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The Spherical Cow: Models and Applications in Geoscience

David Hulslander

I had a great physics teacher in high school, Mr. Dechant. I still use what I learned there. Some vector componentized wind data from NOAA I’m currently wrestling with comes to mind. He probably should have gotten an award just for signing up to be around a bunch of unbalanced teenagers, let alone actually teaching us anything. But he did sign up, and he did a great job teaching us the basics of physics, starting with classical mechanics. Teaching classical physics requires some basic assumptions to get a useable model of reality. Frictionless surfaces, uniform densities, everything in vacuum, perfectly elastic collisions and the like.

Being a bunch of high schoolers, we took great pride in picking on and tearing apart anything and everything. We seized on those necessary assumptions as being fundamentally unrealistic and therefore worthy of ridicule. Mr. Dechant was an excellent sport about it and played along while seriously addressing our objections to the frictionless surfaces. We even gave the model a (uninspired) name: “Physics Land”.  It shares borders with “Economics Land”, where rational consumers inhabit perfectly efficient markets, and “Chemistry Land”, where all reactions run to completion and no electron goes unshared. We didn’t know it at the time, but there’s even a well-worn joke about these sorts of assumptions. The punchline is that the physicist answers the dairy farmer’s milk production question, but the solution only works for spherical cows in a vacuum.

Claiming models, scientific or otherwise, are all incorrect or invalid oversimplifications ignores that we use them all the time and that they work. Machines, economies, businesses and communities all use models one way or another. In fact, they work so well that we don’t even notice them in day to day life. Remote sensing in the geosciences has models, too, and they’re tremendously powerful. Like all powerful tools, we need to be sure we use them correctly and not just make a big mess. Knowing when not to use a model can be just as important; while you would never compare uncalibrated datasets to each other, it might be perfectly fine to compare classification results from two different uncalibrated images. Fortunately, it’s much easier to assure correct usage thanks to modern software. Atmospheric models let us get at better reflectance “fingerprint” signatures of what’s on the ground, opening up great potential for mapping geology, biology, land use and more from the air or even from space. All engineered systems have some sort of imperfections, but calibration models let us maximize their signals and the confidence we can have in their measurements. Geographic models, i.e. map projections, let us take the fantastically complex 3D Earth and put it in to maps we can use for navigation, mapping resources, monitoring human activity, getting a better understanding how our planet works, and more.

Put some models to work for you! Get some data for where/what you’re interested in, from NOAA CLASS, USGS EarthExplorer, or your own favorite depot. Then, try out some calibration models, some atmospheric models, or some analytic models and see what you find! There are some amazing discoveries to be had sojourning in the various Model Lands that make up our world. Who knows, maybe you’ll find a spherical cow.


The images above show, on the left, a calibrated and atmospherically corrected Landsat 5 scene in Karakum Desert, Turkmenistan (R: Band 3, G: Band 2, B: Band 1); an RXD Anomaly detection result is overlain in red, centered. On the right, the brightness temperature calibrated band from the same Landsat 5 scene Band 6 data, showing the anomaly as a bright spot in excess of 300 degrees C. At least 5 models in one workflow! The image of the right demonstrates how improved sensor calibration models for Landsat 8 will allow for much more accurate and precise temperature measurements from the upgraded two-band thermal sensor.  What is it? Make your best guess in the comments. The answer’s here.


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