How much time do we have?

An Engineer looks at Global Warming. Part 1.

This is the first of a three part series. Longer, more detailed versions of these articles are available at gordianknotbook.com.

Time is of the essence.

If you ask an engineer to solve global warming, his first question will be: how much time do I have? Apocalyptic predictions have been with us for some time. In 1982, Mostafa Tolba, executive director of UN Environmental Program proclaimed the ``world faced an ecological disaster as final as nuclear war within a couple of decades unless governments act now." In 2006, Al Gore warned ``the leading experts predict that we have less than 10 years to make dramatic changes in our global warming pollution lest we lose our ability to ever recover from this environmental crisis." A year later Rajenda Pachauri, chief of the UN IPCC gave us less time: ``If there is no action before 2012, it is too late. What we do in the next two or three years will determine our future. This is the defining moment."

These deadlines have come and gone. But new ones keep coming. In 2019, Greta Thunberg counted down the hours. She prophesied "in ten years, 250 days and ten hours we will be in a position where we set off an irreversible chain reaction beyond human control, that will most likely lead to the end of our civilization as we know it. I don't want you to be hopeful. I want you to panic."

My point here is not to poke fun, but rather to point out that these people focused on the right issue. Time. The question is not whether global warming is happening. The key question is how rapidly.

If it is true that we only have 20 or 30 years to drastically cut CO2 emissions, then, as we shall see:

1) we are not going to make it, and

2) we will impoverish and kill billions trying.

As Greta points out, all we can do is panic.

If on the other hand a gradual reduction in CO2 emissions over the next 100 years will suffice, then, if we can avoid our usual stupidities, there is a chance that we can pull it off.

So how much time do we have?

CO2 and Planet Temperature

Thanks to all the fossil fuel we have burned, the CO2 concentration in our atmosphere has risen from 280 to 420 ppm in the last 200 years. The key metric at the center of climate change discussion is Equilibrium Climate Sensitivity or ECS. ECS is the eventual (roughly 500 yrs) increase in planet temperature with each doubling of CO2 concentration.

Think about that for a moment. If the first doubling from say 300 to 600 ppm increases the plant's temperature by 2C, then the second doubling from 600 to 1200 ppm will also increase the the planet's temperature by 2C. The effect of more CO2 is diminishing, as shown in Figure 1.

Figure 1. Eventual warming versus climate sensitivity.

The shape of the curves in Figure 1 is not controversial. It is accepted by essentially all climate scientists. That's why they defined ECS in doubling terms. The dispute is about which of the curves in Figure 1 the planet will follow. But the basic process is self-limiting.

The reason for this logarithmic behavior is saturation. CO2 (and other greenhouse gases) can only absorb the energy being radiated from the earth back to space at certain frequencies. They need to absorb this energy, in order to reradiate some of that energy back to earth. If a CO2 concentration of 100 ppm has absorbed half of the outgoing energy at these frequencies, adding another 100 ppm will have half as much warming effect, since the additional CO2 has half as much energy of the right frequencies which the CO2 can absorb.

The Distribution of the Warming

Another non-controversial feature of the warming is that it will be considerable larger in the high latitudes than the low. Indeed the warming we have seen in the last 100 years has been concentrated in the Arctic. This puts a large part of the warming where humans can most benefit from it, and spares those areas which are near the upper limit of human tolerance from the worst of the warming.

There have been attempts to estimate the social cost of CO2. This is the cost to humanity from emitting one ton of CO2 on the margin. Unsurprisingly, the estimates are all over the place. You can find numbers ranging from negative up to $1000 per ton. But one of the more interesting papers was Ricke et al.¹ These authors attempted to come up with country by country social cost of CO2 (SCC). Figure 2 summarizes their results.

Figure 2. Social Cost of CO2 by Country

According to these mainstream authors, a large portion of the Northern Hemisphere would benefit from global warming. These numbers are the results of a long string of arbitrary assumptions, some of which are bound to be badly wrong; but, from a rough order of magnitude, qualitative point of view, the pattern makes sense. It's almost certainly a net negative to make India hotter. It's probably a net positive to make Canada warmer.

Warming and its effects depend on where you are. Muir Glacier in Alaska has become Muir Inlet, Figure 3, a favorite feeding ground of the humpback whale.

Figure 3. Muir Glacier, 1941 and 2004.

Sea Level Rise

To me the most worrisome effect of global warming is sea level rise. The sea level has been rising since the last glacial maximum about 20,000 years ago. Warming increases sea levels two ways: a) the expansion of the water, b) melting of land ice. Increasing the temperature of the top 500 m of the oceans will increase the sea level by 0.1 meters per degree. Thanks to mixing associated with wave action, this expansion occurs with a time constant of about 10 years. Increasing the rest of the ocean by 0.1 C will increase sea level by about 0.6 m/C. This expansion is very slow, with a time constant of perhaps 1000 years.

On top of that we have land ice melting. If all of Greenland became ice free, it would raise the water level 7 m. If all of Antarctica became ice free, it would raise the water level 60 meters. The good news is this too will take thousands of years. Here's how the IPCC puts it

At sustained warming levels between 2C and 3C, there is limited evidence that the Greenland and West Antarctic ice sheets will be lost almost completely and irreversibly over multiple millenia. At sustained warming levels between 3C and 5C, near complete loss of the Greenland Ice Sheet and complete loss of the West Antarctic Ice Sheet is projected to occur irreversibly over multiple millenia; with substantial parts or all of the Wilkes Subglacial Basin in East Antarctica lost over multiple millenia.² [Emphasis mine.]

The key phrase ``over multiple millenia" is repeated thrice. According to the IPCC, we have time to respond. And the wealthier we are, the better our response can be. We need only look at the Netherlands, Figure 4, to see what is possible. Over the last 700 years, average sea level has risen over a meter. Over that period, the Dutch have increased their land area by about 17%, and drastically improved the protection of all their land.

Figure 4. Holland

Extreme Events

In October of 1780, three of the most deadly Atlantic hurricanes in history occurred within a three week period.³ All three storms followed south to north tracks out of the Caribbean. On October 3rd, the first storm clobbered Jamaica, headed north over eastern Cuba and NNE over eastern Bahamas. Emanuel puts the death toll at 3000. The Great Hurricane of 1780 hits Barbados on the 10th, turns NNW just to the west of the islands, clobbering each in turn; crosses the east end of Hispaniola on the 15th; and then north to Bermuda. Emanuel says 22,000 killed. Solano's hurricane hits the Caymans on the 16th, then the western tip of Cuba on the 18th, reaching the Florida Panhandle on the 22nd. This storm scattered Admiral Solano's fleet, which had set out from Havana to capture Pensacola, killing 2000 sailors/soldiers.

These storms may have changed history. By chance the British Caribbean fleet was hit much harder than the French. The weakened British fleet was unable to defeat the French fleet in the Battle of the Chesapeake Capes a year later, and therefore unable to relieve Cornwallis at Yorktown.

Hurricane clustering is well known. The reason is simple: if conditions are abnormally favorable for hurricane development today, they are more likely to be abnormally favorable a week or two from now. Moreover, there are multi-decadal trends in hurricane frequency, presumably associated with some combination of ocean circulation changes and the El Nino/La Nina cycle.

This clustering has not worked out well for those that argue that the increase in CO2 is increasing hurricane frequency. Between 2005 and 2017, no Cat 3 or larger storm made landfall in the US, the longest such streak since at least 1900. Hurricane Harvey in August 2017, broke a 25 year streak of no Cat 4 or 5 hurricanes hitting the US. 2017 probably marked the end of a favorable period for Atlantic hurricanes and ushered in a difficult period such as we had in the 1930's and 1960's.

All of this makes any attribution of hurricane frequency or strength to manmade greenhouse gases at best speculative. In 2019, the American Meteorological Society surveyed 11 hurricane experts.⁴ Only 1 of the 11 agreed with the statement ``the balance of evidence suggests there has been a detectable increase in North Atlantic Tropical Cyclone activity since the 1970's." This paper received almost no publicity. But if 1780 were to repeat itself next fall, we can be sure the press would know what to blame.

History is replete with extreme events: droughts, heat waves, cold spells, floods, and storms. But climate by definition is a thirty year average of the weather. If we are to blame an increase in extreme events on AGW, we need to see significant changes in 30 year statistics. To make matters worse, we know there are multi-decadal natural variations in the climate. At this point, with the exception of hotter hot spells and milder cold snaps, the statistics just are not there.

What is certain is that our resilience against most extreme events has improved drastically as humanity has become wealthier. In 1912, a typhoon hit Tacloban, a low lying city, in the Philippines, killing roughly half of the inhabitants. In 2013, Super Typhoon Yolanda, one of the strongest storms on record, clobbered Tacloban. Yolanda killed 1 in 80 of the residents. Stronger, better built homes was the main reason for the difference. Between 1986 and 2016, Bangladesh and Myamar accounted for 77% of the fatalities from tropical cyclones, although these two countries represent a tiny fraction of the landfalls.⁵ Wealth is essential to weathering extreme weather.

Methane Bomb

The basic greenhouse process is logarithmic, which tends to stabilize matters. But maybe there is some trigger, some tipping point which all of a sudden floods the atmosphere with oodles of greenhouse gas. The most popular such culprit is methane.

Methane is a greenhouse gas with a global warming potential 28 to 34 times that of CO2 over 100 year period. 1400 gigatons of methane is frozen in the permafrost. The concern is warming in the Arctic could release large amounts of methane with disastrous results. However, current emissions from the permafrost account for less than 1% of global methane emissions. And methane represents about 20% of the radiative forcing of CO2. So we have a ways to go.

When permafrost melts and warms, a race starts:

1) Frozen organic matter is freed up and become fodder for microbes.

2) Depending on the conditions, some of the carbon is turned into methane. Some ends up as CO2.

3) The methane and CO2 percolate toward the surface.

4) Some of the methane becomes fuel for other organisms and is turned into CO2.

5) Plants start to grow on the recently thawed land and begin fixing CO2, Figure 5.

Figure 5. Swedish permafrost transitioning to boreal forest}

Only a portion of the methane makes it into the atmosphere. For deep water hydrates, that portion is near zero. Studies of ice cores indicate that, in former warming periods, very little CH4 was released.\cite{dyonisius-2020} In fact, it is possible for the new plant growth to more than balance the greenhouse gas releases. ``If you're asking who's winning [soil respiration or plant growth], we don't immediately know." Professor Ted Schuur, cofounder of the Permafrost Carbon Network. However, most studies to date show net CO2 fluxes from recently thawed permafrost. This can change as the ground drains and bigger plants become established. The boreal forests are carbon sinks.

There is little talk in the peer reviewed literature of a tipping point. Professor Schuur goes so far as to say ``the idea of a methane bomb is not that helpful. The methane and carbon are not going to be released all at once, but more gradually over time. But the net effect is just as troubling.''⁶ Maybe for a long view, scientist. But for the rest of us, knowing that you have time to respond, makes a difference.

Climate Engineering

In 1991, Mount Pinatubo erupted ejecting 15 to 20 million tons of SO2 into the atmosphere, The result was a 0.5C drop in global average temperature for about 18 months.

Global warming appears to be proceeding at a pace, we can respond to in an orderly way. But large uncertainties exist. Anyone who claims to be able to predict what will happen to the climate over the next 100 years is either a liar or an imbecile. Fortunately, we do have responses if it turns out the doom sayers for once are correct.

The easiest counter to implement is Stratospheric Aerosol Albedo Modification (SAAM), the ridiculously pretentious name for aping Mount Pinatubo. SAAM would spread reflective sulfur particles above the clouds. We only need to increase the reflectivity of the planet by about 2% to counteract a doubling in CO2. This looks cheap, about a billion dollars per year per degree cooling.⁷ It is quick, a matter of a few months, and will go away in a year or two when we stop. Other milder but more expensive methods exists.

The main problem with climate engineering methods is they are delaying tactics. Once started you must keep them going until you have actually reduced the CO2. But an ability to fend off an unexpected consequence of CO2 emission for an indefinite period can be extremely valuable. Opponents talk of moral hazard, meaning the fact that we have a cheap, quick, effective response to an unexpected outcome may slow our tackling of the core problem. True, but, as we shall see, the real moral hazard is responding too fast and too ineffectively to a concern that may be overblown, and the impact that those misguided responses will have on the poor.

A Glance at 2100

Figure 6 shows some 20 different estimates of the average global temperature in 2100 relative to pre-industrial times. This graph indicates that, if we do nothing, we are looking at another 2 or 3C rise, much of which will be in the high latitudes. This sounds worrisome --- the rise won't stop in 2100 --- but hardly cataclysmic in that period. In the temperate USA, there is a migration of people from colder states to warmer. People moving from New York to Florida apparently have no problem with a personal warming of 16C.

Figure 6. 2100 Temperature Relative to Pre-industrial

There are massive uncertainties here. As Roger Revelle put it: ``human beings are now carrying out a large scale geophysical experiment of a kind that could not happen in the past nor be repeated in the future." (Revelle was the guy who in 1957 figured out that the oceans would not absorb nearly as much CO2 as previously thought. But he wasn't worried. He thought that humanity would switch to nuclear power in plenty of time.)

1) Such an experiment is an inherently dangerous undertaking.

2) It appears we have some time. The temperature rise and its effects over the next 100 years may be very expensive but they are probably tolerable.

3) It could be worse than I have pictured. But we have geoengineering weapons which can give us more time if this is the case.

It looks like a sensible, orderly plan is possible. Of course, this view could be horribly wrong. There's a chance that Greta and her colleagues are right. Unless we massively reduce CO2 emissions in 30 years or less the species is doomed. Therefore, we should panic.

I submit we should not. If Greta is wrong, we will have ripped society apart and impoverished and killed billions unnecessarily. If Greta is right, a futile attempt at Net Zero will make very little difference. But that's the subject of Part 2.

1. Ricke, K. and Drouet, L. and Caldeira, K. and Tavoni, M., Country level social cost of carbon, Nature Climate Change, Vol 8, October, 2018.

2. IPCC Working Group 1, Climate Change 2021: The Physical Science Basis, Technical Summary, Sixth Assessment Report, 2021-08-06, p 106.

3. Emanuel, K., Divine Wind. The History and Science of Hurricanes”, Oxford University Press, 2005, pages 63-66.

4. Knutson, T. et al, Tropical Cyclones and Climate Change Assessment, Part 1. American Meteorological Society, Vol 100, October, 2019.

5. Bakkensenm L. and Mendelsohn, R., Risk and Adaptation: Evidence from Global Hurricane Damages and Fatalities, Journal of the Association of Environmental and Resource Economists, Vol 3, No 3, 2016.

6. Federman, A., Abrupt Permafrost Thaw has Scientists Worried, Sierra, December, 2021.

7. Committee on Geoengineering Climate, Climate Intervention. Reflecting Sunlight to Cool the Earth. National Academy of Sciences, 2015. Table 3.4.