Climate Explorations: Obliquity

"True color" approximation for Earth as an ice belt world.

This is the second in a series of climate explorations using the ExoPlaSim model. Last time, we explored different average temperatures; for this post, we’ll keep the temperature (mostly) constant and explore the effect of obliquity, A.K.A. axial tilt. As a reminder, here’s the result of simulating Earth with its approximate pre-industrial conditions, including a tilt of 23.5° (rounded up from the real value of 23.44°):

Refer back to the last post for a discussion of the errors and weaknesses of this model; most obviously, high latitudes are a bit too cold but simultaneously under-glaciated. Still, it should serve well enough as a point of comparison.

Also refer back to that post for the procedure I’m following here; in particular, after changing obliquity I’m also adjusting the CO₂ levels to ensure an Earthlike temperature of 15 °C, which I figure is a better point of comparison.

To reiterate some of our past discussion, Earth’s obliquity is, of course, the predominant cause for our seasons: At 45° latitude, solar irradiance (not accounting for any atmospheric effects) shifts from around 502 W/m² at the summer solstice to 117 W/m² in winter, typically causing a 20-30 °C shift in temperature. The seasonal variation becomes stronger towards higher latitudes, up to a shift between 0 and 544 W/m² at the poles, though minimal seasonal variation occurs not at the equator, but at around 7° latitude; below that latitude, irradiance actually peaks at the equinoxes, when the sun passes directly overhead (435 W/m² at the equator), and drops at the solstices, as solar heating shifts towards the poles (400 W/m²). This gives the equatorial regions a sort of twice-yearly seasonal cycle between high and low irradiance, but for Earth’s current obliquity this is a very subtle effect. Still, it’s worth looking at all of Earth’s seasons for a complete comparison:

Top image is the annual average in all these charts. Because there's a slight lag in temperature changes compared to irradiance changes, the months after solstices and equinoxes are shown.

Grey squares are model cells that received no rain in those months.

Obliquity also affects average heating across the whole year: At the equator, days can never get longer than 12 hours, limiting average irradiance to 435 W/m² at most regardless of obliquity, but at higher latitudes, higher obliquity causes longer summer days with more direct sunlight. It also causes longer winter nights, but because irradiance can’t drop lower than 0 W/m² but it can get much higher (up to 1367 W/m² for Earth with constant direct sunlight), the former effect wins out: At 0 obliquity, the equator would remain at 435 W/m² year-round and the poles would receive essentially no irradiance; but at our current obliquity, the split is 417 and 174 W/m². At about 54° obliquity, average irradiance at the poles surpasses that at the equator; and at 90°, the split is 205 and 512 W/m².

Average temperature by latitude in the baseline model.

So in summary: Higher obliquity means warmer poles relative to the equator on average but stronger seasons, even at the equator.

• Lower Tilt
• 15°
• 5°
• 0°
• Higher Tilt
• 30°
• 35°
• 40°
• 45°
• 60°
• 75°
• 90°
• 15 °C
• -5 °C
• -28 °C    

Previous Exploration: Temperature   

Lower Tilt

15°

Prior Model: Baseline

CO₂ Level: 450 ppm

Average Temperature: 14.2 °C

Lowering the obliquity to 15° initially caused average temperature to drop to 10.8 °C before CO₂ adjustment, with ice caps and tundra extending over much of the baseline continental regions.

After adjustment, the world may look cold, but the vast glaciers and tundra are offset by a larger and hotter tropical belt, and the large deserts regularly reach over 50 °C in summer. In between, most of the temperate regions have disappeared.

The smaller temperature swings are accompanied by less variable wind patterns. Precipitation rates are about the same on average, but more concentrated: both rainforests and deserts have grown at the expense of semiarid (savanna, steppe, Mediterranean) regions.

5°

Prior Model: 15°

CO₂ Level: 540 ppm

Average Temperature: 14.1 °C

I ran this model just for a quick look at a world with minimal but not negligible seasons. Seasonable temperature swings are below 5 °C in most of the tropical and temperate regions, though they can still be as high as 10 °C at the poles.

As a result, continental climates have essentially disappeared, and the temperate regions are being squeezed from both sides, with the tropical belt reaching up to 30° latitude and the ice caps reaching down to 50°. Semiarid climates have also dramatically shrunk, due to little seasonal variation in precipitation.

0°

 

Prior Model: 5°

CO₂ Level: 540 ppm

Average Temperature: 14.1 °C

This is a seasonless world, with nothing to distinguish one half of the year from the other; the sun rises and sets at the same time every day of the year and rises to the same height at noon, passing directly overhead at the equator and remaining perched at the horizon at the poles. Some valleys near the poles may never experience direct sunlight.

There is still daily temperature variation, which averages around 10-20 °C over most of the planet but reaches up to 35 °C on the ice caps. Chaotic weather patterns can also cause moderate temperatures, allowing for occasional nighttime frosts in some temperate regions. Nevertheless, substantial parts of the tropics rarely fall below 30 °C and substantial parts of the ice caps rarely rise above -30 °C.

Under these conditions, continental, Mediterranean, humid subtropical, and monsoon climates are definitionally impossible, and temperate oceanic climates exist as a thin transitional region; tropical rainforest and frigid tundra can be under 1,000 km apart even on flat ground. The lack of seasons means that the contrast between ocean and land thermal inertial doesn’t matter much anymore, so the boundaries between the major climate belts can be remarkably straight.

Winds are consistent too, with remarkably distinct and regular convection cells. The same for precipitation; semiarid regions have greatly shrunk to thin strips, savannas have almost disappeared, and rainforest can give way to desert in under 100 km.

Consistent sunlight and rain could make the equatorial rainforests more productive than any on Earth.

Note that ExoPlaSim’s vegetation model predicts forests in some of the tundra regions here; though we shouldn’t trust this simplistic model too far, it is worth wondering how appropriate the Koppen zone definitions are here, and what sort of life might evolve in an environment with low average temperatures and nightly frosts but no permanent ice formation and consistent high sunlight (though I should also note that the ice caps would probably extend further into these tundra regions in reality).

Higher Tilt

30°

Prior Model: Baseline

CO₂ Level: 173 ppm

Average Temperature: 15.6 °C

Compared to our baseline of 23.5°, this is a smaller change than our previous step down to 15°, but the effect is similar in scale; prior to adjustment, average temperature rose to 19.9 °C.

With temperature adjusted back down, the continental climates have expanded, eating into the temperate belts somewhat and eliminating the ice caps; summer temperatures above 15 °C are not unusual at the poles. Intriguingly, the winter extent of sea ice has expanded somewhat in the northern hemisphere but shrunk in the south without the cooling effect of the ice cap.

Stronger seasonal shifts in temperature lead to greater shifts in wind and precipitation patterns, drying the equatorial region and expanding semiarid regions, neatly in reverse to the lower-obliquity models.

35°

Prior Model: 30°

CO₂ Level: 110 ppm

Average Temperature: 14.4 °C

I ran this and the 40° model after seeing the result of the 45° model, in order to better understand the rather dramatic transition that occurs at these obliquities. This is around the maximum axial tilt with a climate state broadly similar to baseline:

• A warm, wet equator formed by the ITCZ.
• Dry-winter semiarid belts formed by the seasonal motion of the ITCZ.
• Large subtropical deserts at the horse latitudes.
• Dry-summer semiarid belts formed by the seasonal motion of the Ferrel cell and polar front.
• Wetter high latitudes under the year-round influence of the Ferrel cell and polar front with distinct temperate, continental, and subarctic bands due to declining temperatures towards the poles.

No tundra or ice caps in this case, but there is still seasonal ice cover over the poles.

Still, the seasons are stronger, and, for the first time, the south pole gets warmer than the equator in summer. The strong seasons cause a fairly significant seasonal shift in precipitation, such that even the driest deserts get around 40 cm of rain a year (compared to 0.4 cm/year in the baseline). Thus, rainforests and deserts have both shrunk in favor of broader semiarid climates.

40°

Prior Model: 35°

CO₂ Level: 80 ppm

Average Temperature: 16.1 °C

With just a slight increase in obliquity, there’s been a pretty dramatic rearrangement: much of the tropical rainforests and subtropical deserts have disappeared, replaced by a vast patchwork of wet, semiarid, and arid climates over the equatorial regions. Much of the subarctic climate and polar sea ice is gone as well.

Though annual average temperatures remain 20-30 °C warmer at the equator than the poles, during summer the polar landmasses reach to around 10-20 °C warmer than the equator is at the same time.

This causes a huge shift in the ITCZ, moving almost directly over the typical position of the horse latitudes and bringing broad summer rains. Large dry belts also form poleward of the ITCZ in summer, forming broad areas of Mediterranean climates. The large shifts result in rather evenly distributed rainfall; the driest deserts receive 90 cm/year of precipitation on average.

(The average here is a tad warmer than I usually aim to have these models because I guessed at an appropriate CO₂ level rather than running through the whole iterative process.)

45°

Prior Model: 30°

CO₂ Level: 60 ppm

Average Temperature: 15.7 °C

At this point, the arctic and antarctic circles (equaterwardmost extent that experiences 24-hour night at the winter solstice) and the tropics of Cancer and Capricorn (polewardmost extent that has the sun directly overhead at the summer solstice) are at the same latitude. The climate has now completely switched over to an exotic high-obliquity state, which we should explore now in more detail.

The equator is still around 10-20 °C warmer than the poles on average and remains mostly around 15-25 °C throughout the year; still warm, but just about too cold at the solstices to be classified as tropical, save for in a few coastal patches. At higher latitudes, landmasses reach to 40-60 °C in summer and drop to below -20 °C in winter, but coastlines remain mostly within 0-30 °C, and open oceans are even more moderate; sea ice only forms in small coastal patches.

This leads to a large seasonal shift in convection and wind patterns. Rather than a pair of Hadley cells converging at the equator, there’s more like a single convection cell alternating directions with the seasons, forming curved wind patterns as the coriolis effect switches direction at the equator. Strong low-pressure zones over the continents keep some of these winds moving poleward, with wind speeds along some coastlines reaching over 60 km/h.

This one-way Hadley cell creates a wet convergence zone at mid-latitudes in the summer hemisphere, but leaves low latitudes in the winter hemisphere dry. At higher latitudes, the Ferrel cell becomes disorganized and the polar front disappears in summer, and consistently high temperatures makes formation of clouds and rain difficult, leaving the continents dry save for a few patches of strong poleward winds. But these circulation patterns reform in winter, allowing for moderate rain and snow.

Near the equinoxes, temperatures largely equalize and winds weaken globally. As such, the ITCZ sort of skips over the equatorial regions and rains don’t penetrate far inland in these regions, though the driest deserts still get over 40 cm/year of rain on average.

Note that the scale here is shifted down from that in the total precipitation maps, and grey areas get no snow at all.

Altogether, this creates a rather different pattern of climates compared to those at just 10° lower obliquity:

• A dry inland desert belt at the equator with semiarid or wet coasts.
• A dry-winter semiarid belt.
• A subtropical monsoon belt of intense summer rains and blisteringly dry winters.
• At higher latitudes, a vast patchwork of dry-summer (i.e., Mediterranean) and more consistently wet climates, with temperature variation correlated more to distance from the coast rather than latitude; temperate coasts, continental interiors, and a few subarctic patches at the poles and in mountains

These high-latitude dry-summer areas receive little or no light in the wet part of the year, and so might be quite barren compared to similar climates on Earth; any photosynthetic life there would have to either make do with what little photosynthesis it could get done in the moderately wet, moderately sunny spring and fall, or evolve some way to hold onto water from winter all the way to summer.

60°

Prior Model: 75°

CO₂ Level: 38 ppm

Average Temperature: 14.9 °C

At this obliquity, areas at around 60° latitude swing between direct sunlight in summer to 4 months of night at winter. The poles now receive more heat on average than the equator, and polar temperatures are also about 5 °C higher than the equator. But while average temperatures remain between 0 and 25 °C over most of the surface, the interiors of the polar continents can swing between over 70 °C in summer and under -30 °C in winter.

Coastlines are, again, more moderate, with almost no sea ice forming even through the long winter nights. The equatorial regions are also more moderate, with a twice-yearly cycle between around 5 °C at the solstices and 20 °C at the equinoxes. Nights below freezing aren’t uncommon; some amount of snow falls across all of the continents, though some large islands remain consistently above freezing.

As a result, tropical climates have disappeared entirely and even temperate regions are a bit sparser. Past that, much the same patterns as we established for 45° persist, but with smaller equatorial deserts and broader monsoon belts due to a combination of cooler equatorial temperatures and stronger solstice circulation over the equator, which creates a broader summer rain belt and seems to draw some water off the oceans into the equatorial interiors.

75°

Prior Model: 90°, 15 °C

CO₂ Level: 38 ppm

Average Temperature: 14.6 °C

Now that we’ve transitioned solidly into the high-obliquity climates, global climate has become a lot less sensitive to the precise obliquity; note that the 60°, 75°, and 90° models all have roughly the same temperature for the same level of CO₂. Despite heavy snowfall in winter, rapid warming causes a quick spring thaw, so not much solar heating is lost to reflection by snow or ice and even stronger polar heating with higher obliquity doesn’t much change the overall heat balance of the planet.

Almost all land areas beyond 45° latitude reach to over 50 °C in summer, but mostly receive enough winter rains to avoid becoming deserts—though we do have to wonder how much life could survive through the hot, dry summers and dark winters. Prospects may improve in the expanding temperate regions at mid-latitudes.

And, of course, we can see growing regions of tundra replacing the equatorial desert belt, with regular snows at the solstices and growing glaciers in the mountains. Conversely, tropical climates have reappeared in the open waters of the Southern Ocean (though only just, which is why it disappeared in the interpolation map due to slightly oversmoothed sea surface temperatures).

90°

I ran the 90° model from scratch (and then the 75° and 60° models from it), and in the process ran through a few different climate states that might be of interest. At this obliquity, everywhere on the planet sees the sun directly overhead for some part of the year, and everywhere save for the equator experiences daylong night for some part of the year.

15 °C

Prior Model: 90°, -5 °C

CO₂ Level: 38 ppm

Average Temperature: 14.3 °C

Much of the climate map here is basically identical to the 75° case, though the poles are now over 20 °C hotter than the equator on, with some sea ice appearing at the solstices. But the Koppen scheme is concealing the extremes here; summer temperatures of the south pole can reach 100 °C.

However, the oceans retain enough heat to make for mild winters across many of the coasts, and even the landmasses take some time to cool down; the equatorial landmasses remain the coolest parts of the planet to about midwinter. But while the equator warms thereafter, the polar continents continue cooling through the winter night and reach their coldest about a month before equinox, down to below -30 °C in the deep interiors.

Wind patterns are now almost completely dominated by one large convection cell extending from the mid-latitudes of the winter hemisphere almost to the pole of the summer hemisphere, though some remnant of the Ferrel and polar cells survives at the summer pole and in the weak winter winds.

This won't mean much to most of you but I included it for the nerds; This represents an averaged vertical slice through the atmosphere from pole to pole in January (top) and July (bottom), with color representing vertical air motion; red areas show upward convection and blue downward convection.

This one-way circulation creates a by-now familiar pattern of wet summers and cold winters in the subtropical monsoon belts, but a somewhat more unusual pattern forms near the poles. In winter, precipitation is moderate over the cold polar continents and somewhat higher over the warmer oceans. The pattern switches in spring as the equatorial winds switch direction and the continents rapidly warm, pulling in wet air from the oceans. But as the poles continue to warm into summer, it becomes simply too warm for clouds or rain to form; the land remains hot and dry for months even under oppressively humid air. Dropping temperatures in late summer finally allow for rain, with heavy downpours continuing into fall.

This is another pattern the Koppen system doesn’t depict terribly well; areas of “dry-summer” and “dry-winter” climates have been defined here based on the exact distribution of rains, though neither quite describes these dry-summer, dryish-winter, wet-equinox climates.

Altogether, this makes for a fairly hostile environment, with only a few temperate patches hospitable to Earthlike plant life. But we could suppose that some life might evolve to remain dormant through the extreme polar summers and then take advantage of the wetter springs and falls.

-5 °C

Prior Model: 90°, -28 °C

CO₂ Level: 1000 ppm

Average Temperature: -5.2 °C

This is an “ice belt” world, and about as warm as one can be with otherwise Earthlike parameters and topography. Note how much higher the CO₂ value is here than in the warmer model; the ice belt reflects a lot of sunlight, and, much as we saw with the snowball in the last exploration, it takes intense greenhouse heating to overcome it, though not quite to the same extremes. A bit more CO₂ than this and a few degrees of warming will cause the ice belt to rapidly collapse, flipping the climate over to a hothouse with extreme summer temperatures over the poles (hot enough to crash ExoPlaSim if CO₂ is not immediately reduced). Reforming the ice belt would then require intense cooling, perhaps even a complete snowball.

Summer temperatures over the poles still reach to almost 100 °C, while the ice belt drops to below -60 °C at the solstices and rises to about -15 °C at the equinoxes. However, the subarctic monsoon strip mostly remains between -30 and 20 °C, and there are even some pockets of temperate climates on islands and coastlines that remain between 0 and 20 °C.

Though there are no tropical climates currently, small patches in the southern ocean do remain above 11 °C year-round, so a better arrangement of topography or tweaking of other factors (atmospheric pressure, year length, relative solar/greenhouse heating) could conceivably allow tropical climates to exist on an ice belt world.

The overall rain patterns are similar, but the cold ice belt remains fairly dry and the stronger pole-equator temperature contrast seems to cause the equatorial convection cell to shift further into the summer hemisphere, creating a broader, stronger summer rain belt at mid-latitudes.

Life may thus fare rather better in this climate state, as there are more areas that receive rain and sunlight at the same time and at non-insane temperatures.

-28 °C

Prior Model: None

CO₂ Level: 300 ppm

Average Temperature: -27.6 °C

This was the initial result of running up the model from a “cold start” with 90° obliquity and an Earthlike CO₂ level. The ice belt clearly has a strong cooling effect, but the intense summer sunlight keeps the poles warm and the oceans retain the heat through winter, allowing for a stable non-snowball climate at much lower average temperature than for low obliquity. In the future, it might be interesting to see how cool a high-obliquity world can get before crashing to snowball occurs, or if there’s actually a smooth ice belt–snowball transition.

Despite the low average temperature, summers still reach to over 70 °C at the poles. The ice belt, however, drops to -100 °C in the solstices and rarely rises over -30 °C. In the continent interiors, there aren’t many areas that stay between -40 and 40 °C year-round, and temperate regions have disappeared; near-surface air temperatures drop below 0 °C for some part of the year all across the planet, though the sea surface itself manages to remain just above freezing near the poles.

As with the colder worlds at low obliquity we explored before, this is a fairly dry world, especially over the ice belt. The summer rain belt is fairly small and weak, and fall and winter are dry as well; the heaviest rains come with the late spring thaw, though much of this is snow at mid-latitudes.

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That concludes our exploration of obliquity for today, though there's clearly a wide range of possible high-obliquity climates we could explore in the future; more formal research has suggested that multiple circulation patterns could occur for different rotation rates or levels of solar flux. For now, though, the next post will be on day lengths (most likely; I'm still testing out a few different possibilities).

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