# Radiative atmosphere without heat convection

I was reading up on how a universe lacking heat convection would work, and asked a question here that was much too broad. This is me focusing the question much more. How would atmospheres with no heat convection work? I found this article here https://scienceofdoom.com/2014/06/21/radiative-atmospheres-with-no-convection/

It's written by what seems to be anti-climate change believers but the science is very interesting with the conclusion being rapid temperature changes higher or lower you go and a surface temperature of 55C if the theoretical planet has an ocean depth of 5M. However, I'm not sure if the science is sound. If it does work, how would surface temperature change if the ocean depth were extended to 35M instead, and how can I keep the surface temperature at a relatively cool 15C like Earth instead?

Edit: Clarified some things, I'm not very good at science and the article just said an ocean depth of 5M and never specified whether the ocean is across the entire planet, or maybe I didn't read hard enough.

• Much better. Thank you! – JBH Jun 22 '20 at 4:29
• You're quite right now I've read it. Odd simulation. I guess they thought it would take less computer time to calculate rather than using a big heatsink like our ocean. – Tantalus' touch. Jun 22 '20 at 5:03
• An atmosphere with no convection implies one of two things: either the atmosphere is very close to a vacuum, or the gravitational acceleration is very very small. Neither option is pleasant. Any kind of reasonable atmosphere with a reasonable gravitational acceleration will show heat conduction by convection. – AlexP Jun 22 '20 at 11:29
• You will not find reputable sources on the behaviour of atmospheres without convection. Convection is a fundamental property of gasses; if you say "there's no convection" you're implicitly saying that the atmosphere doesn't consist of anything like a real gas. – John Dallman Jun 24 '20 at 8:00

Most of the interesting "weather" and dynamics in the lower atmosphere arise from convection.

I think the link that was posted was mainly about how convection dominates in the lower atmosphere and and radiation effects dominate in the upper atmosphere, and wanted to see what the effect of would be if one artificially looked at the problem without convection. As pointed out in comments and other answers, it is unrealistic to not have convection. The link article by having a thin ocean was mainly trying to set a boundary condition for the model, and if I read it correctly that if the ocean was thick the equilibrium temperature would end up same if you waited long enough. One way to interpret the article is that the convection in the lower atmosphere mixes up the fluid (air) in such a way that the surface doesn't get as hot as it would without having a layer of atmosphere mixing.

From a world building perspective, I think to get at the heart of your question it is about how could you control the temperature of the planet assuming that radiative processes are dominating the heat transfer balance.

The answer I think would be by how much reflectivity (from the surface or perhaps clouds) and emissivity the planet has. From a climate science point of view, this is a big deal. In the air how much to contrails from air traffic change the heat ballance, surprisingly to me, apparently it is measurable. On the ground, or ocean, how much soot from combustion is landing on the snow, or how much ice coverage in the arctic ocean matters in a lot of these models how the light from the sub is trapped or reflected is important.

So for your purposes, you have the light from the sun hitting the planet and the light and heat from the planet radiating into space. Neglecting some details, that the planet may have started out as hot mess of molten rock, and over time new materials from space may be adding water etc. That should come into equilibrium.

A short light article with a graphic is at

https://www.physics-in-a-nutshell.com/article/17/surface-temperature-of-the-earth

The atmosphere acting as a filter as to how to how much of the light and heat from the sun is reflected, how much is transmitted to the surface, and how much of the higher energy photons are absorbed by the gasses in the atmosphere or by the ground and turned into heat (lower energy photons) that would go through the filter and radiate into space.

To dial in the temperature for your world, the easiest thing would be to fiddle how much light is reflected and absorbed. The knobs you can turn (ignoring the convection) would be to add more gasses from volcanoes like CO2 that might absorb and trap heat strongly, but not add a lot of particulates from the volcanos, or clouds in the atmosphere that might reflect more of the light before it gets absorbed. Without CO2, from the volcanos, maybe the oceans are frozen before the eruptions and the earth is very shiny and reflective. Or you could add plants, and they could consume the CO2, and perhaps the plants change the reflectivity of the oceans, or maybe the oxygen from the plants starts to oxidize the land etc.

Volcanoes are not the only thing but just an example of something that can change the heat balance in a short period of time. But basically changing the Albedo of the planet (with or without) a convective atmosphere can change the heat balance and the surface temperature significantly.

Tl;DR: I don't think that a radiative planetary atmosphere is possible. It seems unlikely to meet the key requirements of surface gravity, opacity and temperature that would ensure that radiation would dominate over convection.

We can answer the question of whether radiation or convection dominates energy transport by taking a cue from stellar astrophysics. Many stars form separate radiative and convective zones, while others are fully convective (e.g. very low-mass stars) or fully radiative. For example, the Sun's core is surrounded by a radiative zone that extends about two thirds of the way to the surface; beyond that, convection transports energy the remaining distance to the photosphere. We even see differences in stellar atmospheres; in the atmospheres of hot stars, radiative transport is more important, while in the atmospheres of cool stars, convection is more important.

Let's start by trying to determine whether convection is possible under a given set of conditions. There are a couple of ways we can write the convection criterion. It's often presented in terms of density $$\rho$$ and pressure $$P$$: $$\left|\frac{d\ln P}{d\ln\rho}\right|_{\text{ad}}>\gamma$$ where $$\gamma$$ is the adiabatic index and $$_\text{ad}$$ indicates that we're talking about an adiabatic gradient. However, we can also invoke the ideal gas law and think about temperature, rather than density: $$\left|\frac{d\ln P}{d\ln T}\right|_{\text{ad}}<\frac{\gamma}{\gamma-1}$$ The left-hand side is often denoted by $$\nabla_{\text{ad}}$$. We reach the boundary point when the radiative and convective gradients are equal, $$\nabla_{\text{ad}}=\nabla_\text{rad}$$, and we have a nice expression for the radiative case: $$\nabla_{\text{rad}}=\frac{3F\bar{\kappa}P}{16\sigma T^4g}\propto\frac{\kappa}{g}$$ where $$\kappa$$ is opacity and $$g$$ is acceleration due to gravity.

In short, we need a large radiative gradient $$\nabla_{\text{rad}}$$ for convection to dominate over radiative transport. This occurs in regions of high opacity or low gravitation acceleration; in regions of low opacity or high gravitational acceleration, radiative transport dominates. For radiation to dominate, we need the reverse: we want a planet with a low-opacity atmosphere and strong surface gravity. The surface gravity can be addressed by making our planet small and dense, made of a mixture of iron and silicates, but this may not be enough, and so we still have to consider opacity.

Planetary atmospheres contain sources of both continuum opacities, such as aerosols and water droplets, and line opacities, such as molecules that can undergo vibrational and rotational transitions (Fortney 2018; see also these notes). Line opacities tend to dominate, and so we could argue that we could reduce atmospheric opacity by simply removing some of the most common absorbers: water, methane, carbon dioxide, carbon monoxide, ammonia, etc. For an atmosphere of near-habitable temperatures, water, methane and ammonia are key in the optical and infrared range - perhaps a dry atmosphere could reduce key water vapor absorption bands.

Unfortunately, there's still one problem: $$\nabla_{\text{rad}}$$ has a very strong ($$T^{-4}$$) temperature dependence. Terrestrial planets tend to be quite cool compared to stars, and so we should expect a strong decrease in the radiative gradient from that alone. While it's true that some hot Jupiters may rival stellar atmospheres in temperature, they can't reach the temperatures of the hot, massive stars for which radiation dominates over convection in their atmospheres.

Even without any numbers, I'm inclined to say that it's not possible for you to completely get rid of convection. Sure, you could severely reduce line opacity, but that would require a dry atmosphere, which seems unlikely if you want oceans. You'd also need a high temperature, and even if that was attainable, it would lead to increased evaporation from said oceans, and more water in the atmosphere, and thus a higher opacity. In short, I don't think you're really likely to have a planetary atmosphere without convection.