Time Lag and the Moon’s surface.

The last couple of days have been busy as readers have been driving some interesting discussions.  On one page there was an unexpectedly interesting discussion about the Moon.  It started with an error on my part that was corrected by a reader.  It had to do with the predicted and actual surface temperature of the Moon.  The impact of this could be significant, but that I simply don’t know yet, but the idea is an interesting one that will require some more information.

The predicted (blackbody) temperature of the Moon is 270K (-3°C).  That is a warmer predicted temperature than the Earth has.  This is because the Moon reflects away less energy than the Earth does.  This predicted temperature is not the actual temperature of the Moon though.  The Earth has a predicted temperature 254K (-19°C).  It is warmer than that by 33 °C and the Greenhouse Effect is the common answer as to why the Earth is warmer than this.  Since there is no atmosphere on the Moon, there cannot be a Greenhouse Effect, but the Moon is not the temperature that is predicted by the Stefen-Boltzmann equations.   Most interesting is that it was much warmer during the night and cooler during the day than it was predicted to be.

The reason for this is the ground underneath the surface absorbs energy from the surface.  The lunar surface is not a very strong thermally conductive material, but the surface heats up to about 370K during the day.  That very high temperature causes the surface underneath to warm up just like what happens on the Earth.  When the sun sets the temperature rapidly drops off.  This is because the surface is radiating energy like a blackbody at a high temperature.  As the temperature drops, the amount of energy radiated away from the surface decreases.  Once about 90K is reached the temperature stops dropping and the surface is now colder than the subsurface.  The energy flow then reverses and the surface of the Moon is kept warmer by the energy that is now flowing up from the subsurface and then into space.  The “daily” cycle looks like this.

The Inconvenient Skeptic

(Red) the surface temperature of the Moon. (Green) the temperature of the subsurface of the moon.

One particular item is that the subsurface loses temperature at a constant rate during the night.  At 85-90K the Stefen-Boltzmann for a blackbody is ~3.3 W/m2.  That would indicate that the subsurface is transferring energy to the surface at about that rate.  The total energy is small, but because the rate of heat loss is also low, it is enough to keep the surface temperature from dropping further.

The difference between the theoretical and the actual measured temperature is significant.

The Inconvenient Skeptic

(Red) Predicted temperature of the Moon using Stephan-Boltzmann. (Green) The observed temperature of the Moon from sensors established during Apollo 15.

The energy that is lost to the subsurface during the day prevents the surface from reaching the predicted maximum temperature.  That energy is temporarily stored in the subsurface until the Sun sets.  Then the surface cools and once the subsurface is warmer than the surface, the energy is then transferred to the surface and keeps the temperature from dropping as low as it would otherwise.  The same cycle repeats each lunar day.  The time lag in the observed temperature is evident in the delay between predicted and actual peak temperature.  The surface also is delayed in warming because the subsurface initially is absorbing back the energy that was lost during the night.

According to NASA the maximum depth at which the diurnal temperature change can be noticed is 50cm.  This small region of the Moons surface that stores and releases energy is enough to prevent the Stefan-Boltzmann equation from being an accurate predictor of the surface temperature of the Moon.  If that is enough to prevent the Stefan-Boltzmann from working for the Moon, then how much more error is introduced into the estimated size of the Greenhouse Effect on the Earth by using the Stefan-Boltzmann equation.  The Earth is vastly more complicated than the Moon.  That small region of subsurface is also enough to cause mimic to a small degree the effects that are often attributed to the Greenhouse Effect.  This could be evidence that the stated Greenhouse Effect of 33 °C is inaccurate and that the actual impact of the atmosphere is in fact lower.

Posted in Radiative Heat Transfer and Science Articles - Global Warming by inconvenientskeptic on March 13th, 2011 at 12:38 am.


This post has 10 comments

  1. SoundOff Mar 13th 2011

    OK TIS, I will concede your point. Let’s say ~3.3 W/m2 of the 239 W/m² entering and exiting the Earth’s climate system, or ~0.5°C of the 33°C greenhouse effect, is explained by short-term thermal heat storage in Earth’s solid surface mimicking the greenhouse effect. That still leaves 32.5°C to explain by some other means before concluding it’s an overstated cause of global warming.

    Actually, there is much less diurnal change on Earth due to the true greenhouse effect, oceans and a much shorter day/night length. So the Earth’s solid surface temperature does not change very much over 24 hours. Plus the solid surface is just 29% of the total Earth surface so it is not a big player on that basis alone.

    This all means the Earth’s solid surface isn’t radiating away as much heat as the Moon (or technically it is – where it’s in play – but a stronger than estimated greenhouse effect keeps reheating that solid surface at nearly the loss rate). Therefore, I’m being quite generous if I concede you 0.5°C.

  2. inconvenientskeptic Mar 14th 2011


    But the Earth is a different situation and less energy reaches the Earth’s surface. I am still working through the numbers, but there is the baseline info using Trenberth-2008.

    Only 161 W/m2 reaches the surface. The Earth’s land is also more conductive than the Moon’s surface. This is clearly proven by the fact that 1 week of 380K only results in a detectable temperature change at 50cm, while the Earth’s variation is detectable down to several meters despite a lower temperature gradient.

    You also pointed out that water is the main component of energy storage. With the land and water let’s assume that the Earth transfers about 5x the energy into the surface. That is an estimate and I will refine that number in the future. It could easily be lower, but it could be higher.

    The moon also gets the full solar constant. So the equator at “noon” gets 1367 W/m2, but spatially averaged it would be the same 340 W/m2 that the Earth has at the top of the atmosphere, but it would be the surface only.

    Assuming the 340 W/m2 then the effect on the Moon 1%. The Earth’s surface gets less energy from the sun and transfers more into the surface. If the energy into the subsurface is 16 W/m2, then the effect is 10% of the energy for the Earth’s surface.

    The effect for the Earth could easily be 3°C of the total greenhouse effect and possibly more. The temperature effect on the Moon’s surface is significant.

    I am guessing that the oceans really enhance the overall effect. That is really the wildcard in this. If the oceans could really be a significant factor. There is no point speculating a total percent yet.

    But you have to admit that this effect has been overlooked and if it is greater than 10% of the observed GHE, then it is an important player.

  3. SoundOff Mar 14th 2011

    Whatever excuses either of us comes up with for why the Earth or the Moon is more sensitive to the time lag effect, the real test is how much solid surface temperatures rise and fall over the day/night cycle. More change means more sensitive. The Moon wins this test easily.

    I really don’t want to divert from your “time lag” topic but I don’t think time lags are really that pertinent to blackbody temperatures. Time lags just shave some degrees off the blackbody peaks and troughs, and move those degrees to some later part of whatever lag cycle is being examined. I don’t see how internal shifts within the climate system really matter when analyzing the difference between the actual heat released from the climate system into space versus the blackbody temperature, the latter being just an idealized temperature without all the complications of thermal lags and greenhouse gases.

    If you haven’t seen this link yet, it has a fair amount of overlap with your topic though it’s more ocean-specific.


    Quote: “What might be less obvious until attention is drawn to it (then it is obvious) – the final temperature doesn’t depend on the heat capacity of the liquid. That only affects how long it takes to reach its equilibrium – whatever that equilibrium happens to be.”

  4. inconvenientskeptic Mar 14th 2011


    I started the time lag topic for the purpose of explaining that it should not take years for the “new” equilibrium (steady state) to be reached for a change in CO2 level.

    The lunar aspect is one that I never looked at until our discussion brought it to my attention.

    I do read SoD at times. My approach is very different than his. I used a series of real world examples to estimate the lag. His was a more theoretical.

    His estimate for the change in temperature for a change in forcing is also curious. I would argue that CO2 does not increase the incoming energy at the TOA, which he seems to assume. CO2 should insulate the Earth more effectively so decrease the rate of heat loss from the surface.

    Here are the specific articles.



  5. Richard Sharpe Mar 14th 2011

    I would think that the oceans would play a large part in this equation as well …

  6. SoundOff Mar 14th 2011

    About radiative forcing …

    Any sudden increase in forcing will have its biggest impact in the time just after that forcing occurs. Then the effect decays or tails off very slowly over time. How long depends on the size of the forcing and the length of time that the forcing is sustained. The peak forcing of the solar cycle is a couple years long but it’s a relatively small positive forcing so it decays quickly. A large volcanic eruption is a strong negative forcing but it is usually sustained for only a few months so it decays quickly too. CO2 is a moderate positive forcing but it has been on going for decades and looks like it will be sustained indefinitely (even worse, it’s increasing). CO2 (that is, the overall CO2 flux) has a long residency time too so it compounds, like interest on interest. I don’t think this should be called a lag – it’s really an atmospheric residency time issue.

    It’s not easy to demonstrate the residency time with CO2. Wikipedia says “Carbon dioxide has a variable atmospheric lifetime, and cannot be specified precisely. Recent work indicates that recovery from a large input of atmospheric CO2 from burning fossil fuels will result in an effective lifetime of tens of thousands of years. ” From my readings elsewhere, it seems that half of any CO2 flux is still at work in 25 years, maybe 20% is still active in 100 years, 10% in 500 years and it finally loses all effect after 10,000 years. The residency issue should not be conflated with surface temperature lag (mostly caused by oceans, which is a true thermal lag).

    I read SoD regularly and I’ve never seen him argue that CO2 increases the incoming energy at the TOA, it certainly does not (it does increase surface and lower troposphere energy). CO2 doesn’t exactly insulate the Earth more effectively either, though the effect is similar in result. What’s really happening when CO2 increases is photons are arriving faster than they can leave until the Earth warms up. A warmer Earth forces more photons to leave resulting in a new balance. The entry rate didn’t change but the exit rate decreased for a time due to interference by more CO2 molecules in certain frequencies. Think of it like a daily highway traffic jam that clears up when the government adds more lanes at the expense of hotter taxes.

  7. inconvenientskeptic Mar 14th 2011


    My conclusion on the time factor is different. In every example I can find the climate has a quick and total response very quickly. I have looked.

    It is the case of a negative forcing that would have a longer ocean response. Cool water sinks allowing warm water to rise. A positive forcing warms the water which would then be more biased to collect at the surface.

    It is positive forcing that is more quickly seen in the oceans, not a negative forcing.

    I don’t want this discussion getting into the photon/energy transfer debate. There are several radiative heat transfer articles that can open up that one.

    Do you think that 10% of the total GHE is out of line for this subsurface effect on the Earth?

  8. Malaga View Mar 15th 2011

    The energy going into the surface might be more important than I expected.

    What about the energy released by the cooling planet?

    I guess my question revolves around the observation that the earth is not a black bodythe earth is a warm blue/white/green planet that is cooling into space while being heated by the sun… core heat is being lost through the surface, geothermal activity (warm springs and geysers), volcanic activity and probably deep rooted vegetation.

    It looks like the moon still has some core heat left to radiate… but very very little… areas that never receive direct sunlight, temperatures can dip to within a few tens of degrees of absolute zero. http://www.diviner.ucla.edu/blog/?p=123

    It looks like the interior of the planet earth is a lot bigger and warmer than the moon… as your previous post indicates the soil temperature can stabilise at about 30 feet… and with permafrost (in Yakutsk) this stabilisation happens at about 15 metres (with a temperature of -5C) according to Wikipedia… so the earth does conduct heat in both directions.

    I have no idea how this all adds up… but I guess it contributes to the energy balance

    Time (yr) Permafrost depth
    1 4.4 m (14.6 ft)
    350 79.9 m (262 ft)
    3,500 219.3 m (719 ft)
    35,000 461.4 m (1,514 ft)
    100,000 567.8 m (1,863 ft)
    225,000 626.5 m (2,055 ft)
    775,000 687.7 m (2,256 ft)


  9. SoundOff Mar 15th 2011

    It is the case of a negative forcing that would have a longer ocean response. Cool water sinks allowing warm water to rise. A positive forcing warms the water which would then be more biased to collect at the surface.

    Hmmm. That would mean if we have neither a positive nor a negative forcing happening, a steady state, or if we have only a regular up and down equal forcing (e.g. the solar cycle), then the bias for warm water to rise would mean we would always have a slightly warming atmosphere without any [net] forcing. That is, unless we always have a slightly negative forcing that exactly matches that unforced warming. But wait a minute, there is no forcing to match!!! Gosh but climate science is complicated to understand!

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