Climate Explorations: Eccentricity

"True color" approximation for Earth with 0.6 eccentricity and no obliquity.

Hello! If you've been following this blog or series a while I'll assume you get the basic idea of these explorations, but if not, be sure to check out the first post of the series where I run over my approach and the strengths and weaknesses of the ExoPlaSim model.

Today we'll be looking at the impact of orbital eccentricity, variation in a planet's distance from its star over the course of each orbit. Again you can look to a previous post for a more detailed and technical description of orbital mechanics, but there are a few key points to bear in mind here:

• Planets always follow elliptical paths with the star at one focus of that ellipse such that there is a single point each orbit where the planet is closest to the star, periapsis, receiving the most light, and one point where it is farthest, apoapsis, receiving the least light.
• Eccentricity is (for closed elliptical orbits) defined as the ratio between the difference between the minimum and maximum distance from the star (periapsis and apoapsis) and their sum (the total width of the orbital path, twice the semimajor axis). 0 eccentricity is a perfect circle, and increasing eccentricity implies ever more elongated ellipses with a greater contrast between maximum and minimum light from the star; if eccentricity reaches 1, the planet escapes orbit of the star entirely (there are more fundamental definitions of eccentricity that can be used for parabolic or hyperbolic escape trajectories, but we needn't worry about them here).
• A planet moves faster along its orbit near periapsis and slower at apoapsis, such that at high eccentricity a planet will quickly swing near the star and then spend most of its orbital period crawling along at a greater distance. In spite of this, average heating over a planet's whole orbit increases with greater eccentricity for a given semimajor axis.

Planets moving along orbital paths of equal semimajor axis and (red on the left to pink on the right) 0.0, 0.2, 0.4, 0.6, and 0.8 eccentricity (I don't think the timestamp indicates anything important). Phoenix7777, Wikimedia

Earth's orbital eccentricity is a mere 0.0167, which works out to a bit under a 7% increase in global insolation (light reaching the surface on average) from apoapsis to periapsis. By comparison, at 45° latitude, with Earth's tilt of 23.44°, insolation increases by over 300% from winter solstice to summer solstice. Earth's eccentricity has some subtle effects on global climate—variations of the relative timing of periapsis and the solstices over thousands of years appear to be largely responsible for a cycle of moderately wetter and drier climates in the Sahara, due to the eccentricity either enhancing (when periapsis and summer coincide) or dampening (when periapsis occurs in winter) seasonal temperature variation in the northern hemisphere and so influencing how far north the tropical rain belt reaches in summer—but it's negligible in terms of the broad global patterns of Earth's climate (I've been keeping it set to 0 for all models so far for simplicity's sake), and many a schoolteacher has had to laboriously explain why our seasons are caused not by variation in distance from the sun but the less intuitive way in which angling the planet's surface to the sun spreads out light.

But there are planets out there with higher eccentricity: Mercury's eccentricity is 0.206, the dwarf planet Sedna's is 0.855, and at least one exoplanet has been seen with an eccentricity over 0.95. For such planets (or their moons), insolation variation due to orbital eccentricity may be comparable to or even exceed that caused by obliquity. In such cases where eccentricity dominates, seasons would be globally synchronous rather than offset across hemispheres; the entire planet would warm near periapsis and cool near apoapsis.

For purposes of this post, we'll be looking at planets with only orbital eccentricity and no obliquity; combinations of obliquity and eccentricity are certainly worth investigating but we'll leave them to another time. I have already investigated a "seasonless" world with 0 obliquity and 0 eccentricity, which we'll take as our starting point: it required 540 ppm of CO₂ to balance at a global average temperature of 14.1 °C, and features a rather polarized mix of rainforests, deserts, and ice caps, with only scant transitional semiarid and temperate regions and a somewhat broader tundra belt (which may actually see more glacial coverage on a real planet).

Note, by the way, that ExoPlaSim has only been able to properly model eccentricity over 0.1 since version 3.2.1 (released May 2023), and requires the "Keplerian=True" parameter, so if you installed an older version of ExoPlaSim you may need to update (though there are some potential issues with running version 3.3.0 for some people, so if that's still the latest version you may want to install 3.2.4 instead, using "pip install exoplasim==3.2.4").

• 0.1
• 0.2
• 0.3
• 0.4
• 0.5
• 0.6
  

Previous Exploration: Day Length

0.1

Prior Model: 0 obliquity, 0 eccentricity

CO₂ Level: 540 ppm

Average Temperature: 15.5 °C (13.3 Mar - 17.8 Aug)

Already we can see a marked change from the seasonless world: Savanna, steppe, and temperate climates have greatly expanded, the ice caps have retreated (though the 1.5 °C of warming helps as well), and monsoon, subtropical, Mediterranean, and subarctic climates—all requiring substantial seasonal shifts in temperature or precipitation—have begun to appear.

0.1 eccentricity works out to about a 50% increase in global insolation, which causes a bit over 4 °C swing in global temperatures; locally, most land areas see about 5-10 °C of variation in monthly temperatures, up to 15 °C in the major deserts. This is similar to the seasonal variation seen in the tropics on Earth and so probably wouldn't be obvious across much of the surface, though in cooler temperate areas there may be a clear increase in snowfall and nighttime frosts.

 

Note that for all these runs, I set periapsis (greatest insolation) to July and apoapsis (least insolation) to January (yes, I'm being a bit of a northern hemisphere chauvinist, sorry Australia), but we'll pretty consistently see a lag of a month or two between these extremes of insolation and the actual hottest and coldest months, and this lag is always longer in winter such that fall is longer than spring. For simplicity's sake, I'll mostly be showing maps from the hottest and coldest months, wherever they fall.

This moderate and globally consistent shift in insolation causes fairly little shift in global circulation, but if you look closely there is a tendency for winds to more strongly converge into continents in summer, especially towards the hot deserts.

 

The result is something like a mild monsoon pattern over much of the world, with distinct dry and wet seasons appearing in the semiarid regions flanking the tropics just as we see on our Earth.

0.2

Prior Model: 0.1

CO₂ Level: 243 ppm

Average Temperature: 15.1 °C (10.7 Mar - 20.2 Aug)

Featuring the victorious return of the continental climates. Global insolation now more than doubles between apoapsis and periapsis, similar to local insolation swings between summer and winter at 30° latitude, so this is now decidedly a seasonal world.

 

Seasonal temperature shifts of around 20 °C are common across North America, Asia, and north Africa, with some deserts approaching 70 °C by day in summer, and even the oceans see around 5 °C of variation, but curiously temperatures barely vary in equatorial Africa and South America. This may be related to patterns of circulation.

Much as in the last case, winds converge onto the continents in summer (to the point that we might even consider the ITCZ to divide in two as it passes over Africa), and we can perhaps even see a tendency towards offshore winds in winter, but there's also a marked growth in the width of the Hadley cells in summer, by as much as 10° latitude in the northern hemisphere, as the sudden influx of heat to the tropics drives stronger circulation (even though the proportional increase of insolation across seasons is the same across all latitudes here, the equator still receives far more average insolation than the higher latitudes and so that equivalent proportional increase translates to a substantially greater amount of actual extra heat hitting the surface). This brings more moisture to the tropics and so increased cloud cover that helps keep it cool (and conversely, skies clear in winter as Hadley circulation weakens and converges mostly offshore) but also shifts the polar front and associated rain belts at high latitudes.

The result is a seasonal rain pattern remarkably similar to our Earth: mostly consistent rains over the equator, flanking semiarid regions with summer rains and bone dry winters, the subtropical deserts, and a temperate semiarid belt with dry summers and wet winters (though still mostly restricted to west-facing coasts due to predominantly easterly subtropical winds). The big difference is that this occurs simultaneously across both hemispheres; Christmas in New Zealand is as cool as in Spain or New York. There's also not much space for a wet-summer temperate belt due to the still-rapid drop in temperatures towards the ice caps, so cool Mediterranean climates—a rare oddity on our Earth—are a major climate region here.

0.3

Prior Model: 0.2

CO₂ Level: 60 ppm

Average Temperature: 15.7 °C (8.8 Mar - 24.0 Aug)

Things are starting to look...weirdly normal. Certainly some areas still look out of place and the ice caps are still too large, but the overall distribution of temperate and continental regions is fairly close to our world, there's actually some substantial variation in sea ice cover, and you might be forgiven for mistaking this climate map of the Americas for one of their real climates at a glance.

 

 

The devil's in the details, of course. Substantial parts of North America and Asia see seasonal temperature swings of over 40 °C, which on Earth occurs mostly only in subarctic regions—but here it occurs in the humid subtropics, areas we're used to thinking of as fairly consistently wet and warm with mild winters, but in this case swing between sweltering summers sometimes reaching over 60 °C on hot days and winters cool enough for nighttime snow and frost.

 

Europe is the odd continent out here, still dominated by Mediterranen climates where it isn't just frozen over, but as summer circulation of moisture towards the tropics has gotten even stronger, this type of climate has started appearing even more broadly, even in Japan of all places. ExoPlaSim always seems a bit biased towards Mediterranean-type climates so we should maybe be cautious about interpreting this, but it's never quite manifested in this way so there might be something to it.

There's also a bit more nuance to rain patterns just before and after peak summer, but I'll leave exploration of that to the next model where it's more apparent.

0.4

Prior Model: 0.3

CO₂ Level: 10 ppm

Stellar Flux: 98.6% Earth's

Average Temperature: 15.8 °C (6.2 Apr - 27.6 Aug)

You may note that at this point that I've lowered CO₂ to its minimum value in these models—roughly the minimum where oxygenic photosynthesis is still possible—and I've started lowering the stellar flux instead to counteract the heating effect of higher eccentricity. One issue I've only noticed as I was writing up this post is that ExoPlaSim's simple vegetation model is sensitive to CO₂, such that vegetation growth essentially stops at levels this low, so I won't be showing any data from that (trading off a bit lower sunlight for a bit more CO₂ should let you get a very similar climate more amenable to plant life, so this isn't an issue inherent to this type of climate; in the future I'll set a higher minimum CO₂ threshold for these runs). Note also that the stellar flux here is at the semimajor axis (which appears to be how ExoPlaSim handles the input value for flux); actual average insolation over the whole orbit will be a bit higher.

 

Anyway, the climate is starting to look a bit weird again. This much eccentricity causes over a 5-fold increase in insolation from apoapsis to periapsis, and most of that increase comes in a 4-month peak around periapsis, with little variation from September to April. The global climate varies considerably throughout this brief summer, so I think it's worth it to look through the year in a bit more detail here.

 

 

We'll start with March, where for the most part freezing temperatures reach their maximum extent, far enough south in the northern hemisphere that the temperate band is shrinking again as the continental climates squeeze it out. Otherwise, we see all the typical patterns we've come to expect: cool landmasses cause weak onshore winds (to the point that the trade winds almost seem to reverse couse to avoid Africa) and keep much of the tropics fairly dry, while the higher latitudes are kept moderately wet by the Ferrel cell winds. Overall it's worth noting throughout all these models how clearly distinct the circulation cells are and how uniform the prevailing winds compared to our Earth.

April is technically the coldest month on average, but this is mostly because the oceans are still cooling, whereas land areas are starting to warm again. This causes a slight strengthening of onshore winds that brings more moisture into some equatorial areas.

 

Temperatures over land start rising sharply in May, with a corresponding shift in winds—trade winds now start reversing course to converge onto continents rather than avoid them and the Hadley cell has subtly expanded—and a full tropical rain belt has formed along the ITCZ. Higher latitudes are still fairly wet at this point, though.

Within the next month, average temperatures rise by over 20 °C in many areas. Ocean temperatures lag behind, so winds rapidly reorganize around the new sharp temperature gradients, with gale-force onshore winds appearing on some coastlines. This results in a peculiar precipitation pattern, with intense rains across much of the interiors of the tropical continents but dry coastlines in many areas.

 

The next month sees a similar temperature increase, with averages spiking to over 70 °C in some areas and daytime highs approaching the boiling point. Much of the tropics and subtropics would likely be uninhabitable by humans. Winds continue to reorganize to converge on these warm areas, but more broadly the Hadley cells expand, drawing moisture away from the subtropical regions and concentrating it into the interiors of the equatorial continents; though I suspect we're also seeing something similar to polar summers on high-obliquity worlds, where a rapid rise in summer heat prevents condensation and precipitation of water even at high humidity. Either way, some of the hottest parts of the world are always among the driest (and also incidentally some of the windiest).

(The odd parallel waves of wet and dry strips around the coast are probably an issue with ExoPlaSim related to the limited resolution and discrete timesteps; the physics filters parameter helps reduce this tendency and prevent crashes that can arise from it but don't eliminate it. The actual planet would probably be more uniformly moderately dry in these areas.)

 

August is the warmest month globally, but much as we saw in winter, this is mostly because of the oceans heating up, while land areas have turned the corner and are beginning to cool down. This allows wind patterns to somewhat settle back into more regular convection cell patterns, spreading out moisture somewhat, especially towards coasts, but the Hadley cell remains wide and so the subtropical areas dry.

By September, insolation has already dropped to about 1/3 of its peak in early July. Ocean temperatures begin to catch up to those on land, but winds still generally converge onto continents so we get something of a global wet spell, with heavy rains in many subtropical areas kept dry through much of summer but now with onshore winds again thanks to the shrinking Hadley cells.

Thereafter, the climate enters a long autumn and winter; temperatures gradually decline, the Hadley cells gradually shrink and weaken, and the tropics gradually dry out (as do the poles as they cool down), a trend that continues well past apoapsis until insolation begins to substantially increase again in April. Thus, many areas that appear to have similar climates as they do on our Earth are a bit different in character:

• The tropics see pretty a pretty substantial swing between wet and dry seasons and even 20-30 °C variation in temperature, so rainforests are greatly reduced in favor of what are likely seasonal dry forests and savanna similar to the monsoon regions flanking the tropics on Earth.
• Many of the arid regions actually see fairly substantial rains in summer, but not enough to overcome the intense heat.
• In the temperate and warm continental areas, Mediterranean climates are far more prevalent, but much of these areas remain cold or even freezing through much of winter and early spring and summers are intensely dry, so it's only during fall when the rains return and some of the summer heat lingers that there's much opportunity for growth.
• Humid subtropical and monsoon-influenced climates, which on Earth are some of the most hospitable and productive regions, here see heavy rain only in early and late summer, flanking a couple months of sweltering heat, no rain, and vicious winds; ideal conditions for massive firestorms.

0.5

 

Prior Model: 0.4

CO₂ Level: 10 ppm

Stellar Flux: 91.8% Earth's

Average Temperature: 15.8 °C (3.7 Apr - 31.8 Jul)

The ice cap and tundra climates have finally retreated to about the same extent as our Earth, but, with a 9-fold increase in insolation from apoapsis to periapsis, the rest of the world sees intense summer temperature swings.

 

Large sections of the northern landmasses thaw completely in one month between June and July, and part of Manchuria in particular flips from just below freezing to over 50 °C; a temperature climb of almost 2 °C per day. These intense seasonal swings have squeezed out the temperate band in much of Asia; hot arid climates transition to cold arid and then continental climates. Even much of the formerly tropical regions dip into temperate temperatures in winter.

 

With continents interiors often 30-40 °C hotter than adjacent oceans in July, fierce onshore summer winds ravage many of the coastlines. The prevailing direction of the Hadley cells still dominates over the oceans, though, keeping subtropical areas dry.

 

Though the tropics still see heavy summer rains, the long, dry fall and winter has eliminated much of the wet tropical climates. None of these arid climates in the tropics and subtropics are too dry, though, with how far rains shift around; no part of the planet (at the resolution of this model) receives less than 39 mm of rain per year.

0.6

 

Prior Model: 0.5

CO₂ Level: 10 ppm

Stellar Flux: 83.2% Earth's

Average Temperature: 14.1 °C (-0.5 Apr - 35.6 Jul)

If Earth had this much eccentricity, its orbit would cross those of both Mercury and Mars (even if we shifted it out to get this much stellar flux, though only just for Mercury). About half the total heating the planet receives throughout the year arrives in June and July.

 

As you might expect, this drives an even more extreme temperature spike in early summer. Manchuria now rises by over 70 °C between June and July, and the American midwest isn't far behind. Both areas then drop back down by over 20 °C in August. During that July peak, temperatures in north Africa can approach 150 °C (in an area that also cools enough for light snowfall in winter).

 

Even here, though, the polar ice caps persist, and overall the annual average temperature distribution isn't actually much different from that for the 0.1 eccentricity case, aside from this planet being 1.4 °C colder.

 

The hot summer, of course, drives intense summer winds...

 

...and rapid shifts in precipitation; globally rains almost stop in July. Even the equatorial landmasses only get a couple bursts of rain in early and late summer, so have mostly given over to arid climates. Just to add insult to injury, cloud cover also almost completely clear over much of the planet, giving no respite from the sun by day.

I'm frankly not sure this climate state would prove to be stable against runaway greenhousing in the long term, but it's still interesting to wonder how life might adapt to such conditions; in the harshest regions it might still be possible to shelter through the brief summer—or at least produce seeds or eggs that can endure what adult organisms can't—and then emerge with the late summer rains, onto a landscape that may be cleared and fertilized by widespread wildfires, and grow as much as possible through the long autumn.

This is as far as we'll take it today; all my attempts to simulate a world with 0.7 eccentricity crashed within a few years, even when I lowered the stellar flux enough that the planet froze over. Most likely something about the rapid influx of heat in summer is too much for the model to reliably handle. Reducing the timestep to very low values like 5 minutes or less might help, but I've moved on to other models runs for now; leave a comment if you manage to do any better. There are a few different parameters I might explore next time depending on how the models work out, but most likely it will be combinations of both obliquity and eccentricity.

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