Physics of a reduced global atmosphere

I have been trying to answer a simple question:

“What would happen to our climate if the earth had slightly less atmosphere”

In other words, in which direction would various parameters like temperature, windspeed, precipitation head? What follows is my first attempt to list the possible effects.
Note: I am assuming that a chunk of atmosphere with all the constituents is removed so that (initially) there is no change in proportions of any constituent gases and that the planet allowed to reach a new equilibrium. Also the change is not large enough to cause any dramatic crossing of any threshold or “flip” in the climate.

Pressure

Starting with the obvious, because pressure is the weight of atmosphere divided by surface area, the pressure would drop in proportion to the loss of atmospheric weight.

Oceans gas reserve


There is a huge gas reserve in the oceans. I calculate it thus:
Solubility in sea water of gas @ 4C is about 10mg/l at 1atmosphere, but increases proportional to pressure and so depth. Assuming this relationship holds, at an average ocean depth of 3.5km, bottom pressure would be around 350atmosphere and so the oceans would range from 10mg/l to  3.5g/l and thus the average dissolved gas would be around 1.75% by weight. With ~350 times the weight of ocean as atmosphere and 70% of the world being oceans, this suggests that the oceans hold around 4 atmosphere’s worth of gas.
Thus I expect the long term change in atmospheric pressure to be around a 1/5 of what would be expected if only considering the gas in the atmosphere.

Dry Lapse Rate

Because the specific heat capacity of air per kg is fairly constant with pressure and because dry lapse rate is related to the gravitational acceleration and specific heat capacity, neither of which would change dramatically, then the dry lapse rate would remain the same.

Greenhouse effect (pressure only)

Based on the dry lapse rate, because the atmosphere is thinner, the the average height from which radiation would leave the planet would drop. This means that IR escaping from our planet would come from lower layers of the atmosphere with hotter molecules. This would increase IR loss and therefore result in a cooling of the planet surface.

Moist lapse rate

The moist lapse rate is affected by both pressure and temperature. In normal atmospheric conditions, it increases with lowering temperature and decreases with lowering pressure. Thus because the reduced greenhouse effect means surface temperatures lower with pressure, the two will tend to cancel each other out. However as the greenhouse temperature change is log of pressure, the  greater change is likely to be from the change in pressure rather than overall temperature, so the moist lapse rate should decrease.
This means clouds will tend to extend higher and be less dense.

Greenhouse effect (pressure + moist lapse change)

The total lapse rate will be slightly lower than the standard value that is usually quoted (6.5C/km). Therefore, the greenhouse effect will be lower than expected decreasing planetary temperature even more.

Relative humidity

The overall temperature will drop reducing the water carrying capacity of air. Likewise a drop in pressure also reduces the water carrying capacity of air. Therefore less water will be evaporated from the surface and the importance of water as a heat transport mechanism will reduce. This suggests a change from water-induced cooling of the surface toward IR loss directly from the surface which in turn suggests a change from cloud to more open skies.

Solaration & daily/annual temperature

At high altitudes there is higher proportion of shorter wavelength radiation (violet and ultraviolet), which does not penetrate to lower elevations. This will be the same with lower pressure. Thus there will be more intense radiation both incoming and outgoing. As a result, the diurnal (annual) range of air temperature increases as a result of higher incoming solar radiation in the daytime (in summer) and outgoing radiation in the night-
time (in winter).

Thermal air movement

The heat capacity of air per kg stays the same, but at reduced pressure per volume of air it reduces, and the insulation of the air increases. Therefore, it is less easy to heat air and the scale of  heat transport will reduce. Again this will see a movement away from thermal movement of heat from the surface toward direct IR loss. However countering this to some extent will be the higher differentials in temperature which will tend to increase the thermal heat transfer from warmer to colder areas.

Wind

The quantity of thermal energy moved by rising air and thus driving the winds will reduce, but the mass of that air will also reduce so tending to cancel each other out. The higher differentials from day/night and summer/winter should help to increase wind speeds, however it should be noted that even on Mars with an atmosphere ~1% of the earth’s the wind speeds are similar.

Clouds

Less overall water will be carried into the atmosphere, but the relative humidity may be higher due to more intense solaration during the day and greater transpiration from plants. With the same RH, clouds would form at a similar height, but with higher RH, the cloud base will lower. However with less water per cubic meter, the rate of condensation and thus rate of increase in size of droplets will decrease. Thus clouds should be less dense.

Precipitation

Both lower atmospheric pressure and reduced air movements, should lower the size at which water droplets can no longer be held aloft by rising air and begin to fall as rain. Therefore the size of water as well as overall scale of precipitation should drop. Also, because of lower temperatures, more precipitation would fall as snow.

Land animals

Except for some very high altitude plants and animals, there is a great deal of tolerance to lower air pressures which would be the equivalent of moving uphill both in terms of temperature and pressure. But whilst no individuals would directly die from a slight drop in atmosphere, the overall metabolic rate of “life on earth” ought to tend to drop – albeit compensated by increased solaration. So, drier, higher sunshine and colder.

Oceans

Ocean temperature will reduce. And, whilst colder water can hold more oxygen, this effect is far smaller than the direct reduction in oxygen resulting from pressure (i.e Henry’s law), both reducing temperature and Oxygen content will directly reduce the metabolic rate of ocean life.
 

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7 Responses to Physics of a reduced global atmosphere

  1. Pressure: “Starting with the obvious, because pressure is the weight of atmosphere divided by surface area, the pressure would drop in proportion to the loss of atmospheric weight.”
    That pressure is weight (force in Newtons) divided by area is a very large part of the Meteorological scam, as enhanced by Bill (Stoat) Connelly via wikipedia. Mathematically, normalization has an entirely different connotation that division. Pressure is a Laplacian residue, A the remaining value of stress in Pascals, as the surface normal to that stress approaches zero.
    All the best! -will-

  2. Thus force is proportional to pressure times area (re-normalization). However a one killogram iron sphere sitting on a one sq meter card table has a force (due to gravitational attraction) of 9.8 Newtons. Nowhere is there a pressure of 9.8 Pascals. The pressure exerted by the now deformed table top supporting the sphere at the new contact area is immense, and would approach infinity, were it not for such deformation.
    All the best! -will-

  3. This Earth’s atmosphere at any location expresses exactly zero ‘weight’ as demonstrated by Archimedes 271 BC. Gravity does not accelerate this atmosphere. Gravity instead loosely compresses the whole atmosphere in conformance with the ideal gas law. This both limits the loss of atmosphere to space and also the out-gassing from the surface and oceans.

  4. The approximate columnar mass of Earth’s atmosphere is 101325 Newton per meter squared (Pascals) divided by (PI times the force of gravity in Newtons per kilogram). This value is approximately one third the erroneous value stated in the disgraced wikipedia. Neither value has ever been measured. The amount of atmosphere is undetermined as is any reason for that amount being what it is! The amount of atmosphere by volume would decrease with decreasing temperature. It is likely that the mass of the atmosphere would also decrease with decreasing temperature.
    All the best! -will-

  5. Dry Lapse Rate: “Because the specific heat capacity of air per kg is fairly constant with pressure and because dry lapse rate is related to the gravitational acceleration and specific heat capacity, neither of which would change dramatically, then the dry lapse rate would remain the same.”
    Another scam brought to you by meteorology! Lapse rate has nothing to do with gravity. The temperature decrease with decreasing pressure is always determined by the gamma of that type of gas and has a value of 1.4 for this atmosphere at pressures above 20kPa. Gamma is also called the isentropic exponent in engineering, as atmospheric compression is reversible. It is the partial derivative of pressure with respect to density at any fixed temperature. You are correct that lapse would remain the same.
    All the best! -will-

  6. Scottish-Sceptic says:

    Will, no meteorologist “scammed” me on this – I just worked it out from basic principles. For a rising mass of air, the thermal drop in energy from each kilogram must match the potential energy gained.

  7. T Bone says:

    Here’s something I’ve been wondering about but I don’t have the math skills. I wonder how much more methane is generated by vegans vs meat eaters. Methane is a GH gas too, isn’t it? And I hear it is much more effective too.I find that veggies and carbs give me more gas than meat does, and I’m wondering if vegans are bragging too much about cutting f…er…emissions. 😉

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