC report discusses the “efficacy” of various radiative forcings, which are shown in figure 2.20. I explored the feedback differences between the Sun getting brighter or CO2 increasing, and agree with Anders’ statement that the “climate can’t be incredibly sensitive to changes in solar forcing while having no sensitivity at all to changes in other forcings.”

  26. nuwurld says:

    Ok attps, I can cut to the chase. There are two points that I feel are relevant that would like to address. The first being that thermal radiation, as you know, is closely related to the kinetic distribution of the emitter such that the integration of the Planck function effectively mirrors the distribution of particulate velocities/energies. The solar surface emitting at around 5880K therefore emits a spectrum of photon energies such that the vast majority of photons, upon absorption within a 288K environment have the ability to raise the mean thermal velocity of the kinetic distribution of the absorber. They largely all have sufficient energy to spontaneously downgrade within this environment. So the small but measurable change in TSI is both real and available for work or power.
    Within this 288K environment the THz fluxes which can be calculated, cannot easily be realised. They are not available to spontaneously be absorbed such that they increase the mean thermal velocity. How much of, say, a 4W increase in back radiative forcing, with knowledge that it is spread across the Planck integration from a mean temperature across the optical depth is available to stop the surface losing it’s higher energy kinetics through radiative exchange? This 4W of calculated “forcing” is also unavailable for work or power, if it originates from a cooler emitter within a thermal gradient.

    Do you believe that the spectral distribution of any radiative “forcing” is irrelevant?

    The second point, is that the Earth doesn’t spontaneously evolve towards equilibrium with the TSI. It only has to respond to the portion of the total irradiance thermally absorbed. Spectral variation whilst maintaining TSI can affect the portion thermalised.

  27. Holy Sky Dragon Slayer, Batman!
    Abort! Abort!!!

  28. @DumbSci, yup there is a suggestion of that.

    @nuwurld

    Do you believe that the spectral distribution of any radiative “forcing” is irrelevant?

    Not necessarily, but in the circumstance I’m referring to they are essentially the same. If the solar flux increases so that there is an increase in solar forcing, then the incoming flux (solar) exceeds the outgoing flux (mainly long-wavelength). If we increase greenhouse gas concentrations so that there is an anthropogenic forcing then the same applies. The radiative forcing essentially means that the incoming flux (solar) exceeds the outgoing flux (mainly long-wavelength). Hence the affect of an increase in solar forcing should be the same as an equivalent increase in greenhouse gas forcing.

  29. nuwurld says:

    But, with respect, the solar flux can increase the mean thermal velocity through spontaneous degradation, and back radiation can’t. Irrespective of calculated powers. Does that inability, physically, not bother you, to the extent that you still class them as equivalent?

  30. @nuwurld, I don’t think you understand. When there is a positive radiative forcing the solar flux is increased relative to the outgoing flux. It doesn’t matter what’s caused the forcing.

  31. nuwurld says:

    Wow, I think I do understand. I’ve measured your responses sufficiently to measure your mark. I don’t need to communicate with you further. Any respectful physicist would have wanted the details to be addressed and worked through. It is very easy to communicate a physical misconception. You haven’t addressed any, except to say I “don’t understand”!

  32. @nuwurld, that’s fine. Have a good day.

  33. Tom Curtis says:

    nuwurld:

    1) Do you agree that IR radiation leaving the Earth results in a loss of thermal energy, which all things being equal would result in a loss of mean thermal velocity? That being the case, with TSI held constant, increasing the outgoing IR radiation would cool the Earth, and decreasing it would warm it. Increasing CO2 in the atmosphere decreases outgoing IR radiation until the Earth warms sufficiently to emit the same level of outgoing IR radiation as before.

    2) You do realize that the Earth emits more photons than it receives from the Sun? This follows necessarily from the fact that (a) outgoing IR radiation equals (in equilibrium) the incoming solar radiation, and that (b) the outgoing IR radiation has far less energy per photon then the incoming solar radiation. Therefore even though the effect on thermal velocity per photon is much greater for solar radiation than for outgoing IR radiation, or back radiation, (your only valid point) the total effect of all photons is equal.

    3) The greenhouse effect is not dependent of back radiation, despite some misleading popular presentations of the greenhouse you may have encountered. The greenhouse effect is a function of the temperature in the upper (mid) troposphere from where IR radiation from CO2 (H2O) is radiated to space. Increasing CO2 (H2O) content raises the average altitude from which radiation can reach space, and because increased altitude means cooler temperatures, reduces the radiation reaching space as a result. This must be compensated for by an increase in temperature, and because the lapse rate (change of temperature with altitude) is constrained in the troposphere by convection, that also requires an increase in temperature at the surface. Initially, reduced radiation to space warms the upper (mid) troposphere, which reduces convection, thereby warming the Earth’s surface. Back radiation can also reduce net energy emission by the surface, warming it, but the greenhouse effect is not dependent of that mechanism.

  34. Tom Curtis says:

    I note further that Nuwurld’s assumption that back radiation cannnot increase thermal velocity at the surface assumes that all particles at the surface have the same thermal velocity; rather than there being a very wide distribution of thermal velocities of individual particles, thereby leaving a large number at a lower velocity, and able to increase their individual thermal energy through the absorption of back radiation. Probably telling also that he has left the thermal energy in vibrational modes out of the equation, they being the part of thermal energy directly related to the absorption and emission of radiation.

  35. Thanks, Tom. I think that is one of the best summaries of the greenhouse effect that I have read.

  36. nuwurld says:

    Hi Tom,
    1) Yes. But with respect I was discussing the ability of the solar flux to influence the surface. Not the presumption that decreasing the surfaces ability to radiate through limited spectral bands would limit a dynamic systems ability to still satisfy the thermal gradient set by gravity and the requirement to answer to space. The atmosphere is not in radiative balance. The lapse is mechanical. Dominated by moist convection.

    2)pointless drivel. I don’t care, nor does the physical world how many downgraded near zero energy photons there are. They do not spontaneously upgrade. They fill the expanding universe with it’s background. Within a system influenced by high grade photons and low grade the total effect of all is not equal when describing a drift from equilibrium.

    3 Tom, quantify the ‘greenhouse effect’ then and specify the total effect. AMSU microwave satellite today tells me the globally averaged temperature at 7.5km is -36deg C. That gives a surface equilibrium temperature of 12.75deg C through totally ignoring radiation. So the total of all radiative forcing lies ( did I say ‘lies’?) within two degrees of isentropic equilibrium. That us with a lapse of -6.5K/km purely mechanical. And of course the system is dominated by the latent heat of water (or as you say CO2(H20) wink wink).

  37. nuwurld says:

    Tom, in response to your second response I have only mentioned distribution and mean. I have in no way suggested they where all the same? Re read. Stop making things up!

    I’ll tell you how much I’m making things up Tommy.

    Back radiation is “measured” daily by pyrgeometer readings all over the world. They measure downwhelling flux expressed in Watts/m^2. Typically the downwhelling flux is around 300W/m^2.

    Now, long wave radiation in the THz band can be refracted and reflected and condensed. In particular it can be focussed by surface silvered mirrors. Like those used for astronomy. Now if you take a 5m surface silvered dish, calibrate your panF with a beta lamp as a standard candle and an intensity step tablet your ready to go. Key in the RA and DEC. And the telescope will transit to zenith then pan to field. Then you are left with a 5m condenser focussing all the back radiation from cloudy sky onto a film plane measuring 24mm by 36mm with a black cloth shutter.

    Do the maths. Clear sky gives 300W back radiation. Cloud gives more being warmer and having no spectral window. pi.r^2 where r is 2.5m is 19.6 times the downwhelling flux. Or 5.89kW of downwhelling focussed on a black cloth shutter waiting for the clouds to break. When they do you do your timed exposures at intervals hoping the close variable flare star will perform.

    Did the camera melt. No. It became very cold.

    This is a very real and repeatable experiment.
    Downwhelling radiative flux is not available for work or power.

  38. Tom Curtis says:

    Nuwurld, I have long ago been informed not to debate with fools, lest onlookers will not be able to tell the difference. Clearly, therefore, there is no more point in debating with you. Your effective claim that the “physical world” will violate conservation of energy because it can’t be bothered with the effect of low energy protons makes that abundantly clear. So does your attempt to portray the effect of the greenhouse effect as being the difference between the surface temperature and the calculated surface temperature using a temperature at a height and an approximation of the lapse rate. (It is actually the difference between the radiation to space and what the radiation to space would be if it came directly from the surface at the current global surface temperature, or alternatively it is the lapse rate times the average altitude of radiation to space. Using your numbers, that would make it ~50 degrees C, but actually about 33 C as 7.5 km is not the average altitude of radiation to space.)

  39. Tom Curtis says:

    nuwurld, did you calculate the thermal radiation from the surface blocked by your mirror? No, didn’t think so. All your experiment involves is blocking slightly warmer thermal radiation from the surface and replacing it with slightly cooler thermal radiation from the back radiation. It never ceases to amaze me how many times sky dragon slayers promote experiments as refuting the greenhouse effect when the experimental analysis depends essentially on not calculating all of the relevant energy flows.

  40. The cynic in me notes that typing ‘r’ instead of ‘h’ doesn’t invalidate the physics of the greenhouse effect.

  41. nuwurld says:

    Tom, with respect, having mulled over your arguments, and despite what you may think I do understand the “modern” and “revised”, “greenhouse effect. The raising of spectral bands to lower emitting temperatures such that lower atmospheric temperatures have to be enhanced through the reduced spectral windows to compensate. That I understand.

    That being achieved by reducing the earth’s emissivity through introducing more things that can emit.

    See, even to you that didn’t make sense!

    To quote you,

    ” Initially, reduced radiation to space warms the upper (mid) troposphere, which reduces convection, thereby warming the Earth’s surface.”

    Now, Tom, isn’t this the same warming of the upper troposphere, particularly in the tropics that has never been detected? Isn’t this model the one with zero predictive value with all 73 failing to predict the pause?

    Let’s look at a “warming of the upper (mid) which reduces convection”

    Well hell Tom, isn’t the upper (mid) heated by moist convection as it’s primary energy supply? Sounds like negative feedback.

    Tom, the upper (mid), as you know is above the main radiative components answering to space. Those being the surface and the lower troposphere where your 33K enhancement lies (at mid tropospheric 5km average). At upper (mid) it is subject to the long wave radiation from the surface and the lower troposphere, so warming of it results in less radiative heat transfer from below. You are increasing the lesser temperature component in the full S-B. Negative feedback.

    Plus warming of the upper (mid) due to enhanced radiative components within a low emissivity dominated atmosphere, radiates more to space from altitude from more active triatomics. Negative feedback.

    How is the warming maintained?

    Interesting after decades of declaring that a “greenhouse” works by radiative forcing, then greenhouses actually work by stopping convection that we get to “the upper (mid) warms and reduces convection”!!!!! Forget back radiation, forget long wave trapping,

    ” Initially, reduced radiation to space warms the upper (mid) troposphere, which REDUCES CONVECTION, thereby warming the Earth’s surface.”

    When all the models have zero predictive value.

    And, the telescope was a symmetrical Cassegrain, so the detector was not shielded by the mirror. And I don’t have to account for vibrational modes as they are experimentally determined within Cp, and therefore accounted for in all measured temperatures (unless you believe the atmosphere behaves under non-thermodynamic principles?)

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