Jan 01 2012

Incomplete Global Climate Equations

Published by at 11:45 am under All General Discussions,Global Warming

I know planet-wide science is still very much in its infancy, since we have only in the last 40 years really started exploring our solar system in detail and understanding how planets might work. But one thing you begin to realize rapidly when dealing with space is the issue of scale. A global scale is very hard to get your head around. And sometimes our graphical representations can confuse or mislead us – instead of enlighten us.

For example, the radius of the Earth is on the order of 6,353 – 6384 km (3,947 – 3,968 miles). Another fact is that at the end of 2004 (which is the year for which I found the image I was looking for) there were 367 Geosynchronous Satellites orbiting the Earth. How are these two facts relate? This is a fairly standard representation used for GEO satellite orbital slots around the globe:

Looks damn crowded doesn’t?

But it is an illusion created by the need to get a lot of information onto a small diagram. Nothing (and I mean nothing) is to scale. The Earth’s circumference is 24,901.5 miles (40,075 kilometers). If these satellites were sitting on the ground they would each be 67.8 miles apart.

But they are not on the Earth’s surface. They are in geosynchronous orbit which is approximately 42,164 km (26,199 mi) from the center of the Earth – or over ten times farther out than the surface of the Earth. So you can see how this diagram fools the mind. If to scale, the satellites would be microscopic and far apart.

It is this challenge to think on global scales which, in my humble opinion, has led a lot of people down dead end paths. We keep discussing fractions of degrees extrapolated over 500-1200 km scare grids as a feasible precision (CRU and GISS). The variance on any one day over 100 km is on the order of 2-3°C, so it is impossible to claim we know the mean temp to a tenth of a degree for any month in any given year for a grid box 500-1200 km without hundreds of samples inside the box. We don’t have those hundreds of samples.  Temperature is way too dynamic to take a point measurement and pretend you have measured the region around it for 100′s of kilometers.

My analogy would be to measure ocean wave height in one place, and then pretend you know ocean wave heights to the cm over a 500-1200 km grid. Fantasy.

Anyway, in all climate calculation we only see two elements to the equation: solar flux (and not all that accurately either) and atmospheric factors. Some folks have recently come out with more accurate models which try and actually represent the global physical processes (see here and here for the postings, here and here for my comments).  But they are still woefully incomplete in my opinion. It was a post by Willis Eschenbach on sea temperature data that had me throwing my hands up in frustration at the myopic nature of this debate  (I’m just a lowly engineer and theoreticians sometimes forget they need to sometimes come back down to reality).

Here is the comment:

In addition to the amount measured by Argo floats, Figure 4 shows that there are a number of other oceanic volumes. H2011 includes figures for some of these, including the Southern Ocean, the Arctic Ocean, and the Abyssal waters. Hansen points out that the source he used (Purkey and Johnson,   hereinafter PJ2010) says there is no temperature change in the waters between 2 and 4 km depth. This is most of the water shown on the right side of Figure 4. It is not clear how the bottom waters are warming without the middle waters warming. I can’t think of how that might happen …

At which point I go ARRGHH!

The missing portion of all these equations is the heat coming from the Earth’s core. This really what keeps our planet from freezing (not those green house gases). We always begin with a baseline warmth emanating from underground. But that is not the full story. Because this heat flow is not steady nor constant – no well understood.

Let’s look at the scales we are talking about:

This diagram illustrates how little crust separates us from the hot core of our planet. Ocean crust is only 5-10 kilometers in depth – a thin slice on top of a mass of heat. The core is estimated to be 7000°K, so why are we ignoring this mass of molten metal and hot rock below us in understanding where our heat may be coming from? More here.

Heat flows constantly from its sources within the Earth to the surface. Total heat loss from the earth is 44.2 TW (4.42 × 1013 watts).[12] Mean heat flow is 65 mW/m2 over continental crust and 101 mW/m2 over oceanic crust.[12] This is approximately 1/10 watt/square meter on average, (about 1/10,000 of solar irradiation,) but is much more concentrated in areas where thermal energy is transported toward the crust by convection such as along mid-ocean ridges and mantle plumes.[13]

The obvious answer to Eschenbach’s confusion on what could warm the bottom layers but not the top is obvious. As is the fact the average heat flux from the core is an estimate! What are the error bars? We really don’t have the data to know precisely how much heat is released at any given month or year. It is not steady, and it is not trivial.

So, we have this large heat pad under our feet with massive hot spots along tectonic plate boundaries, most of them under our oceans at their deepest points. See here (click to enlarge).

Since we have barely explored the ocean depths, we barely understand these massive physical processes today, let alone 10, 100 or 1,000 years ago. Any halfway decent energy model would begin with a dynamic core heat source that can heat large amounts of deep ocean water, water which will arise decades later to the surface at upwelling zones. In my view, the oceans are the primary absorption point for energy (not the atmosphere).  It is here the energy from the Sun and Earth’s core is trapped and used to maintain the global temperature balance. This approach puts the primary solar and core heat absorption layer at the oceans (and land, though this portion of the Earth is not as good a heat sink), which are basically at the Earth’s surface.

In my view the atmosphere is a minor attenuation layer that must be taken into account for absorption and emissivity flux, but it is not the driver for thermal balance. It plays the same role as the crust does for the core heat a barrier that attenuates the energy flow, is not the source of the energy. This is completely at odds with the ‘conventional thinking’ – something I have become used to in my life.

Secondly – as the new climate models have discussed – the energy emitting surface of the Earth is many kilometers above the surface of the Earth at the top of the atmosphere. This makes the emitting surface larger in area than the absorption layer of ocean. If our temperature was all solar based, we would have many times the emissivity area than the solar heating area and I doubt we would still be warm. And let me explain why.

The area of solar heating is not as large as one might assume. Yes, we get sun on half the planet, but the solar energy supplied dissipates rapidly with the solar incidence angle:

Figure 2
One sunbeam one mile wide shines on the ground at a 90° angle, and another at a 30° angle. The one at a shallower angle distributes the same amount of light energy over twice as much area.

As the physics shows, at  30° incidence angle the solar energy is cut in half. This means at 60° away from the Sun’s vector, the solar energy has dropped in half.

So while one side of our globe is dark and emitting energy to space , we are not actually getting the full solar flux across the other half in day light, as roughly depicted below:

So we have the entire surface of the Earth being heated by the core, but not in a uniform manner given the mid-ocean ridges and subduction zones. We have the entire top of the atmosphere emitting energy into space (even on the day side). And we have a small circular area around the Sun vector absorbing 100% of the solar flux, which dissipated with angle of latitude and longitude until it reaches 50% at 60° off the solar vector and hits zero at the day night terminator.

Note: This absorption flux is the maximum possible, which will be degraded further by atmospheric effects such as clouds and particles,. These effect become much stronger with lower incidence angle as well, since the solar energy has to travel through much more atmosphere. This is why you cannot use the total solar flux in equations. It must first be degraded by incidence angle and then again by distance traveled through the atmosphere (something we do at NASA all the time when computing RF link performance for LEO satellites).

So any reasonable energy balance model for a point on the Earth must begins with:

Core Heat Transfer + Solar Flux – Energy Emission to Space = Mean energy level over time t

Note here you cannot do an instantaneous equation. For any point on Earth it has to be computed no only a Daily result (to properly model the solar flux incidence over the daytime period), it must then again be computed over the year (to address the season incidence angle effect). It is only over a year that can you truly calculate the maximum possible energy input from the sun (assuming Core Heat Transfer and Energy Emission to Space are steady).

This is all prior to all the atmospheric attenuation effects, which are very dynamic. The atmosphere’s attenuation effect, as discussed above, changes daily with solar incidence angle. It also has a highly dynamic cloud component. And then there are local surface conditions (is the area heavy with vegetation, are the seas calm or choppy, is the ice flat or crumpled). I have yet to see any model that comes close to reflecting the real world dynamics and variation. It is like only using Newton’s gravity equations in aiming long range projectiles – it will never work because Newton leaves out too many other effects like atmosphere and projectile shape, spin, etc.

Is the core heat steady or constant? No, not at all. Another factor that cannot be treated as a geographic or long term constant. Solar flux can be modeled on a daily and annual basis considering incidence angle. Atmospheric effects can be bounded (clear vs. cloudy, ranges of particles, distance traveled by solar radiation, etc). But the dynamics of the core heat transfer are much less defined. I still think we ignore this mass of molten rock and metal at our own risk of continued ignorance.

But all this is still only a local model. To get a regional or global solution, you need to then perform some form of finite element energy transfer across the Earth’s surface – as we do on satellite structures to map the solar and internal systems’ heat flows and dissipation. [Interestingly enough, in space overheating can be more of a problem than cooling.] Only by finite element modeling are you going to create the base energy transfer model of the globe. Now you don’t need to go down to the square meter for each element, but each element has to be characterized in terms of Core Heat and Solar Flux to some degree of fidelity.

I know PhDs like to assume all these real-life dynamics away when creating theoretical models, but you can only do so by adding uncertainties to the results. If you assume constant core heat flux, then you have to add the uncertainty due to literally ignoring the fact core heat flux is not constant in space or time, nor is it well understood. That is how we lowly engineers apply theories, we work out the real life kinks so conveniently bypassed at the theory stage. Same for all factors in the equation, and the variability of the Earth.

As usual, it all comes down to uncertainty and confidence levels. People like Mann and Jones were over-confident with their simplistic models. Laughingly so. They wished away reality and reality came back to bite them.

If you want to know the effect of a minor atmospheric gas on the energy balance of a planet, you don’t begin by reading tree rings and then create assumptions to fit your preconceptions. The answer is neither in the tree rings nor tea leaves. It is in understanding the physical system under scrutiny and dealing with it. And at the planetary scale these are large, dynamic and not well understood.

8 responses so far

8 Responses to “Incomplete Global Climate Equations”

  1. crosspatch says:

    It doesn’t really matter anyway. We are wasting a huge amount of money and resources fighting a non-problem.

    Ok, look at what happens if we do absolutely nothing:

    1. At our current rate of increase in consumption, the price of conventional fossil fuels begin to rise. I am not saying they run out, I am saying that as the easier sources of them are exhausted, it becomes more expensive to extract what remains. Or put another way, as the price rises, more expensive to extract sources become profitable.

    2. As those prices rise naturally, other sources of energy become more cost effective without any subsidies. As prices naturally rise for coal and oil, nuclear, for example, becomes much more cost effective than it is now.

    3. At some point the remaining fossil fuels are too valuable for uses such as paints, plastics, fertilizer and other chemical production to simply burn up. In other words, as the prices rise for oil, everything that has a plastic part anywhere in it or is packaged in plastic or is painted or made of synthetic rubber becomes more expensive. Coal and oil simply become too valuable of a raw material to simply burn up.

    4. At current rate of consumption we might have about 100 to 200 years of supply. If rate of consumption rises only 2% per year, we double our consumption in 35 years. This means that simple math tells us that the entire CO2 from carbon fuel emissions problem is very temporary. It may last only 100 more years and then it’s done.

    5. In the meantime the biosphere responds to increased atmospheric CO2 by scrubbing carbon out of the atmosphere at an increased rate. “Carbon fertilization” impacts result in CO2 being extracted from the atmosphere faster the more CO2 you put in. The moment we stop growing CO2 emissions from carbon fuels, the amount of CO2 in the atmosphere from human activity will begin to immediately decline. In other words, atmospheric CO2 is a self-mitigating problem. Our planet is pretty good about removing CO2 from the air. In fact, it is only the overall balance of CO2 emitted from volcanoes offsetting the CO2 removed by biotic and geological scrubbing from erosion that keep us with enough CO2 to support plant life as it is.

    6. Over the thousands of years CO2 content of the atmosphere has been falling as it is deposited in insoluble carbonates. During the last glacial maximum the atmospheric CO2 fell dangerously close to the minimum required to support most plant species alive today. We are very close to an all time record low CO2 content in the atmosphere. Most plant species alive today evolved when CO2 levels were many times higher than today’s levels.

    7. If we do absolutely nothing, we could end up with a brief period (few hundred years) of elevated CO2 that will begin to be scrubbed out as soon as that consumption rate falls.

    During the Paleocene–Eocene Thermal Maximum there was an absolutely HUGE spike in atmospheric carbon. It lasted for about 20,000 years. Within 200,000 years, the atmosphere had returned to its previous level of CO2. During that period, mammals flourished. But the point is that we saw an injection of an absolutely huge amount of CO2, much larger than what we are doing today with fossil fuels, over the course of time about equal to a single interglacial period and CO2 levels returned to “normal” levels (for that period) within a span equal to two glacial cycles in today’s climate.

    The worst possible consequence of CO2 increase would be a brief (in a geological time frame) increase in sea levels probably lasting less than 1000 years before they begin to recede IF CO2 plays any significant role in temperatures at these levels (which is not proved).

    So if we do absolutely nothing, we might get a little sea level rise but we know that Greenland will not melt and neither will Antarctica. Antarctica has been covered with ice since global temperatures were many degrees higher than now. Greenland didn’t melt in the last interglacial when global temperatures were about 5 degrees higher than now. It is not likely that we will manage to increase Earth’s temperature by 5 degrees C even if we tried to.

    The simple answer is that doing nothing at all is the most cost-effective way of dealing with this temporary problem.

  2. [...] Incomplete Global Climate Equations [...]

  3. Redteam says:

    AJ, very good post
    CP, excellent assessment

    Of course we all know that more and more oil and natural gas is being discovered every year and that the known and proven reserves are now enough to basically last forever and each year that time gets extended. So it’s pretty safe to say the world will not be running out of energy, ever.

    I wonder how the average temperature of the Red sea has changed recently since a new island just sprang up, from a volcano.

    It’s safe to say that very little is known about the historical temperature of the earth (to the nearest 5 degrees or so)

    And I would have thought that all scientists would have known that most heat contained in the oceans is from the core of the earth. I never would have assumed it to come from the sun. Heat from the sun appears to be retained on the earth only for a short time, whereas the majority of the heat comes from the core.

    So, CP, the answer may just be, drill, baby drill….

  4. crosspatch says:

    What people really need to be concerned about, and particularly in places such as the Northern plains and in Canada is the very real possibility that we are headed into a period of significant temperature decline that could result in a shortening of growing season. The historical paleoclimatological record shows us that we experience downturns in temperature when we have weak solar activity. This solar cycle is currently the weakest cycle we have seen since the late 1800′s. The indications so far are that the following cycle will be weak as well.

    If that is the case and if we do head into a period of significant cooling over the next few decades, farmers in those areas will need to adapt by planting varieties that are more tolerant of cool temperatures and have shorter growing seasons.

    If this period of cooler temperatures, God forbid, is amplified by a major volcanic eruption, we could see a major disruption in the global food supply. We will have at least another 20 years of solar activity below the recent norm if cycle 25 is as low as it is looking like it will be. That gives us a 20 year window of vulnerability to such an event having a much greater impact on climate than Pinatubo had during a period of strong solar activity and temperatures were warming.

    The record also shows us that climate regimes can change very quickly. You can get a major change that settles in within only a couple of years and lasts for decades. We need to have plans on the shelf right now on how we are going to adapt to that. Do we have an organized plan right now to shut off biofuel mandates (the subsidies were already shut off but some places like California mandate ethanol in the fuel regardless of subsidy) so that grain can be diverted to food? Do we have a plan in place in such a circumstance to lift restrictions on energy production so that we might produce enough energy to heat cities such as Minneapolis and Chicago in an extremely harsh winter?

    We can deal with a 2 degree rise in temperature without any problem. We can’t deal with a 2 degree drop. An early frost or a freak frost at the wrong time can kill a crop over an entire region. How are we going to deal with the potential loss of that much food?

  5. AJStrata says:


    I agree we have more potential concerns to ‘adapt to’ than higher CO2 levels in the air. One good note, the higher CO2 could offset the lower solar flux because higher CO2 makes the plants more efficient, and from there the rest of the food chain can be supported.

    I recently dropped a comment at WUWT regarding that excellent video summary they have posted (plan to repost here). My point was, after they concluded warming since the late 1800′s could be as low as 0.3°C that it might mean we are not all the way out of the LIA. We have no idea how long it will take to return to the Medieval or Roman warm period levels. None.

    The alarmists have no idea how many unproven assumptions form the foundation of their concepts and theories. They are only now facing the fact their data is crap and their statistics are malformed from a deep desire not to be wrong. But those are only some of their problems.

    Using the uniformitarian principle to assume ecosystems and their species are steady over time is another blatant error (or else Darwin is wrong!).

    So why not also be wrong about the LIA ending?

  6. WWS says:

    Excellent post, AJ, excellent comments, CP. Nothing to add except one note about the LIA – there’s no guarantee, and it actually appears unlikely that we will get back to the temperature levels of the Roman warm period. When you look at the post-glacial temperature record for the last 12,000 years (since the end of the last ice age) there is a slow but measurable decline in the temperature level, interrupted by anomalies and recoveries such as the LIA of the 1600′s and 1700′s.

    Put another way, each temperature recovery to a warm period goes to a little bit lower level than the previous cycle. It does look like we are eventually going to end up in another ice age at some point, but hopefully we still have a few thousand years before we get there.

    or at least a few hundred.