Weather in a 5 mile deep crater

Question

I’ve done a fair bit of research to come up with this scenario. I hope it’s not “too broad” to ask for a reality check. Have I overlooked anything? Does it all sound plausible?

My world takes place in a massive crater, the only habitable place left on the planet. It is roughly 800 x 600 miles and 5 miles deep. At the bottom it is 1.2 atm in pressure, while the surface is at 0.5 atm.

Due to the extreme “altitude” conditions the surface of the planet is cold (would it really be though?) windy, and home to extremophile bacteria mats/mounds, and possibly lichens/moss. The wind here is extremely fast because there’s not much to slow it down.

The sides of the crater are gently sloping downwards, and the wind follows it down. The bacterial mats slowly give way to montane grassland and meadows. Early morning dew from the cold winds is the source of water here. Small gnarled trees grow slowly and are warped by the wind. Meadows are nearby springs, where ancient aquifers were fractured during the meteor impact.

Next comes the treeline and the coniferous forests with fern undergrowth. The wind is slowed by both the trees and its compression at -12,000 feet into the crater. Rain occasionally falls here if the conditions are right. Overall the precipitation is mostly occult. This area has sizable lakes from other meteor impacts which are filled by fractured aquifers and streams from up the crater.

Eventually the heat of the Earth warms the cool air and we reach temperate deciduous forests. Winds are breezy here and carry precipitation from higher up the crater. Evening showers are relatively common. Streams have become rivers by this point. The forests reach all the way to sea level, except where humans have cleared them away for agriculture.

A massive sea covers much of the bottom of the crater, and fortunately it has reached an equilibrium between evaporation and being filled from the aquifers.

In the sea are a series of islands from the complex crater. These islands experience hot moist air, daily rain, and are temperate rainforests. It is here, finally, that the air rises up in a massive updraft. The hot air rises, disperses, and mixes with the atmosphere. Some water vapor finds its way back into the crater, but much more leaves.

I know it’s a big task, but does this all sound plausible? Is there anything I’ve missed or greatly overlooked?

Answer 1

Temperature change is caused by lapse rate

The difference in temperature between the bottom and top of the crater is going to be driven by the lapse rate, and not by the heat of the crust (probably). Lapse rate is the rate at which temperature in Earth's atmosphere decreases with an increase in altitude, or increases with the decrease in altitude. In particular, we can use a chart of moist adiabatic lapse rate to see what the expected temperature changes would be in a 5 mile (8 km) deep crater.

The 'Moist Adiabat's are the dotted lines on the chart. Chicago has a annual mean temp of about 10 C, Washington DC about 15 C, Houston about 20 C, and Miami 25 C. Pick your starting point, then follow the dotted line upwards until it intersects with the line representing 8 km. I get the following:

Floor Temp      Surface Temp   Surface Press
  10 C             -60 C         0.34 atm
  15 C             -45 C         0.36 atm
  20 C             -30 C         0.38 atm
  25 C             -15 C         0.42 atm

So you are looking at quite the different in temps. I also used this chart to double check your pressure estimates. Instead of starting at 1 atm, your crater surface starts at 1.2 atm, so I multiplied the resulting pressure estimates by 1.2. You are pretty close to being right on the pressure.

Overall, the area outside the crater will be very uninhabitable.

Why the Earth won't provide appreciable heating in the crater

The Earth's crust is about 30-50 km deep on the continents, away from tectonic boundaries, and it has a temperature gradient of about 200-400 C in heating between the surface and the boundary with the mantle. The heat flux on continental crust is about 71 mW/m$^2$.

The simplest argument I can make is to compare the heat flux on the continental crust with the heat emitted by the Earth's surface in infra-red radiation. The Earth's surface emits 398 W/m$^2$ in IR radiation to the skies, on average. This is significantly higher than the 71 mW/m$^2$ that comes from inside the Earth.

Lets look at what happens to planetary heat flux when we change the thickness of the crust. Planetary heat flux is controlled by the Fourier's law for head conduction

$$q = -k\nabla T.$$

Here $q$ is heat flux (W/m$^2$), $k$ is conductivity and $\nabla T$ is the heat gradient. If we reduce the distance between crust and surface by 8 km, from 25 km to 17 km, with a constant 300 K temperature differential then $\nabla T$ goes from 12 K/km to 17.6 K/km. This represents a 1.5 times increase in heat flux out of the Earth's surface.

So the Earth is providing something like 120 mW/m$^2$ at the bottom of your crater instead of 70 mW/m$^2$. Still, compared to 160 W/m$^2$ absorbed from sunlight and 80 W/m$^2$ released by evapo-transpiration and IR radiation to space, and back-radiation received from atmosphere and clouds....you get the picture. The change in planetary heat flux is negligible, three orders of magnitude smaller, at least.

Therefore, the temperature gradient between the crater bottom and high surface are going to be driven mostly by lapse rate, the same factor that drives the temperature difference between sea level and the top of Mount Everest on Earth.

Air flow around the crater

Your crater is much hotter than the surrounding air. Hot air tends to rise. The dominant climactic feature will be rising hot air out of the crater. This will cause a variety of follow on effects.

Rising hot air creates cyclones!

Your crater is so large it will induce high speed, cyclonic winds circling around it. In the diagram above, the 'x' and 'o' represent winds into and out of the page around the crater. There will be permanent winds swirling around the crater.

If your crater is entirely in the northern or southern hemisphere (assuming your planet is rotating like Earth) the Coriolis effect will drive the winds into a stable clockwise or anti-clockwise rotation around the crater. If the crater straddles the equator....something will happen, I'm not really sure. if the crater is on the Equator and large enough relative to the size of the planet, the cyclone may actually form a circle around the surface of the planet, but don't quote me on that.

Rising air releases moisture as it cools

As your air rises, it will lose its ability to hold moisture. You can see this from the thermodynamic diagram at the top of the page. If we assume a jungle-y 25 C average temperatures at the bottom of the crater, then that air can hold about 20 g of water per cubic meter. Elevate that air to 8 km, and it can hold about 3.5 g, leaving the remainder to fall as rain.

The center of your crater will be constantly raining. The temperature gradient between crater bottom and surface is going to be much higher than the temperature gradient between day and night, therefore, you will always have a steadily rising column of hot air.

Various wind conditions might blow around pockets of warm air, especially towards the edges, but you can assume the center of the crater will see rain every single day. The hotter the crater, the higher the magnitude difference in saturation mixing ratio will be, so the more rain you will get. A 10 C crater will get light rain every day, a 25 C crater will see permanent torrential rainfall.

Descending cold air will enter the crater like a blast furnace

From the cyclone swirl, descending cold air will spiral into the basin to take the place of the air that rose out. The force of gravity will ram this wind into higher pressure areas at the bottom of the crater, and the resulting molecular friction will be expressed as adiabatic heating.

These are foehn winds. The 8 km drop means that you would see an expected 30-60 C of adiabatic heating as the wind rushes downhill. Given that the wind already has high kinetic energy from the hurricane swirl at the top, the result near the bottom with be superheated blast-furnace winds. If conditions are right at the top, with extra solar heating for whatever reason, you could easily see steady 45 C or higher gale-force winds at the bottom of the crater.

No trees will live on the slopes of the crater, due to the high wind speeds and highly variable temperatures. The slopes could easily see temperature changes of 30 C in a matter of minutes, as one air mass blast past and is replace by another.

Answer 2

I'll try to tackle each of your points, so reaslistically on the face of it, its fairly plausible

My world takes place in a massive crater, It is roughly 800 x 600 miles and 5 miles deep. At the bottom it is 1.2 atm in pressure, while the surface is at 0.5 atm.

Pressure variance is reasonable and plausible, my only question though, what happened to the rest of the world to the crater being:

the only habitable place left on the planet.

That sentence suggests that something happened else where and that something could very easily transfer into this crater which could very easily effect life, but that's an aside

Due to the extreme “altitude” conditions the surface of the planet is cold(would it really be though?) windy, and home to extremophile bacteria mats/mounds, and possibly lichens/moss. The wind here is extremely fast because there’s not much to slow it down.

This is a tough one, if the "surface" is fairly uniform in terms of height, and it is just this crater that goes deep below this surface then actually the "altitude" would be basically ground level and would be receiving similar amounts of energy from the sun to that of the crater. so while the surface would have lower pressure and indeed lower temperatures, significantly lower tempretures are not a given, again there would be a gradient

The sides of the crater are gently sloping downwards, and the wind follows it down. The bacterial mats slowly give way to montane grassland and meadows. Early morning dew from the cold winds is the source of water here. Small gnarled trees grow slowly and are warped by the wind. Meadows are nearby springs, where ancient aquifers were fractured during the meteor impact.

This is easily possible, although craters aren't just a big hole in the ground, the rim of the crater protrudes the bedrock somewhat, even on very old and weathered craters. now this rim is mere metres on Meteor Crater in the US, and is definitely not uniform. however that is a mere kilometre or so across, not 600-800 miles. so that rim is going to be a small mountain range all the way along it. which means anything on one side will have similar on the outside of the rim

Next comes the treeline and the coniferous forests with fern undergrowth. The wind is slowed by both the trees and its compression at -12,000 feet into the crater. Rain occasionally falls here if the conditions are right. Overall the precipitation is mostly occult. This area has sizable lakes from other meteor impacts which are filled by fractured aquifers and streams from up the crater.

A 600-800 miles diameter crater will still have significant heating and cooling, its big enough to not stop high level winds effecting the weather or climate within the crater and also big enough to easily generate its own weather, so the trees.

Eventually the heat of the Earth warms the cool air and we reach temperate deciduous forests. Winds are breezy here and carry precipitation from higher up the crater. Evening showers are relatively common. Streams have become rivers by this point. The forests reach all the way to sea level, except where humans have cleared them away for agriculture.

Don't discount the power of the sun. if there is trees and life then the sun has to be able to get through to power photosynthesis. which means its not just the heat of the earth that will warm up air.

As for the forests and the rest, yes perfectly plausible

A massive sea covers much of the bottom of the crater, and fortunately it has reached an equilibrium between evaporation and being filled from the aquifers.

This is perfectly reasonable, but it the water and clouds do extend past the rim then that water is lost as it freezes and settles. aquifers are fairly constant water sources, if you had a particularly warm year where ice melted on the surface more than average then those aquifers would let it all roll downhill and you crater bottom sea has no where lower to send the water so keeping that homeostasis would be unlikely, but not impossible.

In the sea are a series of islands from the complex crater. These islands experience hot moist air, daily rain, and are temperate rainforests. It is here, finally, that the air rises up in a massive updraft. The hot air rises, disperses, and mixes with the atmosphere. Some water vapor finds its way back into the crater, but much more leaves.

All of this is fine, but i'd even with a massive updraft its still unlikely to have most of the water leave, most rainclouds are within the first 5 miles of atmosphere so those clouds wouldn't escape the crater walls

I cannot stress enough i am not a meteorologist, This is all just some basic research and my understanding. hope it helps