Ignored Heat Capacity

Something that has often bothered me about climate models and rain water is how the energy transfer to the rock is handled.   Each climate model I’ve read seems to address the problem in similar ways with bulk conductivity parameters that appear to ignore anything but conductive energy transfer to significant depths with basic flows of energy at shallow depths.   The result is that there doesn’t appear to be much effective thermal mass in our land area on Earth.  The consequence of this is that  land thermal mass holds nothing of great effect with respect to global warming.   Climate models are absolutely missing something important here.

I’m not sure what reference would best illustrate the point,  Trenberth has a powerpoint presentation up at this link which summarizes the complex parameterization of climate model land usage.  The reference is pithy but explains quite clearly how modern science interprets ground thermal mass.


The rock is treated as a solid non-moving mass

Land:  Small heat capacity, small mass involved (conduction)

Water storage varies: affects sensible vs latent fluxes

Wide variety of features, slopes, vegetation, soils

Mixture of natural and managed

The heat capacity is treated as small which on the surface (some pun intended) seems reasonable.   However, conduction is almost always a minimal factor in a situation where fluids are present and physical mass flow exists.   In the surface of the ground on earth, we have significant physical thermal mass flow —>downward.   Always downward.. well nearly always anyway.

The magnitude of heat capacity

Did you know that a century of today’s worst case global warming heat can be stored in the deep oceans with only an approximate 0.1C rise in temperature and that 0.1c is leaves the oceanic mass very near freezing in temperature?

Did you know that the huge oceanic thermal mass is only 10% of the water in Earth’s crust?

In effect, the only thing which conceptually allows our temperature to measurably rise with today’s minimal CO2 forcing is the lag in thermal transfer to these huge thermal masses.  Oceans are said to mix on over-century timescales.  Water and ocean, conduction and convection effects are stated by modern science to be too slow and therefore dangerous warming can occur.  Interestingly, land thermal mass seems to have a very high transfer rate and is quite nearly ignored.   I don’t believe this very significant aspect of global warming has been vetted thoroughly and you shouldn’t either.

While we do have a huge amount of water on Earth and contrary to public schooling, will not run out due to human usage, we have a lot more rock in the Earths crust than we have water.

This is how modern climate science thinks of land:

Moreover, heat penetration into land is limited by the low thermal conductivity of the land surface; as a result only the top two meters or so of the land typically play an active role in heat storage and release (e.g., as the depth for most of the variations over annual time scales). Accordingly, land plays a much smaller role than the ocean in the storage of heat and in providing a memory for the climate system.

This type of paragraph is surprisingly common argument, presented as a mere handwave rationale to define the necessary land depths used in climate models.   While annual temperature invariance of deeper soils sounds like a reasonable rationale to cut off the depths of modeling layers, it fails to take into account the relatively lower thermal mass of water passing through the soil on an annualized basis, and the continuing nature of the increased energy input to that same soil caused by warmer atmosphere.

Another example of a climate paper which discusses only conductivity of soil without discussion of net flow.

It seems really obvious to me that the heat from rain, and the slow but regular downward convection of fluid through the massive amount of rock will lead to little seasonal temperature change of the soil but a very large heat storage device.   The capacity for this storage can easily eliminate the higher frequency seasonal variations and yet ignore the conductive heat transfer of decadal term climate signals.  The result would be vastly underestimated thermal absorption by the thin surface layer conduction models used in modern climate science.   As an example, California’s rain has to pass through hundreds of feet of rock before it reaches ground water.   Does anyone expect a few inches of rain to affect the seasonal temperatures of rock?  I don’t, but over time the heat from 0.6C warmer than average rain will certainly be stored there.   The heat will have a great deal of difficulty conducting upward due to low rock conductance and a continuing downflow of new rain water percolating through the rock material.  Yet conduction is what climate science recognizes and a few meters of surface material seems to be the critical part of land thermal mass modeling.

This is wholly inconsistent with the much better known science of hydrogeology.  Here is an article showing the age of water in a typical well. The oldest being ~ 300 ft deep and 30 years old.   So gradual down-flowing rain has been pushing extra heat from globally warming temperatures into this rock for at most 30 years.  A hundred meters of rock over 30 years as a typical measure of land mass thermal absorption.  The water went through the rock, the heat definitely reached equilibrium with the rock over that time and the water holding the global warming heat is still contained within the rock!

Of note, while the wells in the paper seem to stop at 100meters, the water certainly didn’t.

Do you think climate models take into account this massive heat storage capacity?

Here is what GISS had for ground layers in 2005

Continents: each 4×3 cell is
either all ocean or all continent
1. Resolution: fixed
fractions of continental cell are
ground, land ice, or lake,
ground can be partially covered by snow,
lake can be partially covered by lake ice;
ground has 4 layers plus fith layer for snow,
ground layer thicknesses: .0625, .25, 1, 4 (m);
land ice has 4 layers;
liquid lake has 2 layers,
lake ice is treated like sea ice

So we know from my link above that water can regularly get into a 100 meter well in 30 years or less, yet this climate model only calculates the first 1.4 meters, and apparently only for thermal conductivity.  I’m just not seeing the convection parametrization you would expect for downward water flow, not that I couldn’t have missed something in this model while reading another, but it does not appear to be there.

Numerous modern climate models suffer the same lack of depth (again some pun intended – sorry):

Our latest version, CRCM4.2 is even more in-line than CRCM 3.7 with the CCCma GCM3 package (Scinocca and McFarlane, 2004). The most important change consisted in the implementation of GCM3’s multi-layer surface scheme CLASS 2.7 (Canadian LAnd Surface Scheme; Verseghy, 1991; Verseghy et al., 1993) in the CRCM to provide a more realistic description of water and energy exchange between the land surface and atmosphere. Starting from the surface, CLASS uses three soil layers with thicknesses of 0.1 m, 0.25m and 3.75 m, corresponding approximately to the depth influenced by the diurnal cycle, the rooting zone and the annual variations of temperature, respectively. CLASS includes prognostic equations for energy and water conservation for the three soil layers and a thermally and hydrologically distinct snowpack where applicable (treated as a fourth variable-depth soil layer).

I know that in our house, we have a cracked basement wall, and after a very hard rainstorm our wonderful finished basement can get water in that particular corner.   The wall is 2.5 meters underground at the base and it takes literally hours for the water to reach that depth. We have had some specialists out twice for the problem and they will be coming back again.   However, 1 day isn’t an unreasonable expectation on any percolating soil to over 2 meters depth.    The increased heat added to the ground of a single rain at that depth is going to take months to measurably influence the rock, and if another rain hits, it will be dragged further downward instead of conducting up to the surface.  

The heat capacity of water is 4 Kj/kg-K  and the heat capacity of sand is 0.19 or about 21 times less than water.   However the density of sand is 1600 Kg/m^3 and water is 1000Kg/m^3.   If you get 0.1 meters of rain in a month, as we approximately do, an equal heat capacity layer of sand has a depth of 1.3 meters.  If the water is 1 C warmer, and was contained to 1.3 meters, then the land should warm by 0.5C at that depth and the water should cool by 0.5C.  In practice, the continuing downflow will carry that warmth to an even greater depth.  New rainfall continues the process, carrying the new heat ever deeper.

Of course we would expect very little monthly temperature variance at 3 meters depth because the thermal mass of the rock has dampened the variations in rain water temperature.  I hope I have explained well enough to show that while this thermal capacitance dampens high frequency signals, it does nothing to preclude energy from hundred year warming caused by CO2 from penetrating to great depths.

To me this is a very big problem with climate modeling.   It is not a minor issue to be brushed off as current modeling does, and this missing heat should be considered carefully.   Perhaps I’m missing something special here, it wouldn’t be the first time, but at this point I can’t imagine what that might be.



Update per request from Mark Cooper.  A typical soil temperature range vs depth in winter and summer seasons.  The graph shows net power flow is upward in the winter and downward in summer.  For some reason the graph won’t upload to wordpress, so the link is the best I can do.I tried to make the point that the net direction of heat flow is not the important factor with respect to global warming but rather the change in magnitude of heat flow due to warmer temperatures is the critical factor.  That may not be clear in the post above.












27 thoughts on “Ignored Heat Capacity

  1. Are there any long term temperature measurements at depth?

    If seems to me that if this theory is correct (and if the Globe is warming) the temperature 10 M down in porous areas should be at an all time high?

    The perfect test in other words.

        1. I found this somewhat interesting paper (abstract) http://www.ipgp.fr/fr/long-term-climate-change-and-surface-versus-underground-temperature-measurements-in-paris

          “Underground temperatures, unaffected by surface fluctuations and averaging procedures, show a 0.9 degrees C increase and thus confirm the trend indicated by the surface records.”

          Why aren’t the warmers trumpeting this? Could it be the warming has been consistent over a long time period? Prior to 1950?

          1. Here is another one using Borehole temps that is interesting http://www-personal.umich.edu/~shaopeng/annurev00.pdf

            This was the quote regarding Greenland.

            “Because these boreholes are deep and in a very-low-noise environment, they enable surface temperature reconstructions back through much of the Holocene, and well into the late Pleistocene at the GRIP and GISP2 sites. These reconstruc- tions (Dahl-Jensen et al 1998, Clow 1998, Clow & Waddington 1999) show that at the time of the last glacial maximum, ca 25 ka, the temperature in central Greenland was about 20–25 K colder than the present-day temperature there. From that temperature minimum, the temperature increased steadily to some 1.5–
            2.5 K warmer than present in the time interval 8–4 ka, a period sometimes referred to as the climatic optimum. The last millennium began with temperatures about 1 K warmer than at present, but by the middle of the nineteenth century these had cooled to 0.5–1.0 K below the present temperature in the closing stages of the Little Ice Age. The area then warmed again in the first half of the twentieth century, but it has cooled somewhat in the decades that followed.”

          2. Not to thread bomb but this chart on page 352 was very interesting.

            It shows warming definitely starting in the 1500 and gradually accelerating to today. Obviously they were driving SUV’s in the 1500’s to get the global warming rolling.

  2. Sorry, but I think you make a wrong assumption that heat flow is downward.
    The earth itself is a radiating heat body, which contributes about 45 Terawatts to the atmosphere.

    The average sedimentary geothermal gradient is about 2.5c per 100m. For Igneous rock, it is a lot higher due to radioactivity within the rock itself- it can be up to 5c/100m. So I don’t think +0.6c rain water will not have any impact…

    What I do find odd is that surface rugosity is ignored in climate models. Although the Earth’s surface land area is 29%, if you flattened it out with a giant rolling pin, it would cover more than 50% of the planet’s surface.

    1. Don’t brush this off so easily, the story is more complex than that!

      Soil temperature is an interesting thing.


      The gradient is first negative then positive in this graph depending on the season. This means that in summer months, the soil layer is absorbing (net downward) and in winter, it is emitting (net upward). Perhaps I should be more clear in the article but power is a mixed up language. The net direction of power is actually irrelevant to the article as the mass of the water is continually downward. Thus the change in power transfer from rain is continually downward. My point though is that the net magnitude of this long term downward movement is not insignificant. Large amounts of power are being transported downward through the rock being carried by the mass of the water. The heat capacity of a thick layer of rock is not insignificant in comparison to the power of global warming.

      1. Well, it’s all very complex, If it wasn’t everyone would be in agreement? 🙂
        Would be good if you include that sketch in your post?

        But I think even if the top couple of meters might be a temporary heat sink, over the year the net effect would still be heat flow from land to atmosphere… Slightly off topic, but I think that in winter, trees transfer a lot of heat from under the ground to the atmosphere by heat convection, one reason (IMHO) why trees that live in places with a cold winter do not freeze…

  3. Having looked at soil temperature I doubt water movement is important.

    Behaves as a thermal delay line. Related to this is some of UHI.
    Mentioned some of it in blog articles.
    Just remembered, if you go to my blog, not the Talkshop and type delay into the search box it will show two articles about delay, one has some real soil temperature data. This is corrected Armagh Obs. data, long story.

    Also needs remembering water movement upwards is via trees, a lot into leaves. An wind scour.

    For real fun, sublimation of ice, crosses two phase change points, heat is sum of the two.

  4. Yes Geoff the climate models all but ignore heat capacity. As Dr. Miskolczi stated in 2007 earth’s surface is treated as if it is a black body. A black body surface having no heat capacity.

    On a planet that the surface of which is 71% covered by on average 2.5 mile deep oceans it is ridiculous.

    If you want to find more equally ridiculous modelling assumptions that the current models still model all one has to do is read LFR 1922….

    For instance it is assumed wind, particularly local gustiness (omitted totally by the grid structure of the models) does not effect evapouration rates….

    There is a lot more to be said in a near future article I am currently putting together…

  5. Jeff,
    As I think you are saying, the issue isn’t whether there is a big thermal mass, but to what extent heat can get to it. So you are really saying that percolating water increases thermal conductivity.

    But moving fluid only advects heat when there is a temperature gradient. Once water enters a porous medium, temperature between liquid and solid is completely equilibriated. So moving water will only convey heat when the combined medium has a temperature gradient. The flux is ρ c_p v.∇T.

    And the numbers are small. Only a small fraction of rain escapes evaporation, rainfall and evap – say 100mm/year. Water might be 30% of the medium, and there are about 32e+6 seconds in the year, so that is about 1e-8 m/s. And of course, what goes down must come up. but let’s just look at downflow.

    ρ c_p is aabout 4e+6. The temperature gradient you want is the extra due to AGW – maybe 1°C over the thickness of the heat sink region – say 100m. ie |∇T| ~ .01 1°C/m.

    Put it together, and it’s 1e-8*4e+6*.01=.0004 W/m2. Truly negligible.

    1. Nick,

      Your comment is convincing. I need to read up on water volume deposited across the land of the whole planet but even at 10X your value it is still small.

    2. Nick,

      I agree that the amounts are not very significant but

      I am having problems with balancing the units:

      ρ c_p v.∇T.

      is I think Kg/m^3 * J/Kg/ºC * m/s * ºC/m = J/s/m^3 (W/m^3) which I think would be correct for the exchange of heat between the fluid and the substrate per metre squared of area per metre of depth, not the flux per unit area.

      I do not understand why you have corrected the velocity in the way you have as I believe it is the effective flow rate across the whole area that matters, not the actual velocity in this particular case

      So the result I would get would be more like 0.01 W/m^2.

      Sorry to be a pain.

      1. Would you mind putting in the values you used. I’ve read the comment a couple of times and can’t quite figure out how you arrived at 0.01.

        1. Hi,

          I have used the product of the mass flow rate 100Kg/Yr

          The specific heat ~4000 J/Kg/ºC

          The change in temperature 1ºC

          giving ~400,000 J/Yr =~ 0.013 W

          I think the actual temperature gradient and the depth are not needed only their integral, the change in temperature between the input and output boundaries, in this particular case.

  6. Jeff: I suspect you can draw some deductions about heat flux into and out of the ground by considering how far seasonal changes in surface temperature penetrate into the ground. In general, most caves have the same temperature year round – whether the cave is dry or wet. So the heat flux driven by a 20 degC seasonal change in surface temperature is negligible over six months. If you have a basement sump pump, that will provide access to ground temperature below the concrete floor in a basement. As long as the temperature in the basement remains fairly constant, any seasonal change in the temperature of the water in the sump should come from the surface. Footers and foundations need to reach below the “frost line” so they don’t heave when water in the ground freezes in the winter. Building codes call for digging holes at least 24″ below the surface where I live and the lowest temperature we experience for several days is probably in the single digits.


    1. Franktoo, sorry I duplicated your point about cave temperatures. A moving frost line would be expected as well, if serious warming into the ground was taking place. But that dog does not seem to be barking either, does it?

  7. Caverns and mineshafts should be decent proxies since they are subject to groundwater movement/migration and have existed a long time.
    If I recall caves are famous for stable temperatures in ~60.0o range.
    The heat sink of earth must be vast. The interesting point you bring up about the influence of sea bottom on ocean temps is one worth exploring more.

  8. Jeff, you’ve found the missing heat! Don’t squander it; disappear this post, write up a research proposal to measure the heat as the water seepage carries it ever downward, and apply for a research grant. Design your experiment so that you track the fleeing heat for several years, that way you can get a multiyear grant.

    Contact Trenberth, I bet he’ll be delighted to support your grant application (provided he’s lead author).


    1. I don’t know, I’m sure we can work something out. The heat is still interesting to me but I really think Nick is right and it simply isn’t large. Still need to look at it closer though but am working on a plant layout and can’t seem to get the time. It is pretty difficult to find useful information on the topic.

  9. I do not come to this blog often because there are too many “lukewarmers” who do not understand the basics of engineering science (ie thermodynamics, heat&mass transfer, fluid dynamics, reaction kinetics, engineering mathematics etc)
    Jeff you have obviously not been down a deep mine. i went down a mine in Canada when the surface temperature was around -35C in a blizzard. The ground was covered by metres of snow and ice. Underground some 900m down below sea level the temperature was around 20C. The temperature is a combination of the lapse rate (below sea level) and heat rising from the mantle. I was also down in a deep mine in a warm country. The surface temperature was about 30c but underground it was necessary to use air conditioning to have a pleasant working temperature around 30C. Some may have read about diamond mines in South Africa where miners can only work in conditions without air conditioning for 30 minutes.
    Engineering is about measured data and experience not as Feyman said of science guesses and hypothesis most which have no reality (as applies for CAGW)

  10. Cementafriend,

    I have of course been down a deep mine. Rock has a tremendous heat capacity so I don’t know why you would expect to feel a 1C change in the deep ground. This post is purely conjecture about heat transfer from rain water. The reason it is interesting to me is because the oceanic heat capacity is so large by itself that all of global warming could literally vanish within it with basically no change in water temperature. NIck’s quick calculation above shows that the rate of heat transfer due to the limited nature of rainfall is apparently several orders of magnitude lower than it would need to be to have any appreciable impact. I strongly suspect we could get a couple of those orders of magnitude back with slightly different assumptions but that still would be a really low and uninteresting transfer rate.

    As to your comments about lukewarmers misunderstanding thermodynamics, I agree that more people should take thermodynamics. It is an old argument here and rather a silly one IMHO.

  11. Sorry for the late comment but I find your article interesting.

    This inspired me to do a calculation as follows with assumptions stated

    Water covers 71% of planet surface area so a calculation for water might be a rough guide to overall effect.
    Water is reasonably mixable given the calculated long time obtained.
    Time chosen is length of time to raise mass of water by one Kelvin
    Accepting for the sake of the calculation the excess heat imbalance per square metre that worries the IPCC.

    Click to access lecture_03.pdf

    Formula used

    Power x Time = S.M.∇T.

    p = net climate imbalance( IPCC) figure = 0.58w/m2
    S = specific heat capacity = 4200J/kgK
    M = mass of water =1.35 x 10^21kg
    ∇T = one Kelvin

    Excess heat supplied by Sun to water = 0.58 x surface area of water = 0.58x 3.6×10^14

    Time = 5.67 x 10^24/ 2.09 x 10^14

    Time taken = 860 years

    => I won’t lose any sleep tonight worrying about global warming!

    1. Bryan,

      This is the same reason I don’t worry about global warming doom EVER actually happening.


      It simply isn’t possible for CO2 to create dangerous warming and a lot of ‘scientists’ know it. For it to occur we have to assume there is unreasonably low heat mixing in the oceans and that somehow the amplification from water in the air is ridiculously high. It simply isn’t something I’m going to lose any sleep over.

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