Friday, March 18, 2022

Land Gained and Lost: A Fermi Estimate

Climate change affects the amount of land usable by humans in at least three different ways. Land is lost through sea level rise. Land is lost because it becomes too hot for human use. Land is gained because it becomes warm enough for human use. Exact calculations of the size of all three effects, if possible at all, would require much more expertise and effort than I am bringing to the problem so what I offer are Fermi estimates, numbers based on very crude approximations. For all three estimates I will be assuming warming of 3°C above current temperatures and sea level rise of .6 m above present sea level, roughly what the latest IPCC report projects for the end of the century under SSP3-7.0.

Land Lost to Sea-level Rise

The amount of land lost equals the length of coastline times the amount by which it shifts in. For the total length of the world’s coastline I found a figure of 356,000 km. The amount by which coastline shifts in with a given amount of sea level rise depends on the slope of the coastal land. I came across a figure of a hundred feet of shift for every foot of sea level rise in a book discussing the situation on the U.S. Atlantic coast; since I do not have figures for every coast in the world, I will use that.

60m coastline shift x 356,000 km of coastline = 21,436 km2

That is my very approximate estimate of land lost to sea level rise.

Land Lost to Rising Temperature

How much does temperature rise in hot parts of the world with 3° more of global warming? Figure SPM.5b of the latest IPCC report[1] shows a map of projected average temperature change due to a 4° increase relative to 1850-1900 in average global temperature, roughly 3° relative to current temperature. Parts of the Earth that are both hot and densely populated appear to warm by a little less than the global average. Table 11.SM.2 shows the effect of different levels of global warming on maximum temperatures. It looks from that as though 3° of global warming would raise the maximum temperature of the relevant regions[2] by about 3°. So if we knew at what temperature, average or maximum, the Earth’s surface becomes too hot for human habitation, we could conclude that any area currently within three degrees of that would, with our assumed level of global warming, become too hot for humans.

The simplest approach to doing this is to compare a map of global temperature (Figure1 ) to a map of population density (Figure 2) and see at what temperature population density goes to close to zero. Comparing the two maps we observe that while the coldest areas of the globe are essentially empty, the hottest are not; some, such as the Philippines, Senegal, and Malaysia, are densely populated. If there is a temperature at which the Earth’s surface becomes unliveable, these maps do not show it. Our estimate of the amount of land lost by the direct effect of heating, calculated in this way, is zero.

We may be able to do a little better by looking at data on cities. The hottest city, by average temperature, is Assab, Eritrea, at 30.5°C, with several others nearly that warm. Hence we can conclude that any city whose average temperature after climate change is less than 30.5° will not be unliveably hot while cities whose temperature is higher than that might be. There are 28 cities with an average temperature of 28°C or more. Their a combined population is about 33 million, which is roughly .7% of the urban population of the world. If we use urban population ratio as a very rough proxy for total population ratio and that as a very rough proxy for land ratio and calculate.7% of the non-arctic land area of Earth, we get 

149 million km2 (Land area) – 5.5 million (Antarctica) - .8 million (Greenland) = 143 million km2

143 million km2 x.007 = 1 million km2

That gives us a very approximate upper bound for the amount of land that becomes unlivable due to global temperature increasing by three degrees. It is only an upper bound because we do not know that a city would be unliveable at an average temperature of 31°, only that there are no cities that hot.

Both of these calculations are based on average temperature. Arguably what habitability depends on is be maximum temperature. If it gets unendurably hot during a summer day, the fact that winter nights are cold is little compensation.

Figure 3 is the equivalent of Figure 1 for maximum temperatures. The highest temperature regions it shows include densely populated parts of India as well as more sparsely populated parts of Africa and Arabia. Insofar as one can tell from that map, there are no places large enough to show on the map where maximum temperatures are too high for human habitation. It is possible that some would be that hot after an additional three degrees of warning but the combined evidence of Figures 2 and 3 suggests not, since some of the hottest regions are densely populated.

I have been defining usable land as land humans can live on. While there are parts of Earth that seem crowded, average land per person is about five acres, so human populations are not limited by the amount of space to put them in. They might, however, be limited by not enough land to feed them, so it might make more sense to define usable land as land suitable for growing crops.

Is there any significant amount of land that is too hot to grow crops? So far as I can tell, there is not. Maps showing yield of various crops can be found online; some regions with high average and maximum temperatures show substantial yields. The yields shown are averaged over countries, but a map of agriculture in India shows crops being grown across areas within India of both high average and high maximum temperature.

My conclusion from these calculations is that there is probably no substantial amount of land area that will become either uninhabitable or unable to grow crops solely because of temperature with global warming of 3°C.

This does not mean that there is no area that will become either uninhabitable or unable to grow crops as a result of global warming, only that there is no area where it will happen solely because of temperature. Looking at Figure 2, one observes a wide region of northern Africa with almost nobody living there — the Sahara. That area is less hot than some populated regions, so temperature is not the entire reason it is empty, but it can be, almost surely is, part of the reason, so increased temperature might expand it.

On the other hand, the latest IPCC report suggests the possibility that climate change might have the opposite effect:

Some climate model simulations suggest that under future high-emissions scenarios, CO2 radiative forcing causes rapid greening in the Sahel and Sahara regions via precipitation change (Claussen et al., 2003; Drijfhout et al., 2015). For example, in the BNU-ESM RCP8.5 simulation, the change is abrupt with the percentage of bare soil dropping from 45% to 15%, and percentage of tree cover rising from 50% to 75%, within 10 years (2050-2060) (Drijfhout et al., 2015). However, other modelling results suggest that this may  be a short-lived response to CO2 fertilization (Bathiany et al., 2014).

In summary, given outstanding uncertainties in how well the current generation of climate models capture land-surface feedbacks in the Sahel and Sahara, there is low confidence that an abrupt change to a greener state will occur in these regions before 2100 or 2300.

Figuring out all consequences of climate change for the amount of land available for human use is a much more complicated problem than I am trying to solve.

Land Gained Due to Rising Temperature

Human land use at present is limited by cold, not heat, as shown on Figure 2 above — the equator is populated, the polar regions are not. It follows that global warming, by shifting temperature contours towards the poles, should increase the amount of land warm enough for human habitation. Making Antarctica habitable would require a lot more than three degrees of global warming and the southernmost land masses north of it are already inhabited, so any land gains from warming will be in the northern hemisphere.

Figure 11.SM.1 of the sixth IPCC report shows minimum temperature of areas such as North America and Northern Asa going up by between 2 and 3.4 degrees per degree of global warming. Since warming is greater in colder climates, I take 3 degrees per degree as a reasonable guess for the increase in temperature in the northern part of those zones. It follows that three degrees of global warming will increase the temperature in the colder parts of those zones by about nine degrees. To estimate how much land will shift from not quite habitable to at least barely habitable we need two numbers — what length of the contour dividing barely habitable from not quite habitable is over land and how far a nine degree increase in temperature will shift it.

It seems likely that habitability depends more on minimal temperature than on average temperature. Figure 4 shows temperatures in January, which should be close to the minimum, with contours every five degrees — much more precise information than Figure 1 provides for average temperatures. Combining the temperature information on Figure 4 with the population density information on Figure 2, the border of habitability appears to be at about -15°C. Nine degrees of warming will raise the January temperature of land currently at -24° to -15°, so shift the land between those two contours from not quite habitable to barely habitable. I estimate the distance between the -15° and -25° contours to average about 800 km, making the distance between -15° and -24° about 720 km, and the length over land of those contours to total about 15,000 km. Hence the area between them is about 10,800,000 km2.

This land is being warmed from not quite habitable to at least barely habitable, from a population density of less than two per square km to a population density of more than two but in some areas less than ten. At the same time, the land a little farther south is being warmed from barely habitable to more than barely habitable, and the land south of that …  . Combining those effects, 10.5 million square km is a rough estimate of the increase in fully usable land.

The analysis so far has used population density as the measure of habitability. As I suggested earlier, it may make more sense to use the ability to grow crops. Crop production maps for Canada and Russia show crops growing in about the same areas that appear habitable by population density, so I have not tried to redo the calculation on that basis.


On the basis of these calculations, I find, for the effect of climate change by the end of the century under SSP3-7.0:

Loss of usable land by flooding due to sea level rise: 21,436 km2

Loss of usable land due to the direct effect of warming: Probably close to zero, with one calculation giving an upper bound of one million km2.

Increase of usable land due to the direct effect of warming: 10.8 million km2.

All of these numbers are very approximate but they imply a large net increase, due to climate change, in the amount of land usable by humans — more than twice the area of the United States. They also imply that nearly five hundred times as much land is gained through warming as is lost through sea level rise, which makes it odd that only the latter is commonly included in discussions of the effects of climate change.

P.S. Two commenters on this in different places asked why I didn't discuss other work along these lines and one of them provided a link to “Climate change impacts on global agricultural land availability” by Xiao Zhang and Ximing Cai 2011 Environ. Res. Lett. 6. It is a more elaborate analysis than mine, focusing on the amount of arable land and trying to take account of a  wider range of constraints including soil quality and humidity. It finds increases in some regions, decreases in others, with the net effect, not including land not available because of population increase, ranging from -.8 million km2 to +1.2 million km2. Details of their analysis are difficult to extract from the article — I could not tell, for example, whether the effect of CO2 fertilization on the water requirement of plants is one of the effects they take into account. The analysis in this chapter is less sophisticated but much easier for the reader to audit, to figure out what I am doing and whether to trust the result.

A similar calculation is done in Ramankutty N et al 2002,  The global distribution of cultivable lands: current patterns and sensitivity to possible climate change,” Global Ecol. Biogeogr. 11 377–92. That article explicitly takes account of the reduction in water requirements due to CO2 fertilization. The authors conclude “In the GCM-simulated climate of 2070–99, we estimate an increase in suitable cropland area of 6.6 million km2.” Since I am estimating land warm enough for human use and they are estimating land suitable for cultivation, taking account of a variety of constraints, it is not surprising that their figure is lower than mine. The Sahara, for example, is warm enough for human use — there are densely populated regions that are warmer — but not suitable for cultivation.


This is a draft of a chapter for a book I am working on. I am looking for two sorts of comments:

1. Easy ways of doing my calculations better. There are obviously ways I could make my results more accurate by more complicated calculations but since I don't really care if the real number is twice mine or half it, that isn't worth doing. On the other hand, if there are ways just as easy but smarter, giving a more reliable result, I am interested.

2. Major mistakes. My conclusions are pretty dramatic and I want to know if they are, for some reason, wildly wrong.

[1] This and other references to IPCC figures in this chapter are to IPCC AR6 WGI Full Report.

[2] SAS, EAS, SEA, and CAF in the table.



At 3:00 AM, March 19, 2022, Blogger Benjamin Cole said...

Interesting. I too have wondered about certain northerly bands becoming habitable.

Anecdotally, I am told winters in Montana are milder than 70 years ago, and accounts for some population growth of the state.

Add on: Higher CO2 level are often artificially induced in greenhouses, for obvious reasons.

But also: The Mojave river used to flow pretty well, and in the 1920s people built thoroughbred horse farms out there. No more.

So, there will be winners and losers. Venice, Italy may wish to recalculate matters.

At 7:53 AM, March 19, 2022, Anonymous Anonymous said...

Nicely thought out and structured.

I understand that there isn't really space fo it in this discussion, but are you looking to draw any parallels to the Medieval Warm Period? Even though it is considered an anomaly, and much more localized, the effects of the changes in weather on society and culture were remarkable and, while some may take that as an endorsement of the issue, certainly a point of discussion.

Thank you, a good read for a late saturday morning.

At 7:57 AM, March 19, 2022, Anonymous Anonymous said...

More comments on this post here:

At 8:17 AM, March 19, 2022, Blogger Unknown said...

Well posited, dispassionate and balanced. Well done!

At 11:46 AM, March 19, 2022, Blogger László said...

This does not take into account the inevitable collapse of ecosystems that cannot adapt to such temperature changes, even if humans could. We need those to survive in the long run, so the "gains" would be worth very little.

At 1:23 PM, March 19, 2022, Blogger Modern Mugwump said...

Nice job calculating, but just a glance at the globe and the shapes of the continents yeilds the same conclusion - there's an awful lot of too-cold land in the northern hemisphere (I've been pointing this out for 20 years).

But politically, Change Is Bad. All change (even if it's good). People are spring-loaded to see the negatives of change and ignore the positives.

And for those who want to control the world, Bad Is Good. In the immortal words of Rahm Emanuel, "You never want a serious crisis to go to waste". Nothing motivates people to give up power to central authorities like fear and crisis.

At 4:21 PM, March 19, 2022, Anonymous Anonymous said...

This doesn't quite fall into the two categories you ask for, but (last I was aware) the warming predictions have more detail than a flat increase to all temperatures. That 3 degrees of average warming is mostly due to higher low temperatures, not to higher high temperatures, which has significant implications for the section on "what if habitability is mostly due to maximum temperatures rather than average temperatures?".

At 4:41 PM, March 19, 2022, Blogger David Friedman said...


I was looking at the effect on maximum temperature:

"Table 11.SM.2 shows the effect of different levels of global warming on maximum temperatures. It looks from that as though 3° of global warming would raise the maximum temperature of the relevant regions by about 3°."

At 4:51 PM, March 19, 2022, Blogger David Friedman said...


This is a change occurring over almost eighty years, which is enough time for most species to shift their range accordingly. The major exception would be trees. Could you go into more detail on what ecosystems you expect to collapse, and why, if average global temperature increases by about three degrees?

Also, were you aware of the effect I describe and its magnitude? If not, might that suggest that you have gotten a very biased account of climate change issues, omitting positive consequences? If so, might that suggest that your views on the effect of warming on ecosystems — I am guessing that it isn't based on your own research — might be due to a biased account?

There are two objectives to this essay, supposing that nobody points out serious errors in it. One is to persuade readers that the effects of climate change are substantially better than they believe by demonstrating one large positive effect they were unaware of. The other is to persuade readers that their present views are based on a badly biased account of the evidence, as demonstrated by that account omitting a large positive factor.

For the second, do you really want to claim that not mentioning the addition of ten million square kilometers to the habitable land mass of the Earth is not evidence of bias, just because you can think of a problem, one you already knew about, that you think somehow balances it?

At 4:55 PM, March 19, 2022, Blogger David Friedman said...


I have discussed CO2 fertilization at some length on my blog in the past. It's another example of an effect of climate change that usually gets left out of discussions.

At 8:29 AM, March 20, 2022, Blogger Ernie said...

Here is a video on the effects of a carbon tax. The model used has a 1 deg X 1 deg resolution of the world. Migration and effects on land are included.


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