Author Archives: Andreas Muenchow

Rotations, Spin, and People

I hate to rotate. It makes me sick. And yet, every day I spin at 800 miles per hour, because living on a spinning earth does this to me. Why does the earth spin at all? [CalTech answer.] Did it always spin the way it does now? [No.] Could it spin in the other direction that would make the sun rise above the horizon in the West rather than the East? [No.] If not, why not? [Not sure yet.] I am pondering these questions as I will teach my first undergraduate class in ten days:

I plan to introduce how oceans and atmospheres circulate to distribute heat, water, and “stuff” like food and plastics across the globe. There is lots of rotation, lots of angular momentum, lots of torque and I am unsure, if a text book and lecture via Zoom will make much sense. So, today I discovered several fun and smart and insightful videos that I may even pose to my students as Homework or Exam questions 😉

The first set of videos I discovered today is Derek Muller’s Veritasium channel on YouTube. He covers a range of physics, math, and even biology topics, but I here focus on his wing nut problem. He entertains by explaining a strange and even bizarre observation made in space some 30 years ago. A Russian engineering astronaut noticed a rotating wing nut change its rotational axis repeatedly. Russia kept the observation top secret for over 10 years for reasons not entirely clear, but here is a modern attempt to explain what happened. It also applies to how tennis rackets rotate:

Now this reminded me of a problem that I encountered during my third year studying physics in Germany. I never solved or understood this so-called spinning-hard-boiled-egg problem that the Physics Girl describes so well. Her real name is Dianne Cowern and I use her videos in my graduate statistics class where her voice and physics shatters wine glasses via resonance. Today I discovered many more of her PBS Digital videos that all are filled with fun, beauty, and smart explanations. She plays with vortices in air and water and in between.

Now how does this relate to oceanography and meteorology? Well, we all live somewhere on the spinning top or egg or peanut that we call earth. Gravity keeps us grounded, but rotating objects can do strange things as the above two videos show. And when rotation becomes important we are not just dealing with linear momentum, but also angular momentum. When rotation becomes important, we must consider torques that generate angular momentum in ways similar to how forces generate linear momentum.

Rotation adds a strong and often counter-intuitive element because unlike a force that accelerates a car in the same direction that the force is applied, a force applied to a rotating system generates a torque perpendicular to both the force and the direction to the rotational axis. This can be confusing and one has to either watch the movies or go through advanced vector calculus. Furthermore, a rotating sphere acts differently than a rotating spheroid which acts differently from a rotating triaxial spheriod. Our peanut earth is the latter and thus has at least three axes of orientation (a and b and c) that all have different kinetic energy and angular momentum states. This makes for wobbly rotations which are sensitive to changes in both force balances and the distribution of masses like ice and water that can move to different locations at different times and stay there for a while.

For a perfect sphere three perpendicular lines from the center to the surface all have the same distance a (top) while for a spheriod only two of the three perpendicular lines have the same distance from the center (bottom right). If all three perpendiculars are different then we have something called a triaxial spheroid [Adapted from WikiPedia].

And how does this relate to climate science and my beloved glaciers in Greenland? Well, there is the “global wobbling” that caused ice ages and warm periods as the earth’s principal axis or rotation changes or wobbles. The “global wobble” was discussed in hilarious way a few years ago by the United States House of Representative’s “Committee on Science, Space, and Technology.” Closing this essay, I let Jon Steward of the Comedy Channel speak and hope you find his commentary and live experiment as funny as I do:

Data Obsessions while in Self-Quarantine

I sit in my home office looking into a garden which explodes in yellow from the forsythia with splashes of pink from the camellias. Both flourish after a large shading cherry tree fell down a few years ago. The tree stump is covered by moss and provides a natural border. My native American Flame azaleas (Rhododendron calendulaceum) now stand 8 feet tall in front after I planted them in 2001 as 3 inch sticks. They are the pride of my garden along with Piedmont, Sweet, Okonee, and Plum azaleas all purchased from Callaway Gardens in Georgia. They grow well, because I correctly predicted that the warmer climate zones of Georgia would move northward towards Delaware. Here are the azaleas in blooms in early May or four weeks from now:

These are distractions, because I need to process and analyze ocean velocity data off Greenland. My student from South Korea rightfully expects numbers that she can work with for her Masters degree. We plan to meet via Zoom video call every Friday and Wednesday. She is ordered to stay at home in Maryland while I am ordered to stay at home in Delaware. We also meet Monday and Wednesday evenings when I teach “Waves” via Zoom to eight University of Delaware graduate students from China, South Korea, Thailand, and the USA. Our topic yesterday was the waves in the wakes of a ship or a duck or an island. To me physics are as beautiful as are the flowers in my garden:

Now these are the things that I should work on during my self-quarantine, but I am obsessed and distracted with new data. The Johns Hopkins University in Baltimore, MD distributes data on the number of people who were diagnosed with Covid-19, who died of it, and who have recovered. While it is easy to access their excellent data displays as global health authorities report them, the actual raw digital data files are accessible at

These data require computer programming and data handling skills that a well trained physical ocean, climate, or data scientist masters. The raw data, however, do not tell a story, because it just looks like gibberish,

but there is a most orderly system to this madness. With 143 lines of computer code (one C-shell and two awk scripts) I convert these data into a single graph to tell a story:

First, I focus only on the number of people who have died, because I consider this the most reliable (albeit morbid and depressing) estimate of how the virus is spreading.

Second, I present the number of people who died relative to the population. It hardly seems fair to compare the numbers from the USA with 327 million people to those of Malta with only 0.5 million people. The technical term is “normalization,” that is, all numbers are relative to 1 Million people. So, 5 dead in Malta give 10 dead per million. The same 10 dead per million correspond to 3270 dead Americans. This way I am comparing apples to apples as opposed to Americans to Maltese.

Third, I want to compare the spread of the pandemic over time on different continents, different countries, different states, and different cities. This requires to time-shift countries hit by the virus earlier than others. In the above graph, for example, I moved the curve for Italy 14-days forward and that of Spain 6-days forward relative to all other places listed.

Fourth, I am most interested in New York State (population 20 million), because it contains New York City (population 8 million) and, I believe, it gives Americans a good idea what is coming. Furthermore, I believe, that the Government of New York State is a little more efficient, smart, and forward-thinking than many other government entities. It also has resources not necessarily available to less affluent communities.

The curve for New York State initially (until Mar.-25) followed the trajectory of Italy 14 days earlier, but then it switched over to the steeper trajectory of Spain 6 days earlier. Notice that Italy’s curve has a flatter trajectory than the steep curve of Spain and New York State. From Mar.-28 to Mar.-31 the New York curve was almost exactly that of Spain 6 days ago, but yesterday, the number of people dying in New York grew even faster than those in Spain or Italy ever did. This is scary stuff.

Yesterday, New York State had about 111 dead per million people. While this is still less than the 180 dead per million people that both Italy and Spain had yesterday, it may take only 4-5 additional days for New York State to reach those numbers also, but I still do not know what these numbers mean. I do not “feel” them. So I try to compare them to other causes of death such as people getting killed every month in (a) car accidents (9 per million) or (b) gun violence (8 per million) or (c) cancer (126 per million). These references help me to visualize the scale and impact of this pandemic.

So, while Covid-19 has killed about as many people in the US the last 4 weeks as people died in car accidents, in New York State the number of Covid-19 dead is about to exceed those who died of cancer in this same period. The hardest hit place in the US, however, is not New York City (160 dead per million), but New Orleans (295 dead per million). The County or Parish of New Orleans, Louisiana has about 400,000 people or a little less than New Castle County in Delaware where I live, but New Orleans has 115 dead compared to 5 in New Castle County (9 dead per million).

There are a few bright spots and I want to close on those. Los Angeles (7 dead per million) and California (5 dead per million) are doing remarkable well as does Germany (11 dead per million). Despite physical separations from others, I feel closer to friends, family, and neighbors both overseas and across the street. With more than 10 feet distance we have impromptu get-togethers between the door and the end of the driveway of 4 different households. I am happy to know that my neighbor Joyce from Kenya is safe back home living quarantined across the street with her African friends from Mali. She runs Water for Life which is a small non-profit that provides clean drinking water for rural communities in Kenya. It makes me happy to know her as a neighbor across the street.

And then there are the true warriors who fight this virus while endangering themselves to help others. Here is a nurse from Spain whose photo at work I took from her Twitter feed. We are all surrounded by wonderful and beautiful people.


Almost 300 years ago a brave scientist boldly stated that everything can be described as waves. It took mathematicians another 200 years to prove that Joseph Fourier, the bold scientist, had it right. I am comforted by this fact while the Covid-19 pandemic appears to grow without bounds. And yet, bounds do exist, because Fourier states that what goes up must come down. This includes the global Covid-19 pandemic of 2020/21 as well as the Influenza pandemic of 1918/19. The latter had three distinct peaks in the United Kingdom that varied both in amplitude and duration:

Adapted from Taubenberger, J.K. and D.M. Morens: 1918 Influenza: The mother of all pandemics, Emerging Infectious Diseases, 12 (1), 2006.

This pandemic of 100 years ago came in three distinct pulses in the spring of 1918, in the fall of 1918, and in the winter of 1919. The graph shows that during the first wave about 0.5% of all infected people died while the second and third wave were more deadly with 2.5% and 1.3% fatality rates. These rates are somewhat similar to those we see today with Covid-19, but there is much we do not yet know.

We do not yet know, for example, how long it will take for the Covid-19 waves to pass through populations. We do not know the amplitude of the waves either, because it all depends on how well we distance ourselves from each other both now and into the future to minimize transmission of the virus. There is no control, yet, because no vaccine exist, but smart distancing will impact how many people will get infected (the amplitude) over time (the period).

These two factors (amplitude and duration) will determine how many of our friends, partners, parents, brothers, and sisters we will lose to the virus. As the German Chancellor Angela Merkel said yesterday: “Im Moment ist nur Abstand Ausdruck von Fuersorge,” which translates as “At the moment only distance is an expression of care.”

German Chancellor Angela Merkel on Mar.-18, 2020 on German TV.

Waves change as they propagate from one medium to another. As ocean wave forms move from deep to shallow water they change both amplitude and speed until they eventually break. I view today’s Covid-19 waves in a similar way.

Covid-19 waves will propagate through all societies on our planet, but they will propagate differently in different regions, countries, and societies. Amplitudes, periods, and propagation speeds will differ. Some of this is already visible by global statistics that are collected and shared in real time:


The spread of the virus in China differs from that in South Korea which differs from that in Iran, Italy, Germany, and the United States. Different political systems, different skills of and trust in governments, and different personal behaviors all provide a different medium within which these waves propagate and, eventually, will dissipate.

This is day-8 for me and my wife to distance ourselves from our friends, family, and neighbors. We are fine. My wife turns the bedroom into a painted mural while I read and write at home and spent much time in the spring garden. It slowly sinks in, that this will not be over next week or next month. The goal is to make the amplitude as small as possible by spreading the period out as long as possible which will allow our hospitals, nurses, and doctors to provide the best care for those who need it. As a wise woman said yesterday: “At the moment only distance is an expression of care.”


Taubenberger, J.K. and D.M. Morens: 1918 Influenza: The mother of all pandemics, Emerging Infectious Diseases,, 12 (1), 2006.”

Peanut Earth

I got in trouble in class today. When the earth was introduced as a sphere, I disagreed and stated that the earth was shaped like a peanut instead. While it got me laughs from some students, not everyone was amused. And yet, I am serious on two counts:

First, a sphere is a well defined shape that depends only on its radius. A sphere is a perfect mathematical idealization without a blemish such as a scratch, a bump, or a hole. It is also perfectly symmetric in two angles that I call longitude and latitude.

Second, a peanut eludes definition, because each peanut differs slightly from the next. It approximates a sphere poorly. Perhaps a spheroid is better approximation. It results when an air-filled beach ball is squished at its North-Pole. Still this does not look like a peanut, but instead of one parameter (its radius a), we now use two parameters (a and b) to describe it better. Or better yet, let us use three parameters (a and b and c).

For a perfect sphere three perpendicular lines from the center to the surface all have the same distance a (top) while for a spheriod only two of the three perpendicular lines have the same distance from the center (bottom right). If all three perpendiculars are different then we have something called a triaxial spheroid [Adapted from WikiPedia].

We can keep going like this for many, many more parameters by fancy sounding mathematical constructs. Still, neither peanut nor earth will ever be defined by perfectly defined mathematical objects, but a finite sum of them may approximate a true shape well enough. Both peanut and earth occur in nature and thus reflect physics, biology, and chemistry. As such our peanut earth can only be approximated by something mathematical, but the mathematics are always off by an amount that we can always make smaller by adding more parameters to describe the shape. In my glacier work off Greenland I use about 2200 such parameters to describe the shape of the earth to accurately represent its floating ice shelf.

Closing my argument, I find that the little peanut has more in common with our planet earth than a sphere. Peanut and earth may look different from a distance, but the closer we look, and the better our sensors become, and the more accuracy we require, the closer our approximation of earth resembles our approximation of the peanut. The sphere is just the first of many approximations of the real thing. The real thing has a name and the Smithonian Institution defines and describes geoid much better than I do here calling it peanut earth.

The colors in this image represent the gravity anomalies measured by GRACE. One can define standard gravity as the value of gravity for a perfectly smooth ‘idealized’ Earth, and the gravity ‘anomaly’ is a measure of how actual gravity deviates from this standard. Red shows the areas where gravity is stronger than the smooth, standard value, and blue reveals areas where gravity is weaker. [Credit: NASA/JPL/University of Texas Center for Space Research]

How big is Greenland?

Maps of Greenland were sketched with broken bones, frozen limbs, and starved bodies of men and dogs alike. On April 10, 1912 four men and 53 sled dogs crossed North Greenland from a small Inuit settlement on the West Coast where today the US Air Force maintains Thule Air Base. In 1912 Knud Rassmussen, Peter Freuchen, Uvidloriaq, and Inukitsoq searched for two explorers lost somewhere on Greenland’s East Coast 1200 km (760 miles) away. They returned 5 months later with 8 dogs without finding Einar Mikkelsen or Iver Iversen. These two arrived in North-East Greenland to find diaries, maps, and photos of three earlier explorers who had starved to death in the fall of 1908. Mikkelsen and Iverson found the records, but struggled to survive the winters of 1910/11 and 1911/12 alone stranded before a passing ship found them. I ordered their 1913 Expedition Report yesterday.

Dog sled teams drive across Greenland’s Inland ice in April 1912 from Clemens Markham’s Glacier in the west to Denmark Fjord in the east. All 4 explorers returned, but only 8 dogs did.
Map of Greenland as included in the Report of the First Thule Expedition 1912 by Knud Rasmussen.

I worked along these coasts in 2014, 2015, 2016, 2017, and 2018 on German research vessels, Swedish icebreakers, Greenland Air helicopters, and American snowmobiles. We explored the oceans below ice and glaciers with digital sensors but without hunger, cold, or lack of comfort. I feel that I know these coasts well, read what others have written and suffered. I make my own maps, too, to reveal patterns of oceans, ice, and glaciers that change in space and time. And yet, I am often lost by distances and areas. I do not know how big Greenland is.

Clockwise from top left: Ocean observatory on sea ice off Thule Air Base (Apr.-2017); refuelling helicopter in transit to ocean observatory on Petermann Gletscher (Aug.-2016); Swedish icebreaker in Baffin Bay (Aug.-2015); and deployment of University of Delaware ocean moorings from Germany’s R/V Polarstern off North-East Greenland at 77 N latitude (Jun.-2014).

At home I know distances that I walk, bicycle, or drive as part of my daily routine. I know areas where I live from weather and google maps, weekend strolls, and where family and friends live. Once we travel in unfamiliar lands, however, we are lost. Americans rarely know how small most European countries are while Europeans rarely know how far the Americas stretch from Pacific to Atlantic Oceans. Nobody knows the size of Greenland or Africa. On World Atlases Greenland appears as large as Africa, but this is false. Just look at this map:

The size of Africa on the same scale as the USA (green), Greenland (orange), and Germany (blue). Germany is about the same size as Botswana while Greenland is a tad larger than Kongo and the USA is about as big as the Sahara.

Thus North Greenland’s explorers walked distances similar to walking across Texas, Mississippi, and Florida (and back) or distances similar to walking Germany from its North Sea to the Alps (and back) or distances similar to walking across Kenya (and back). Making these maps, I found the tool at These playful maps compare Greenland’s size by placing its shape onto North-America, Europe, and Asia:

Three explorers starved and froze to death November 1907 because they underestimated their walking area. Their shoes wore thin and they walked barefoot. Daylight disappeared and was replaced by polar night. Food vanished with no game to hunt. Jorgen Bronland, Niels Hoeg Hagen, and Ludvig Mylius-Erichsen were 29, 30, and 35 years young when they died mapping Greenland. I sailed the ice-covered coastal ocean. I was helped by maps they made walking.