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.