Tornadoes
Detection/inference from radar
One of the biggest advancements of remote sensing (via radars) came with the discovery of Doppler shift measurable by weather radars. In the United States, the weather radar network, commonly referred to as "NEXRAD" utilized by the National Weather Service, Federal Aviation Administration and the Department of Defense, upgraded the national network to estimate this Doppler shift. These upgraded radars are called the WSR-88D. In doing so, the radar network was able to also make an estimate about the velocity of particles in the air either moving toward or away from the radar.
Legacy algorithms
This set the stage for some of the early work for being able to use the WSR-88D radar for determining the location of tornadoes, particularly in supercell thunderstorms (the most dangerous variant of thunderstorms on Earth). In a nutshell, if a storm is exhibiting rotation, which is necessary for a tornado, we should be able to observe this in the radial velocity afforded by Doppler frequency shift. How? That's the million dollar question! Let's explore a theoretical tornado, and then look at a real example.
Our "tornado" is occurring and splitting between two rays of the radar beam.
On the right side, scatterers/particles caught in the flow of the tornado are moving away from the radar and are generally colored in shades of red. While on the left side, scatterers/particles caught in the flow of the tornado are generally moving toward the radar and typically colored in shades of green or blue. This is known as "gate-to-gate" shear and is a classic sign of rotation in a radar with the ability to signal process the Doppler frequencies.
With this in our belt of tools, let's shift gears to look at an ongoing tornado using real radar data. 
Here, in the circled section we can see red colors, indicating the scatterers moving away from the radar, right next to green colors which we know to be scatterers moving toward the radar.
Polarimetric algorithms
Around 2012, the NEXRAD radar network underwent yet another upgrade, to give the radar polarimetric capabilities. After this upgrade, new insights into tornadic storms and rotating storms became possible.
Diagnostic indicators
With the advent of polarimetric capability, one of those most clear indicators of a tornado on the ground causing structural damage was now possible. By using the correlation coefficient (commonly referred to as RhoHV) debris within a tornado can become strikingly obvious. This "debris signature" can act as an indicator to a meteorologist that a tornado is on the ground and causing damage, which can aid in clarifying emergency messaging to first-responders, emergency managers, and media outlets, just to name a few. 
Looking now to real data, in the above image, we see reflectivity. Note the circled area of higher values. In the image below, the circle is in the same area with extremely low values of RhoHV. This indicates that in that area the radar is sampling a high variation of things, or debris. 
Potential prognostic indicators
Some of the most powerful indicators that polarimetric radars give us insight into are that of low-level shear, which is necessary for rotation in supercell storms. Without shear, storms can't acquire the rotation they need to become tornadic. While this area of research is in its infancy, GWG has been part of this work from as early as 2012 and sees potential in the application of this science to our nowcasting and forecasting products.
Take me back to the learning resources!
References
American Meteorological Society, 2012: AMS Glossary. Accessed March 2023,
https://glossary.ametsoc.org/wiki/Tornado