Time Lags in the Climate System

Interstellar Bill says: June 18, 2012 at 1:27 pm
“Also, this inquiry is scientifically useless because there’s no parameterized supercomputer model of all the soil on Earth.

Yes, but we took a handful of sand and extrapolated

I’ve always wondered about this. When people talk about the surface temperature of the earth what exactly does that mean. It seems like surface *AIR* temperature is merely a proxy for the true surface temperature of the earth.
Let’s next ask if we need to factor in the temperature of the ocean depths and ocean crust, to get an estimate of the surface temperature of the earth. If you look at trends this might not be important, but whenever I see people doing that elementary zero dimensional model of the earth’s surface, I wonder if they don’t overestimate when they say the average surface temperature of the earth is 12, 13 or 14 degrees C.

Much cheaper used copies are available on abe.com
http://www.abebooks.com/servlet/SearchResults?sts=t&tn=%93The+Climate+Near+The+Ground%94

Interstellar Bill says: June 18, 2012 at 1:27 pm
“Also, this inquiry is scientifically useless because there’s no parameterized supercomputer model of all the soil on Earth.”
And just what do you think all that hammering is about ?? Willis has PLANS !!!! 😉

@Steve Skinner,
Its been several years since I did soil properties at uni, but I remember that these things are related to :
grain size, and grain size distribution
water content
type of grain (if the grains are “sticky” or not)
carbon matter
compactness
etc etc etc
so yes, the type of soil has a huge bearing on the heat holding capacity.

Another interesting topic. In other fields ‘diffusivity’ is called ‘thermal transfer coefficient’ and is measured in W/(m2K). As you know, temperature is not heat.
I hope you’re not really pounding nails.
I have an extra paslode cordless if you were not joking and are serious about getting work done.

vukcevic says:
June 18, 2012 at 2:09 pm
To the climate of the Northern Hemisphere an 11 lag between summers Icelandic Low and the AMO is of critical importance

11 of what unit of measure? I think this is years if I remember what I saw of your work in the past. Ok, just confirmed that by visiting the provided link. 11 year lag.

Gradually and finally people start to catch up with what climatology understood, taught and was researching 30 years ago. It speaks to my charge that the IPCC has set climatology back 30 years.
All of the issues discussed here were included in the textbook I was involved with in 1989. I used to tell my students a lab experiment would prove insolation doesn’t penetrate far into the ground by quickly pulling up worms and measuring how quickly they reacted by blinking.
Lags speak to the ongoing problem of climatology – cause and effect. Maybe soon we will hear about the lag between Earth’s peak Gaussian strength and temperature, daily and annually or the many other lags that require investigation and explanation. If you want a good overview you might begin with Oliver and Fairbridge’s Encyclopedia of Climatology published in 1987 and a far better more complete and up to date summary than all the IPCC Science Reports combined.
It is going to take a long time to wash of the stink of politics. If and when we do we will find that we have even less data than 30 years ago because in order to achieve their political science they adjusted, threw out, truncated, or lost, large amounts of data. They closed data collection sites so even if re-established them continuity is virtually impossible.
I am glad Willis is acknowledging the work of Geiger. Let me add to the list the names of Thornthwaite, Penman, Budyko, Herman and Goldberg, Imbrie and Imbrie, Claiborne, Eddy, Douglas, Koppen, Grove, Libby, Labitzke, Van Loon, Emiliani, Bryson among many others and of course, Lamb who must roll in his grave at what happened at the Climatic Research Unit.
I am glad Willis is doing this, but it is too little too late. The public have moved on. The only lag left is between final exposure of what the IPCC have done and complete withdrawal of funding.

“This is because it takes time for the heat to warm the earth, and that heat comes back out of the earth during the times in the temperature cycles when there is less forcing.”
It takes an 8.hour morning to warm a back yard, and since the sun reduces power at a slow pace after peak power, the influx of energy from the sun will overpower the leaving of thermal energy for a couple of hours into the afternoon barbecue.

The seasonal lags for the ocean are about 82 days, freshwater lakes are about 49 days and land surfaces are 34 days.
You can turn some of these equations into joules/m2/second. At the height of the day, the sun is shining in at something like 960.0 joules/m2/second, but the ground is accumulating that solar energy at an exceedingly tiny number; something like 0.007 joules/m2/second. Even though there is a lag of 2.6 hours, the rate that the energy is accumulating (and then leaves at night when the Sun goes down) is several orders of magnitude smaller. The lags are really very, very small rates of accumulation/net loss (small compared to how much the incoming energy changes over a 24 hour epriod.) It is big part of the picture; energy flows over time, that are not being addressed in the theory.

More coincidence? 1/8 = ½^3, so 3 degrees of freedom/dimensions.
Thx for the D/L link and warning. 13 seconds on my ancient P4, 15 mbps, 518 pages. 😉 Compared to graphics and video files, kinda trivial.

Hi Wilis,
If the load was purely conductive the temperature would be in phase with the forcing, i.e. a phase lag of 90º for a sinusoidal signal.
For a purely capacitive load it would be 90º and for a purely diffusive load 45º.
That is as measured at the surface and is true for all frequencies (provided pure means pure)
A spacial mix of mostly conductive and mostly capacitive loads will be somewhere between 0º and 45º but will vary somewhat with frequency.
There is a file abstem3 (?) that contains all the gridded normals (the monthly climatology) for the Hadley temperature dataset. So it contains the average seasonal component so you can see how the phase varies around the world. The annual signal is cleanest at aroung 45 North or South where the semi-annual signal is weakest.
You will see that the phase of the annual cycle varies quite a bit from ~25º in Mongolia (highly land locked in the direction of the prevailing wind) to ~70º near about 3/4 around the equator bound leg of each gyre.
That is my memory serves me well.
Alex

Oops Wrong Angle!
A spatial mix of mostly conductive and mostly capacitive loads will be somewhere between 0º and 90º but will vary somewhat with frequency.

Willis, you might also want to do some reading on adobe construction. In a book on adobe construction I read many years ago they mentioned this thermal lag. It is actually central to determining the ideal thickness of the adobe wall to use in a home. If the wall is the right thickness the peak temperature thermal pulse will reach the interior surface of the adobe wall early in the morning when additional heating would be needed, and the cool thermal pulse from the early morning hours will reach the interior surface of the adobe wall during the heat of the day.
At the proper thickness the wall acts as a thermal capacitor charging and discharging with a time constant that is exactly opposite of the exterior temperature cycle.
This is why wine cellars interior temperatures approximate the ground temperature although the walls are only about 2 ft thick, they stabilize the interior temperature at the local annual average temperature.
I was noticing the same thing if you look at the climate records for an area and find the historically hottest day of the year, you will find the local climatic time lag with respect to the summer solstice. The same applies to the historically coldest day of the year with regard to the winter solstice. I am sure that local micro climate and seasonal flow patterns will slightly shift the local climate cycle time lag slightly due to changes in prevailing wind directions and such but I doubt it differs more than a week or so for most locations on the surface of the earth.
As far as thermal lags for water, you might also want to look into studies aimed at solar thermal storage ponds as they have lots of actual test data for how the water pool heats and cools and how that changes with depth. Highest water temperatures are achieved with relatively shallow water with a bottom that can be directly heated by the sunlight as there is less water being heated by the solar isolation in a relatively shallow body of water, than a deep water pool that is heated through out a considerable depth.
Hurricane studies show this hot shallow water can partially compensate for land fall in swampy areas where the abundance of relatively hot water counter balances the normal cut off of heat supply to the hurricane at landfall.
Interesting information!
Larry

Thank you Willis for yet another good article. –
“How heat is transmitted through the Earth’s crust” is a complicated study and there is not much written about it since ‘Fourier 1824’. I have mentioned his writings before as I have learnt a lot from it and feel I shall have to re-read him.
However originally I come from a place in the world which is positioned approximately 60 degrees north (60° N) and there, back in the 1940s, the yearly frost that solidified the ground reached down to approximately 2 metres (or meters as you may write it). – Well, that frost was thawed out by late May – early June. Of course it was the water in the soil and not the soil itself that froze solid during the winter.
But, further north, in places where the rays from the Sun have less impact there is something else called “Permafrost” where the temperature of the soil is less than 0° C year after year.
Wikipedia says the permafrost can reach as far down as 1493 meters (m), which is a heck of a depth. Here where I live now (around 50° N there is no permafrost at all and I can only assume it is all down to the Sun.
So a question that bugs me now is: “Does the heat from the Sun percolate down to accumulate at the centre of the Earth, or is it more likely that there is a never-ending energy source down there that keeps the fire burning for billions of years? (Is it maybe burning Uranium or Thorium – no, it surely cannot be fossilfuels?)
I really must re-read Fourier – but – as you have started this line of study I shall be watching the progress with interest.

@Interstellar Bill aid “there’s no parameterized supercomputer model of all the soil on Earth.”
There is also no accurate parametized supercomputer model of the oceans, ionosphere, trophosphere and gulf stream that has sub-routines for calculating the effect of incoming Solar winds/waves.
Which is why most of the Nasa modeling scientists found themselves jobless in 2003.
USGS and various mining departments globally have reasonably geological topographical infrared models which could be used to create a global supercomputer model, however I think the article stipulates that this is an inconvenient truth, therefore ignored by climate change “scientists”,

Tim Ball says on June 18, 2012 at 3:24 pm:
“Gradually and finally people start to catch up with what climatology understood, taught and was researching 30 years ago. It speaks to my charge that the IPCC has set climatology back 30 years. —— —-
I am glad Willis is doing this, but it is too little too late. The public have moved on. The only lag left is between final exposure of what the IPCC have done and complete withdrawal of funding.“
============
Well said Tim Ball, I would like to hear (read) more from you too!

Thanks for the link to the textbook, I will enjoy reading it if it is as empircal as you say.
But I think you are missing a mechanism related to the atmosphere – I assume that is you point mentioning CERES? – that is not really present for solids.
The “thermal diffusivity” is related to the specific heat capacity, which under quantum theory is related to the number of degrees of freedom, i.e. it is not really a constant
e.g. take a look at things like “pressure broadening”…

“The beach air is hot, and your feet can still get burnt.”
You probably didn’t mean it as it is written but insolation and sand type have much more to do with hot sand than air temperature.

the lag between max solar input and max temperatures varies with latitude….for example I am in Trivandrum at about 8 degrees north….over here it is hottest in April when the sun is directly overhead

eyesonu says:
June 18, 2012 at 6:27 pm
Sleepalot says:
June 18, 2012 at 3:24 pm
I keep looking at this temperature graph taken during a solar eclipse.
http://www.shadowchaser.demon.co.uk/eclipse/2006/thermochron.gif
========================
Wow. 20 C temp drop over ~90 min and then a corresponding increase. I have not seen that graph.

I also saw the reports of the very rapid temperature drops during totality of eclipses. It is apparently a sharp enough chill that eclipse watchers are recommended to bring a jacket even in warm environments.
It also implies a radiation rate for heat loss. In dry climates the temperature climb from the evening low to the peak temp of the day is typically less than 30 deg F (17 deg C), which is comparable to the heat loss shown in only the time duration of the progression into totality.
Where is all that CO2 backradiation when you need it ??? /no so much sarc
Larry

Two brief comments.
1. It is standard practice at synoptic climate stations to measure soil temperature at different depths down to about 1 to 1.5 m.
2. In hydrological modelling the effect of soil heat flux is well known. During spring evaporation rates are lower than calculated from meteorological data, as soils warms up. During autumn the rates are higher as the soil gives up its heat.

“A steady slow increase, on the other hand, wouldn’t show such a lag. At least, that’s my current thinking …”
You can only define a lag time (or phase lag) if you have a cyclic (essentially sinusoidal) change since this produces a responce of similar forn to the driving force.
The responce to a step change is an exponential. You cannot define a phase or time lag in the same but this is still a lagged response.
It may be interesting to look at the tropical zone as gopal panicker suggests. The equator has 6 month cycle with geometrical maxima at the equinoxes , not 12m as it is outside the tropics, so this may be an interesting test of your 1/8 lag.

Willis, I have two words for you that might provide answers to your observations – Thermal Conductivity. It involves a time quotient which can be used to explain your observations.
As an engineer, I have been involved in Thermodynamics on a real world level for most of my adult life, and it amazes me that most of these ‘scientists’ involved in climatological studies ignore,dismiss, or attempt to refute the laws of Thermodynamics – a science in its own right which is centered on the study and use of heat. Thermodynamics is, in a large way, related to Climatology; for example it relies on models to predict the effect of temperature differences, heating and cooling, and energy differences. The big difference is that the models in Thermodynamics accurately predict the outcomes while the Climatological models have yet to predict an accurate outcome. One of the big failings of the models in climatology, from my perspective, is that they refuse to look at the problem from a thermodynamic point of view. If you look at the climate as a gigantic and extremely complex heat engine, I believe you will be better able to predict the outcomes of any changes in climate. For example, saying that global warming will cause extreme weather conditions is a fallacy from a thermodynamic perspective because the amount of work you can get out of a heat engine is based on the difference between the ‘hot’ side and the ‘cold’ side. In other words what is the temperature difference across a weather front – that will determine how violent the storms will be. The interesting thing is that for meteorologists the thermodynamic point of view is more valid than the climatological viewpoint. Climatology can produce models which will accurately predict climate change, but until they go through all the experimental challenges that Thermodynamics went through, adopt proper scientific methodology, and take into effect all the extra complexities involved instead of getting dragged into political decisions they rank no more higher than a Cult in my opinion.

Willis said:

It is only in cyclical fluctuations, where heat is moving both into and out of the ground, that we see a lag. A steady slow increase, on the other hand, wouldn’t show such a lag. At least, that’s my current thinking …

I think there can be no difference between a steady slow increase and a cycle of infinite length.
Therefore it can have no impact at all (or after a lag of 0.11 * ∞ years)

“the peak temperature during the day doesn’t occur until about three hours after noon, and the hottest months of the summer are about a month and a half after the summer solstice. This is because it takes time for the heat to warm the earth, and that heat comes back out of the earth during the times in the temperature cycles when there is less forcing.”
The reason for that phase lag is that even when the driving force has passed its maximum (noon for example) it is still well above the cycle mean and remains above it for a full quarter of a cycle. The max temperature will lie somewhere between the point of max driving force and the point at which if falls to the cycle mean.
Just where in this interval it lies, depends of the restoring forces cooling the system and the intertia (thermal in this case) of the system. Similar arguments show why it’s coldest in mid Feb not 21st December (NH).

@HankHenry says:
June 18, 2012 at 2:24 pm
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Further to the observation made by HankHenry
When considering the extent of so called GHG warming (said to be about 33degC), I question the correctness of assessimg ocean temperature solely on the basis of SST and not taking account of the average temperature of the ocean.
After about 4 billion years of heat input from the sun and ocean over turning, the deep ocean is only about 4 degC. This is material. If ocean temperature was more uniform (say if the deep and mid oceans were nearer the range of 12 to 15 degC), the prospects for ice ages would greatly diminish.
The temperature of the deep ocean comes back to bite and permits the development of ice ages.

eyesonu says:
June 18, 2012 at 6:27 pm
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And yet Trenberth and the Team would have one believe that DWLWIR is greater than solar irradiance. Funny that all those GHGs didn’t keep and maintain temperatures up for very long.

Thanks for your post. Interesting.
But the earth is never in thermal equilibrium is it. The sun is rising and setting. Night follows day. A cyclic system is never at equilibrium by the very nature of the cycles.

FYI 4 Willis – diurnal overturn is limited to about the top 1 meter
The Near-surface Layer of the Ocean: Structure, Dynamics And Applications
By Alexander Soloviev, Roger Lukas
http://books.google.com/books?id=4p6gNsSs-vIC&pg=PA250&lpg=PA248&ots=8HlIBxX8UP&dq=ocean+diurnal+overturning
It would be interesting to see the tautochrones for the moon. Apollo 15 & 17 missions placed regolith heat transfer experiments with temp probes at regular intervals between surface and up to 3 meters (or as deep as they could drill). The experiments radioed data back to earth for 4 years. Last I checked some sort of SNAFU at NASA.com had made the experiment data unavailable but it was there a year or two ago and available to the public.

Nick “Why the difference?” my guess would be something to do with all that water sloshing about in the oceans acting as a massive damper. Home as I call it 🙂

I just clicked on: http://www.shadowchaser.demon.co.uk/eclipse/2006/thermochron.gif and all I got was a page displaying: “This site is unavailable because it is too busy.” Well, well, well –Watts up with that?

Willis you are presenting a classic boundary value problem of the heat equation see
http://thevirtuosi.blogspot.nl/2012/05/how-cold-is-ground-ii.html
buy a text book instead of reinventing the wheel yourself.
try eg Geodynamics by Turcotte and Schubert.

Willis, I think you might have flipped a sign. You took equation two, substituted into three, but two is negative and the ‘z’ in three is negative and seems your 1/2π (0.159) in four ends up positive. If that correct it’s no problem here, I’m human too and have that slip occur regularly. Seems more the s2/s1 should have been s1/s2 to make eq. 2 positive, for it seems do want log(1/2) in the eq. 4.
But now to the substance. I downloaded the Geiger book, have read about a hundred pages and that is a well needed breath of fresh air. I’ll enjoy that one, thanks. I follow you up to equation four, then I lose the logic, the sign doesn’t bother me, the result 0.11 doesn’t bother me, I have tracked that lag here at my home over the last two summers and I was getting ~0.108, basically a match. But, equation three says if the depth ‘z’ is zero then the lag ‘t1’ is also zero. Right? This was Geiger saying the first part of the chapter was theoretical and he ends right after showing the actual empirical tautochron relation where you then expand. What’s you logic going from half gradient magnitude ratio across a depth in the soil to the temporal lag at the surface. I’ve tried but can’t seem to find your logical tie between the two and you don’t go very deep right at that point. Can you clarify?
The reason I ask these picky points is this plays directly into a global energy relationship I have working on (on and off) for a couple of months now, and thanks for the link to Geiger’s book, it holds some estimate numbers I’ve been looking for and it does have included a relation to lags also.

Willis: While these equations show how the time lag changes as you go down in a solid surface, I think the more relevant equations for the sort of time lags that you are interested in for the climate system is to start looking instead at box models for the climate system.
For example, a one-box model can be written in the form of a differential equation as:
C*dT/dt = F(t) – lambda*T.
Here, T is the temperature, t is time, C is the heat capacity (the specific heat times mass) of the system, lambda is a constant with 1/lambda equal to the climate sensitivity, and F(t) is the forcing vs time. If you have a periodic sinusoidal forcing of angular frequency omega and amplitude F_0, then F(t) = F_0*cos(omega*t).
These equations can be solved exactly in the long-time limit and the result that one gets is that the time lag varies as a function of omega*tau where the time constant tau = C/lambda. The easiest way to write the solution is that T(t) = the real part of (F_0/lambda)*exp(i*omega*t) / (1 + i*omega*t) where i is the square root of -1.
When omega*tau is much less than 1, the temperature response is roughly in phase with the forcing; when omega*tau is much greater than 1, the temperature response lags the forcing by pi/2, i.e., a quarter of a cycle. And, of course, for in-between values of omega*tau, you get a lag somewhere in between 0 and 1/4 of a cycle.
This result makes sense: If the system has a very small heat capacity, the temperature is basically just proportional to the current value of the forcing. If the system has a very large heat capacity, then the temperature increases when the forcing is above its time-average value and decreases when the forcing is below its time-average value.
With a two (or more)-box model, as is presumably necessary to realistically model the Earth’s climate system, things are more complicated. However, I think it is still true that the time lag will be somewhere between 0 and 1/4 of a cycle.