Qiusheng Wu, University of Tennessee

If you want to track changes in the Amazon rainforest, see the full expanse of a hurricane or figure out where people need help after a disaster, it’s much easier to do with the view from a satellite orbiting a few hundred miles above Earth.

Traditionally, access to satellite data has been limited to researchers and professionals with expertise in remote sensing and image processing. However, the increasing availability of open-access data from government satellites such as Landsat and Sentinel, and free cloud-computing resources such as Amazon Web Services, Google Earth Engine and Microsoft Planetary Computer, have made it possible for just about anyone to gain insight into environmental changes underway.

I work with geospatial big data as a professor. Here’s a quick tour of where you can find satellite images, plus some free, fairly simple tools that anyone can use to create time-lapse animations from satellite images.

For example, state and urban planners – or people considering a new home – can watch over time how rivers have moved, construction crept into wildland areas or a coastline eroded.

Environmental groups can monitor deforestation, the effects of climate change on ecosystems, and how other human activities like irrigation are shrinking bodies of water like Central Asia’s Aral Sea. And disaster managers, aid groups, scientists and anyone interested can monitor natural disasters such as volcanic eruptions and wildfires.

Putting Landsat and Sentinel to work

There are over 8,000 satellites orbiting the Earth today. You can see a live map of them at keeptrack.space.

Some transmit and receive radio signals for communications. Others provide global positioning system (GPS) services for navigation. The ones we’re interested in are Earth observation satellites, which collect images of the Earth, day and night.

Landsat: The longest-running Earth satellite mission, Landsat, has been collecting imagery of the Earth since 1972. The latest satellite in the series, Landsat 9, was launched by NASA in September 2021.

In general, Landsat satellite data has a spatial resolution of about 100 feet (about 30 meters). If you think of pixels on a zoomed-in photo, each pixel would be 100 feet by 100 feet. Landsat has a temporal resolution of 16 days, meaning the same location on Earth is imaged approximately once every 16 days. With both Landsat 8 and 9 in orbit, we can get a global coverage of the Earth once every eight days. That makes comparisons easier.

Landsat data has been freely available to the public since 2008. During the Pakistan flood of 2022, scientists used Landsat data and free cloud-computing resources to determine the flood extent and estimated the total flooded area.

Sentinel: Sentinel Earth observation satellites were launched by the European Space Agency (ESA) as part of the Copernicus program. Sentinel-2 satellites have been collecting optical imagery of the Earth since 2015 at a spatial resolution of 10 meters (33 feet) and a temporal resolution of 10 days.

GOES: The images you’ll see most often in U.S. weather forecasting come from NOAA’s Geostationary Operational Environmental Satellites, or GOES. They orbit above the equator at the same speed Earth rotates, so they can provide continuous monitoring of Earth’s atmosphere and surface, giving detailed information on weather, climate, and other environmental conditions. GOES-16 and GOES-17 can image the Earth at a spatial resolution of about 1.2 miles (2 kilometers) and a temporal resolution of five to 10 minutes.

How to create your own visualizations

In the past, creating a Landsat time-lapse animation of a specific area required extensive data processing skills and several hours or even days of work. However, nowadays, free and user-friendly programs are available to enable anyone to create animations with just a few clicks in an internet browser.

For instance, I created an interactive web app for my students that anyone can use to generate time-lapse animations quickly. The user zooms in on the map to find an area of interest, then draws a rectangle around the area to save it as a GeoJSON file – a file that contains the geographic coordinates of the chosen region. Then the user uploads the GeoJSON file to the web app, chooses the satellite to view from and the dates and submits it. It takes the app about 60 seconds to then produce a time-lapse animation.

There are several other useful tools for easily creating satellite animations. Others to try include Snazzy-EE-TS-GIF, an Earth Engine App for creating Landsat animations, and Planetary Computer Explorer, an explorer for searching and visualizing satellite imagery interactively.

Qiusheng Wu, Assistant Professor of Geography and Sustainability, University of Tennessee

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Manil Suri, University of Maryland, Baltimore County

March 14 is celebrated as Pi Day because the date, when written as 3/14, matches the start of the decimal expansion 3.14159… of the most famous mathematical constant.

By itself, pi is simply a number, one among countless others between 3 and 4. What makes it famous is that it’s built into every circle you see – circumference equals pi times diameter – not to mention a range of other, unrelated contexts in nature, from the bell curve distribution to general relativity.

The true reason to celebrate Pi Day is that mathematics, which is a purely abstract subject, turns out to describe our universe so well. My book “The Big Bang of Numbers” explores how remarkably hardwired into our reality math is. Perhaps the most striking evidence comes from mathematical constants: those rare numbers, including pi, that break out of the pack by appearing so frequently – and often, unexpectedly – in natural phenomena and related equations, that mathematicians like me exalt them with special names and symbols.

So, what other mathematical constants are worth celebrating? Here are my proposals to start filling out the rest of the calendar.

The Golden Ratio

For January, I nominate the Golden Ratio, phi. Two quantities are said to be in this ratio if dividing the larger by the smaller quantity gives the same answer as dividing the sum of the two quantities by the larger quantity. Phi equals 1.618…, and since there’s no Jan. 61, we could celebrate it on Jan. 6.

First calculated by Euclid, this ratio was popularized by Italian mathematician Luca Pacioli, who wrote a book in 1509 extravagantly extolling its aesthetic properties. Supposedly, Leonardo da Vinci, who drew 60 drawings for this book, incorporated it into the dimensions of Mona Lisa’s features, a choice some claim is responsible for her beauty.

The first inkling that phi occurs in nature came from another Italian, Fibonacci, while studying how rabbits multiply. A common reproductive assumption was that each pair of rabbits begets another pair every month. Start with a single rabbit pair, and successive populations will then follow the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256 and so on – that is, get multiplied by a monthly “growth ratio” of 2.

What Fibonacci observed, though, was that rabbits spent the first cycle reaching sexual maturity and only began reproducing after that. A single pair now gives the new, slower progression 1, 1, 2, 3, 5, 8, 13, 21, 34… instead. This is the famous sequence named after Fibonacci; notice that each population turns out to be the sum of its two predecessors.

How does phi show up amid all these randy rabbits? Well, progressing through the sequence, you see that each number is about 1.6 times the previous one. In fact, this growth ratio keeps getting closer and closer to 1.618…. For instance, 21 equals about 1.615 times 13, and 34 equals about 1.619 times 21. This means the rabbits settle down to reproducing with a growth ratio that is no longer 2, but rather, gets closer and closer to the Golden Ratio.

Actual rabbits are unlikely to follow this rule precisely. For one, they have the unfortunate tendency to get eaten by predators. But the Fibonacci numbers – like 5, 8, 13 and so on – show up extensively in nature, like in the number of spirals you might see in a typical pine cone. And yes, phi itself makes a few appearances as well, perhaps most notably in the way leaves arrange themselves around a stem to maximize exposure to sunlight.

The constant ‘e’

February offers another blockbuster constant, Euler’s number e, which has the value 2.718…. So mark next Feb. 7 for the shindig.

To understand e, consider “doubling” growth again, but now in terms of the “population” of dollars in your bank account. By some miracle, your money in this example is earning you 100% interest, compounded each year. Each $1 invested becomes $2 at year’s end.

Suppose, however, the interest is compounded semiannually. Then 50% of the interest is credited midyear, giving you $1.50. You get the remaining 50% interest on this $1.50 at the end of the year, which works out to $0.75, giving you $2.25 ($1.50 + $0.75). So your investment gets multiplied by 2.25, rather than 2.

What if a war broke out between banks, each offering to compound the same 100% interest over shorter and more frequent intervals? Would the sky be the limit in terms of your payout? The answer is no. You could raise your growth ratio from 2 to about 2.718 – more precisely, to e – but no higher. Although you get more frequent credits, they have progressively diminishing returns.

In the late 17th century, the discovery of calculus led to a quantum leap in people’s ability to grapple with the universe. Math could now analyze anything that changed – which extended its domain to most phenomena in nature. The constant e is famous because of its iconic role in calculus: It turns out to be the most natural growth factor to track change. Consequently, it shows up in laws describing many natural processes – from population growth to radioactive decay.

Next on our calendar of mathematical constants would come pi, of course, for March. My nominee for April is Feigenbaum’s constant delta, which equals 4.669… and measures how quickly growth processes spin off into chaos.

I’ll wait for my first batch to achieve official holiday status before going any further – happy to consider any candidates you want to nominate.

Manil Suri, Professor of Mathematics and Statistics, University of Maryland, Baltimore County

This article is republished from The Conversation under a Creative Commons license. Read the original article.