User:William M. Connolley/Atmospheric general circulation on tidally locked planets

Planets near their sun may become tidally locked, as the Moon is tidally locked to the Earth. Indeed, for potentially habitable planets of red dwarf stars the expectation is that all will be tidally locked, since they must be near their stars for the insolation to be high enough to support life. Such planets have two major features that distinguish their atmospheric circulation from "normal" planets like Earth: the insolation remains centered one one hemisphere, instead of varying; and the rotation rate is the same as the "year" and hence is low, typically of the order of 30 days. This latter effect leads to a weakened but non-negligible role for the Coriolis force.

The modelled planet
A range of possible planets can be modelled. For the purposes of discussion, we shall think of a planet of roughly Earth-like characteristics (mass, radius, albedo, atmospheric thickness and constituents) except orbiting a red dwarf at a distance such that its insolation is roughly comparable to Earth's. In particular, in the absence of other information, we shall assume where necessary that the atmospheric grenhous effect is largely provided, as on earth, by water vapour and carbon dioxide.

mention red-sunlight affect on GHE and on albedo

The radius of the orbit and rotation rate depend on the assumed mass (and hence luminosity) of the star. For a red dwarf of 0.1 solar masses, the orbital period is approximately 6 days and the orbital radius ~0.02 AU. For 0.5 solar masses, the period is ~60 days and radius ~0.2 AU. The simulations discussed below assume a period of 16 days, like Titan.

The point underneath the star is called the sub-stellar point; the point opposite that, the anti-stellar point. The side that is lit is called the dayside; the side unlit, the nightside.

The unrealistic radiative-convective case
In the absence of horizontal atmospheric transport, heat is distributed by radiation and by vertical convection. In this case, the sub-stellar point becomes scorchingly hot (400 K at the surface), and the nightside freezingly cold (200 K), because the atmosphere does not effectively transport heat.

This case, however, is not realistic: even a thin atmosphere of ~50 mb is enough to strongly moderate the temperature difference.

Including atmospheric transport
When atmospheric transport is included, heat will be transported as sensible heat from the dayside to the nightside, reducing the temperature contrast. A full GCM is required to accurately simulate this process, but simple estimates can be made.

The timescale for advection of heat from the dayside to the nightside is simply L/U, where L is the day-night difference and U a typical windspeed. With an assumed windspeed of 10 m/s, this becomes 20 days. The timescale for radiative equilibrium is more complex ($$t_r = c_p p_0 / \sigma g T^3$$ explain these) and is approximately 160 days for Earth. Hence, on Earth, radiative equilibrium is never reached, because the advective timescale is always shorter. On a plausible exoplanet, the same is likely to be true. This can be seen by observation of polar night atmospheres on Earth, which do not collapse to very low temperatures.

When atmospheric transport is included, the sub-stellar point temperature is approximately 300 K, decreasing towards 275 at the poles; the anti-stellar point is at 265 K. Hence, substantial portions of the planet are habitable, by Earthly standards; habitability is by no means restricted to the terminator. '''Is this surprising? This is warmer than polar temperatures on Earth. Lack of Coriolis allows more heat transport around the equator?'''

[add more]

Atmospheric collapse
A question of interest for tidally locked planets is "atmospheric collapse". At atmosphere, chilled, may collapse due to components condensing out. In order, the water vapour may condense as ice; the CO2 may freeze; and then the bulk atmosphere may freeze. On a tidally locked planet these effects can cause collapse if the atmosphere is cold enough at any point (if that occurs, the consituent starts freezing out at that point, and progressively depletes the rest of the atmosphere). On Earth, with diurnal and seasonal variation, rather more of the surface has to cool before this is possible.

The anti-stellar point is likely to be below the freezing point of water. Hence, water vapour will condense there and effectively dessicate the entire atsmophere, unless some mechanism - glacial flow, or ocean transport - returns the ice to regions where the temperature is above zero. To some extent, this depends on the amount of water available. Were the planet similar to Earth, it would not be possible to deposit all the water as ice on the night side, since there is a practial limit of about 5km height for an ice sheet, and all the ice just would not fit.

A nightside temperature cold enough to freeze out CO2 is unlikely, unless the atmospheric thickness is less than ~100 mb.

And freezing out the nitrogen is well out of order.

[expand]

Work in progress
So: the paper is written with the Reading SGCM. There is various wurble in it saying that it is good enough (physics is fairly simple, it is mainly a GCM for doing atmos dynamics), as is its T10 truncation; I'm a little dubious about that but probably the later follow-up paper justifies that more.

The basic point is that if you just consider radiative-convective models, you'll find that the dayside is v hot and the nightside v cold. But if you include atmospheric advection, this is radically modified. Aside: this should be no great surprise. We know it gets cold in the polar winter on earth, but it doesn't get *very* cold. See-also "coreless winter".

There is a nice piece of scale analysis about radiative and advective timescales. The advective timescale is how long it takes to move some atmosphere from day to night (L/U; on earth, about 20 days). The radiative relaxation timescale is more complex and for earth is ~160 days. Which means that (on earth) you'll never see radiative relaxation timescales; advection will always upset things. Given what is known about Gg I think about all you can say is that these timescales are likely to be similar; the radiative one might be shorter and the advective one longer, but still the advective one is going to dominate.

Then we get onto the GCM circulation results. The paper has some slightly silly pic in it (because climatologists *always* draw zonal average pic, they do too, even though a zonal average is meaningless for a planet with so disimilar day and night sides). Anyway, ignoring those, you get what you would expect: a strong vertical rising flow under the sub-stellar point. Due to the tidal locking the Coriolis force is less, but still there, and it does modify the flow: you *don't* get a sort of symmertical flow under the sub-stellar point. And conservation of momentum still matters, which means you get odd things due to only having much inter-layer stress in the near-surface layers. Which means that although you get night-to-dayside surface flow over the poles (pretty well as you'd expect) you actually get light-to-dark flow over the equator. But the end result is that the atmosphere acts to transfer heat from the day to the nightside.

Then you can play fun games with "atmospheric collapse" depending on atmospheric thickness overall, and constituents. So, if the atmos is thin enough, and insolation low, you can end up with bits of the nighside cold enough to condense CO2, whereupon all the CO2 condenses out and it gets colder. So you might end up left with a substantially N2 atmosphere. But N2 can still transport heat, and it never gets cold enough to freeze out the N2, so you always get left with an atmosphere of some sort.

A more interesting sort of collapse is losing all the water. There is a section on this, but it wasn't quite clear - maybe I should re-read it. Certainly in their "standard" run the sfc T on the nightside at the "antistellar point" drops below 270 oC, so water will freeze out (meanwhile, substellar, its about 305 K, so quite tolerable really. Large portions of the dayside look to get habitable temperatures). Unless something acts to move that ice back onto the dayside so it can melt, you're going to lose all your water to the nightside. Which will (a) kill everything and (b) reduce the GHE effect so cooling things a bit.