The Planetary Geometry of Extreme Climate Migration

Adam Sobel and I have a new paper on Potentially Extreme Population Displacement and Concentration in the Tropics Under Non-Extreme Warming.

The paper is a theoretical exercise making a simple point: tropical populations that migrate to maintain their temperature will generally have to move much further that their counterparts in middle latitudes. This results from well established atmospheric physics that aren't focused on by the researchers who usually think about climate change and migration. One reason this result is interesting is that, in a sense, the physics of the tropical atmosphere "amplify" the impact of warming (at least in this dimension) so that even small climate changes can produce really large population displacements in the tropics (theoretically). Here's the story...



The tropical atmosphere is very different than the atmosphere in the middle latitudes (Adam has written a short tutorial about why). One of the main reasons is because the atmosphere doesn't "feel" like its rotating in the tropics the way it does in the middle latitudes; in fluid mechanics we say that the tropical atmosphere has limited planetary vorticity (Kyle Meng and I have already tried once to explain how profound this point is to economists). This sounds boring/dumb/weird, but it actually matters a lot. First I'll explain what the issue is, then why it matters in a general sense, then what this all has to do with the new paper.

What do I mean when I say the tropical atmosphere doesn't "feel the earth's rotation"? The atmosphere has angular momentum (the thing that that makes ice skaters spin faster when they pull their arms in close and helps your bike stay upright when the wheels spin) because the earth is rotating once a day. If you stood on the north pole, you'd spin in a circle every 24 hrs. But if you stand at different latitudes, you feel this spin differently. An easy way to see this is to imagine a sheet of paper with two red dots on it placed on the ground. At temperate latitudes, you can see that the two dots appear as if the rotate around one another each day: one dot is closer to the sun in the morning, and 12 hrs later the other dot is closer to the sun. But if the sheet of paper is on the equator, the two dots no longer rotate around each other and instead just travel parallel to each other around the planet each day (yes, this is kinda weird). Here's a cartoon of these two sheets of paper from the article with Kyle:

From Hsiang & Meng (2015)

Why does this matter? Well, the spinning of the atmosphere, relative to the surface of the planet, is what generates the Coriolis effect (go ahead and click on that link, then you'll appreciate how simple my diagram is). This is the "force" that determines which direction hurricanes spin and governs how weather systems behave in the temperate latitudes (video), but it is pretty much missing from the tropical atmosphere because the tropics don't feel like they are spinning.  Ever wonder why photos of the earth from space have big swirly looking clouds? This happens because the Coriolis "force" is always pushing against pressure gradients in the atmosphere (caused by temperature gradients), causing the atmosphere to swirl and preventing temperature gradients from collapsing. If the Coriolis force didn't balance pressure gradients, then all our air would just quickly flow from high to low pressure regions and the pressure everywhere would equalize immediately (like in a bathtub). This balance between pressure gradient forces and the Coriolis force is one of the most important relationships governing how the atmosphere behaves in middle latitudes (see here if you love math), but it does not play a governing role in the tropics, which is why the tropical atmosphere doesn't look nearly as swirly as further north and south:

Because the Coriolis force is so weak in the tropics, it can't balance out large pressure gradient forces and so tropical air doesn't swirl and instead just sloshes around, more or less, kind of like water in your bathtub. If one part of the tropical atmosphere heats up, it creates an area of high pressure which moves into low pressure regions quickly, spreading the warmth rapidly.  So temperature gradients in the tropical atmosphere dissipate quickly, which causes large regions of the tropics to have pretty uniform temperatures (imagine: it's hard to keep one half of a bath tub full of hot water and the other end full of cold water without them mixing). Because temperatures are pretty uniform in the tropics, there are not strong temperature gradients. 

So to recap: (1) the atmosphere in the tropics doesn't "feel" the earth's rotation, (2) so there is not a strong Coriolis effect, (3) which means there is no Coriolis "force" to balance horizontal pressure gradients, (4) which causes pressure gradients (and thus temperature gradients) in the tropics to collapse quickly (like in a bathtub). This is why the tropics have weak horizontal temperature gradients.  (Note: one of Adam's important contributions is developing useful approximations of this phenomenon.)

Okay, so the tropics have weak temperature gradients while the middle latitudes have strong gradients. What does this have to do with migration and climate change? Well, there is a lot of literature pointing out that as the climate changes, populations of plants and animals move around to adapt, finding locations that have similar temperatures (see references 1-25 in the paper)---you're probably familiar with the idea of polar bears moving further north and species moving up mountains as things warm up. This is probably less true for humans, since we have lots of ways to cope with warming besides moving, but there is some evidence that people move in a pattern that is related to temperature. For example, we all know what happened during the dustbowl and in this paper we showed that people in Indonesia have a higher probability of moving (mostly to the cooler city) when temperatures get hotter:

Migration probability of Indonesian households, from Bohra-Mishra et al (2014)

So for the sake of theoretical clarity, Adam and I assume that whatever population we are looking at moves in space in such a way as to always preserve its environmental temperature. In reality, things could get more complicated.

The main point of the paper is that in the tropics these temperature-preserving migrations look very different than in temperate latitudes because the tropics have such weak temperature gradients (due to the dynamics described above). The can been seen with a simple geometric argument.  

Here's my cartoon for what temperatures look like for two populations, one in the tropics and one at higher latitudes. The red solid lines show temperature as a function of latitude and the dashed blue lines show the temperature that each of the two populations like to live in.  One population likes it hot (T_tropical) so it lives at a lower latitude than the population that prefers a warmer temperature (T_temperate):

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Now imagine that every location gets a little bit warmer due to climate change (orange arrows below). In response, populations move to preserve their initial temperature (in this simplified model). In high latitudes, this leads to some movement but it is modest so long as the amount of warming is modest (length of the green arrow below). But in the tropics, these displacements become really large  because the temperature gradient is so flat.  Adam and I point out that the length of temperature preserving migrations will be inversely proportional to the strength of the initial horizontal temperature gradient.

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Since I like analogies: if you're lying on the beach near the water at low tide and then the tide comes in, how far do you have to move to avoid getting wet?  It depends on how sloped the beach is right at the water's edge. If the beach is pretty steep, then the rising tide won't move to far inland and you might not need to move your blanket. But if you're at a really flat beach, then an incoming tide can force you to pick up your stuff and move inland pretty far.  If the height of the sand were instead the temperature at each location, then you can see why the steepness of the temperature gradient matters for distance traveled.

So is the simple cartoon above a reasonable model for the actual planet? You need temperature gradients to be low in the tropics and warming to be relatively uniform across all latitudes. In our analysis, we treat the oceans and continents separately, since we assume no species are going to go from one to the other when migrating. Looking at average surface temperatures as a function of latitude:

we can look at what the temperature gradient is at each location:

and we see that these gradients do indeed approach zero near the equator, and are small for a band in the tropics.

Finally, we check what average temperature changes are in a climate change scenario where global mean temp warms 2C:

and we see that temperature changes are pretty uniform across latitudes. So this simple model might actually perform pretty well.

We then take a bunch of climate model projections and compute actual temperature-preserving migrations in this scenario. To do this, we look for the minimum distance a population originating in location i would need to travel in order to preserve its temperature (subject to the constraint that continental locations stay on land, and visa versa for oceans). We then plot this distance (in logs) at the origin location i. Here is what we get:

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In the tropics, to preserve their temperature, populations have to travel roughly an order of magnitude further than at higher latitudes. In places that are medium-dark pink, temperature preserving migrations are >1000 km, for just a +2C change in global mean temp.

There are several places where the simple model approximations break down, for example mountain regions behave differently, and locations on the far southern coasts of Africa, Australia, etc behave oddly because the search algorithm is trying to move the populations over oceans (since they are constrained to remain on land). Also, coastal upwelling on the eastern boundaries of ocean basins produces strong temperature gradients that reduce migration distances.

An second interesting insight emerges if you ask where all the populations undertaking these extreme migrations end up.  To consider this, we simulate a scenario where there is a completely uniform initial distribution of populations all over the planet (imagine we spread and even layer of peanut butter over the entire earth). We then allow each pixel of population to move according to the temperature preserving migration above. This is the map of population density describing where populations (peanut butter) end up:

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Large tropical areas basically empty out, and populations end up highly concentrated at the edges of the tropics or the foothills of mountains, achieving population densities that are sometimes >400% of the initial population density. This concentration occurs because tropical populations are moving into the subtropics faster than subtropical populations move out.  This "traffic jam" of populations in the tropical margins is kind of like when fast moving cars on a highway suddenly encounter cars that are moving in the same direction, but not as fast.

We think this kind of population concentration is a bit worrisome, since if it actually occurred there were be tremendous strain on resources in the regions where the population densities climb. To drive this point home, we developed a simple thought-experiment with a well-known initial population distribution that's a little more structured than peanut butter: people. Here is the global population distribution before and after +2C of warming, if everyone were to follow a temperature preserving migration (assuming no population growth):

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Things would get almost inconceivably crowded in a lot of locations (take a look at India, and note that this is a log scale). Clearly, this isn't what's going to happen, since people don't just pick up and move cities like this. But it does provide some sense of proportion for these calculations.

This exercise also allows to consider the distribution of distances individuals would travel under this scenario. Here's a histogram of hypothetical distances traveled:

Roughly a third of the world would have to move more than 500 km and 12.5% of the world would have to move more than 1000 km. This is a lot of movement and it would be extraordinarily costly.

What are the main take-aways from this kind of theoretical exercise? First, when people think about climate-induced migration, they often focus on polar regions or mountain sides, but we want people to realize that the tropics are also an important place to pay attention to because the temperature gradients are small---so if populations start to move, they might move (and concentrate) a lot. The dynamics that govern these temperature gradients (i.e. Coriolis effects) are a little more sophisticated than what most folks are usually focused on in this research space, but they are extremely generalizable and may have first-order significance in lots of cases.

Second, this is a theoretical exercise about "potential migration and concentration" which almost certainly won't play out exactly as depicted because of all the various ways populations adapt to climate changes.  But the extremity of these results should flag for us how important it is to understand migration and climate change better. We currently know very little about how populations move in response to climate and what the knock on effects of these movements are (especially for people), and we desperately need to know more. Large-scale migrations and population concentration can be massively destabilizing, for human or natural systems (consider the current European crisis), so we need to understand these dynamics better and develop a better sense for how much they are affected by climate change. Even if our theoretical calculations here differ from reality by a factor of five, these types of changes would be dramatic.