A Toy Model of Climate Change

Introduction

A screenshot of the online book
Math for the People.

In Introductory Physics for Medicine and Biology, Russ Hobbie and I make use of toy models. Such mathematical descriptions are not intended to be accurate or realistic. Rather, they‘re simple models that capture the main idea without getting bogged down in the details. Today, I present an example of a toy model. It’s not related to medicine or biology, but instead describes climate change. I didn’t originally derive this model. Much of the analysis below comes from other sources, such as the online book Math for the People published by Mark Branson and Whitney George.

Earth Without an Atmosphere

First, consider the earth with no atmosphere. We will balance the energy coming into the earth from the sun with the energy from the earth that is radiated out into space. Our goal will be to calculate the earth’s temperature, T.

The power density (energy per unit time per unit area, in watts per square meter) emitted by the sun is called the solar constant, S. It depends on how far you are from the sun, but at the earth’s orbit S = 1360 W/m². To get the total power impinging on our planet, we must multiply S by the area subtended by the earth, which is πR², where R is the earth’s radius (R = 6.4 × 10⁶ meters). This gives SπR² = 1.8 × 10¹⁷ W, or nearly 200,000 TW (T, or tera-, means one trillion). That’s a lot of power. The total average power consumption by humanity is only about 20 TW, so there’s plenty of energy from the sun.

We often prefer to talk about the energy loss or gain per unit area of the earth’s surface. The surface area of the earth is 4πR² (the factor of four comes from the total surface area of the spherical earth, in contrast to the area subtended by the earth when viewed from the sun). The power per unit area of the earth’s surface is therefore SπR²/4πR², or S/4.

Not all of this energy is absorbed by the earth; some is reflected back into space. The albedo, a, is a dimensionless number that indicates the fraction of the sun’s energy that is reflected. The power absorbed per unit area is then (1 – a)S/4. About 30% of the sun’s energy is reflected (a = 0.3), so the power of sunlight absorbed by the earth per unit of surface area is 238 W/m².

What happens to that energy? The sun heats the earth to a temperature T. Any hot object radiates energy. Such thermal radiation is analyzed in Section 14.8 of Intermediate Physics for Medicine and Biology. The radiated power per unit area is equal to eσT⁴. The symbol σ is the Stefan-Boltzmann constant, σ = 5.7 × 10^–8 W/(m² K⁴). As stated earlier, T is the earth’s temperature. When raising the temperature to the fourth power, T must be expressed as the absolute temperature measured in kelvin (K). Sometimes it’s convenient at the end of a calculation to convert kelvin to the more familiar degrees Celsius (°C), where 0°C = 273 K. But remember, all calculations of T⁴ must use kelvin. Finally, e is the emissivity of the earth, which is a measure of how well the earth absorbs and emits radiation. The emissivity is another dimensionless number ranging between zero and one. The earth is an excellent emitter and absorber, so e = 1. From now on, I’ll not even bother including e in our equations, in which case the power density emitted is just σT⁴.

Let’s assume the earth is in steady state, meaning the temperature is not increasing or decreasing. Then the power in must equal the power out, so 

(1 – a)S/4 = σT⁴. 

Solving for the temperature gives

T = ∜[(1 – a)S/4σ] .

Because we know a, S, and σ, we can calculate the temperature. It is T = 254 K = –19°C. That’s really cold (remember, in the Celsius scale water freezes at 0°C). Without an atmosphere, the earth would be a frozen wasteland.

Earth With an Atmosphere

Often we can learn much from a toy model by adding in complications, one by one. Now, we’ll include an atmosphere around earth. We must keep track of the power into and out of both the earth and the atmosphere. The earth has temperature T_E and the atmosphere has temperature T_A.

First, let’s analyze the atmosphere. Sunlight passes right through the air without being absorbed because it’s mainly visible light and our atmosphere is transparent in the visible part of the spectrum. The main source of thermal (or infrared) radiation (for which the atmosphere is NOT transparent) is from the earth. We already know how much that is, σT_E⁴. The atmosphere only absorbs a fraction of the earth’s radiation, e_A, so the power per unit area absorbed by the atmosphere is e_AσT_E⁴.

Just like the earth, the atmosphere will heat up to a temperature T_A and emit its own thermal radiation. The emitted power per unit area is e_AσT_A⁴. However, the atmosphere has upper and lower surfaces, and we’ll assume they both emit equally well. So the total power emitted by the atmosphere per unit area is 2e_AσT_A⁴.

If we balance the power in and out of the atmosphere, we get 

e_AσT_E⁴ = 2e_AσT_A⁴. 

Interestingly, the fraction of radiation absorbed by the atmosphere, e_A, cancels out of our equation (a good emitter is also a good absorber). The Stefan-Boltzmann constant σ also cancels, and we just get T_E⁴ = 2T_A⁴. If we take the forth root of each side of the equation, we find that T_A = 0.84 T_E. The atmosphere is somewhat cooler than the earth.

Next, let’s reanalyze the power into and out of the earth when surrounded by an atmosphere. The sunlight power per unit area impinging on earth is still (1 – a)S/4. The radiation emitted by the earth is still σT_E⁴. However, the thermal radiation produced by the atmosphere that is aimed inward toward the earth is all absorbed by the earth (since the emissivity of the earth is one, e_E = 1), so this provides another factor of e_AσT_A⁴. Balancing power in and out gives

(1 – a)S/4 + e_AσT_A⁴ = σT_E⁴ .

Notice that if e_A were zero, this would be the same relationship as we found when there was no atmosphere: (1 – a)S/4 = σT_E⁴. The atmosphere provides additional heating, warming the earth.

We found earlier that T_E⁴ = 2T_A⁴. If we rewrite this as T_A⁴ = T_E⁴/2 and plug that into our energy balance equation, we get

(1 – a)S/4 + e_AσT_E⁴/2 = σT_E⁴ .

With a bit of algebra, we find

(1 – a)S/4 = σT_E⁴ (1 – e_A/2) .

Solving for the earth’s temperature gives

T_E = ∜[(1 – a)S/4σ] ∜[1/(1 – e_A/2) ] .

If e_A were zero, this would be exactly the relationship we had for no atmosphere. The fraction of energy absorbed by the atmosphere is not zero, however, but is approximately e_A = 0.8. The atmosphere provides a dimensionless correction factor of ∜[1/(1 – e_A/2)]. The temperature we found previously, 254 K, is corrected by this factor, 1.136. We get T_E = 288.5 K = 15.5 °C. This is approximately the average temperature of the earth. Our atmosphere raised the earth’s temperature from –19°C to +15.5°C, a change of 34.5°C.

Climate Change

To understand climate change, we need to look more deeply into the meaning of the factor e_A, the fraction of energy absorbed by the atmosphere. The main constituents of the atmosphere—oxygen and nitrogen—are transparent to both visible and thermal radiation, so they don’t contribute to e_A. Thermal energy is primarily absorbed by greenhouse gases. Examples of such gases are water vapor, carbon dioxide, and methane. Methane is an excellent absorber of thermal radiation, but its concentration in the atmosphere is low. Water vapor is a good absorber, but water vapor is in equilibrium with liquid water, so it isn’t changing much. Carbon dioxide is a good absorber, has a relatively high concentration, and is being produced by burning fossil fuels, so a lot of our discussion about climate change focuses on carbon dioxide.

The key to understanding climate change is that greenhouse gasses like carbon dioxide affect the fraction of energy absorbed, e_A. Suppose an increase in the carbon dioxide concentration in the atmosphere increased e_A slightly, from 0.80 to 0.81. The correction factor  ∜(1/(1 – e_A/2) ) would increase from 1.136 to 1.139, changing the temperature from 288.5 K to 289.3 K, implying an increase in temperature of 0.8 K. Because changes in temperature are the same if expressed in kelvin or Celsius, this is a 0.8°C rise. A small change in e_A causes a significant change in the earth’s temperature. The more carbon dioxide in the atmosphere, the greater the temperature rise: Global warming.

Feedback

We have assumed the earth’s albedo, a, is a constant, but that is not strictly true. The albedo depends on how much snow and ice cover the earth. More snow and ice means more reflection, a larger albedo, a smaller amount of sunlight absorbed by the earth, and a lower temperature. But a lower temperature means more snow and ice. We have a viscous cycle: more snow and ice leads to a lower temperature which leads to more snow and ice, which leads to an even lower temperature, and so on. Intermediate Physics for Medicine and Biology dedicates an entire chapter to feedback, but it focuses mainly on negative feedback that tends to maintain a system in equilibrium. A viscous cycle is an example of positive feedback, which can lead to explosive change. An example from biology is the upstroke of a nerve action potential: an increase in the electrical voltage inside a nerve cell leads to an opening of sodium channels in the cell membrane, which lets positively charged sodium ions enter the cell, which causes the voltage inside the cell to increase even more. The earth’s climate has many such feedback loops. They are one of the reasons why climate modeling is so complicated.

Conclusion

Today I presented a simple description of the earth’s temperature and the impact of climate change. Many things were left out of this toy model. I ignored differences in temperature over the earth’s surface and within the atmosphere. I neglected ocean currents and the jet stream that move heat around the globe. I did not account for seasonal variations, or for other greenhouse gasses such as methane and water vapor, or how the amount of water vapor changes with temperature, or how clouds affect the albedo, and a myriad of other factors. Climate modeling is a complex subject. But toy models like I presented today provide insight into the underlying physical mechanisms. For that reason, they are crucial for understanding complex phenomena such as climate change.

Transitioning to Environmentally Sustainable, Climate-Smart Radiation Oncology Care

“Transitioning to Environmentally
Sustainable Climate-Smart
Radiation Oncology Care,”
by Lichter et al.,
IJROBP, 113:915–924, 2022.

Loyal readers of this blog may have noticed an increasing number of posts related to climate change, and the intersection of global warming with health care and medical physics. This is not an accident. I’m growing increasingly worried about the impact of climate change on our society. One way I act to oppose climate change is to write about it (here, here, here). So, I was delighted to read Katie Lichter and her team’s editorial about “Transitioning to Environmentally Sustainable, Climate-Smart Radiation Oncology Care” (International Journal of Radiation Oncology Biology Physics, Volume 113, Pages 915–924, 2022). Their introduction begins (references removed)

Climate change is among the most pressing global threats. Action now and in the coming decades is critical. Rising temperatures exacerbate the frequency and intensity of extreme weather events, including wildfires, hurricanes, floods, and droughts. Such events threaten not only our ecosystems, but also our health. Climate change’s negative effects on human health are slowly becoming better understood and are projected to increase if emissions mitigation remains inadequate. Emerging research notes a disproportionate effect of climate change on vulnerable populations (e.g., older populations, children, low-income populations, ethnic minorities, and patients with chronic conditions, including cancer) who are the least equipped to deal with these outsized effects.

Then Lichter and her coauthors get specific about radiation oncology.

More than half of cancer patients will require radiation therapy (RT) during the course of their illness. As most RT courses are delivered using fractionated external beam radiation (EBRT), patients undergoing EBRT are vulnerable to treatment disruptions from climate events. Notably, disruption of RT treatments due to severe weather events has been shown to affect patient treatment and survival. As radiation oncologists, it is imperative to recognize and further investigate the effects of climate change on health and cancer outcomes and understand the specific vulnerabilities of patients receiving RT to the effects of climate change. We must also advance our understanding of the contribution of radiation oncology as a specialty to green house gas (GHG) emissions, and what measures may be taken in our daily practices to join the international efforts in reducing our negative environmental impact.

Next the authors present their four R’s to address oncology care: reduce, reuse, recycle, rethink. This is sort of an inside joke among radiation biologists, because radiation biology famously has its own four R’s: repair, reassortment, reoxygenation, and repopulation. Lichter et al.’s four R’s explain how to lower radiation oncology’s effect on the climate.

1. Reduce means to lower the energy needs for imaging and therapeutic devices, and to minimize medical waste.
2. Reuse means to favor reusable equipment and supplies (such as surgical gowns) whenever possible.
3. Recycle means to recycle any single-use supplies than cannot be reused. Much now finds its way to urban landfills rather than to recycling centers.
4. Rethink means to reconsider all medical radiation oncology processes and procedures in light of climate change. Can some things be done by telemedicine? Can we reduce the number of fractions of radiation a patient receives so fewer visits to the hospital are required? Can some professional conferences be held virtually rather than in person? Sometimes the answer may be yes and sometimes no, but all these issues need to be reexamined.

Lichter’s editorial concludes (my italics)

The health care system contributes significantly to today’s climate health crisis. All efforts addressing the crisis are important due to their direct emissions reduction potential, and the example they set for the health care system and the patients who need the care. Although the effects of increasing global temperatures on human health are well studied, the effects of health care, and specifically oncology and radiation treatments, on contributing to climate change are not. The radiation oncology community has a unique opportunity to use our technological expertise and awareness to assess and minimize the environmental impact of our care and set the standard for sustainable health care practices for other specialties to emulate. 

Thank you Katie Lichter and your whole team for all the important work that you are doing to fight climate change! Your four R’s—reduce, reuse, recycle, and rethink—apply beyond radiation oncology, and even beyond health care, to all of our society’s activities. Perhaps writers of textbooks such as Intermediate Physics for Medicine and Biology need to reduce, reuse, recycle, and especially rethink how our books impact, and are impacted by, global warming.

 

Listen to Katie Lichter talk about her climate journey.

https://www.youtube.com/watch?v=ccnz3V8WAh4

The Million Person Study: Whence It Came and Why

A screenshot of the article
“How Sound is the Model Used to
Establish Safe Radiation Levels?”
on the website physicsworld.com.

Last fall, physicsworld.com published an editorial by Robert Crease asking “How Sound is the Model Used to Establish Safe Radiation Levels?” This question is addressed in Chapter 16 of Intermediate Physics for Medicine and Biology, and I have discussed it before in this blog. Crease begins

Ionizing radiation can damage living organisms, that’s clear. But there are big questions over the validity of the linear no-threshold model (LNT), which essentially states that the risk of cancer from radiation and carcinogens always increases linearly with dose. The LNT model implies, in other words, that any amount of radiation is always dangerous and that zero risk is present only at zero dose.

Crease notes that alternative models are the threshold model in which there is a minimum dose below which there is no risk, and the hormesis model which says that small doses are beneficial by triggering repair mechanisms. He explains that by adopting such a conservative position as the linear no-threshold model we may cause unforeseen negative consequences.

What sort of negative consequences? One of the most urgent and dire health hazards faced by humanity is climate change. Addressing the danger of a warming climate, with all its implications, must be our top priority. Climate change is caused primarily by the emission of greenhouse gasses such as carbon dioxide that result from the burning of fossil fuels to generate electricity, warm our homes, power our vehicles, or make steel and concrete. One alternative to burning fossil fuels is to use nuclear energy. But nuclear energy is feared by many, in part because of the linear no-threshold model, which implies that any exposure to ionizing radiation is dangerous. If, in fact, the linear no-threshold model is not valid at the low doses associated with nuclear power plants and nuclear waste disposal then the public might be more accepting of nuclear power, which may help us in the battle against climate change. Crease concludes

One of the many reasons for the need to study the validity of LNT is that convictions of its accuracy continue to be used as an argument against nuclear power plants, in connection with their operation as well as their spent fuel rods. Nuclear power may be undesirable for reasons other than this. But the critical need to find a workable alternative to fossil fuels for energy production requires an honest ability to assess the validity of this model.

In my opinion, determining if the linear no-threshold model is valid at low doses is one of the greatest challenges of medical physics today. It’s a critical example of how physics interacts with medicine and biology. We need to figure this out. But how?

Screenshot of The Million
Person Study website.

One way is to conduct an epidemiological study of low-dose radiation exposure. But such a study would have to be huge, because it’s looking for a tiny effect influencing an enormous population. What you need is something like The Million Person Study. Yes, medical physics has its own “big science” large-scale collaboration. The Million Person Study’s website states

There is a major gap in epidemiological understanding, however, of the health effects experienced by populations exposed to radiation at lower doses, gradually over time.

The foundation of the Million Person Study is to fill that gap, using epidemiological methods of assessing rate and quality of mortality on a study group of one million persons exposed to this type of radiation.

The website notes that there are many reasons to assess the risk of low doses of radiation, including determining 1) the side effects of medical imaging procedures such as computed tomography, 2) the danger of nuclear accidents or terrorism (dirty bombs), 3) the safety of occupations that expose workers to a slight radiation dose, 4) the hazards of environmental exposure such as from radon in homes, and 5) the uncertainty of space and high altitude travel such as when sending astronauts to Mars. The Million Person Study not only focuses on the level of exposure, but also on the duration: was it a brief exposure as if from an nuclear accident, or a low dose delivered over a long time?

The cover of a special issue of the
International Journal of Radiation Biology
about The Million Person Study.

Want to learn more about The Million Person Study? See the paper by John Boice, Sarah Cohen, Michael Mumma, and Elisabeth Ellis titled “The Million Person Study: Whence it Came and Why,” published in the International Journal of Radiation Biology in 2022 (Volume 98, Pages 537–550). Its abstract is printed below.

Purpose: The study of low dose and low-dose rate exposure is of immeasurable value in understanding the possible range of health effects from prolonged exposures to radiation. The Million Person Study (MPS) of low-dose health effects was designed to evaluate radiation risks among healthy American workers and veterans who are more representative of today’s populations than are the Japanese atomic bomb survivors exposed briefly to high-dose radiation in 1945. A million persons were needed for statistical reasons to evaluate low-dose and dose-rate effects, rare cancers, intakes of radioactive elements, and differences in risks between women and men.

Methods and Materials: The MPS consists of five categories of workers and veterans exposed to radiation from 1939 to the present. The U.S. Department of Energy (DOE) Health and Mortality study began over 40 years ago and is the source of ∼360,000 workers. Over 25 years ago, the National Cancer Institute (NCI) collaborated with the U.S. Nuclear Regulatory Commission (NRC) to effectively create a cohort of nuclear power plant workers (∼150,000) and industrial radiographers (∼130,000). For over 30 years, the Department of Defense (DoD) collected data on aboveground nuclear weapons test participants (∼115,000). At the request of NCI in 1978, Landauer, Inc., (Glenwood, IL) saved their dosimetry databases which became the source of a cohort of ∼250,000 medical and other workers.

Results: Overall, 29 individual cohorts comprise the MPS of which 21 have been or are under active study (∼810,000 persons). The remaining eight cohorts (∼190,000 persons) will be studied as resources become available. The MPS is a national effort with critical support from the NRC, DOE, National Aeronautics and Space Administration (NASA), DoD, NCI, the Centers for Disease Control and Prevention (CDC), the Environmental Protection Agency (EPA), Landauer, Inc., and national laboratories.

Conclusions: The MPS is designed to address the major unanswered question in radiation risk understanding: What is the level of health effects when exposure is gradual over time and not delivered briefly. The MPS will provide scientific understandings of prolonged exposure which will improve guidelines to protect workers and the public; improve compensation schemes for workers, veterans and the public; provide guidance for policy and decision makers; and provide evidence for or against the continued use of the linear nonthreshold dose-response model in radiation protection.

 Lead on Million Person Study, and thank you for your effort. We need those results!

Black Carbon and Radon

Drawdown

In a previous post, I reviewed the book Drawdown: The Most Comprehensive Plan Ever Proposed to Reverse Global Warming. Sometimes I visit the book’s associated website, drawdown.org, because it has so much to teach me about climate change. Recently, I read one of their publications about Reducing Black Carbon. The executive summary begins:

Black carbon—also referred to as soot—is a particulate matter that results from the incomplete combustion of fossil fuels and biomass. As a major air and climate pollutant, black carbon (BC) emissions have widespread adverse effects on human health and climate change. Globally, exposure to unhealthy levels of particulate matter, including BC, is estimated to cause between three and six million excess deaths every year. These health impacts—and the related economic losses—are felt disproportionately by those living in low- and middle-income countries. Furthermore, BC is a potent greenhouse gas with a short-term global warming potential well beyond carbon dioxide and methane. Worse still, it is often deposited on sea ice and glaciers, reducing reflectivity and accelerating melting, particularly in the Arctic and Himalayas.

Therefore, reducing BC emissions results in a triple win, mitigating climate change, improving the lives of more than two billion people currently exposed to unclean air, and saving trillions of dollars in economic losses.

As I learned more, I found that black carbon is only one type of fine particles in the air. I begin to wonder “where have I heard about the risk of particulate matter before?” Then it hit me: Section 17.12 of Intermediate Physics for Medicine and Biology, which is about radon. Russ Hobbie and I wrote

Uranium, and therefore radium and radon, are present in most rocks and soil. Radon, a noble gas, percolates through grainy rocks and soil and enters the air and water in different concentrations. Although radon is a noble gas, its decay products have different chemical properties and attach to dust or aerosol droplets which can collect in the lungs. High levels of radon products in the lungs have been shown by both epidemiological studies of uranium miners and by animal studies to cause lung cancer.

Aha! Perhaps black carbon is an effective carrier of radon decay products into the lungs. This is just a hypothesis, but I did find a reference that supported the idea (Wang et al., “Particle Radioactivity from Radon Decay Products and Reduced Pulmonary Function Among Chronic Obstructive Pulmonary Disease Patients,” Environmental Research, Volume 216, Article Number 114492, 2023). Below I present part of their introduction (references removed)

Consistent with the existing literature on ambient particulate matter (PM) exposure, our previous studies found that indoor PM was associated with increased systemic inflammation and oxidative stress and reduced pulmonary function among [chronic obstructive pulmonary disease] patients in Eastern Massachusetts. It has recently been recognized that an attribute of PM with potential to promote pulmonary damage after inhalation is radionuclides attached to PM, referred to as particle radioactivity (PR). Though ionizing radiation has many sources (e.g., cosmic radiation and medical procedures), the majority of natural background radiation (and, thus, of PR) is from radon (²²²Rn), which decays into α-, β-, and γ-emitting decay products. Although radon gas itself is rapidly exhaled, freshly generated radon decay products (also referred to a radon progeny) can rapidly attach to particles in the ambient and indoor air and be inhaled into the airways. After deposition, particles continue to emit radiation in the lungs with a residence time that can range from several days to months. Compared to β- and γ-emissions from radionuclides, α-emitting particles are considered the most toxic due to their high energy and large mass. Since α-radiation cannot penetrate the intact epidermis, inhalation is the predominant route of exposure, and evidence that α-radiation may cause pulmonary damage is suggested by its effects on inducing inflammation and reactive oxygen species in human lung fibroblasts as well as up-regulating gene pathways in human pulmonary epithelial cells associated with inflammatory and respiratory diseases.

I didn’t find any mention of radon in Drawdown’s publication Reducing Black Carbon or in the World Health Organization’s publication Health Effects of Black Carbon. I don’t know if radon is an important part of the mechanism by which black carbon causes health hazards. Yet, I wonder. I know that radon is a more serious hazard among smokers compared to nonsmokers, and smoking should have similarities to breathing soot. This black carbon/radon hypothesis raises some interesting questions. Is black carbon more effective than other types of particulate matter in transporting radon decay products? Does global warming increase lung cancer? Is black carbon more dangerous in areas with high radon concentrations? Is black carbon more hazardous for people living in poorly ventilated buildings rather than in well-ventilated buildings or outdoors?

Soot is clearly bad news. As drawdown.com says, it’s a triple threat: climate, health, and well-being. They offer several ideas for reducing black carbon:

1. Urgently implement clean cooking solutions
2. Target transportation to reduce current—and prevent future—emissions
3. Reduce BC from the shipping industry
4. Regulate air quality
5. Include BC in nationally determined contributions and the United Nations Framework Convention on Climate Change
6. Improve BC measurements and estimates

The item about regulating air quality makes me speculate if a positive feedback loop could underlie the impact of black carbon on the climate: Soot in the air increases global warming; increased global warming increases the number of forest fires, and an increased number of forest fires increases the amount of soot in the air. Again, this is just a hypothesis, and I don’t know it’s true. But I do know that in my 25 years living in Michigan, the only serious problem with air pollution and soot I’ve experienced was caused by last summer’s Canadian forest fires, and such fires appear, at least to me, to be related to global warming.

 

Black carbon may be one of the places where climate change and IPMB intersect. It’s an important topic and deserves closer study.

Bernard Leonard Cohen (1924–2012)

The Nuclear Energy Option: An Alternative for the 90s.
by Bernard Cohen.

Today is the one hundredth anniversary of the birth of American nuclear physicist Bernard Cohen. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss Cohen mainly in the context of his work on the risk of low levels of ionizing radiation and his opposition to the linear no threshold model. Today, I will examine another aspect of his work: his advocacy for nuclear power. In particular, I will review his 1990 book The Nuclear Energy Option: An Alternative for the 90s.

Why read a 35-year old book about a rapidly changing technology like energy? I admit, the book is in some ways obsolete. Cohen insists on using rems as his unit of radiation effective dose, rather than the more modern Sievert (Sv). He discusses the problem of greenhouse gases and global warming, although in a rather hypothetical way as just one of the many problems with burning fossil fuels. He was optimistic about the future of nuclear energy, but we know now that in the decades following the book’s publication nuclear power in the United States did not do well (the average age of our nuclear power plants is over 40 years). Yet other features of the book have withstood the test of time. As our world now faces the dire consequences of climate change, the option of nuclear energy is an urgent consideration. Should we reconsider nuclear power as an alternative to coal/oil/natural gas? I suspect Cohen would say yes.

In Chapter 4 of The Nuclear Energy Option Cohen writes

We have seen that we will need more power plants in the near future, and that fueling them with coal, oil, or gas leads to many serious health, environmental, economic, and political problems. From the technological points of view, the obvious way to avoid these problems is to use nuclear fuels. They cause no greenhouse effect, no acid rain, no pollution of the air with sulfur dioxide, nitrogen oxides, or other dangerous chemicals, no oil spills, no strain on our economy from excessive imports, no dependence on unreliable foreign sources, no risk of military ventures. Nuclear power almost completely avoids all the problems associated with fossil fuels. It does have other impacts on our health and environment, which we will discuss in later chapters, but you will see that they are relatively minor.

He then compares the safety and economics of nuclear energy with other options, including solar and coal-powered plants for generating electricity. Some of the conclusions are surprising. For instance, you might think that energy conservation is always good (who roots for waste?). But Cohen writes

Another energy conservation strategy is to seal buildings more tightly to reduce the escape of heat, but this traps unhealthy materials like radon inside. Tightening buildings to reduce air leakage in accordance with government recommendations would give the average American an LLE [loss of life expectancy] of 20 days due to increased radon exposure, making conservation by far the most dangerous energy strategy from the standpoint of radiation exposure!

His Chapter 8 on Understanding Risk is a classic. He begins

One of the worst stumbling blocks in gaining widespread public acceptance of nuclear power is that the great majority of people do not understand and quantify the risks we face. Most of us think and act as though life is largely free of risk. We view taking risks as foolhardy, irrational, and assiduously to be avoided….

Unfortunately, life is not like that. Everything we do involves risk.

He then makes a catalog of risks, in which he converts risk to the average expected loss of life expectancy for each case. This LLE is really just a measure of probability. For instance, if getting a certain disease shortens your life by ten years, but there is only one chance out of a hundred of contracting that disease, it would correspond to an LLE of 0.1 years, or 36 days. In his catalog, the riskiest activity is living in poverty, which has an LLE of 3500 days (almost ten years). Smoking cigarettes results in an LLE of 2300 days. Being 30 pounds overweight is 900 days. Reducing the speed limit on our highways from 65 to 55 miles per hour would reduce traffic accidents and give us an extra 40 days. At the bottom of his list is living near a nuclear reactor, with a risk of only 0.4 days (less than ten hours). He makes a compelling case that nuclear power is extraordinarily safe.

Cohen summarizes these risks in a classic figure, shown below.

Figure 1 from Chapter 8 of The Nuclear Energy Option.

Our poor risk perception causes us (and our government) to spend money foolishly. He translates societies efforts to reduce risk into the cost in dollars to save one life.

The $2.5 billion we spend to save a single life in making nuclear power safer could save many thousands of lives if spent on radon programs, cancer screening, or transportation safety. This means that many thousands of people are dying unnecessarily every year because we are spending this money in the wrong way.

He concludes

The failure of the American public to understand and quantify risk must rate as one of the most serious and tragic problems for our nation.

I agree.

Cohen believes that Americans have a warped view of the risk of nuclear energy.

The public has become irrational over fear of radiation. Its understanding of radiation dangers has virtually lost all contact with the actual dangers as understood by scientists.

Apparently conspiracy theories are a problem we face not only today but also decades ago, when the scientific establishment was accused of hiding the “truth” about radiation risks. Cohen counters

To believe that such highly reputable scientists conspired to practice deceit seems absurd, if for no other reason than that it would be easy to prove that they had done so and the consequences to their scientific careers would be devastating. All of them had such reputations that they could easily obtain a variety of excellent and well-paying academic positions independent of government or industry financing, so they were to vulnerable to economic pressures.

But above all, they are human beings who have chosen careers in a field dedicated to protection of the health of their fellow human beings; in fact, many of them are M.D.’s who have foregone financially lucrative careers in medical practice to become research scientists. To believe that nearly all of these scientists were somehow involved in a sinister plot to deceive the public indeed challenges the imagination.

To me, these words sound as if Cohen were talking now about vaccine hesitancy or climate change denial, rather than opposition to nuclear energy. 

What do I think? I would love to have solar and wind supply all our energy needs. But until they can, I vote for increasing our use of nuclear energy over continuing to burn fossil fuels (especially coal). Global warming is already bad and getting worse. It is a dire threat to us all and to our future generations. We should not rule out nuclear energy as one way to address climate change.

Happy birthday, Bernard Cohen! I think if you had lived to be 100 years old, you would have found so many topics to write about today. How we need your rational approach to risk assessment. 

 Firing Line with William F. Buckley Jr.: The Crisis of Nuclear Energy.

https://www.youtube.com/watch?v=ipOrGaXn-r4&list=RDCMUC9lqW3pQDcUuugXLIpzcUdA&start_radio=1&rv=ipOrGaXn-r4&t=52

Gauss and von Humboldt

The Age of Napoleon,
by Will and Ariel Durant,
Volume 11 of The Story of Civilization.

Regular readers of this blog may recall that over the last few years I’ve been reading Will and Ariel Durant’s magnificent The Story of Civilization. I’m almost done.  I’m currently finishing the final chapters of the last volume: The Age of Napoleon. In the chapter about the German people is a section on science. It states

Two men especially brought scientific honors to Germany in this age—Karl Friedrich Gauss (1777–1855) and Alexander von Humboldt (1769–1859).

Humboldt is never mentioned in Intermediate Physics for Medicine and Biology, but Gauss is everywhere. When speaking of Gauss, the Durants write

We shall not pretend to understand, much less to expound, the discoveries—in number theory, imaginary numbers, quadratic residues, the method of least squares, the infinitesimal calculus—by which Gauss transformed mathematics from what it had been in Newton’s time into an almost new science, which became a tool of the scientific miracles of our time. His observations of the orbit of Ceres (the first planetoid, discovered on January 1, 1801) led him to formulate a new and expeditious method of determining planetary orbits [least squares is discussed in Chapter 11 of IPMB]. He made researches which placed the theory of magnetism and electricity upon a mathematical basis [Gauss’s law for calculating the electric field is discussed in Chapter 6 of IPMB; the now somewhat obsolete unit of magnetic field strength is the gauss]. He was a burden and blessing [definitely a blessing] to all scientists, who believe that nothing is science until it can be stated in mathematical terms. [He also invented the Gaussian probability distribution, which plays a major role in diffusion, discussed in Chapter 4 of IPMB]…. He is now ranked with Archimedes and Newton.

Humboldt was more of a naturalist, and his name never appears in IPMB. But the Durants devoted even more space in their history to him than to Gauss.

The other hero of German Science in this age was Wilhelm von Humboldt’s younger brother Alexander…. In 1796 he began, by accident, the long tour of scientific discovery (rivaling Darwin’s on the Beagle) whose results made him, according to a contemporary quip, “the most famous man in Europe, next to Napoleon.”

Humboldt is particularly famous for his work in geography and geology. I become familiar with him when I taught earth science. I was a new, untenured faculty member at Oakland University when the physics department needed someone to teach our earth science class. OU does not have a geology department, but some students do need a course in earth science, so the physics department was in charge of it. When the faculty member who traditionally taught it retired, I was asked to take it over. I knew nothing about earth science, but neither did anyone else in the department, and being the newest member of the department I didn’t feel that I could say no. I taught the class for about five years, and found that I enjoyed it. Most students in the course were elementary education majors. They weren’t the strongest science students I ever taught, but they were some of the nicest.

Here is what the Durants had to say about Humboldt.

He discovered (1804) that the earth’s magnetic force decreases in intensity from the poles to the equator. He enriched geology with his studies of the igneous origin of certain rocks, the formation of mountains, the geographical distribution of volcanoes. He provided the earliest clues to the laws governing atmospheric disturbances, and thereby shed light on the origin and direction of tropical storms. He made classic studies of air and ocean currents…. His Essai sur la geographie des plantes began the science of biogeography—the study of plant distribution as affected by the physical conditions of the terrain. These and a hundred other contributions, modest in appearance but of wide and lasting influence, were published in thirty volumes from 1805 to 1834 as Voyages de Humboldt et Bonpland aux regions equinoxiales du nouveau continent.

Humboldt is particularly relevant these days as one of the first environmentalists and discoverer of the concept of human-induced climate change. The closest he came to IPMB may be his work on muscle excitation and bioelectricity. In “Alexander von Humboldt and the Concept of Animal Electricity” (Trends in Neurosciences, Volume 20, Pages 239–242, 1997), Helmut Kettenmann wrote

More than two hundred years ago, Alexander von Humboldt helped to establish Galvani's view that muscle and nerve tissue are electrically excitable. His 1797 publication was a landmark for establishing the concept of animal electricity. Almost half a century later, von Humboldt became the mentor of the young du Bois-Reymond. With the help of von Humboldt's promotion, du Bois-Reymond demonstrated convincingly that animal tissue has the intrinsic capacity to generate electrical activity, and thus laid the ground for modern electrophysiology. 

Gauss and Humboldt; what a pair. Put them together with Goethe and Beethoven and Germany around 1800 becomes a pretty interesting place.

Oh, what will I do with myself now that my reading of The Story of Civilization is complete? I guess I will have to focus on the 6th edition of IPMB.

 

My favorite Gauss story, about how as a child he added all the numbers from 1 to 100.

https://www.youtube.com/watch?v=cD9rI4wSc7o

Ken Jennings narrates this video about Alexander von Humboldt.

https://www.youtube.com/watch?v=fj7tRMdmOgs

Alexander von Humboldt and the discovery of climate change.

https://www.youtube.com/watch?v=fYrXE_umWCw

Drawdown

Drawdown,
Edited by Paul Hawken.

This blog is about physics applied to medicine and biology, but if we don’t solve the climate crisis there’s no use developing fancier ways to do medical imaging or radiation therapy; we’ll all be dead. So today I’m going to tell you about a book I just read, titled Drawdown: The Most Comprehensive Plan Ever Proposed to Reverse Global Warming. It’s the book I’ve been looking for. It analyzes all the different ways we can address global warming, and ranks them by impact and importance. Here’s how the editor Paul Hawken begins Drawdown.

The genesis of Project Drawdown was curiosity, not fear. In 2001 I began asking experts in climate and environmental fields a question: Do we know what we need to do in order to arrest and reverse global warming? I thought they could provide a shopping list. I wanted to know the most effective solutions that were already in place, and the impact they could have if scaled. I also wanted to know the price tag. My contacts replied that such an inventory did not exist, but all agreed it would be a great checklist to have, though creating one was not within their individual expertise. After several years, I stopped asking because it was not within my expertise either.

Then came 2013. Several articles were published that were so alarming that one began to hear whispers of the unthinkable: It was game over. But was that true, or might it possibly be game on? Where did we actually stand? It was then that I decided to create Project Drawdown. In atmospheric terms drawdown is that point in time at which greenhouse gases peak and begin to decline on a year-to-year basis. I decided that the goal of the project would be to identify, measure, and model one hundred substantive solutions to determine how much we could accomplish within three decades towards that end.

Many solutions are presented in Drawdown, but here I count down the top ten, ranked according to their total atmospheric carbon dioxide reduction, with a brief quote from Drawdown accompanying each.

10. Rooftop Solar

As households adopt rooftop solar… they transform generation [of electricity] and its ownership, shifting away from utility monopolies and making power production their own.

9. Silvopasture

Silvopasture is… the integration of trees and pasture or forage into a single system for raising livestock… Trees create cooler microclimates and more protective environments, and can moderate water availability. Therein lies the climatic win-win of silvopasture: As it averts further greenhouse emissions from one of the world’s most polluting sectors, it also protects against changes that are now inevitable.

8. Solar Farms

Any scenario for reversing global warming includes a massive ramp-up of solar power by mid-century. It simply makes sense: the sun shines every day, providing a virtually unlimited, clean, and free fuel at a price that never changes. Small, distributed clusters of rooftop panels are the most conspicuous evidence of the renewables revolution powered by solar photovoltaics (PV). The other, less obvious iteration of the PV phenomenon is large-scale arrays of hundreds, thousands, or in some cases millions of panels [solar farms] that achieve generating capacity in the tens or hundreds of megawatts.

7. Family Planning

Increased adoption of reproductive healthcare and family planning is an essential component to achieve the United Nations’ 2015 medium global population projection of 9.7 billion people by 2050. If investment in family planning, particularly in low-income countries, does not materialize, the world’s population could come closer to the high projection, adding another 1 billion people to the planet.

6. Educating Girls

Girls education, it turns out, has a dramatic bearing on global warming. Women with more years of education have fewer, healthier children and actively manage their reproductive health… Synchronizing investments in girls’ education with those in family planning would be complementary and mutually reinforcing. Education is grounded in the belief that every life bubbles with innate potential. When it comes to climate change, nurturing the promise of each girl can shape the future for all.

5. Tropical Forests

In recent decades, tropical forests... have suffered extensive clearing, fragmentation, degradation, and depletion of flora and fauna… One of the dominant storylines of the nineteenth and twentieth centuries was the vast loss of forestland. Its restoration and re-wilding could be the twenty-first-century story.

4. Plant-Rich Diet

Eat food. Not too much. Mostly plants.

3. Reduced Food Waste

Whether on the farm, near the fork, or somewhere in between, efforts to reduce food waste can address emissions and ease pressure on resources of all kinds, while enabling society more effectively to supply future food demand.

2. Wind Turbines

Ongoing cost reduction will soon make wind energy the least expensive source of installed electricity capacity, perhaps within a decade.

1. Refrigerant Management

As temperatures rise, so does reliance on air conditioners. The use of refrigerators, in kitchens of all sizes and throughout “cold chains” of food production and supply, is seeing similar expansion. As technologies for cooling proliferate, evolution in refrigerants and their management is imperative.

While reading Intermediate Physics for Medicine and Biology, let’s turn up the thermostat a bit during warm days. Between chapters, let’s ditch the hamburger and eat a salad instead (and if you can’t finish it, save the rest for leftovers). Let’s make sure girls in particular are encouraged to read IPMB (or whatever else that will help with their education). And let’s write our congressional representatives and encourage them to support solar and wind energy sources.

If you don’t have the time to read Drawdown, or don’t have easy access to it, then visit the website drawdown.org or watch the videos below, which summarize the plan to reverse global warming.

Climate Solutions 101. Unit 1, Setting the Stage

https://www.youtube.com/watch?v=qT_O2F5zgXc&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=1

Climate Solutions 101. Unit 2, Stopping Climate Change 

https://www.youtube.com/watch?v=bkDherHOymo&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=2

Climate Solutions 101. Unit 3, Reducing Sources 

https://www.youtube.com/watch?v=EiE2DbUOmgc&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=3 

Climate Solutions 101. Unit 4, Supporting Sinks and Improving Society

https://www.youtube.com/watch?v=n_ysjDqZlDw&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=4 

Climate Solutions 101. Unit 5, Putting It All Together

https://www.youtube.com/watch?v=t3tZi7aTym8&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=5

Climate Solutions 101. Unit 6, Making It Happen

 https://www.youtube.com/watch?v=xmt1oOUis0E&list=PLwYnpej4pQF7UPnt0nkZEa8sxR9TmWR1B&index=6

Radiology in Our Changing Climate: A Call to Action

Schoen et al. (2021)
“Radiology in Our Changing Climate:
A Call to Action,”
JACR, 18:1041–1043.

Lately I’ve been thinking more and more about the importance of combating climate change, which may be the most urgent technological challenge of our time. But you haven’t seen much about it in this blog, because climate change doesn’t have much to do with Intermediate Physics for Medicine and Biology. Or does it? Last year, Julia Schoen, Geraldine McGinty, and Cody Quirk published an opinion piece in the Journal of the American College of Radiology titled “Radiology in Our Changing Climate: A Call to Action” (Volume 18, Pages 1041–1043). It’s short, clear, and well worth reading. The introduction begins:

Just as early radiologists did not understand the dangers of high radiation doses, today we are naive to imaging’s carbon footprint and its implications for public health. The world’s temperature has already risen more than 1 °C from preindustrial levels. We see the effects of climate change across the world, from extreme wildfires and stronger storms to rising sea levels and ocean acidification. If we continue with “business as usual,” children born today will experience a planet that is 4 °C warmer than in preindustrial times and the associated health consequences. These consequences are disproportionately felt by children, the elderly, those with preexisting conditions, and outdoor workers. As our climate crisis worsens, radiologists must urgently consider our role in climate change.

According to Schoen et al., the health care system may be responsible for nearly ten percent of American’s greenhouse gas emissions. TEN PERCENT! Yikes. They suggest that radiology departments are “likely a major contributor to energy use within hospital systems.” They identify four ways to address the energy use in radiology.

Imaging Exams

Schoen et al. claim that “over a year, the energy use of one CT [computed tomography] scanner was comparable with that of 5 four-person households, and the energy use of one MR [magnetic resonance] scanner was close to that of 26 four-person households.” I always thought MRI was the ideal imaging method, but it turns out it’s an energy hog, contributing significantly to radiology’s carbon footprint. There are few easy ways to reduce energy use; perhaps use ultrasound more when appropriate and adopt new technologies that shorten imaging time.

Scanners in the Off State

Imaging systems use a lot of energy even in standby mode. You must keep the superconducting coil of a MRI scanner cold all the time, not just when it’s imaging. Solutions are not simple. Schoen et al. suggest using scanners 24 hours a day (patients won’t like that) and working with manufacturers to find ways of reducing energy use when a scanner is not operating.

Wasteful Habits

We have to cut the waste in radiology departments. Simple improvements would be to turn off computers and picture archiving and communication systems (PACSs) at night or when not in use, and reducing excess packaging. I support these easy changes, but wonder if they’ll have a major impact on our carbon footprint.

Energy Sources

Alternative energy sources—including ones like wind, solar, and nuclear—will reduce greenhouse gas emissions. This is something individual radiologists, or even radiology departments, have little control over, but if major health care systems demand cleaner energy sources they might be able to influence regional utilities and politicians.

Conclusion

Schoen, McGinty, and Quirk discuss an important issue, and I thank them for raising it. Their call to action must be addressed by radiologists in collaboration with hospital administrators, academic researchers, and medical device companies. All of us—including the past, present, and future patients needing radiological services—must advocate for reducing our impact on the climate.

I’ll give Schoen et al. the last word by quoting the eloquent final paragraph of their publication.

Radiology faces many challenges, from improving diversity to changes in reimbursement in a budget-neutral system. Addressing climate change is an opportunity to protect vulnerable populations and increase our value in the health care system. Initiatives to address climate change align with the ACR’s [American College of Radiology’s] core purpose of serving both patients and society. Our field has made great strides in patient safety by decreasing radiation doses. Similarly, through our technological expertise and awareness, we can decrease our carbon footprint, with the ultimate goal of mitigating climate change and preventing a looming public health crisis.

 

Listen to a podcast of Julia Schoen discussing sustainability and radiology.

https://www.youtube.com/watch?v=_66M2PgnTxA

The group “Radiologists for a Sustainable Future” is on Twitter. Follow them at @Rads4SF.