Energy for Future Presidents

Physics for Future Presidents

by Richard Muller, physics professor at UC Berkeley. Cofounder of the Berkeley Earth Surface Temperature project.

Notes inspired by the books. Work in progress, I will inform Dr. Muller when more complete.

Better explanation of CO2 warming based on adiabatic cooling with altitude

The usual explanation of increased CO2 "thickening" the atmosphere is easy but wrong. It attracts a lot of skepticism from the 80% informed, as I was before I learned some atmospheric science. A better explanation is slightly more complicated, but it can convert informed skeptics into informed believers. The climate debate needs fewer smart people poking holes in careless parodies of the scientific arguments. If you show more respect for your intelligent audience, they will show more respect for you.

The "temperature of the earth" is an equilibrium between the black body emission of the earth and solar input. The "earth" as viewed from space is "colored" infrared ball, at some wavelengths the top of the opaque CO2 layer, at other wavelengths the top of the opaque water vapor layer.

Temperature decreases with increasing altitude. One can think of this as the gas molecules slowing down as they move upwards, or as the energy lost due to the work performed as an adiabatically-isolated volume of gas rises and expands and cools. The cooled gas has a much lower vapor pressure of water - the excess water condenses and falls. Above the tropopause, there is very little water, so the infrared bands blocked by water vapor can radiate freely into space. In those bands, the earth appears opaque at the tropopause, and the radiation in those bands is the black body radiation of gas at the temperature at the top of the tropopause. If the bottom of the atmosphere gets warmer, the tropopause moves up, so that the temperature lapse rate ( temperature per vertical distance) stays approximately the same.

Since CO2 does not condense at atmospheric temperatures, its pressure versus altitude decreases exponentially, but never drops abruptly to zero. As it gets thinner, the absorption length goes up inversely proportional to density. When it gets thin enough, it approaches transparency in its absorption bands. The temperature of the atmosphere at that altitude determines the black body radiation in those infrared bands.

So, if the CO2 density lapse rate is 5km (WAG), and the CO2 doubles, then the "transparency altitude" moves up by 3.3km, colder by the temperature lapse rate of (6.5K / km ) or 21K. To radiate the same amount of heat in the IR band, it would need to increase the temperature at those altitudes by 21K - which means increasing the temperature of the whole column underneath by 21K, all the way to the ground. Fortunately, the CO2 opacity wavelengths are only a small percentage of the whole IR spectrum, so the net result is a small percentage increase of 21K, with a little more IR emitted by water vapor and a lot more by the surface. Much depends on the IR albedo of the surface, which is a lot lower for ocean water than for sea ice, so increased temperatures at the poles and on land will send significantly more heat into space.

The exponential decrease in pressure with altitude is ultimately where the observed ln(P,CO2,) temperature dependence comes from, not a "widening of the CO2 absorption band with temperature". Do the math.

Of course, the whole picture is complicated, and while the atmospheric scientists are making great strides with models and measurements, they are still struggling to produce simple but accurate explanations that fit into sound bites. The "heat blanket" sound bite is simple but misleading, and creating a lot of opposition. Better explanations, probably relying on computer graphics and analogies between IR and visual color, would go a long way towards adding accuracy to "both sides" of the debate.

CO2 increase - don't ignore agriculture

Note: I need to find a good graph of CO2 versus time back to 1750. Most of these graphs start at 1900CE, when there is already a distinct upslope in CO2. This is not commensurate with global industrialization rates, but is strongly related to the clearing of forests and their replacement by tillage agriculture, which releases enormous amounts of CO2 into the atmosphere from wood and soil.

This is not to say that agriculture is to blame for CO2 increases, and mechanical CO2 creation is not. However, if our agricultural practices generate more CO2 than wild nature does, and sequesters less, then we should minimize the amount of agriculture we do, no more than that necessary to feed the world's population. If "green energy" increases the amount of agriculture, or replaces wild lands with sunlight-blocking solar cells, then it increases CO2, and does not reduce it.

While the ocean contains far more CO2 than the air, there is far more carbon in soil and rock than both. The carbon "long cycle" is the biological injection of carbon into soil and rock. Weathered rock contains potassium and phosphorus - plant roots replace those cations and anions with carbonates, absorbing the nutrients and binding the carbon to the rocks. This is a slow process, but steady. Between the building of deep carbon-laden soils (mostly humus), the carbonization of rocks, the volcanic burial of rock, and the accumulation of plant and animal remains on the sea floor, in the long term life buries carbon, adding it to land and ocean bedrock.

So the big question is whether agriculture, and recent changes for higher productivity, increase or decrease the long term geological sequestration of carbon. It is plausible that many of our high yield crops, fed with artificial fertilizers, do not send down deep roots to wrest these nutrients from the soil and rock. Less root means more biomass for food. That is a good thing in that it reduces the land needed to feed the world, but it comes at a price of reduced carbon sequestration in the soil. If we plow up wild lands to plant shallow-rooted biofuel crops, and feed those crops with energy-intensive fertilizers, we are doing far more harm than good.

Most "deserts" are lands unfit for pasture or crop agriculture - but very few are lifeless. Desert biological productivity is surprisingly high (higher than Iowa farmland, for example), but occurs in the crust of the soil, conserving scarce water by not creating tall evaporative leaves and stalks. Most of the world's mineral deserts are the result of prehistoric herding, which stripped the land of the fragile grasses and ground cover that held down the sand. Now they are sand dunes. While those dunes reflect a lot of sunlight back into space, and convert less to heat, they are not compatible with life. We should think long and hard before we turn living deserts into "solar deserts" of PV cells, creating an expensive dribble of electricity while destroying a vast amount of CO2-sequestering life.


220 ppm CO2 is 60 ppm elemental carbon. The air column has a mass of about 10,000 kg/m2, so assuming uniform vertical mixing that is about 600 grams of carbon per square meter. If 15% of the earth's surface is fertile enough to grow some kinds of plants (including most non-mineral deserts), that is around 4 kilograms of carbon per square meter in fertile areas. For an average soil depth of a meter, and an average density of 2000 kg/m3, then an additional 0.2% carbon-by-weight captured in the soil will sequester 220 ppm CO2. Carbon is good for soil - the deep, high carbon terra preta soils in the Amazon basin are very good for agriculture compared to the low nutrient clay soils nearby.

Some of the permaculture community is enamored of biochar; so am I (unless I learn something different). This is the heating of organic waste to drive off the volatiles, leaving a charcoal residue that is buried in the soil. Besides sequestering carbon, the charcoal buffers the soil pH, and makes large surface areas of microcavity pores for bacterial substrates, while impeding their consumption by nematodes and other larger-but-still-microscopic predators. The whole story is probably very complicated, and deserves deep study by agricultural and soil scientists. But if we can store kilotons per hectare of carbon in deep soils, we've gone a long way towards cleaning up the atmosphere.


Liquid methane for aviation

First things first - before greatly expanding shale gas production, we need to manage water better:

Jet aircraft may be the best transportation use for methane, possibly from fractured shale. Tupolev is designing planes to run on natural gas. Unlike passenger vehicles, aircraft travel between major airports, with fuel systems operated by professionals. Aircraft fuel is stored in huge, easy to insulate tanks. Liquid methane must be kept cryogenically cold, but the heat of evaporation can maintain temperature for the duration of a flight. If the tank and liquid are pressurized, that may require wing redesign, but the pressure can help stiffen the wing, much like the thin tanks on the Atlas rocket. LCH4 is only 60% as dense as normal jet fuel, but the energy per weight is higher and fuel cost and the pollution are lower. This increases fuel economy, lowers takeoff weight, and makes aircraft operation cheaper. This reduces the need for a recooler after the intake compressor in the engine. Under pressure the boiloff displaces air from the ullage above the remaining liquid. Managed correctly, this should prevent air-fuel explosions like TWA Flight 800 in 1996.

Drawbacks: The cryogenic liquid can lead to icing, stuck valves, and mechanical problems in the wings. There may be safety problems while maintenance crews learn new techniques and procedures. Ultracold metal can be more brittle.

Wikipedia paragraph about LNG for aviation

Magnetic/Ballistic Power Storage Loop

Flywheel speeds are limited because the structural mass rotates - even very expensive carbon fiber has a limited strength to mass ratio, so v2 is proportional to a×r and S/ρ .

Magnetic levitation is weaker than structural materials, but a magnetic field is massless. The strength of a magnetic field is \mu H^2/2 ; for an average 1 Tesla field, that is 800KPa .

Imagine a horizontal rotating ring of iron in vacuum (axis pointed vertically, supported by magnetic levitation, with very strong stationary electromagnets inside the ring providing centripedal acceleration. By Earnshaw's theorem, the magnetic suspension is unstable, but the ring-to-magnet spacing can be controlled by distance measurement (optical, capacitance, ...) and rapid (10s of microseconds) electronic adjustment of the electromagnet current. If the ring has radius R, height H, velocity V, and mass M, then the pressure P_R necessary to counteract centrifugal acceleration is P_R = M V^2 / 2 \pi H R^2 . The energy E stored in the ring is E = \pi P_R H R^2 . Unlike a flywheel, a small ring does not store much energy, but a very large ring with large R can move incredibly fast and store a huge amount of energy in ordinary steel, costing perhaps $300/tonne.

If the ring is a meter high, a centimeter thick, and the diameter of an agricultural pivot irrigator (1km), it weighs about m = 80 kg/meter, or 250 tonnes for the ring (the stationary magnets weigh more). the velocity is \sqrt{ P_R H R / m } or 2200 m/s , and the energy stored is 6.3e11 joules or 170 MW-h , as much as 6800 Beacon Power flywheels.

This is proportional to R2.   A ring 12.5 km diameter would use 10 times as much material, 12.5 times as much power for the magnet windings, 12.5 times as much electronics. But it would move \sqrt{12.5} times as fast ( 7900 m/s ), store 12.5 times as much energy per meter, and 156 times as much total energy as a 1 km diameter ring, in this case 26 GW-h, more than a million flywheels.

7900 m/s is interesting - it is orbital velocity. If we cut our ring in half, and insert long straight sections between the halves, we add total mass and total energy storage without increasing velocity. The "straight" sections follow the curvature of the earth. Nominally they do not need magnet support - but since we are speeding and slowing the loop to add and subtract energy, and we must move the rotor during earthquake accelerations, we will need about 800 Pa/meter of control magnets - about 0.1% of the magnets needed for the D shaped turnarounds. If we added 180 km of straight section, the energy stored goes up 10X. This loop would store 260 GW-h, perhaps 160 GW-h recoverable from speeds between 4900 and 7900 m/s (slower than that, and we need to put more average power into our straight section magnets to provide lift). The two straight sections could be converged into one track for most of the distance, perhaps under a railroad right-of-way.

7900 meters per second is fast - if the system breaks and throws chunks, they go a long way. This must be deeply buried - but we can use horizontal well drills to make the tunnels, or put it underwater.

If a sand particle gets loose between the moving iron rotor and the stationary magnet track (stator), it may cause a "hypervelocity spalling cascade", with material from the rotor knocking loose material from the stator and vice versa. But we can make the rotor thicker and slower, increasing the mass of the rotor and the straight section magnets while reducing the velocity and the spalling energies. We can also coat the rotor and stator surfaces with diamond (now a common industrial process), which is lighter and stronger - less energy per particle, and more tightly bound surfaces.

Imagine a loop running underwater, following the continental shelf around the Pacific, from China past Alaska to Mexico, and back, a total length of around 30,000 km. This loop could provide 12 terawatt-hours of usable energy storage, while efficiently sharing power between the US and Asia. The loop would be expensive - perhaps 30 billion dollars at 1 thousand dollars per mass-produced meter - but if the cost difference between peak and trough demand prices was 1 cent per kilowatt hour, it would produce 120 million dollars per cycle. With two deep cycles per week, it would pay for itself in 2.5 years. In 2012, the peak-to-trough prices vary a lot more, but a very large system will eliminate most of that variance.

This is all wildly speculative, and will need a lot of development, but the physics is well understood. See for more.

380 Trillion Terawatts


Muller (last edited 2014-12-09 18:11:10 by KeithLofstrom)