Category Archives: Weather

Locked down so long, it’s looking up: the up-side of COVID-19.

I’m not crazy about the COVID isolation, but there are up-sides that I’ve come to appreciate. You might too. Out of boredom, I was finally got into meditation. It was better than just sitting around and doing nothing.

It’s best not to look at isolation as a problem, but an opportunity. I’ve developed a serious drinking opportunity.

And it’s an opportunity to talk to myself. I told myself I’ should quit drinking. Then I figured, why should I listen to a drunk who talks to himself.

A friend of mine was on drugs, but then quit. Everyone in his house is happy, except for the lamp. The lamp won’t talk to him anymore.

The movies are closed, and the bars, and the gyms. It gives me another reason not to go to the gym.

Did you know that, before the crowbar was invented, crows used to drink at home.

The real reason dogs aren’t allowed in bars: lots of guys can’t handle their licker.

There’s time to spend with my children. And they look like me.

I like that I don’t commute. Family events are over zoom, funerals (lots of funerals), meetings, lectures. They come in via the computer, and I don’t have to dress or attend. No jacket, no pants… no travel …. no job.

My children are spending more time with us at home. We have virtual meals together. I discovered that I have a son named Tok. He seems to like my dad-jokes.

My wife is finding it particularly tough. Most every day I see her standing by the window, staring, wondering. One of these days, I’ll let her in.

I asked wife why she married me. Was it for my looks, or my income, or my smarts. She smiled and said it was my sense of humor. 🙂

My wife is an elementary school teacher. She teaches these days with a smart board. If the board were any smarter, it would go work for someone else. It’s necessary, I guess. If you can’t beat them, you might as well let the smart board teach. I think the smart board stole the election. It began by auto-correcting my spelling. Then it moved to auto correct my voting. The board is smarter and better than me (Hey, who wrote this?)

some mask humor
I’ve learned to love masks, though some of them are hot.

You’d think they’d reduce the number of administrators in the schools, given that it’s all remote. Or reduce the price of college. It would be nice if they’d up the number of folks who can attend. So far no. Today the Princeton alumni of Michigan is sponsoring video-talk by Princeton alumnus, George Will. I wanted to attend, but found there was limited seating, so I’m on the waiting list (true story). By keeping people out, they show they are exclusive. Tuition is $40,000 / year, and they keep telling us that the college is in service of humanity. If they were in the service of humanity, they’d charge less, and stream the talk to whoever wants to listen in. I have to hope this will change sooner or later.

Shopping for toilet paper was a big issue at the beginning of the pandemic, but I’ve now got a dog to do it for me. He goes to the store, brings it back. Brings back toothpaste too. He’s a lavatory retriever. (I got this joke from Steve Feldman; the crowbar joke too.)

I don’t mind that there are few new movies. There are plenty of old movies that I have not seen, and old TV shows too.

This fellow is the new head of Biden’s COVID-19 task force. He’s got a science-based plan for over-population and the disease.

I like that people are leaving New York and LA. It’s healthy, and saves on rent. Folks still travel there, mostly for the rioting, but lockdowns are nicer in Michigan.

More people are hunting, and hiking, and canoeing. These are active activities that you can do on lockdown. The old activities were passive, or going out to eat. Passive activities are almost a contradiction in terms.

We’re cooking more at home, which is healthier. And squirrel doesn’t taste half bad. If I live through this, I’ll be healthy.

I’m reading more, and have joined goodreads.com. I’ve developed a superpower: I find can melt ice cubes, just by looking at them. It takes a while but they melt.

A lot more folks have dogs. And folks have gotten into religion. Wouldn’t it be great, if after death we fond that dyslexic folks were right. There really is a dog.

Let’s love the virus. If we don’t, the next crisis will be worse.

There was an election last week. My uncles voted for Biden, which really surprised me. They were staunch Republicans when they were alive. My aunt got the ballot and convinced them. She was a Democrat when she was alive.

I got pneumonia vaccine shot, and a flu shot. That wasn’t a joke. I think it’s a good idea. Here’s why. People mostly die from pneumonia not the virus.

Before COVID, the other big crisis was global warming. Al Gore and Greta Thunberg claimed we had to shutter production and stop driving to save the planet. COVID-19 has done it. The next crisis is over-population. COVID is already curing that problem — not so much in China, but in the US, Europe, and South America.

Just As a final thought, let’s look at the bright side of the virus. If we don’t, the next crisis will be worse. Take Monty Python’s advice and Always look at the bright side of life.

Robert Buxbaum, November 20, 2020.

When was America great last? Before October 24, 1945, United Nations Day.

Last night a CNN reporter was going around a Trump rally asking ‘When was America ever great?” It’s a legitimate question for anyone wearing a MAGA hat. “Make America Great AGAIN” suggests that America was once great and is no more. The answer the reporter pushed for, I think, was the one given by NY’s Governor Cuomo: “America was never that great.” Alternately, the answer of Michelle Obama, who claimed in 2008, “For the first time in my adult life, I am really proud of my country.” The attendees attempted other answers, like 1776, but the reporter shot them down, saying that people were enslaved in 1776, and telling the home audience that even later, women didn’t have the right to vote, or the LGBT community was denied the rights to which it was entitled. I was not there, and might have got shot down too, but I suspect the question deserves an exact answer: the last time America was great was just before October 24, 1945, United Nations Day, the day we submitted to be part of a world government.

Jackie Robinson, the first black American in major league baseball. Signed October 23, 1945.

By October 23, 1945 WWII was over. We had peace and plenty, the most powerful military, and the most powerful economy. Besides this, we had a baby boom (Children are a bedrock of success, IMHO). Also, on October 23, 1945, the Brooklyn Dodgers signed Jackie Robinson, the first black, major Leaguer since the late 1800s. We thus took a major step against the greatest of our original sins. These were aspects of US greatness, but they were were not guaranteed. They were based on two pre-requisites: a national dedication to self-improvement, and the sovereign control we had over our self-improvement. Total control ended on October 24, 1945 when we joined with the Soviet Union, the United Kingdom, China, France, and several other nations accepting (limited) control by the United Nations organization.

By accepting United Nations oversight, we gave over a significant chunk of sovereignty to other countries whose desire, mostly, was that the US should not be greater than them, and largely that it should not be great at all. To that end they endeavored to insure that we did not have the most powerful economy, the most powerful military, or a baby boom. From tat day on, other countries would sit in judgment on our behaviors and goals. More and more, they would demand remedies that served their interests and diminished US greatness, its exceptionalism. To the patriot this is a disaster. The New York Times declares that anti-exceptionalism is the road to world peace and prosperity. The MAGA crowd disagree.

The United Nations officially came into existence on October 24, 1945, after the United States, the Soviet Union, the United Kingdom, China, France ratify the UN Charter. The charter, once signed, was handed to Truman’s assistant, Alger Hiss.

It’s not that the MAGA Republicans are against world peace or prosperity. No sane person is, but they claim that the best way to achieve these things is for us to be exceptional and work in our own best interests. It is only a sad peace that is achieved by having a foreign body decide that we are at fault in every conflict, and that we should pay reparations to all who lag. There are many poor, socialist countries choosing judges, and these judges tend to rule that the US, as a rich nation, is always at fault and should always pay — both for “development” of the poor nations -overseen by them — and for the the UN too. We knew that their judges would rule this way, but likely didn’t care, or realize how much of our greatness rested on sovereignty. Without sovereignty, even the greatest of world powers will be brought down. Alger Hiss, the person Truman handed the signed UN charter to, was a spy for the Soviet Union. It was a telling beginning.

One of the big promises of Donald Trump is that he will limit the reach of the UN and of its ability to reach into our pockets. He already renegotiated or rejected trade agreements, like TPP that would have sent our jobs and technology abroad. Trump also placed import taxes (tariffs) on some foreign goods. The MAGA folks approve, but the Obama internationalists are scandalized. As depicted in the book “Fear”, long time (Obama) staffers at the White House stole tariff bills from the president’s desk to save the world by keeping them from Trump’s signature. Tariffs have been used throughout American history, and can be a benefit for jobs, and diplomacy and for American manufacturers. They are not radical, but some people lost out. Larely, those were US consumers of foreign goods who suffered. Things improved most for black and hispanic workers though. The intellectual class who claim to represent black and hispanic interests have removed Trump and supporters from social media. It’s their way of winning the argument.

Henry Cabot Lodge, Wilson’s main opponent ito the US joining the League of Nations,.

A major anti-MaGA goal is to stop global warming. This is done by globe-trotting folks in private jets who’ve agreed we should shut US industry and pay $1B/ year, while permitting unlimited coal use by China and India. They were the largest CO2 sources, and also among the least efficient producers.Their share of CO2 output is huge and growing. The globe-watchers don’t care. By the way, is a cold world is something we really need?

Trump also limited the power of the world trade organization and of the world court. It’s something that Henry Kissinger recommended In the Journal “Foreign Affairs 2001. Kissinger wrote that “The danger [in too much power for the world court] consists of substituting the tyranny of judges for that of governments; historically, the dictatorship of the virtuous has often led to inquisitions and even witch-hunts.” Trump also built up the military, and claims he will eliminate a postal agreement that gives low, subsidized rates, to China and poor countries so they can mail goods to the US for far less than we can to ourselves. Joe Biden has pushed for “the dictatorship of the virtuous” and promises to raise taxes to pay for it. He’s also suggested packing the supreme court. To me, this is far more radical than tariffs.

The MAGA divide between Trump and Obama/ Biden is not new. It’s existed to a greater or lesser extent between most Democrats and Republicans as far back as the civil war. One major cause of the civil war was tariffs. Then as now, tariffs benefit the manufacturer and worker, and hurt the aristocrat.

In 1918, the MAGA divide played flared because of Wilson’s support of the League of Nations. Republican, Henry Cabot Lodge opposed joining the League of Nations over the same complaints that Trump has raised. Trump’s MAGA claim is that he’ll make US agreements serve US interests. Also that he’s making the US military strong again, and making the US economy strong again. For all I know, the plan for the next four years is to try to ignite another baby boom, too. This, as I understand it, is the MAGA message.

As a side issue, I note that virtually every rapper is for Trump, and virtually every orthodox rabbi too. Yet the internationalist claim he’s racist. His approval among black voters is polled at 46%. Unless you hold that Jewish and black voters don’t understand their own interests. it would seem that Trump is not the racist he’s claimed to be. A recent, “jews for Trump” parade in NY was attacked with rocks, eggs, fists, and paint thrown on participants by white Democrats. The racists who run the NY Justice Department decided not to prosecute.

Robert Buxbaum, October 27-28, 2020. I figured it was time someone explained what “Make America Great Again” meant. I’ve also speculated on Trump’s religion here, and on his mental state, here.

Eight ways to not fix the tower of Pisa, and one that worked.

You may know that engineers recently succeed in decreasing the tilt of the “leaning” tower of Pizza by about 1.5°, changing it from about 5.5° to about to precisely 3.98° today –high precision given that the angle varies with the season. But you may not know how that there were at least eight other engineering attempts, and most of these did nothing or made things worse. Neither is it 100% clear that current solution didn’t make things worse. What follows is my effort to learn from the failures and successes, and to speculate on the future. The original-tilted tower is something of an engineering marvel, a highly tilted, stone on stone building that has outlasted earthquakes and weathering that toppled many younger buildings that were built straight vertical, most recently the 1989 collapse of the tower of Pavia. Part of any analysis, must also speak to why this tower survived so long when others failed.

First some basics. The tower of Pisa is an 8 story bell tower for the cathedral next door. It was likely designed by engineer Bonanno Pisano who started construction in 1173. We think it’s Pisano, because he put his name on an inscription on the base, “I, who without doubt have erected this marvelous work that is above all others, am the citizen of Pisa by the name of Bonanno.” Not so humble then, more humble when the tower started to lean, I suspect. The outer diameter at the base is 15.5 m and the weight of the finished tower is 14.7 million kg, 144 million Nt. The pressure exerted on the soil is 0.76 MPa (110 psi). By basic civil engineering, it should stand straight like the walls of the cathedral.

Bonanno’s marvelous work started to sink into the soil of Pisa almost immediately, though. Then it began to tilt. The name Pisa, in Greek, means swamp, and construction, it seems, was not quite on soil, but mud. When construction began the base was likely some 2.5 m (8 feet) above sea level. While a foundation of clay, sand and sea-shells could likely have withstood the weight of the tower, the mud below could not. Pisano added length to the south columns to keep the floors somewhat level, but after three floors were complete, and the tilt continued, he stopped construction. What to do now? What would you do?

If it were me, I’d consider widening the base to distribute the force better, and perhaps add weight to the north side. Instead, Pisano gave up. He completed the third level and went to do other things. The tower stood this way for 99 years, a three-floor, non-functional stub. 

About 1272, another engineer, Giovanni di Simone, was charged with fixing the situation. His was the first fix, and it sort-of worked. He strengthened the stonework of the three original floors, widened the base so it wold distribute pressure better, and buried the base too. He then added three more floors. The tower still leaned, but not as fast. De Simone made the south-side columns slightly taller than the north to hide the tilt and allow the floors to be sort-of level. A final two stories were added about 1372, and then the first of the bells. The tower looked as it does today when Gallileo did his famous experiments, dropping balls of different size from the south of the 7th floor between 1589 and 1592.

Fortunately for the construction, the world was getting colder and the water table was dropping. While dry soil is stronger than wet, wet soil is more plastic. I suspect it was the wet soil that helped the tower survive earthquakes that toppled other, straight towers. It seems that the tilt not only slowed during this period but briefly reversed, perhaps because of the shift in center of mass, or because of changes in the sea level. Shown below is 1800 years of gauge-based sea-level measurements. Other measures give different sea-level histories, but it seems clear that man-made climate change is not the primary cause. Sea levels would continue to fall till about 1750. By 1820 the tilt had resumed and had reached 4.5°.

Sea level height history as measured by land gauges. Because of climate change (non man-made) the sea levels rise and fall. This seems to have affected the tilt of the tower. Other measures of water table height give slightly different histories, but still the sense that man change is not the main effect.

The 2nd attempt was begun in 1838. Architect, Alessandro Della Gherardesca got permission to dig around the base at the north to show off the carvings and help right the tower. Unfortunately, the tower base had sunk below the water table. Further, it seems the dirt at the base was helping keep the tower from falling. As Della Gherardesca‘s crew dug, water came spurting out of the ground and the tower tilted another few inches south. The dig was stopped and filled in, but he dig uncovered the Pisano inscription, mentioned above. What would you do now? I might go away, and that’s what was done.

The next attempt to fix the tower (fix 3) was by that self-proclaimed engineering genius, Benito Mussolini. In 1934. Mussolini had his engineers pump some 200 tons of concrete into the south of the tower base hoping to push the tower vertical and stabilize it. The result was that the tower lurched another few inches south. The project was stopped. An engineering lesson: liquids don’t make for good foundations, even when it’s liquid concrete. An unfortunate part of the lesson is that years later engineers would try to fix the tower by pumping water beneath the north end. But that’s getting ahead of myself. Perhaps Mussolini should have made tests on a model before working on the historic tower. Ditto for the more recent version.

On March 18, 1989 the Civic Tower of Pavia started shedding bricks for no obvious reason. This was a vertical tower of the same age and approximate height as the Pisa tower. It collapsed killing four people and injuring 15. No official cause has been reported. I’m going to speculate that the cause was mechanical fatigue and crumbling of the sort that I’ve noticed on the chimney of my own house. Small vibrations of the chimney cause bits of brick to be ejected. If I don’t fix it soon, my chimney will collapse. The wet soils of Pisa may have reduced the vibration damage, or perhaps the stones of Pisa were more elastic. I’ve noticed brick and stone flaking on many prominent buildings, particularly at joins in the chimney.

John Burland’s team cam up with many of the fixes here. They are all science-based, but most of the fixes made things worse.

In 1990, a committee of science and engineering experts was formed to decide upon a fix for the tower of Pisa. It was headed by Professor John Burland, CBE, DSc(Eng), FREng, FRS, NAE, FIC, FCGI. He was, at the time, chair of soil mechanics at the Imperial College, London, and had worked with Ove, Arup, and Partners. He had written many, well regarded articles, and had headed the geological aspects of the design of the Queen Elizabeth II conference center. He was, in a word, an expert, but this tower was different, in part because it was an, already standing, stone-on stone tower that the city wished should remain tilted. The tower was closed to visitors along with all businesses to the south. The bells were removed as well. This was a safety measure, and I don’t count it as a fix. It bought time to decide on a solution. This took two years of deliberation and meetings

In 1992, the committee agreed to fix no 4. The tower was braced with plastic-covered, steel cables that were attached around the second and third floors, with the cables running about 5° from the horizontal to anchor points several hundred meters to the north. The fix was horribly ugly, and messed with traffic. Perhaps the tilt was slowed, it was not stopped.

In 1993, fix number 5. This was the most exciting engineering solution to date: 600 tons of lead ingots were stacked around the base, and water was pumped beneath the north side. This was the reverse of the Mussolini’s failed solution, and the hope was that the tower would tilt north into the now-soggy soil. Unfortunately, the tower tilted further south. One of the columns cracked too, and this attempt was stopped. They were science experts, and it’s not clear why the solution didn’t work. My guess is that they pumped in the water too fast. This is likely the solution I would have proposed, though I hope I would have tested it with a scale model and would have pumped slower. Whatever. Another solution was proposed, this one even more exotic than the last.

For fix number 6, 1995, the team of experts, still overseen by Burland, decided to move the cables and add additional tension. The cables would run straight down from anchors in the base of the north side of the tower to ten underground steel anchors that were to be installed 40 meters below ground level. This would have been an invisible solution, but the anchor depth was well into the water table. So, to anchor the ground anchors, Burland’s team had liquid nitrogen injected into the ground beneath the tower, on the north side where the ground anchors were to go. What Burland did not seem to have realized is that water expands when it freezes, and if you freeze 40 meters of water the length change is significant. On the night of September 7, 1995, the tower lurched southwards by more than it had done in the entire previous year.  The team was summoned for an emergency meeting and the liquid nitrogen anchor plan was abandoned.

Tower with the two sets of lead ingots, 900 tons total, about the north side of the base. The weight of the tower is 14,700 tons.

Fix number 7: Another 300 tons of lead ingots were added to the north side as a temporary, simple fix. The fix seems to have worked stabilizing things while another approach was developed.

Fix number 8: In order to allow the removal of the ugly lead bricks another set of engineers were brought on, Roberto Cela and Michele Jamiolkowski. Using helical drills, they had holes drilled at an angle beneath the north side of the tower. Using hoses, they removed a gallon or two of dirt per day for eleven years. The effect of the lead and the dirt removal was to reduce the angle of the tower to 4.5°, the angle that had been measured in 1820. At this point the lead could be removed and tourists were allowed to re-enter. Even after the lead was removed, the angle continued to subside north. It’s now claimed to be 3.98°, and stable. This is remarkable precision for a curved tower whose tilt changes with the seasons. (An engineering joke: How may engineers does it take to change a lightbulb? 1.02).

The bells were replaced and all seemed good, but there was still the worry that the tower would start tilting again. Since water was clearly part of the problem, the British soils expert, Burland came up with fix number 9. He had a series of drainage tunnels built to keep the water from coming back. My worry is that this water removal will leave the tower vulnerable to earthquake and shedding damage, like with the Pavia tower and my chimney. We’ll have to wait for the next earthquake or windstorm to tell for sure. So far, this fix has done no harm.

Robert Buxbaum, October 9, 2020. It’s nice to learn from other folks mistakes, and embarrassments, as well as from their successes. It’s also nice to see how science really works, not with great experts providing the brilliant solution, but slowly, like stumbling in the dark. I see this with COVID-19.

Greenland is warm, and I’m not sure that’s bad

I got the graph below from a global warming blog called “factcheck.” The blue line on the graph below shows Greenland temperatures, constructed by Vinther et al. (2009) using data from six ice cores smooth to 20 year steps. The black line at the right are observed temperatures from Berkeley Earth, with a 20-year smooth applied. To make the graph, the observed temperatures, and ice temperatures were aligned over the 1880-1960 period. According to many this shows a disaster that we caused, and that we must reverse by stopping US industry. I’m not so sure.

It is seen that theGreeland temperature has risen 1.5°C over the last century, or 4°C since 1710. The first issue is that the rise since 1710 to 1810 is rather substantial, about 1.3°C and the level of world industrialization was a lot less, but more importantly, when I look at this curve, the part that worries me is not the spike at the right, but the bit at the left. I’m far more comfortable with another degree or three of Greenland heating, than I am with an ice age and the 50°C drop that entails.

As for stopping US industry to cure the rise, that too seems like a bad idea since most of the carbon dioxide comes not from us, but from China, with quite a bit from India. If we stop our poroduction, we merely hurt ourselves while moving production, and CO2 to China. I suspect that those behind this are Chinaphiles — Sinophiles.

Robert Buxbaum July 28, 2020

Sweden v Michigan: different approaches, same outcome.

Sweden has scientists; Michigan has scientists. Sweden’s scientists said to trust people to social distance and let the COVID-19 disease run its course. It was a highly controversial take, but Sweden didn’t close the schools, didn’t enforce masks, and let people social distance as they would. Michigan’s scientists said to wear masks and close everything, and the governor enforced just that. She closed the schools, the restaurants, the golf courses, and even the parks for a while. In Michigan you can not attend a baseball game, and you can be fined for not wearing a mask in public. The net result: Michigan and Sweden had almost the same death totals and rates, as the graphs below show. As of July 28, 2020: Sweden had 5,702 dead of COVID-19, Michigan had 6,402. That’s 13 more dead for a population that’s 20% smaller.

Sweden’s deaths pre day. There are 5,702 COVID dead since the start, out of a population of 10.63 million. There are 79,494 confirmed COVID cases, but likely a lot more infected.

Sweden and Michigan are equally industrial, with populations in a few dense cities and a rural back-country. Both banned large-scale use of hydroxy-chloroquine. Given the large difference in social distance laws, you’d expect a vastly different death rate, with Michigan’s, presumably lower, but there is hardly any difference at all, and it’s worthwhile to consider what we might learn from this.

Michigan’s deaths pre day. There are 6,426 COVID dead since the start, out of a population of 9.99 million. There are 88,025 confirmed COVID cases, but likely a lot more infected.

What I learn from this is not that social distance is unimportant, and not that hand washing and masks don’t work, but rather it seems to me that people are more likely to social distance if they themselves are in control of the rules. This is something I also notice comparing freezer economies to communist or controlled ones: people work harder when they have more of a say in what they do. Some call this self -exploitation, but it seems to be a universal lesson.

Both Sweden and the US began the epidemic with some moderate testing of a drug called hydroxychloroquine (HCQ)and both mostly stopped in April when the drug became a political football. President Trump recommended it based on studies in France and China, but the response was many publications showing the didn’t work and was even deadly. Virtually ever western country cut back use of the drug. Brazil’s scientists objected — see here where they claim that those studies were crooked. It seems that countries that continued to use the drug had fewer COVID deaths, see graph, but it’s hard to say. The Brazilians claim that the anti HCQ studies were politically motivated, but doctors in both Sweden and the US largely stopped prescribing the drug. This seems to have been a mistake.

US hospitals stopped using HCQ in early April almost as soon as Trump recommended it. Sweden did the same.

In July, Henry Ford hospitals published this large-scale study showing a strong benefit: for HCQ: out of 2,541 patients in six hospitals, the death rate for those treated with HCQ was 13%. For those not treated with HCQ, the death rate was more than double: 26.4%. It’s not clear that this is cause and effect. It’s suggestive, but there is room for unconscious bias in who got the drug. Similarly, last week, a Yale researcher this week used epidemiological evidence to say HCQ works. This might be proof, or not. Since epidemiology is not double-blind, there is more than common room for confounding variables. By and large the newspaper experts are unconvinced by epidemiology and say there is no real evidence of HCQ benefit. In Michigan and Sweden the politicians strongly recommend continuing their approaches, by and large avoiding HCQ. In Brazil, India and much of the mideast, HCQ is popular. The countries that use HCQ claim it works. The countries that don’t claim it does not. The countries with strict lock-down say that science shows this is what’s working. The countries without, claim they are right to go without. All claim SCIENCE to support their behaviors, and likely that’s faulty logic.

Hydroxychloroquine and COVID-19 fatality rates in different countries as of early June 2020. This isn’t enough to prove HCQ effectiveness, but it’s promising, and suggests that increased use is warranted, at least among those without heart problems.

Given my choice, I’d like to see more use of HCQ. I’m not sure it works, but I’m ,sure there’s enough evidence to put it into the top tier of testing. I’d also prefer the Sweden method, of nor enforced lockdown, or a very moderate lockdown, but I live I’m Michigan where the governor claims she knows science, and I’m willing to live within the governor’s lockdown.There is good, scientific evidence that, if you don’t you get fined or go to jail.

Robert Buxbaum, July 29, 2020. As I side issue, I think iodine hand wash is a good thing. I may be wrong, but here’s my case.

Why the earth is magnetic with the north pole heading south.

The magnetic north pole, also known as true north, has begun moving south. It had been moving toward the north pole thought the last century. It moved out of Canadian waters about 15 years ago, heading toward Russia. This year it passed as close to the North pole as it is likely to, and begun heading south (Das Vedanga, old friend). So this might be a good time to ask “why is it moving?” or better yet, “Why does it exist at all?” Sorry to say the Wikipedia page is little help here; what little they say looks very wrong. So I thought I’d do my thing and write an essay.

The motion of the magnetic (true) north pole over the last century; it's nearly at the north pole.

Migration of the magnetic (true) north pole over the last century; it’s at 8°N and just passed the North Pole.

Your first assumption of the cause of the earth’s magnetic field would involve ferromagnetism: the earth’s core is largely iron and nickel, two metals that permanent magnets. Although the earth’s core is very hot, far above the “Curie Temperature” where permanent magnets form, you might imagine that some small degree of magnetizability remains. You’d be sort of right here and sort of wrong; to see why, lets take a diversion into the Curie Temperature (Pierre Curie in this case) before presenting a better explanation.

The reason there is no magnetism above the Curie temperature is similar to the reason that you can’t have a plague outbreak or an atom bomb if R-naught is less than one. Imagine a magnet inside a pot of iron. The surrounding iron will dissipate some of the field because magnets are dipoles and the iron occupies space. Fixed dipole effects dissipate with a distance relation of r-4; induced dipoles with a relation r-6. The iron surrounding the magnet will also be magnetized to an extent that augments the original, but the degree of magnetization decreases with temperature. Above some critical temperature, the surrounding dissipates more than it adds and the effect is that the original magnetic effect will die out if the original magnet is removed. It’s the same way that plagues die out if enough people are immunized, discussed earlier.

The earth rotates, and the earth's surface is negatively charged. There is thus some room for internal currents.

The earth rotates, and the earth’s surface is negatively charged. There is thus some room for internal currents.

It seems that the earth’s magnetic field is electromagnetic; that is, it’s caused by a current of some sort. According to Wikipedia, the magnetic field of the earth is caused by electric currents in the molten iron and nickel of the earth’s core. While there is a likely current within the core, I suspect that the effect is small. Wikipedia provides no mechanism for this current, but the obvious one is based on the negative charge of the earth’s surface. If the charge on the surface is non-uniform, It is possible that the outer part of the earth’s core could become positively charged rather the way a capacitor charges. You’d expect some internal circulation of the liquid the metal of the core, as shown above – it’s similar to the induced flow of tornadoes — and that flow could induce a magnetic field. But internal circulation of the metallic core does not seem to be a likely mechanism of the earth’s field. One problem: the magnitude of the field created this way would be smaller than the one caused by rotation of the negatively charged surface of the earth, and it would be in the opposite direction. Besides, it is not clear that the interior of the planet has any charge at all: The normal expectation is for charge to distribute fairly uniformly on a spherical surface.

The TV series, NOVA presents a yet more unlikely mechanism: That motion of the liquid metal interior against the magnetic field of the earth increases the magnetic field. The motion of a metal in a magnetic field does indeed produce a field, but sorry to say, it’s in the opposing direction, something that should be obvious from conservation of energy.

The true cause of the earth’s magnet field, in my opinion, is the negative charge of the earth and its rotation. There is a near-equal and opposite charge of the atmosphere, and its rotation should produce a near-opposite magnetic field, but there appears to be enough difference to provide for the field we see. The cause for the charge on the planet might be due to solar wind or the ionization of cosmic rays. And I notice that the average speed of parts of the atmosphere exceeds that of the surface —  the jet-stream, but it seems clear to me that the magnetic field is not due to rotation of the jet stream because, if that were the cause, magnetic north would be magnetic south. (When positive charges rotate from west to east, as in the jet stream, the magnetic field created in a North magnetic pole a the North pole. But in fact the North magnetic pole is the South pole of a magnet — that’s why the N-side of compasses are attracted to it, so … the cause must be negative charge rotation. Or so it seems to me.  Supporting this view, I note that the magnet pole sometimes flips, north for south, but this is only following a slow decline in magnetic strength, and it never points toward a spot on the equator. I’m going to speculate that the flip occurs when the net charge reverses, thought it could also come when the speed or charge of the jet stream picks up. I note that the magnetic field of the earth varies through the 24 hour day, below.

The earth's magnetic strength varies regularly through the day.

The earth’s magnetic strength varies regularly through the day.

Although magnetic north is now heading south, I don’t expect it to flip any time soon. The magnetic strength has been decreasing by about 6.3% per century. If it continues at that rate (unlikely) it will be some 1600 years to the flip, and I expect that the decrease will probably slow. It would probably take a massive change in climate to change the charge or speed of the jet stream enough to reverse the magnetic poles. Interestingly though, the frequency of magnetic strength variation is 41,000 years, the same frequency as the changes in the planet’s tilt. And the 41,000 year cycle of changes in the planet’s tilt, as I’ve described, is related to ice ages.

Now for a little math. Assume there are 1 mol of excess electrons on a large sphere of the earth. That’s 96500 Coulombs of electrons, and the effective current caused by the earth’s rotation equals 96500/(24 x3600) = 1.1 Amp = i. The magnetic field strength, H =  i N µ/L where H is magnetizability field in oersteds, N is the number of turns, in this case 1, µ is the magnetizability. The magnetizability of air is 0.0125 meter-oersteds/ per ampere-turn, and that of a system with an iron core is about 200 times more, 2.5 meter-tesla/ampere-turn. L is a characteristic length of the electromagnet, and I’ll say that’s 10,000 km or 107 meters. As a net result, I calculate a magnetic strength of 2.75×10-7 Tesla, or .00275 Gauss. The magnet field of the earth is about 0.3 gauss, suggesting that about 100 mols of excess charge are involved in the earth’s field, assuming that my explanation and my math are correct.

At this point, I should mention that Venus has about 1/100 the magnetic field of the earth despite having a molten metallic core like the earth. It’s rotation time is 243 days. Jupiter, Saturn and Uranus have greater magnetic fields despite having no metallic cores — certainly no molten metallic cores (some theorize a core of solid, metallic hydrogen). The rotation time of all of these is faster than the earth’s.

Robert E. Buxbaum, February 3, 2019. I have two pet peeves here. One is that none of the popular science articles on the earth’s magnetic field bother to show math to back their claims. This is a growing problem in the literature; it robs science of science, and makes it into a political-correctness exercise where you are made to appreciate the political fashion of the writer. The other peeve, related to the above concerns the game it’s thoroughly confusing, and politically ego-driven. The gauss is the cgs unit of magnetic flux density, this unit is called G in Europe but B in the US or England. In the US we like to use the tesla T as an SI – mks units. One tesla equals 104 gauss. The oersted, H is the unit of magnetizing field. The unit is H and not O because the English call this unit the henry because Henry did important work in magnetism One ampere-turn per meter is equal to 4π x 10−3 oersted, a number I approximated to 0.125 above. But the above only refers to flux density; what about flux itself? The unit for magnetic flux is the weber, Wb in SI, or the maxwell, Mx in cgs. Of course, magnetic flux is nothing more than the integral of flux density over an area, so why not describe flux in ampere-meters or gauss-acres? It’s because Ampere was French and Gauss was German, I think.

James Croll, janitor scientist; man didn’t cause warming or ice age

When politicians say that 98% of published scientists agree that man is the cause of global warming you may wonder who the other scientists are. It’s been known at least since the mid 1800s that the world was getting warmer; that came up talking about the president’s “Resolute” desk, and the assumption was that the cause was coal. The first scientist to present an alternate theory was James Croll, a scientist who learned algebra only at 22, and got to mix with high-level scientists as the janitor at the Anderson College in Glasgow. I think he is probably right, though he got some details wrong, in my opinion.

James Croll was born in 1821 to a poor farming family in Scotland. He had an intense interest in science, but no opportunity for higher schooling. Instead he worked on the farm and at various jobs that allowed him to read, but he lacked a mathematics background and had no one to discuss science with. To learn formal algebra, he sat in the back of a class of younger students. Things would have pretty well ended there but he got a job as janitor for the Anderson College (Scotland), and had access to the library. As janitor, he could read journals, he could talk to scientists, and he came up with a theory of climate change that got a lot of novel things right. His idea was that there were  regular ice ages and warming periods that would follow in cycles. In his view these were a product of the precession of the equinox and the fact that the earth’s orbit was not round, but elliptical, with an eccentricity of 1.7%. We are 3.4% closer to the sun on January 3 than we are on July 4, but the precise dates changes slowly because of precession of the earth’s axis, otherwise known as precession of the equinox.

Currently, at the spring equinox, the sun is in “the house of Pisces“. This is to say, that a person who looks at the stars all the night of the spring equinox will be able to see all of the constellations of the zodiac except for the stars that represent Pisces (two fish). But the earth’s axes turns slowly, about 1 days worth of turn every 70 years, one rotation every 25,770 years. Some 1800 years ago, the sun would have been in the house of Ares, and 300 years from now, we will be “in the age of Aquarius.” In case you wondered what the song, “age of Aquarius” was about, it’s about the precession of the equinox.

Our current spot in the precession, according to Croll is favorable to warmth. Because we are close to the sun on January 3, our northern summers are less-warm than they would be otherwise, but longer; in the southern hemisphere summers are warmer but shorter (southern winters are short because of conservation of angular momentum). The net result, according to Croll should be a loss of ice at both poles, and slow warming of the earth. Cooling occurs, according to Croll, when the earth’s axis tilt is 90° off the major axis of the orbit ellipse, 6300 years before or after today. Similar to this, a decrease in the tilt of the earth would cause an ice age (see here for why). Earth tilt varies over a 42,000 year cycle, and it is now in the middle of a decrease. Croll’s argument is that it takes a real summer to melt the ice at the poles; if you don’t have much of a tilt, or if the tilt is at the wrong time, ice builds making the earth more reflective, and thus a little colder and iceier each year; ice extends south of Paris and Boston. Eventually precession and tilt reverses the cooling, producing alternating warm periods and ice ages. We are currently in a warm period.

Global temperatures measured from the antarctic ice showing stable, cyclic chaos and self-similarity.

Global temperatures measured from the antarctic ice showing stable, cyclic chaos and self-similarity.

At the time Croll was coming up with this, it looked like numerology. Besides, most scientists doubted that ice ages happened in any regular pattern. We now know that ice ages do happen periodically and think that Croll must have been on to something. See figure; the earth’s temperature shows both a 42,000 year cycle and a 23,000 year cycle with ice ages coming every 100,000 years.

In the 1920s a Serbian Mathematician, geologist, astronomer, Milutin Milanković   proposed a new version of Croll’s theory that justified longer space between ice ages based on the beat frequency between a 23,000 year time for axis precession, and the 42,000 year time for axis tilt variation. Milanković used this revised precession time because the ellipse precesses, and thus the weather-related precession of the axis is 23,000 years instead of 25,770 years. The beat frequency is found as follows:

51,000 = 23,000 x 42,000 / (42000-23000).

As it happens neither Croll’s nor Milanković’s was accepted in their own lifetimes. Despite mounting evidence that there were regular ice ages, it was hard to believe that these small causes could produce such large effects. Then, in a 1976 study (Hayes, Imbrie, and Shackleton) demonstrated clear climate variations based on the mud composition from New York and Arizona. The variations followed all four of the Milankocitch cycles.

Southern hemisphere ice is growing, something that confounds CO2-centric experts

Southern hemisphere ice is growing, something that confounds CO2-centric experts

Further confirmation came from studying the antarctic ice, above. You can clearly see the 23,000 year cycle of precession, the 41,000 year cycle of tilt, the 51,000 year beat cycle, and also a 100,000 year cycle that appears to correspond to 100,000 year changes in the degree of elliptic-ness of the orbit. Our orbit goes from near circular to quite elliptic (6.8%) with a cycle time effectively of 100,000 years. It is currently 1.7% elliptic and decreasing fast. This, along with the decrease in earth tilt suggests that we are soon heading to an ice age. According to Croll, a highly eccentric orbit leads to warming because the minor access of the ellipse is reduced when the orbit is lengthened. We are now heading to a less-eccentric orbit; for more details go here; also for why the orbit changes and why there is precession.

We are currently near the end of a 7,000 year warm period. The one major thing that keeps maintaining this period seems to be that our precession is such that we are closest to the sun at nearly the winter solstice. In a few thousand years all the factors should point towards global cooling, and we should begin to see the glaciers advance. Already the antarctic ice is advancing year after year. We may come to appreciate the CO2 produced by cows and Chinese coal-burning as these may be all that hold off the coming ice age.

Robert Buxbaum, November 16, 2018.

What drives the jet stream

Having written on controversial, opinion things, I thought I’d take break and write about earth science: the jet stream. For those who are unfamiliar the main jet stream is a high-altitude wind blowing at about 40,000 feet (10 km) altitude at about 50° N latitude. It blows west to east at about 100 km/hr (60 mph), about 12% of the cruising of a typical jet airplane. A simple way to understand the source of the jet stream is to note that the earth spins slower (in mph) at the poles than at lower latitudes, but that the temperature difference between the poles and equator guarantees that air at high altitude is always traveling toward the poles from the lower latitudes.

Consider that the earth is about 40,000 km is circumference and turns once every 24 hours. This suggests a rotation speed of 1667 km/hr at the equator. At any higher latitude the speed is 1667 cos latitude. Thus it’s 1070 km/hr at 50° latitude, 0 km/hr at the north pole; 1667km/hr cos 50°= 1070 km/hr.

Idealize north-south circulation of air around our globe.

Idealized north-south circulation of air around our globe.

It’s generally colder at the poles than it is at lower latitudes — that is nearer the equator (here’s why). This creates a north-south wind where the air becomes more compact as it cools in northern climate (50°latitude  and further north), and this creates a vacuum at high altitudes and a high pressure zone at low altitudes. The result is a high altitude flow of air towards north, and a flow of low altitude air south, a process that is described by the idealized drawing at right.

At low altitudes in Detroit (where I am) we experience winds mostly from the north and from the east. Winds come from the east — or appear to — because of the rotation of the earth. The air that flows down from Canada is moving west to east at a slower speed than Detroit is moving west to east. We experience this as an easterly wind. At higher altitudes, the pattern is reversed. At 9 to 12 km altitudes, an airplane would experience winds mostly from the south-west. Warm air from lower latitudes is moving eastward at 1200 or more km/hr because that’s the speed of the earth. As it moves north, it discovers that the land is moving eastward at a much slower speed, and the result is the jet stream. The maximum speed of the jet stream is about 200 km/hr, the difference in the earth’s east-speed between that at 40°N and at 50°N, while the typical speed is about half of that, 100 km/hr. I’d attribute this slower speed to friction or air mixing.

One significance of the jet stream is that it speeds west-east air-traffic, e.g. flights from Japan to the US or from the US to Europe. Airlines flying west to east try to fly at the latitude and altitude of the jet stream to pick up speed. Planes flying the other way go closer to the pole and/or at different altitudes to avoid having the jet stream slowing them down, or to benefit from other prevailing winds.

I note that Hurricanes are driven by the same forces as the jet stream, just more localized. Tornados are the same, just more localized. A localized flow of this sort can pick stuff up here’s how they pick stuff upRobert Buxbaum, May 22, 2018

What drives the gulf stream?

I’m not much of a fan of todays’ kids’ science books because they don’t teach science IMHO. They have nice pictures and a few numbers; almost no equations, and lots of words. You can’t do science that way. On the odd occasion that they give the right answer to some problem, the lack of math means the kid has no way of understanding the reasoning, and no reason to believe the answer. Professional science articles on the web are bad in the opposite direction: too many numbers and for math, hey rely on supercomputers. No human can understand the outcome. I like to use my blog to offer science with insight, the type you’d get in an old “everyman science” book.

In previous posts, I gave answers to why the sky is blue, why it’s cold at the poles, why it’s cold on mountains, how tornadoes pick stuff up, and why hurricanes blow the way they do. In this post, we’ll try to figure out what drives the gulf-stream. The main argument will be deduction — disproving things that are not driving the gulf stream to leave us with one or two that could. Deduction is a classic method of science, well presented by Sherlock Holmes.

The gulf stream. The speed in the white area is ≥ 0.5 m/s (1.1 mph.).

The gulf stream. The speed in the white area is ≥ 0.5 m/s (1.1 mph.).

For those who don’t know, the Gulf stream is a massive river of water that runs within the Atlantic ocean. As shown at right, it starts roughly at the end of Florida, runs north to the Carolinas, and then turns dramatically east towards Spain. Flowing east, It’s about 150 miles wide, but only about 62 miles (100 km) when flowing along the US coast. According to some of the science books of my youth this massive flow was driven by temperature according to others, by salinity (whatever that means), and yet other books of my youth wind. My conclusion: they had no clue.

As a start to doing the science here, it’s important to fill in the numerical information that the science books left out. The Gulf stream is roughly 1000 meters deep, with a typical speed of 1 m/s (2.3 mph). The maximum speed is the surface water as the stream flows along the US coast. It is about 2.5 metres per second (5.6 mph), see map above.

From the size and the speed of the Gulf Stream, we conclude that land rivers are not driving the flow. The Mississippi is a big river with an outflow point near the head waters of the gulf stream, but the volume of flow is vastly too small. The volume of the gulf stream is roughly

Q=wdv = 100,000 x 1000 x .5 =  50 million m3/s = 1.5 billion cubic feet/s.

This is about 2000 times more flow than the volume flow of the Mississippi, 18,000 m3/s. The great difference in flow suggests the Mississippi could not be the driving force. The map of flow speeds (above) also suggest rivers do not drive the flow. The Gulf Stream does not flow at its maximum speed near the mouth of any river.  We now look for another driver.

Moving on to temperature. Temperature drives the whirl of hurricanes. The logic for temperature driving the gulf stream is as follows: it’s warm by the equator and cold at the poles; warm things expand and as water flows downhill, the polls will always be downhill from the equator. Lets put some math in here or my explanation will be lacking. First lets consider how much hight difference we might expect to see. The thermal expansivity of water is about 2x 10-4 m/m°C (.0002/°C) in the desired temperature range). To calculate the amount of expansion we multiply this by the depth of the stream, 1000m, and the temperature difference between two points, eg. the end of Florida to the Carolina coast. This is 5°C (9°F) I estimate. I calculate the temperature-induced seawater height as:

∆h (thermal) ≈ 5° x .0002/° x 1000m = 1 m (3.3 feet).

This is a fair amount of height. It’s only about 1/100 the height driving the Mississippi river, but it’s something. To see if 1 m is enough to drive the Gulf flow, I’ll compare it to the velocity-head. Velocity-head is a concept that’s useful in plumbing (I ran for water commissioner). It’s the potential energy height equivalent of any kinetic energy — typically of a fluid flow. The kinetic energy for any velocity v and mass of water, m is 1/2 mv2 . The potential energy equivalent is mgh. Combine the above and remove the mass terms, and we have:

∆h (velocity) = v2/2g.

Where g is the acceleration of gravity. Let’s consider  v = 1 m/s and g= 9.8 m/s2.≤ 0.05 m ≈ 2 inches. This is far less than the driving force calculated above. We have 5x more driving force than we need, but there is a problem: why isn’t the flow faster? Why does the Mississippi move so slowly when it has 100 times more head.

To answer the above questions, and to check if heat could really drive the Gulf Stream, we’ll check if the flow is turbulent — it is. A measure of how turbulent is based on something called the Reynolds number, Re#, it’s the ratio of kinetic energy and viscous loss in a fluid flow. Flows are turbulent if this ratio is more than 3000, or so;

Re# = vdρ/µ.

In the above, v is velocity, say 1 m/s, d is depth, 1000m, ρ = density, 1000 kg/m3 for water, and  0.00133 Pa∙s is the viscosity of water. Plug in these numbers, and we find a RE# = 750 million: this flow will be highly turbulent. Assuming a friction factor of 1/20 (.05), e find that we’d expect complete mixing 20 depths or 20 km. We find we need the above 0.05 m of velocity height to drive every 20 km of flow up the US coast. If the distance to the Carolina coast is 1000 km we need 1000*.05m/20 = 1 meter, that’s just about the velocity-head that the temperature difference would suggest. Temperature is thus a plausible driving force for 0.5 m/s, though not likely for the faster 2.5 m/s flow seen in the center of the stream. Turbulent flow is a big part of figuring the mpg of an automobile; it becomes rapidly more important at high speeds.

World sea salinity

World sea salinity. The maximum and minimum are in the wrong places.

What about salinity? For salinity to work, the salinity would have to be higher at the end of the flow. As a model of the flow, we might imagine that we freeze arctic seawater, and thus we concentrate salt in the seawater just below the ice. The heavy, saline water would flow down to the bottom of the sea, and then flow south to an area of low salinity and low pressure. Somewhere in the south, the salinity would be reduced by rains. If evaporation were to exceed the rains, the flow would go in the other direction. Sorry to say, I see no evidence of any of this. For one the end of the Gulf Stream is not that far north; there is no freezing, For two other problems: there are major rains in the Caribbean, and rains too in the North Atlantic. Finally, while the salinity head is too small. Each pen of salinity adds about 0.0001g/cc, and the salinity difference in this case is less than 1 ppm, lets say 0.5ppm.

h = .0001 x 0.5 x 1000 = 0.05m

I don’t see a case for northern-driven Gulf-stream flow caused by salinity.

Surface level winds in the Atlantic.

Surface level winds in the Atlantic. Trade winds in purple, 15-20 mph.

Now consider winds. The wind velocities are certainly enough to produce 5+ miles per hour flows, and the path of flows is appropriate. Consider, for example, the trade winds. In the southern Caribbean, they blow steadily from east to west slightly above the equator at 15 -20 mph. This could certainly drive a circulation flow of 4.5 mph north. Out of the Caribbean basin and along the eastern US coat the trade winds blow at 15-50 mph north and east. This too would easily drive a 4.5 mph flow.  I conclude that a combination of winds and temperature are the most likely drivers of the gulf stream flow. To quote Holmes, once you’ve eliminated the impossible, whatever remains, however improbable, must be the truth.

Robert E. Buxbaum, March 25, 2018. I used the thermal argument above to figure out how cold it had to be to freeze the balls off of a brass monkey.

Why is it hot at the equator, cold at the poles?

Here’s a somewhat mathematical look at why it is hotter at the equator that at the poles. This is high school or basic college level science, using trigonometry (pre calculus), a slight step beyond the basic statement that the sun hits down more directly at the equator than at the poles. That’s the kid’s explanation, but we can understand better if we add a little math.

Solar radiation hits Detroit at an angle, as a result less radiation power hits per square meter of Detroit.

Solar radiation hits Detroit or any other non-equator point at an angle, As a result, less radiation power hits per square meter of land.

Lets use the diagram at right and trigonometry to compare the amount of sun-energy that falls on a square meter of land at the equator (0 latitude) and in a city at 42.5 N latitude (Detroit, Boston, and Rome are at this latitude). In each case, let’s consider high-noon on March 21 or September 20. These are the two equinox days, the only days each year when the day and night are equal length, and the only times when it is easy to calculate the angle of the sun as it deviates from the vertical by exactly the latitude on the days and times.

More specifically the equator is zero latitude, so on the equator at high-noon on the equinox, the sun will shine from directly overhead, or 0° from the vertical. Since the sun’s power in space is 1050 W/m2, every square meter of equator can expect to receive 1050 W of sun-energy, less the amount reflected off clouds and dust, or scattered off or air molecules (air scattering is what makes the sky blue). Further north, Detroit, Boston, and Rome sit at 42.5 latitude. At noon on March 31 the sun will strike earth at 42.5° from the vertical as shown in the lower figure above. From trigonometry, you can see that each square meter of these cities will receive cos 42.5 as much power as a square meter at the equator, except for any difference in clouds, dust, etc. Without clouds etc. that would be 1050 cos 42.5 = 774 W. Less sun power hits per square meter because each square meter is tilted. Earlier and later in the day, each spot will get less sunlight than at noon, but the proportion is the same, at least on one of the equinox days.

To calculate the likely temperature in Detroit, Boston, or Rome, I will use a simple energy balance. Ignoring heat storage in the earth for now, we will say that the heat in equals the heat out. We now ignore heat transfer by way of winds and rain, and approximate to say that the heat out leaves by black-body radiation alone, radiating into the extreme cold of space. This is not a very bad approximation since Black body radiation is the main temperature removal mechanism in most situations where large distances are involved. I’ve discussed black body radiation previously; the amount of energy radiated is proportional to luminosity, and to T4, where T is the temperature as measured in an absolute temperature scale, Kelvin or Rankin. Based on this, and assuming that the luminosity of the earth is the same in Detroit as at the equator,

T Detroit / Tequator  = √√ cos 42.5 = .927

I’ll now calculate the actual temperatures. For American convenience, I’ll choose to calculation in the Rankin Temperature scale, the absolute Fahrenheit scale. In this scale, 100°F = 560°R, 0°F = 460°R, and the temperature of space is 0°R as a good approximation. If the average temperature of the equator = 100°F = 38°C = 560°R, we calculate that the average temperature of Detroit, Boston, or Rome will be about .927 x 560 = 519°R = 59°F (15°C). This is not a bad prediction, given the assumptions. We can expect the temperature will be somewhat lower at night as there is no light, but the temperature will not fall to zero as there is retained heat from the day. The same reason, retained heat, explains why it is warmer will be warmer in these cities on September 20 than on March 31.

In the summer, these cities will be warmer because they are in the northern hemisphere, and the north pole is tilted 23°. At the height of summer (June 21) at high noon, the sun will shine on Detroit at an angle of 42.5 – 23° = 19.5° from the vertical. The difference in angle is why these cities are warmer on that day than on March 21. The equator will be cooler on that day (June 21) than on March 21 since the sun’s rays will strike the equator at 23° from the vertical on that day. These  temperature differences are behind the formation of tornadoes and hurricanes, with a tornado season in the US centering on May to July.

When looking at the poles, we find a curious problem in guessing what the average temperature will be. At noon on the equinox, the sun comes in horizontally, or at 90°from the vertical. We thus expect there is no warming power at all this day, and none for the six months of winter either. At first glance, you’d think the temperature at the poles would be zero, at least for six months of the year. It isn’t zero because there is retained heat from the summer, but still it makes for a more-difficult calculation.

To figure an average temperature of the poles, lets remember that during the 6 month summer the sun shines for 24 hours per day, and that the angle of the sun will be as high as 23° from the horizon, or 67° from the vertical for all 24 hours. Let’s assume that the retained heat from the summer is what keeps the temperature from falling too low in the winter and calculate the temperature at an .

Let’s assume that the sun comes in at the equivalent of 25° for the sun during the 6 month “day” of the polar summer. I don’t look at equinox, but rather the solar day, and note that the heating angle stays fixed through each 24 hour day during the summer, and does not decrease in the morning or as the afternoon wears on. Based on this angle, we expect that

TPole / Tequator  = √√ cos 65° = .806

TPole = .806 x 560°R = 452°R = -8°F (-22°C).

This, as it happens is 4° colder than the average temperature at the north pole, but not bad, given the assumptions. Maybe winds and water currents account for the difference. Of course there is a large temperature difference at the pole between the fall equinox and the spring equinox, but that’s to be expected. The average is, -4°F, about the temperature at night in Detroit in the winter.

One last thing, one that might be unexpected, is that temperature at the south pole is lower than at the north pole, on average -44°F. The main reason for this is that the snow on south pole is quite deep — more than 1 1/2 miles deep, with some rock underneath. As I showed elsewhere, we expect that, temperatures are lower at high altitude. Data collected from cores through the 1 1/2 mile deep snow suggest (to me) chaotic temperature change, with long ice ages, and brief (6000 year) periods of warm. The ice ages seem far worse than global warming.

Dr. Robert Buxbaum, December 30, 2017