GOING CORONAVIRAL-- A COMMENT ABOUT EXPONENTIAL GROWTH

We humans are pretty good at understanding linear change. It's all around us:

--eat more, gain some weight; eat less, lose some weight
--press on the gas pedal, speed up; press on the brake, slow down
--turn up the heat, feel warmer; turn down the heat, feel cooler
--someone can't hear you, talk louder; someone moves closer, talk more softly
--and thousands of other daily experiences in which a small change produces a small result and a larger change produces a larger result.

However, some events don't behave linearly. There are situations where a small change can quickly produce a big effect. We're living through at least two of them right now--climate change and the Covid-19 pandemic. We're failing miserably in understanding and dealing with both of them.

A sneeze--a few tiny droplets can cause massive disruption

Photo credit: CDC

Let's do a little math--please bear with me:

Step number     Linear growth (n x 2)     Exponential growth (2 to the n) 

         1                        2                                                    2                                       
         2                        4                                                    4                                         
         3                        6                                                    8                                         
         4                        8                                                   16                                       
         5                      10                                                   32                                       
         6                      12                                                   64                                       
         7                      14                                                 128                                       
         8                      16                                                 256                                         
         9                      18                                                 512                                         
       10                      20                                               1024 
       11                      22                                               2048                                     

Let's pretend that these numbers represent two different responses to the Covid-19 virus.

The steps might represent weeks. The first column might represent a situation where the virus is fairly well controlled (e.g. through some combination of social distancing, mask wearing, testing, tracing and isolating people likely to shed the virus). On average one infected person infects approximately one other person, with the result that the number of cases grows linearly. The third column represents exponential growth--where the virus truly is "going viral." All that takes is for one infected person to pass the virus on to more than one new victim.

Notice the enormous and rapidly expanding difference as the weeks tick by. At week three, exponential growth has infected just two more people than in the linear growth model, but at ten weeks the difference is more than 1,000, and one week later, more than 2,000.

So, our first takeaway is that when we're dealing with any situation involving exponential growth, at first it's hard to distinguish from a normal linear situation that we're used to, but sooner or later it takes off explosively.

Now let's examine that phrase "sooner or later."

      Week    Doubling stopped sooner           Doubling stopped later
         1                        2                                                    2                                     
         2                        4                                                    4                                       
         3                        8                                                    8                                       
         4                      16                                                   16                                       
         5                      18                                                   32                                       
         6                      20                                                   64                                       
         7                      22                                                 128                                       
         8                      24                                                 256                                         
         9                      26                                                 258                                         
       10                      28                                                 260 
       11                      30                                                 262
Total Cases:          198                                               1290

What a difference a delay makes.  This might represent two states, one of which sees the exponential handwriting on the wall after just four weeks, institutes effective controls and ends up with 198 cases, while the other delays control measures one month more and ends up with with 6.5 times as many cases. (Or these numbers could equally well represent deaths, in which case that one month delay would have caused over a thousand needless deaths.

Obviously the numbers above are meant to be an illustration; they don't match exactly with the real world. However, you can see this in the real world if you compare the impact of a one-week delay in responding to the pandemic in New York vs. California. Here's a zerospinzone.blogspot post from March 30:

In this comparison of coronavirus cases in New York vs California, you can see what difference even a few days lag in imposing strict stay-at-home orders makes. California--population 39.5 million, first state to impose strict controls: current # of cases 6358, deaths 132. New York--population 19.5 million, delayed a week before imposing controls: current # of cases 60,679, deaths 1063. The number of cases per population in NY is 19 times greater than in California, and the number of deaths per population 17 times greater. What a tragic difference a week's delay makes.

A lot has happened in New York and California in the subsequent three months, with start-and-stop openings and closings in both states. Through all that, however, California has managed to keep a tighter lid on the explosive potential of the coronavirus. As of today, June 28, New York has documented 416,769 cases and 31,483 deaths while Callifornia has had 215,575 cases and just 5,934 deaths. Adjusted for population, late-starting New York has suffered nearly four times as many cases and more than ten times as many deaths as California. Clamping down just one week earlier in California almost certainly saved tens of thousands of lives.

Our second takeaway, then, is that when dealing with the potential for exponential growth, getting control of the rate of growth as early as possible--before the number of cases explodes-- makes a huge difference.

It's pretty clear that we, as a species, aren't very good at dealing with things that have the potential for exponential growth, and so can blast out of control at any time.  We're seeing the results of this globally as we try to put a cap on the coronavirus. Similarly, experts have been warning us for decades that, because of a number of looming tipping points, climate change too has the potential to spin wildly out of control.

However, we don't have a good excuse for continued ignorance; it's not as though the potential for dangerous exponential growth has been a secret. Consider this old proverb, a version of which goes like this:

For want of a nail a horseshoe was lost,
for want of a horseshoe a horse went lame,
for want of a horse a rider never got through,
for want of a rider a message never arrived,
for want of a message an army was never sent,
for want of an army a battle was lost,
for want of a battle a war was lost,
for want of a war a kingdom fell,
and all for want of a nail.

Clearly we've had folk knowledge about exponentially large consequences from a small event for a lot time.

Even more ancient is a story from India about a chess-loving king who promised to reward a visitor with whatever he wanted. The visitor "modestly" asked for one grain of rice on the first square of a chessboard, 2 grains on the second square, 4 on the third, 8 on the fourth, etc. It didn't take the King many squares before he realized he'd taken on an impossible task. Sixty-four doublings would have required some 18,000,000,000,000,000,000 grains of rice, enough to cover all of India a meter deep.

That ancient king learned a striking and costly lesson about exponential growth. It seems as though we--and our current leaders--need to learn it all over again, and quickly. That is, if we don't want our kingdom to fall for want of an adequate response to this microscopic but immensely dangerous virus.

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REA

ONE MORE DEGREE COULD TRIGGER A COLLAPSE OF GREENLAND'S ICE SHEET

The latest and best reconstruction of temperatures near Greenland over that last 450,000 years shows that much of Greenland's vast ice sheet could melt from sustained warming of less than one degree. That means that the world risks triggering a devastating 7 meters (23 feet) of sea-level rise before the end of this century.

 Greenland Ice Sheet at Risk

Credit: cake@cake0

Writing in the prestigious Proceedings of the National Academy of Sciences (PNAS), researchers at the University of Bergen, Norway, and at Rutgers University, New Brunswick, New Jersey, analyze 450,000 years of sea surface temperatures off the coast of Greenland. They were able to track four interglacial (warm) periods, during one of which Greenland's southern ice sheet completely disappeared. During that 30,000-year-long warm period centered around 400,000 years ago, temperatures were only slightly higher than they are today--within one degree C--and well within the projections of climate models for the end of this century--if we continue on a business-as-usual trajectory.

Comparing the four warm periods it became clear that the amount of warming was not the only factor impacting how much of Greenland's ice melted. The other key was the duration of the warming. Even with temperatures just 0.8 degrees C warmer than today, the longer duration of the warm period centered around 400,000 years ago led to almost complete melting of Greenland's southern ice sheet.

According to the authors, their findings support climate models that find a tipping point somewhere between 0.8 and 3.2 degrees C warmer than today, beyond which melting of Greenland's ice sheet is inevitable even if temperatures go back down. Paleoclimatologist Nil Irvali, at the University of Bergen, explains that the tipping point occurs when melting reduces the altitude of the ice surface to the point where the even-warmer temperatures at the lower elevation guarantees runaway melting. "The elevation effect becomes dominant over time," she says, "melting accelerates, and may even continue even though the climate cools again."

The risk, she clarifies, is not that the Greenland Ice Sheet will melt before the end of the century, but that by the end of the century atmospheric warming caused by a continuation of current policies and emissions could easily trigger irreversible melting and an eventual, and devastating, 7-meter sea-level rise.

Actually, Irvali points out, it's even worse than that, since both atmospheric carbon dioxide and warmer ocean waters have extremely long lifetimes. "It is also important to note that CO2 we put into the atmosphere will have a long lifetime even if we cut emissions, and as more and more heat accumulates in the ocean it commits us to a longer timescale of warming," she says, "So our current activities will impact climate for millennia to come."

The authors conclude, "Notably, the critical temperature threshold for past [Greenland Ice Sheet] decay will likely be surpassed this century. The duration for which this threshold is exceeded will determine Greenland's fate."

To which we must add, and the fate of millions of Americans and hundreds of millions of people worldwide.**

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**In case this paleo-historical study seems too theoretical, recent observations by a completely different set of researchers show that Greenland is losing ice 7 times faster than it was two decades ago, in line with the IPCC's worst-case scenario, putting some 400 million people at risk of coastal flooding by 2100.

REA

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An ill wind . . .

Third Roadsign Report from the institute

We sailed past yet another warning sign on our crash course towards irreversible climate change a few days ago.

As reported by the AP, two German-flagged cargo ships navigated the "northeast passage," powering their way from South Korea to Siberia (and on towards Rotterdam) via an arctic route that until now has always been blocked by ice.

Scientists cited in the AP story say that this is a clear indication of human-caused climate change, which has long been predicted to show up most dramatcally in Earth's arctic and antarctic regions.

It may be good news for shippers and other business interests who are eager to exploit the arctic, but it's not good news for the rest of us.

Earth's rapidly melting ice is thought to be one of the most likely triggers for irreversible climate change. Since ice reflects the sun's energy back into space, it helps to keep the planet cool. When ice is replaced with open ocean or terrain, solar energy is absorbed and retained. This sets up a feedback loop that melts more ice, which means more energy is absorbed--you get the idea.

At least, with President Obama rather than Bush in the White House, the U.S. is no longer actively blocking progress towards international agreements to fight climate change. However, the political will and skill to attack this enormous global problem still lag dangerously far behind the accelerating pace of global warming and climatic disruption.

Robert Adler

for the institute

How much atmospheric CO2 can we live with?

That’s the question James Hansen, director of the NASA-Goddard Institute for Space Studies, addressed on October 7 at the Joint Annual Meeting of the Geological Society of America, in Houston, Texas.

His short answer is less than 350 parts per million—the level Hansen believes will preserve Earth’s ice sheets, mountain glaciers, and head off a devastating sea-level rise.

The fact that we have now surged past 387 parts per million of CO2, with no effective control in sight, is alarming. 

A state of emergency

“I believe we’ve reached a state of emergency,” Hansen said, “although it’s not easy to see. But if you look at the science, it becomes clearer and clearer.”

It’s enough of an emergency to force him to rethink nuclear power, an issue on which he’s previously been “an agnostic.” Renewable energy alone in sufficient quantities, he said, would be too costly.

 

Hansen walked the audience through the science—ice cores that reveal CO2 levels over the past 800,000 years, microscopic shells from under the sea floor that track ocean bottom temperature and salinity for the past 35,000,000 years, reconstructions of past glaciations and sea levels, the current rates at which the Earth is warming and its ice sheets disintegrating, and computer models of the climate system.

The bottom line is that the amount of CO2 in the atmosphere drives Earth’s climate, and that we are driving CO2 off the charts.

“All we have to do is graph the greenhouse gas forcing over the past several hundred thousand years,” says Hansen. “When we choose the right scale, it’s a hand and glove fit. Humans are now completely in charge of the composition of the atmosphere. CO2 and methane are far outside the range they’ve been in for millions of years.”

We’re in charge but out of control

Did you catch that—“Humans are now completely in charge of the composition of the atmosphere.” In charge, but out of control, like airplane without a pilot.

We’re not even close to heading in the right direction. Even countries that signed on to the Kyoto Accord have increased their carbon emissions. There’s more CO2 in the atmosphere than at any time in the last 650,000 years, and the rate at which it’s increasing is itself increasing.

“The actual actions of countries worldwide are inconsistent with stopping the CO2 rise,” Hansen said. “Energy departments around the world are assuming we can burn all the remaining fossil fuel. That will double or triple atmospheric CO2.”

What that means, he said, is that unless global carbon emissions are cut drastically, and soon, we’re headed for “. . . a completely different planet than the one that’s existed in the past. Obviously, it would be an ice-free planet, warmer than it’s been in any of the recent interglacials.” 

Among other impacts Hansen foresees is the disappearance of glaciers in the Himalayas, Rockies, and Andes within the next few decades, threatening the water and food supplies of hundreds of millions of people. 

Hmm. Where would they go, and what kinds of upheavals would that kind of mass migration cause?

Irreversible tipping points

Hansen also warned about climatic and environmental tipping points, “where the dynamics of the system take over and you don’t need any more forcing and there’s the potential to lose control.”

One example is the disintegration of the ice sheets. “It takes thousands of years to build up an ice sheet from snowfall,” he said. “If we cause the West Antarctic ice sheet to disintegrate, that’s essentially irreversible.”

“I think that the metric for what is dangerous should be headed by these irreversible effects, such as the extermination of species,” he said. “We know that when there have been warmings of several degrees in the past, more than half of the species on Earth at that time went extinct.”

Remarkably, Hansen remains optimistic about our ability to push CO2 levels back below 350 parts per million and turn this looming catastrophe around. The keys are technology and public policy.

One necessary ingredient, he says, is to cut back immediately on the burning of coal as well as other fossil fuels. “We could say that we’ll only use coal at power plants where we will capture and sequester it,” he said.

Hansen also wants to see carbon emissions taxed. “The public has to understand that we have to put a price, a tax, on carbon emissions,” he said. “That has to be given back, so the person who reduces his carbon emissions more than average will make money.”

Hansen is now re-examining nuclear power. In principle, he says, fourth generation reactors can burn nuclear fuel far more efficiently than in the past, while generating much less--and less dangerous--waste.

“I think we should be doing the research on nuclear power and having a trial of fourth generation technology, because that may very well be necessary,” he said.

Crimes against humanity and nature

From Hansen’s point of view, business-as-usual versus re-stabilizing the climate is an intergenerational conflict with enormous moral and legal implications.

“It’s an inequity and an injustice for the young and the unborn,” he said. I think it raises ethical and legal questions about liability. There has been intentional misinformation of the public, which makes the companies that engage in that and fund the contrarians to misinform the public ethically and I think legally liable for what I call crimes against humanity and nature.”

Hansen does not believe that the free market alone can or will solve this problem. “The profit motive seems to be so strong that I don’t think we can rely on their conscience to change things,” he said. “We have to rely on public policy.”

Hansen has consistently and courageously advocated on behalf of a stable climate and a viable future for our children. We need to make sure our leaders know he's not alone, and that this may be our last chance to act.

Bush and Cheney--lame ducks or dangerous dinosaurs?

Here’s a real-life scene worthy of a Hollywood thriller:

Three U.S. senators huddle over a document, closely watched by a team of White House lawyers. The senators have been granted a quick view of a zealously guarded report. They’re allowed to scribble a few notes before the papers are whisked away.

What could this eyes-only document be? A warning of an impending terror attack? The discovery of a killer asteroid plummeting towards Earth? The truth about UFOs?

None of the above. This scene, which took place in the U.S. Senate on 25 July, was just a skirmish in one of many battles that the Bush administration continues to wage as their final five months in power tick away--in this case furthering their program to derail any meaningful action on climate change.

For the lame ducks that they supposedly are, Bush et al. continue to show a lot of teeth and claws.

The much-fought-over document is a report on the impacts of greenhouse-gas-driven climate change on the U.S. It was grudgingly prepared by the U.S. Environmental Protection Agency (EPA) only after the U.S. Supreme Court ordered the agency to determine if greenhouse gas emissions threaten public health or the environment.

The study reportedly corroborates what most of the world has long accepted—that the world’s climate is changing in response to greenhouse gas emissions, that future emissions will exacerbate climate change, and that those changes will impact the U.S.—not to mention the rest of the world—to such a degree that unchecked emissions are likely to endanger public welfare.

Those conclusions are far from radical today, but remain anathema to President Bush and especially Vice President Cheney—who has strenuously pushed the agenda of the most reactionary of the petrochemical and coal behemoths on energy and climate issues.

If the EPA findings were to become official policy, the agency could be mandated to regulate greenhouse gas emissions as a pollutant under the Clean Air Act. To an administration that has done everything in its power to block public awareness of climate change in the U.S., and, a fortiori, official studies, recognition of the problem, or—heaven forebid—national or international action, the report had to be derailed.

So, when the EPA emailed the report to the White House in December of 2007, Bush et al. finessed the potential threat by the remarkable ploy of simply refusing to open the email. Remember those hear-no-evil, see-no-evil, speak-no-evil monkeys?

That report is not the only casualty in the administration’s climate-and-energy war. Last October, for example, John Marburger, the President’s chief science advisor, reportedly gutted a study by the U.S. Centers for Disease Control on the health effects of climate change. In December, Stephen Johnson, who heads the EPA, overrode his own staff recommendation, and scuttled California’s attempt to regulate its own greenhouse gas emissions. The National Oceanic and Atmospheric Administration and NASA have also run into the administration’s climate-change firewall.

On the international front, this administration has consistently sabotaged attempts to limit greenhouse gas emissions and other meaningful steps to head off potentially catastrophic climate change at meetings of the G8 and at the UN climate summit at Bali, Indonesia, in December, 2007. As the world tries to craft a successor to the Kyoto accord, the U.S. continues to push any numerical caps to carbon dioxide production into the distant future.

The conventional wisdom in the U.S. and much of Europe right now has it that Bush and Cheney are lame ducks waddling towards the door, and that the world should look past them to a hopefully more enlightened administration.

That would be fine if action on climate change were not so urgent. A series of recent studies in leading science journals has made it clear that the pace of climate change is accelerating to a degree that is surprising and alarming to many climatologists. Runaway ice melt, carbon-dioxide-bubbling permafrost, methane-belching seafloors, and changing ocean currents are just a few of the dangerous tipping points that Earth's climate could soon cross.

Testifying before Congress on 23 June, 2008, NASA climatologist Jim Hansen redlined six “tipping elements” that Earth’s climate is likely to crash through unless we cut atmospheric carbon dioxide from the current 385 parts per million to 350 or less. This is crucial, Hansen writes, “if humanity wishes to preserve a planet similar to that on which civilization developed and to which life on earth is adapted.”

Even economists have started to sense the same urgency. Rajendra Pachauri, an IPCC economist says—"If there's no action before 2012, that's too late. What we do in the next two to three years will determine our future. This is the defining moment."

The community of nations is now preparing to negotiate the agreement that will replace Kyoto. That new accord, which needs to be in place by December of 2009, looks to be our last best chance to head off catastrophic climate change.

If this is in fact “the defining moment” for Earth’s climate, then the Bush administration’s continued determination to block or delay any meaningful domestic or international action until they are ushered from the White House makes them look a lot more like velociraptors than lame ducks.

The U.S. Congress needs to be encouraged to redouble its efforts to reign in this still dangerous administration and act forcefully on climate change, and the international community needs to do everything it can to ensure that the next president is committed to getting the U.S. up and running on this vital issue from his first day in the oval office.

If instead we let the dinosaurs continue to run the world, we should not complain when we find ourselves back in the Cretaceous.

Robert Adler

Fifty thousand Earth scientists call for climate action, but is anyone listening?

The American Geophysical Union, representing some 50,000 scientists and students in 137 countries, has staked out significant new ground on the issue of climate change. The question is, have they gone far enough?

At a press conference in Washington, DC on 24 January, they released a terse statement saying that “Earth’s climate is now clearly out of balance and is warming,” that many facets of the climate system “are now changing at rates and in patterns that are not natural,” and that these changes are best explained by increased levels of greenhouse gases and aerosols generated by human activity.

They were equally clear about probable impacts—reduced agricultural productivity worldwide, widespread loss of biodiversity, and, if warming greater than two degrees Celsius continues over centuries, melting ice sheets leading to a sea level rise of several meters.

“The scale of change we’re seeing is something modern society has never seen,” said Michael Prather, who chaired the AGU committee and was also lead author of the 2007 Intergovernmental Panel on Climate Change report.

Nor did the group rule out the possibility of “surprises that may cause more dramatic disruptions than anticipated.”

Unlike the Bush administration, which has steadfastly resisted international efforts to set specific targets for greenhouse gas emissions, the AGU was not afraid to lay out numbers. “If this two degrees Celsius warming is to be avoided,” they write, “then our net annual emissions of carbon dioxide must be reduced by more than 50 percent within this century.”

When I asked the AGU panel to explain the statement that Earth’s climate is out of balance, Prather said it meant that the climate is no longer cycling slowly within a fixed range. “It’s not a balanced system,” he said. “We’re starting to slide.”

Does that mean that we’re sliding toward an irreversible tipping point? Prather would only say, “We’re moving.” He would not say if that meant “crossing a single critical threshold” or “death by 1000 knives.”

In either case, the panel agreed, concerted, coordinated, and targeted international action is needed.

“If you don’t start on a trajectory downward [for greenhouse gas emissions], you won’t be able to stabilize climate change,” said Prather. “We have to turn it over and bring it down. What we’re really looking for are much larger reductions, greater than 50 percent, by the end of the century.”

Given the clarity and urgency with which the AGU presented the case for urgent action, I was disappointed by their lack of a specific action plan, even for their own organization. “It’s our responsibility to go out and talk,” said Prather, and of course to provide society with the best science possible. But individual members need to decide just what they want to do.

AGU president Tim Killeen also emphasized education, outreach and greater interaction with policy makers, but cautioned that the AGU is determined to stay within its scientific role and not be drawn into “debilitating political controversies”.

Clearly, the AGU deserves kudos for stating the science clearly and for issuing yet another strong wake-up call to citizens and policy makers worldwide.

Still, given the powerful economic and political interests who are fighting any caps or cuts in greenhouse gas emissions, much less 50 percent reductions, I suspect that the AGU is overestimating the impact of good science, education, and outreach alone. After all, energy producers, smokestack industries, automakers and other great producers of greenhouse gasses are not shy about exerting all the political influence they can muster or buy.

To the extent that the AGU and its members take their own work and warnings seriously, and want those warnings to lead to real change, they are going to have to venture out of their comfort zone and into that unfamiliar and risky political arena both farther and faster than they might like.

Robert Adler

for the institute