Climate Explorations: Planet Size

Hello, this is the seventh part of a series where I explore different possible climates with the ExoPlaSim model. As always, you may want to check the first post in the seriesfor details on my approach and some of the limitations of the model, and thismore recent post describing the new climate classification system I’ve started using.

Today we’re looking at different planet sizes. The “size” of a planet can mean a few different things, but here I’ve taken what seems to me the most straightforward approach: I’ve picked a range of planet masses from 1/10 to 10 times Earth’s mass—which based on previous discussions is an optimistic but reasonable estimate for the potential range of habitable Earth-like planets—and then used the mass-radius formulas from Fortney et al.2007 to estimate the radius of each planet, assuming an Earth-like composition of 32% metal core and 68% rocky mantle and crust, with the results ranging from 0.489 to 1.795 Earth’s radius (and thus 0.85 to 1.73 times the density, a significant departure from the occasional shortcut of assuming an Earthlike density). From mass and radius, we can then get the surface gravity, ranging from 0.418 to 3.105 Earth’s gravity. Conveniently enough I made this graphic a while back with the same formulas and picking mostly the same sizes, excluding just the smallest one here, so it may help you visualize the range of planets we’re looking at.

For topography, I’ve simply kept our standard Earth map with the same elevations (though because ExoPlaSim takes topography inputs as geopotential—surface elevation times gravity—I had to create separate inputs and start each model from scratch, rather than restarting from a previous model as I usually do). This likely isn’t totally realistic, for one because surface gravity can potentially influence terrain elevation in a number of ways, and for another because landmasses likely wouldn’t just scale directly with the planet’s surface area (note that surface area scales with the square of radius, so the smallest planet here has less than 1/4 Earth’s surface area and the largest over 3 times as much, and so their copied landmasses from Earth are scaled by the same amount). There’s at least some chance that the geometry of plate motion over the surface and convection of the mantle would tend to scale such that larger planets would tend to have larger landmasses, but we really can’t be sure—we don’t even know that that all these planets would have plate tectonics. But trying to create realistic surface topography for each case is beyond the scope of this exploration and not even something we could attempt with much confidence based on current research, so we’ll just have to make do.

A planet’s size doesn’t directly influence the distribution of solar heating over the surface or the overall necessary balance of heating to radiative cooling, but there are still a couple reasons to expect it to influence climate. For one, as the planet’s radius increases or decreases, distances across the surface scale by the same amount. In particular, for a larger radius the distance between the equator and the pole increases, which makes it harder for heat to diffuse between them. A greater radius also influences the Coriolis effect, as the tangential velocity of the equator will be greater and there will be more distance for north- or south-blowing winds to be deflected over, so we can generally expect to see more atmospheric circulation cells for larger planets. With our scaled topography, larger planets will also have a greater distance from the continental coasts to their interiors, but again it’s hard to say how representative that is of the tendencies of real planets with varying geography.

The surface gravity could also have a subtle influence. Higher gravity compresses the atmosphere more, effectively making it “shorter” as pressure drops quicker with altitude. For a given level of water content, a shorter atmosphere has less total water, and so a weaker greenhouse effect, and it also carries less total heat and so there’s even weaker transport of heat from warm to cool areas.

There is something of a common assumption that larger planets should have thicker atmospheres (in terms of total surface pressure). This isn’t entirely unfounded, as greater surface gravity and escape velocity could reduce atmospheric escape to space and a proportionally larger and warmer interior could potentially outgas more volatiles to the surface, but there’s various other processes that influence atmospheric evolution other than just these factors, and there may be a substantial element of simple luck in terms of the exact composition of a planet as it forms and early atmospheric losses to large impacts (surface tectonics may also influence the movement of gasses between the atmosphere and interior). So we might expect some overall correlation between planet mass and atmospheric pressure, but I don’t think we can assume that any planet twice as massive as Earth would necessarily have more atmosphere than a planet half as massive. For this exploration I’ve given every planet the same surface pressure (though because of the effect of gravity on atmospheric height, this does effectively imply proportionally less atmospheric mass per surface area for the larger planets), though I wouldn’t be opposed to trying out different combinations of planet size and surface pressure in the future.

These theoretical considerations in mind, let’s see how they’ve played out in practice.

• Smaller Planets
• 0.5 Earth Mass
• 0.25 Earth Mass
• 0.1 Earth Mass
• Larger Planets
• 2 Earth Mass
• 4 Eath Mass
• 10 Earth Mass 

Previous Exploration: Pressure 

Smaller Planets

0.5 Earth Mass

Planet radius: 0.820 Earth radii

Surface gravity: 0.743 g

Stellar Flux Relative to Earth: 0.965

Average Temperature: 15.4 °C

By the magic of cubic scaling, this planet probably wouldn’t look much different from Earth despite having half its mass, and indeed it may not seem all that different in its surface properties and general geology.

As per usual for a first test, the differences here are subtle but definitely present when looking closely. As expected, shrinking the planet has warmed it slightly, requiring stellar flux to be lowered to maintain an Earth-like temperature.

This is probably mostly due to a taller atmosphere giving it a stronger greenhouse effect, though slightly reduced ice cover may help as well. The winds are near indistinguishable from baseline, but with less distance to carry heat, they’re more effectively balancing heat across latitudes: Relative to the baseline, this planet is about 5-8 °C cooler in the tropics and over 10 °C warmer at the poles.

Perhaps the clearest shift is in precipitation patterns: The tropics have become generally wetter, due not just to lower evapotranspiration in the cooler climate but also higher precipitation, and the desert belts have shifted slightly poleward, drying out parts of southern Eurasia. On the whole precipitation is slightly lower on average, but only modestly so.

0.25 Earth Mass

 

Planet radius: 0.661 Earth radii

Surface gravity: 0.572 g

Stellar Flux Relative to Earth: 0.932

Average Temperature: 15.7 °C

Still 2/3 Earth’s radius and over 2/5 it’s surface area, thanks in part to being about 13% less dense than Earth.

The differences here are a bit clearer: The ice caps are largely gone, with both poles seeing brief summers up to 5-10 °C. The tropics have become milder in turn, with few areas outside of deserts reaching more than 30 °C averages.

 

 

The effect on wind patterns is subtle but can be picked out on close inspection: the Hadley cells have slightly expanded, and the polar cell has essentially disappeared in the northern hemisphere, while in the south it persists through most of the year but mostly dissipates in the warm summer months.

 

 

The rains have shifted with the winds: much of Eurasia and North America have turned over to desert and steppe, while the subtropical deserts of Africa and Australia have shrunk instead. There's notably less area of true desert, because the transitional zones around the edges of the deserts haven't scaled down with the planet.

0.1 Earth Mass

Planet radius: 0.489 Earth radii

Surface gravity: 0.418 g

Stellar Flux Relative to Earth: 0.904

Average Temperature: 15.8 °C

This planet is now slightly less massive than Mars, and somewhat denser as well so a fair bit smaller. Though Mars’s small size may have helped cause the loss of its atmosphere, it’s not implausible that a luckier planet around this size could hold onto a thick atmosphere and stable climate for longer.

With less than half the distance to the poles and a tall atmosphere, there’s now less than a 30 °C difference in average temperature between the equator and poles. Some patches of permanent ice have returned, but this is likely because the warmer polar seas, now ice-free year-round, are producing more moisture to snow down on glaciers.

Note as well the lack of highland tundra in any of the major mountain ranges here; though ExoPlaSim always struggles to show mountain climates properly due to resolution limitations, in this case the lower gravity is causing less of a temperature drop with altitude, so mountaintops at the same elevation are closer to the nearby lowland climates.

For winds, there’s a somewhat clearer expansion of the Hadley cells and poleward shift in the Ferrel cells, with only a hint of a southern polar cell in midsummer. Notably though we don’t see the tropical winds consolidating into one large equator-crossing cell as we saw in our lookat a terraformed Mars or the single near-global cell of modern Mars—the ITCZ doesn’t even move much farther with the seasons. So while planet size plays some role in circulation patterns, the long year, hemispheric asymmetry, and surface pressure also factor into Mars’s particular patterns.

This shift in circulation has of course spread semiarid climates across much of the northern mid-latitudes, and the world as a whole is still modestly drier than baseline, but really this isn’t so much an expansion of the arid belt as it staying about the same width while the rest of the world shrinks—and note that there are fewer completely dry areas here, perhaps in part because the continental interiors are all closer to the sea.

Larger Planets

2 Earth Mass

Planet radius: 1.213 Earth radii

Surface gravity: 1.359 g

Stellar Flux Relative to Earth: 1.035

Average Temperature: 14.1 °C

Another world that might look quite similar to Earth at a glance and on the surface despite having a substantially different mass and volume. Some models have suggested that worlds even modestly larger than Earth may be prone to retain thick hydrogen atmospheres, at least in orbit of smaller stars, but other models vary and this could vary between specific planets.

The trends in climate are unsurprisingly about the reverse as for smaller planets: increasing the planet’s size as made it tend cooler, requiring more stellar flux to retain its temperature, and increased the temperature gradient between equator and pole, giving the tropics sweltering 40 °C summers and the poles -70 °C winters. Tibet has also acquired its own large glacier in the shallower atmosphere.

Wind patterns are broadly similar to baseline, but with some notably stiff winter winds out of the major mountain plateaus, which can become cooler than nearby lowlands thanks to more cooling with altitude and greater area.

Oddly, precipitation is also slightly below baseline here, and while the desert belts have slightly expanded towards the equator and retreated in North America and Australia, they haven’t shrunk much in Eurasia, perhaps because greater distance from the coasts and warmer subtropics is offsetting any shift in wind patterns that might bring more rain to these latitudes.

4 Earth Mass

Planet radius: 1.447 Earth radii

Surface gravity: 1.910 g

Stellar Flux Relative to Earth: 1.079

Average Temperature: 14.3 °C

A definitive superearth, probably unlikely to have an identical atmosphere to Earth but perhaps not impossible.

There is of course a greater temperature gradient with latitude, and as we’ve seen in previous cases with weak heat transport, this manifests as fairly uniform temperatures across the tropics (though desert summer days can still reach over 60 °C) and then a sharper drop in the mid-latitudes, where heat transport is weaker outside the Hadley cells and there’s less direct light and more ice cover in winter, down to polar winters reaching below -90 °C. There’s actually a bit less ice cover in Antarctica here, but likely just because less moisture can reach it from the distant unfrozen seas.

For winds, there’s a clearer difference here but not quite what we might expect: in the south, the circulation cells are clearly delineated and a fourth circulation cell has appeared near the pole; but in the north, the Ferrel cell dominates most of the high latitudes in winter with a remnant polar cell centered over Greenland; and then in summer, the Hadley cell expands but much of the rest of the hemisphere is a confused tangle of winds, with wind circulation between warm and cold areas often more prominent than global circulation patterns.

It is perhaps these more irregular wind patterns, as well as increased distances and stronger orographic effects from mountains because of the higher gravity, that accounts for the overall patchiness of wet and dry climate zones. But on the whole the average precipitation is about the same as baseline, just a bit more broadly distributed across the mid latitudes rather than concentrated along the ITCZ and polar fronts.

10 Earth Mass

Planet radius: 1.795 Earth radii

Surface gravity: 3.105 g

Stellar Flux Relative to Earth: 1.131

Average Temperature: 14.7 °C

An order of magnitude more massive than Earth, and yet still less than twice the radius; getting a rocky planet that looks clearly much larger than Earth is actually fairly hard to do. I had been somewhat expecting a larger planet to have more even climate bands evocative of a gas giant’s cloud bands, but the opposite seems to be the case, though perhaps this is at least in part due to my choice to keep the same continents scaled to the surface area.

As typical for many of the more extreme climates we’ve looked at, much of the planet is split between torrid tropics and permanently frozen polar wastelands, but there is a thin strip in between that remains tolerable for human habitation year-round. There’s a particularly vicious hotspot in South America, the center of which remains about 60 °C year-round, due perhaps to air heating and drying as it descends from the Andes (west India has the same issue in summer, but at least cools in winter.

We can again see fairly clear circulation cells in the southern hemisphere, though they’re a bit less distinct here, appearing more as cyclones in each ocean basin that don’t properly connect across the continents. In the north there’s a more general chaos, as winds mostly fail to organize into latitudinal circulation cells and instead blow more directly between cold and hot spots that appear as the 3-times-larger continents warm and cool with the seasons and air masses struggle to move over even more modest mountain ranges. Particular stiff winds descend from large highland glaciers, with those off Tibet reaching over 140 km/hour in winter.

Thus, rather than concentrated in large latitudinal belts, rains are more patchily distributed along fronts or against mountains, with strongly seasonal rain patterns in many areas due to local rainshadows. Again though, the total average precipitation is about the same as the baseline.

This in turn makes for a fairly chaotic vegetation distribution, with the thickest forests appearing in strips along the edges of mountains or in a few large stretches of subtropical lowlands.

A chart of average temperature by latitude across all the models here and the baseline.

That’ll do for today, a fairly straightforward case after some of our recent explorations teasing out complex seasonal patterns, but one with a couple surprises nonetheless. The next exploration will be one I’ve been looking forward to for a while, altering the planet’s ocean area.

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