Category Archives: Uncertainty

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]

Is Petermann Gletscher Breaking Apart this Summer?

I am disturbed by new ocean data from Greenland every morning before breakfast these days. In 2015 we built a station that probes the ocean below Petermann Gletscher every hour. Data travels from the deep ocean via copper cables to the glacier surface, passes through a weather station, jumps the first satellite overhead, hops from satellite to satellite, falls back to earth hitting an antenna in my garden, and fills an old computer.

A 7-minute Washington Post video describes a helicopter repair mission of the Petermann data machine. The Post also reported first result that deep ocean waters under the glacier are heating up.

Sketch of Petermann Gletscher’s ice shelf with ocean sensor stations. The central station supports five cabled sensors that are reporting hourly ocean temperatures once every day. Graphics made by Dani Johnson and Laris Karklis for the Washington Post.

After two years I am stunned that the fancy technology still works, but the new data I received the last 3 weeks does worry me. The graph below compares ocean temperatures from May-24 through June-16 in 2017 (red) and 2016 (black). Ignore the salinity measurements in the top panel, they just tell me that the sensors are working extremely well:

Ocean temperature (bottom) and salinity (top) at 450-m depth below Petermann Gletscher from May-25 through June-16 2017 (red) and 2016 (black). Notice the much larger day-to-day temperature ups and downs in 2017 as compared to 2016. This “change of character” worries me more than anything else at Petermann right now.

The red temperature line in the bottom panel is always above the black line. The 2017 temperatures indicate waters that are warmer in 2017 than in 2016. We observed such warming for the last 15 years, but the year to year warming now exceeds the year to year warming that we observed 10 years ago. This worries me, but three features suggest a new ice island to form soon:

First, a new crack in the ice shelf developed near the center of the glacier the last 12 months. Dr. Stef Lhermitte of Delft University of Technology in the Netherlands discovered the new crack two months ago. The new rupture is small, but unusual for its location. Again, the Washington Post reported the new discovery:

New 2016/17 crack near the center of Petermann Gletscher’s ice shelf as reported by Washington Post on Apr.-14, 2017.

Second, most Petermann cracks develop from the sides at regular spaced intervals and emanate from a shear zone at the edge. Some cracks grow towards the center, but most do not. In both 2010 and 2012 Manhattan-sized ice islands formed when a lateral crack grew and reached the central channel. The LandSat image shows such a crack that keeps growing towards the center.

Segment of Petermann Gletscher from 31 May 2017 LandSat image. Terminus of glacier and sea ice are at top left.

And finally, let’s go back to the ocean temperature record that I show above. Notice the up and down of temperature that in 2017 exceeds the 2016 up and down range. Scientists call this property “variance” which measures how much temperature varies from day-to-day and from hour-to-hour. The average temperature may change in an “orderly” or “stable” or “predictable” ocean along a trend, but the variance stays the same. What I see in 2017 temperatures before breakfast each morning is different. The new state appears more “chaotic” and “unstable.” I do not know what will come next, but such disorderly behavior often happens, when something breaks.

I fear that Petermann is about to break apart … again.

How to Power Modern Economies: Read Your Meter

Read you meter at home. This fun-filled advice was given by Sir David MacKay in a wonderful TEDx talk about how we heat our homes, get to work, run our computers, and how it all scales across countries and continents. The idea is really about how we run our lives while also trying to pass on a livable planet to our grand-children without the politically correct “greenwash” and self-righteous “claptraps”. Read your meter, do some algebra, and embrace the adventure to explore your home, your life, and the energy it all takes. If you read this far, watch the movie

David MacKay taught physics and information theory at the University of Cambridge in England. I learnt of him via Ruth Mottram in one of her many tweets. Dr. Mottram studies climate impacts of Greenland glaciers and works at the Danish Meteorological Institute. The tweet made me buy the book “Information Theory, Inference, and Learning Algorithm’s” that David MacKay wrote a few years back. It arrived today.

What piqued my interest was the advanced math that goes into designing networks that send and transform information such telephone calls via wireless, computer networks, and how to deal with imperfect channels of communication. My marriage comes to mind, too, because what I say is not always what I mean which is not always what my wife hears and vice versa, but I digress. Imperfect communication channels are one challenge we will face in an experiment to explore acoustic underwater data transmissions that hopefully will take place next year out of Thule Air Force Base, Greenland. Water and ice are imperfect communication channels that we need to use wisely to make our whispers carry far. Try to talk to a person across a busy street in Manhattan with all its hustle and bustle; you need to find something smarter and more effective than just simple shouting.

David MacKay wrote a second book that is close to his TEDx talk and is called “Sustainable Energy without the Hot Air.” Experimenting at home like any good physicist does, he discovers that “… the more often I read my meter, the less gas I use!”

There is so much more to this man, his work, and ideas as a physicist with a keen interest in the big picture without skipping the details. Sadly, he died yesterday of cancer too early only 48 years of age.