## Math, Doppler And The Missing Jetliner

I just finished reading some technical data from Inmarsat and Ministry of Transport Malaysia concerning the analysis of satellite data transmissions from MH370. It’s this data that’s shifted the searchers from MH370’s planned route to a tract in the Southern Indian Ocean well west of Australia–nearly the opposite direction expected!

It is a brilliantly concocted method to get usable information from what should have been meaningless housekeeping transmissions.

Radio signals travel at the speed of light. If we know how long those signals take to go satellite-to-plane (or vice versa) we can start doing calculations and find the distance between the two.

Inmarsat was then able to calculate the range of the aircraft from the satellite, and the time it took the signal to be sent and received, to generate two arcs of possible positions – a northern and a southern corridor.

As you probably know the northern track was thrown out. But why? That’s where the plane should have been flying. It was the most logical direction.

Enter Doppler!

Because the satellite and plane were both moving, their radio waves were subject to Doppler shift. This is an expected part of satellite work and equipment to compensate for it is built into the system.

The Inmarsat technique analysed the difference between the frequency that the ground station expected to receive and the one actually measured, known as the Burst Frequency Offset.

Because the satellite wasn’t at the midpoint of the two project tracks, the expected northbound offset or shift was different than the southbound shift. What was actually seen only matched the southern track.

Depending on the plane’s speed the same Doppler shift could indicate slightly different positions. Unfortunately, that’s an unknown. It’s a good guess to estimate 400-450 knots. That’s why the area now being searched isn’t a single point, but a larger area.

Obviously, the plane hasn’t been found, there’s still no real explanation for what went wrong. However, this clever use of math helps bring those looking one step closer.

I know this is somewhat complex. I’m not 100% sure my explanation will be clear to everyone. Questions are welcome.

## When I Watch Radar Here’s What I Watch

He was an astronomer and mathematician. Today he’d be a nerd, but back then he was just crazy smart!

I’m hearing thunder in the distance so I fired my browser to take a look at the radar. NEXRAD, the Weather Service radar really is a marvel of technology. There’s a lot to see if you know what to look for.

A little background first. When I arrived in Connecticut there was a single radar available. It was a model WSR57. That stood for Weather Surveillance Radar 1957. Like most good government projects this 1957 radar didn’t become operational in most spots until the 1960s.

Hands up if you’re surprised?

As radars go the WSR57 up on Soapstone Mountain in Somers sucked! It was sited in a bad place for weather radar. Precipitation of the same intensity would produce different results depending on where it was. It was pretty much blind to snow. There was a huge area continually blocked by ground clutter. It was all we had.

Today’s NEXRAD radars are model WSR88D. The “D” stands for Doppler. It’s a big step up. NEXRAD is more powerful, more versatile and since much of what it does is software driven easily upgraded.

Radar is pretty simple. You bounce radio waves off hydrometeors (the official name we assign to the precipitation being measured). Since radio waves move at the speed of light if you measure the time it takes for the wave to return you can figure out the distance.

The intensity of that returned wave is the deciding factor for the colors you see. Stronger rain or hail or sleet produce stronger radar returns. Radar waves bouncing off light rain, drizzle or most snow are much weaker.

I’m looking at some rain south of Connecticut now which is really intense. The colors on the display are hot. The rain is coming down in buckets!

One of the things NEXRAD’s software makes possible is analyzing the radar returns to decide how much rain has actually fallen. It’s a neat trick involving math much more complex than you might expect. In potential flooding situations this ability is a life saver… literally! Some areas (mostly over the ocean at this moment) are seeing as much as 1.5″ of rain per hour!

All of this is geekily cool and we haven’t even touched Doppler!

Please note, it’s Doppler with a capital “D.” It’s someone’s name. Christian Doppler lived in the first half of the 19th Century. He was an astronomer and mathematician. Today he’d be a nerd, but back then he was just crazy smart!

Doppler postulated his principle (later coined the Doppler effect) that the observed frequency of a wave depends on the relative speed of the source and the observer, and he tried to use this concept for explaining the colour of binary stars. – Wikipedia

What works for stars seems to work for any wave. Take sound as an example. If you stand along a highway as cars approach the pitch of the sound of their engines rises until the car is upon you. As it moves away the pitch shifts downward. We call that Doppler shift.

As a hydrometeor being picked up on Doppler radar moves toward you the frequency of the radar wave bouncing off it shifts higher. If it’s moving away the radar frequency that returns is lower. NEXRADs software allows us to plot that.

What meteorologists look for are adjacent areas that show motion in opposite directions. That’s a signature found in tornadoes. There’s no way to see that without Christian Doppler’s work from the early 1840s!

Most of the time here in the Northeast that Doppler feature is unneeded and unused. However, when conditions warrant the WSR88D’s capability is nothing short of amazing.