The sky is the limit, mathematically speaking

Today is a beautiful sunny day in Missouri, so I brought my laptop out to the porch. When I work outside, I can’t help but watch the wind and the clouds, hyper-aware of the sounds in my surroundings. As the distant whir of a jet passed far above, I whimsically observed that the sound was coming from a point well behind the plane itself. Replacing whimsiness with my insufferable engineering mindset, I started rattling off some quick calculations, literally on the back of an envelope.

The source of the sound was approximately 30 seconds behind the plane as it flew overhead, which means that the plane was about 6 miles straight up because sound travels a mile every 5 seconds. This is a reasonable answer since it is close to 40,000 feet, the cruising altitude for commercial jetliners. The speed of sound is a useful conversion factor, and I use it all the time to tell me the distance of lightning strikes. There are a few ways to calculate the jet’s speed: you could again use the speed of sound when the jet is in the distance, or you can estimate its angular velocity as it passes overhead at a known altitude. I used the latter, comparing the perceived length of the plane’s vapor tail a minute apart to estimate an angle. This calculation pegged the plane at 550 mph, again reasonable at around 90% of the speed of sound. It took 6 minutes for the plane to leave my view after passing directly overhead, which means I could see it when it was over 100 miles away. Not coincidentally, you can often see over 100 miles from the window seat of a plane. The farthest view from a mountaintop I have ever seen was another mountain 80 miles away, but increasing in altitude from 1 to 6 miles does wonders for visibility, due to both the curvature of the earth and the lower particulate matter concentrations higher up in the atmosphere.

A line of clouds materialized in the distance. To me, it’s no mystery how far away they are or how long they would take to approach. Meteorologists use a metric called “lifted condensation level” (which basically means cloud height) to forecast rain showers and severe thunderstorms, and due to the sharp temperature gradients in our atmosphere, the base height of cumulus clouds is almost guaranteed to fall between 1-2 kilometers. Lower LCL values beget higher chances for severe weather, and, conversely, thunderstorms have lower cloud bases than fair-weather cumulus. You can calculate the LCL using the dew point or relative humidity…I used to tell my chemical engineering students that those weather apps that tell you temperature, humidity, and dew point are redundant because with two of those values you can calculate the third. I also used to tell them to, when they’re having deep conversations with a significant other while gazing into the sky, impress their date by calculating the cloud height on the spot. Anyway, the point of all this, if there is one at all: there are a lot of interesting things to learn by keenly observing your surroundings. The world is full of not only fascinating math but also a natural beauty that defies calculation.

Hurricane Irma: a disaster as forecast

Just three months ago, I was basking in the Caribbean paradise, cruising from Florida to the Bahamas, St. Thomas, and St. Maarten. Now, many islands lay in ruins, battered by the up-to-180 mph sustained winds of Hurricane Irma, a monstrous Category 5 storm at its strongest. While pictures of Barbuda, an island of around 1400 people where over 95% of structures were totaled, conveyed the totality of devastation most widely and poignantly, the islands of St. Martin/Maarten, Anguilla, the Virgin Islands, and Turks and Caicos also suffered widespread damage to a majority of buildings. The death toll has continued to climb this week, as relief efforts in the Caribbean are limited by accessibility.  I really, really hope the disaster response is strong, despite that our full attention was on the potential for a direct hit to Florida (an event that could have been unimaginably disastrous had Irma remained a Category 4-5 storm as it made landfall). Luckily, Irma weakened as it lingered off the coast of Cuba on Friday, and Florida was spared from the worst of the wind damage.

Looking at our GFS model forecasts from Thursday 9/7, 3 days in advance, this was a miracle, better-than-best case scenario for Florida as a whole. By these forecasts, Miami and much of Florida’s Atlantic coast were almost guaranteed a direct hit, which would have brought catastrophic wind damage and long-lasting flooding from up to 12-foot storm surges. The European model (ECMWF) afforded more variability, simulating 51 possible tracks compared to the American model’s 21, but the true track was still a rather unexpected edge case. After nailing the projection for Harvey’s unprecedented rain in Houston, our forecasts missed the ball on both path and intensity projections for Irma, which is especially alarming when many people evacuated the Miami area and drove west into the eventual path.

For more information about the differences between the European and American models, check out this article from Mashable. My understanding of hurricane paths is far more simplistic, with hurricanes moving away from high pressure and toward low pressure systems, fueled by warm water (which in turn, creates low pressure feedback forcings…then everything starts getting complicated!)  So for now, I’m comfortable leaving the forecasting to supercomputers, especially as input data improves in accuracy.

September 11th

16 years later, today will be a normal day for most Americans. We won’t be attending vigils or watching hours of special programming in remembrance. Our War on Terror has been replaced by new fears of North Korean proliferation. In fact, a vast subset of young Americans do not remember the gravity of the events or fully understand the drastic changes that followed. The rest of us, myself included, have the tragedies of 16 years ago emblazoned on the inside of our hearts and will always remember the date even though much of the grief/horror/fear has subsided.

This disconnect struck me a few weeks ago at a “brainstormers” gathering, wherein it was actually a point of debate whether 9/11 was an extremist attack or a conspiratorial power grab by the U.S. Government. I found it tremendously insulting on many levels, particularly to the victims and their families, veterans, government employees, but also to anyone who feels patriotic appreciation for America. In the immediate aftermath, people from all political affiliations, ethnicities, and walks of life banded together in solidarity, in patriotism. Above the sense of fear, there was an emboldened sense of community. The ghost of 9/11 haunted us for about a decade, during which preventing terrorism was our top national priority, then something happened.

We started to forget. It’s natural to be desensitized over time, even from the most world-altering tragedy of my lifetime. Maybe we were exhausted of war and willing to accept the demise of Bin Laden in 2011 as the end of a story. Or the Arab Spring of 2012 fostered hope for a future without dictatorial or terrorist regimes. Perhaps the Great Recession added daily pressures, or frustrations about social issues finally reached a tipping point. The media largely reflects a change in priorities, though many conservative outlets still cover anti-terrorism efforts with the same fervor as 10 years ago. We were reluctant to intervene directly in the Syrian conflict (despite the rise of ISIS, perhaps the largest terrorist network to date), a notable departure from our typical anti-terrorist interventionism. I, for one, am fine with that, as the threat of terrorism does indeed seem to be diminishing. But as times change, we cannot forget how we felt as a country in the aftermath. I will always remember this date, for its horror and tragedy but also for perseverance and recovery.