Climate Explorations: Combining Obliquity and Eccentricity
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"True" color approximation of hemispherically mirrored Earth with 45° obliquity and 0.5 eccentricity |
Hello, this is part of a series where I explore different possible climates with the ExoPlaSim model. As per usual, you can check the first post in the series for details on my approach and some of the limitations of the model. This will also be my first exploration using my new climate classification system, so you may want to take a quick look at that if you’re not familiar and compare how it looks with previous explorations.
We’ve already looked at the individual effects of
different rotational obliquities
on a world with zero eccentricity and
different orbital eccentricities
on a world with zero obliquity. For the most part, I want to go through each
individual parameter in turn throughout this series before I start exploring
their combinations, but in this case I couldn’t resist seeing how these two
seasonal forcings work together.
To review, obliquity creates
seasons through the shifting orientation of the planet relative to the star
(due to the orbit; it doesn’t actually change in absolute terms), causing an
offset seasonal cycle between hemispheres: summer solstice (the point of
maximum heating and longest daylight at high latitudes) in one hemisphere
coincides with winter solstice (minimum heating and daylight) in the other,
with mild equinoxes (equivalent heating and daylight between hemispheres) in
between. Higher obliquity brings more heat on average to the polar regions
but also greater seasonal changes in heating, and at high obliquity the
equatorial regions also experience their own twice-yearly seasonal cycle,
with warm equinoxes and cold solstices.
Eccentricity creates
seasons through shifting distance from the star, causing a simultaneous
global seasonal cycle: the entire world experiences the same warm periapsis
(closest approach to the star) and cold apoapsis (farthest point from the
star). Higher eccentricity causes more intense changes in heating, but also
affects the length of seasons; the planet moves faster through its orbit
near periapsis and slower near apoapsis, so higher eccentricity creates
shorter summers and longer winters, though in practice this seemed to
manifest as a short spring warming just before periapsis and then gradual
fall cooling thereafter.
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Movement of planets at different eccentricities (0.0 to 0.8). Phoenix7777, Wikimedia |
How seasons play out on a planet with both substantial obliquity and eccentricity will depend on exactly how these two cycles align. In this post, we’ll look at the particular case of periapsis aligning with northern summer solstice. This creates an asymmetrical seasonal pattern, where the northern hemisphere sees a greater range in heating from the sun (the sun is both highest in the sky and closest in space in summer and both low in the sky and distant in winter) but the southern seasons are dulled by an offset pattern (the sun is high but distant in summer and low but close in winter). But again, eccentricity also affects the lengths of seasons; obliquity causes seasons because of the shifting relative orientation of the planet’s rotation and the sun, and as the planet moves faster in its orbit near periapsis, that relative orientation shifts faster. Currently, Earth’s equinoxes are in March and September, at about the 21st in both months, such that each hemisphere gets about the same period of greater light. If periapsis coincided with northern summer solstice at June 21 (instead of falling in January as in reality), then at 0.1 eccentricity, the solstices would shift to April 2 and September 8; at 0.3 eccentricity, they’d be at April 25 and August 17; and at 0.5 eccentricity, they’d be at May 16 and July 26, with only 71 days between them in norther summer but 294 days through northern winter.
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Movement of planet around the sun in this scenario (eccentricity exaggerated) and orientation of the planet relative to sunlight at these points (with the rotational axis shown, north pole on top). |
Thus, the northern hemisphere experiences short, hot summers and long, cold winters, while the southern hemisphere experiences long, cool summers and short, mild winters. This all balances out such that the average heating across the whole year is still symmetrical across hemispheres. Higher eccentricity increases global average heating, but in proportional terms it doesn’t affect the distribution of average heating across latitudes, only how that heating is distributed throughout the year.
The tricky thing is that, even neglecting its slight eccentricity, Earth already has a somewhat asymmetric climate due to the different distribution of continents across the hemispheres, with the northern hemisphere generally having stronger seasons due to its greater land area (land warms and cools faster than oceans and so sees stronger seasons). To get a better sense of how combining obliquity and eccentricity can create asymmetric climates across the hemispheres, I want to work with a more symmetric baseline. The solution I’ve found to this is to take the topography of Earth’s northern hemisphere and simply flip it over into the south:
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The greyscale heightmap used in this exploration, with seas marked in blue. |
(For anyone who missed the last post, these plates show the uninterpolated climate map in my new bioclimate system in the top left, the interpolated map below with the key, and a Koppen-Geiger map in the upper right with the same color scheme as in my previous explorations and on Wikipedia.)
The result is about 3 °C cooler than actual Earth, likely because the
higher land area (39% of the surface to actual Earth’s 29%) gives it a
higher albedo, and it appears to have a somewhat stronger monsoon around the
East Asian ocean, which is typically underestimated in ExoPlaSim models of
actual Earth at this resolution.
Look closely and you’ll still
see some discrepancies between hemispheres, which can be attributed to some
combination of A, random noise that the 10-year sampling period didn’t
completely filter out: B, ExoPlaSim’s default year is slightly offset from
the periapsis-apoapsis cycle (to match Earth’s year, with periapsis in early
January), which subtly influences how the monthly averages turn out; and C,
perhaps some slight biases somewhere in the internal workings of
ExoPlaSim—I’m not aware of any specifically, but they’re not unusual in
models of this type and ExoPlaSim in particular has in past versions had
issues with the ways data at different latitudes is split between CPU cores
and combined back together. Regardless, any such bias looks to be small
enough for this to serve as a decent baseline for the sort of asymmetric
seasons we’ll be seeing today.
To cover the range of reasonable
obliquities and eccentricities, I’ve picked out 3 levels of each to combine:
23.5°, 45°, and 90° obliquity and 0.1, 0.3, and 0.5 eccentricity.
One
final note is that rather than altering CO2 levels to adjust temperature, as
I have done in previous explorations, I’ve switched to holding CO2 at 300
ppm and altering stellar flux (the average level of sunlight, before
adjusting for eccentricity). This is because I’ve found that part of
ExoPlaSim’s vegetation growth model varies with the CO2 level. This does
make some of the vegetation maps I’ve included with previous explorations a
bit suspect, but it’s hard to say how much, especially for the cases with
higher CO2—for what it’s worth, maximum vegetation growth is also limited by
water availability and temperature in the model.
23.5° Obliquity
This is roughly the obliquity of modern Earth, so any shift in seasonality will be due largely to the influence of eccentricity. Earth’s slight orbital eccentricity of 0.0167 does actually have a subtle influence on our climate, with shifts in the alignment of the obliquity and eccentricity cycles particularly influencing the humidity of northern Africa (because alignment between periapsis and northern summer create stronger northern seasons which pull the ITCZ farther north in summer). But the eccentricities here will all be greater than any Earth has ever experienced, so far as we can tell.0.1 Eccentricity
Prior Model: Symmetric Earth baselineStellar Flux Relative to Earth: 1.004
Average Temperature: 15.5 °C
To start off with, the asymmetry here is moderate but still obvious at a glance: the combination of periapsis with summer solstice in the north gives it more intense seasonal swings in temperature and precipitation, while the south sees more regular rain and less hostile extremes but also a shorter growing season at high latitudes.
0.3 Eccentricity
Prior Model: 23.5° obliquity, 0.1 eccentricityStellar Flux Relative to Earth: 0.96
Average Temperature: 14.4 °C
Here we see a more obviously asymmetrical climate, with a major ice cap in one hemisphere and only seasonal ice in the other (and this is another case where the Pasta bioclimate system more clearly shows how dramatically the extreme seasons are affecting the north compared to Koppen-Geiger). Again, both hemispheres receive the same total amount of light in a year, so this is due only to how sunlight is distributed across the year. In particular, the extent of ice is largely limited by summer melt: so long as winters remain below freezing, the exact temperature doesn’t much affect rates of ice accumulation, but summer temperatures do substantially affect rates of melt and so the overall balance of melt to accumulation; thus, even though the north has a longer and dimmer winter, the hot summers keep the ice at bay, while the south has gradually iced over, which raises its albedo and so does ultimately create an imbalance in total effective heating of each hemisphere. The northern polar regions are even balmy enough to see significant vegetation growth in their few summer months (though this is partially a consequence of the automatic global temperature adjustment; to maintain the same global average temperature, a colder southern hemisphere has to be counterbalanced with a warmer north).
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Average temperature by latitude throughout the year. |
The equatorial regions are wetter, but starting to see significant seasonality and their own monsoon cycle from a mix of obliquity- and eccentricity-related effects: near periapsis/northern summer, the ITCZ shifts north and the equator warms enough to widen the Hadley cell and generally intensify global winds, but not so much as to suppress rain, so heavy rains reach into much of north Africa; near apoapsis/northern winter, the ITCZ shifts back towards the equator and the Hadley cell narrows, keeping the equator wet but leaving north Africa dry.
In the south, for the most part weak thermal seasons come with correspondingly little precipitation variation, with the deserts largely staying dry and temperate regions staying wet, but there is still a substantial Mediterranean strip between the deserts and tundra; the same intensifying of winds near periapsis also draws moisture away from these areas, which are also hottest at around the same time, creating a dry-summer precipitation pattern.
0.5 Eccentricity
Prior Model: 23.5° obliquity, 0.3 eccentricityStellar Flux Relative to Earth: 0.821
Average Temperature: 14.4 °C
This case is in some ways a bit more symmetrical than the last case, because eccentricity is starting to dominate over obliquity in forcing seasons, though it’s fairly clear that the south still offers better prospects for survival despite the vast ice caps.
The overall result is another entry in our collection of marginally habitable worlds, with a region of fairly hospitable climates trapped between extremes. Though, because the alignment of the eccentricity and obliquity cycles tends to shift over time (on Earth, over a roughly 21,000-year cycle), the durability of this habitable region is questionable.
45° Obliquity
If you’ve been following my previous explorations, you may remember that 45° obliquity represented a somewhat interesting intermediate state, with the tilt high enough to show a high obliquity circulation pattern of predominantly equator-crossing winds, creating equatorial deserts and a mid-latitude monsoon belt; yet low enough that the equator remains the warmest part of the planet on average. I figured then that it would be worth seeing how this responds to asymmetrical seasons as well as the low- and high-obliquity cases.0.1 Eccentricity
Prior Model: 23.5° obliquity, 0.1 eccentricityStellar Flux Relative to Earth: 0.998
Average Temperature: 15.3 °C
To start out with, much as with the first 23.5° case, the differences in temperature are modest at first, with the average temperature profile still largely symmetrical, but there are some notable differences.
0.3 Eccentricity
Stellar Flux Relative to Earth: 0.915Average Temperature: 16.0 °C
Again as with the 23.5° cases, this intermediate eccentricity shows some of the clearest asymmetries.
0.5 Eccentricity
Stellar Flux Relative to Earth: 0.82Average Temperature: 15.7 °C
As with 23.5°, the high eccentricity begins to dominate seasons at low latitude and so make them more symmetrical, but the bulk of the southern hemisphere manages to remain moderate as the north gives way to sweltering desert; after all, anywhere beyond 45° south simply gets no light in midwinter no matter how close the sun is.
In the south, there is a heat wave in the lower latitudes in August when the planet rapidly speeds through equinox while still close to the sun. But at higher latitudes, this rapid winter is a boon, lasting just long enough to save the surface from the intense periapsis sun but quickly passing to give prolonged periods of summer sun. The winter freeze only lasts about a month, and recall that, given the timing of the equinoxes, even the south pole only has to endure about 70 days of winter night and then passes the rest of the year in continuous light.
The sun still gets a bit more distant towards apoapsis, which gives many of these areas curious double-seasons: Warming from the brief winter freeze in July to an initial post-periapsis high of 10-25 °C in September, then gradual cooling back down to a ~5-10 °C low in February with widespread mountain frosts, and then warming again as the sun grows closer to another high in May before the rapid onset of winter.
90° Obliquity
Of course, I had to see how eccentricity would combine with extreme obliquity. For these cases I have presumed that people are particularly interested in the potential for such worlds to develop equatorial ice belts, so rather than 15 °C I aimed to balance these cases at -5 °C, the highest average temperature where we found a stable ice belt in our previous exploration of high-obliquity worlds.0.1 Eccentricity
Stellar Flux Relative to Earth: 0.998Average Temperature: -5.0 °C
Previously it seemed like -5 °C made for a happy medium for high-obliquity worlds, not so hot to be completely desiccated by the summer heat but not so cold that too little water evaporates to produce much rain, but in this case that hasn’t worked out quite as well and much of the continental interiors in both hemispheres are fairly inhospitable.
All in all, the south hemisphere still probably offers the best prospects for habitability, but it’s a narrow margin
0.3 Eccentricity
Stellar Flux Relative to Earth: 0.926Average Temperature: -4.7 °C
As per usual, now we start to see more significant asymmetry, and again the south appears to be the big winner in terms of habitability, but there’s some benefit to the lower latitudes in the north as well.
The south, on the other hand, sees a more gradual temperature climb over its long summer to a blistering but more survivable summer peak in March, and then typically a 3-4 month freeze.
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Sea ice cover through the year |
The other highlight here is of course that the precipitation patterns in the north show the typical dry summer and fall downpour, but the south’s more moderate warming allows it to retain rains through summer, with the only dry periods in winter when the hemisphere cools and moisture is all pulled north.
0.5 Eccentricity
Stellar Flux Relative to Earth: 0.799Average Temperature: -5.0 °C
For this case, I couldn’t get a stable permanent ice belt to form, but I kept to a -5 °C average for comparison.
That’ll do for this exploration. This is, of course, just one possible alignment for eccentricity and obliquity seasons, and at some point I may want to look at what happens If periapsis coincides with an equinox rather than solstice. But we’ve still got a fair few individual parameters still to explore, so next time we’ll be looking at varying surface atmospheric pressure. See you then.
HOLY COW IT FINALLY CAME
ReplyDeleteOMG this is so great
Say there is a continent stretching about as far north as south from the equator like Africa. Then entire ecosystems could migrate between hemispheres over the Milankovitch cycle. Such a continent would have an advantage in evolving large animals. They would not be limited to small sky islands half the cycle. Such sky islands would also get severely cold in winter creating another difficulty for evolution.
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