The sky, like a summer smile, is smudged with clouds, and the unwarm spring air baffles the jacket I grabbed on my way out of the house. I turn a corner, and there he is, walking towards me, eyes big with recognition. A few paces back, a woman in her fifties trails behind. It’s his mother, I know.

I see him often on my walks through the broad sides of the town, lying on the sidewalk, or sprawled against a curb, gazing at the meaning of things, his mother nearby but unobtrusive, though his age is at least sixteen. His discourse is with the wind, the texture of concrete, the colors of an oil slick.

Today, he sees me.

“Richard, Richard, Richard!” he shouts in an explosion of joy.

“It’s Mike,” I say. “You got it right last time, John.”

“Mike, Mike, Mike!” He extends his hand to shake. I take it. Like the sidewalk, it is surprisingly rough. A dark cloud scuds past, revealing the sun that was there all along.

We part, each of us with spring in his step.

The mountains and the sea, Part 2

Ah, GPS!  What would we do without it?  Those satellites tell us exactly where we are. That’s what they do, isn’t it?

Well, not exactly.  In fact, the only thing a GPS satellite does is tell you what time it is up there.  For that to tell you where you are, two things are required: two perfectly synchronized clocks, one in the satellite and one in the receiver, and a way to tell exactly how long the signal from above takes to get to you.  The clocks in the satellites are atomic clocks; they’re be accurate for many millennia.  The clocks here are quartz clocks, like your fancy wristwatch; they’re cheaper and you can easily reset them if they get off, something you can’t do to the satellite clocks.  The satellites just send out regularly timed strings of pseudo-random numbers.  The necessary calculations to figure out where we are all done down here.  The receivers generate the same, and then compare the signals to get the lag.  Since we know the speed of light, which is the same as radio waves, calculating the precise distance is easy peasy.

A little sidebar of interest: you know those equations Einstein came up with you thought were only good for bombs and nuclear reactors?  Without them, GPS wouldn’t work worth a damn.  You see, the satellites orbit at about 12,000 miles, far enough for them to be moving significantly faster that anything on the surface of the earth.  So fast, in fact, that time actually slows down for them relative to the earth.  If you don’t take that into account, you’ll end up thinking you’re in the middle of the ocean somewhere.

Cool.  There are enough satellites (27) so that you can get at least 3 or 4 from anywhere on the planet, and can thus pinpoint your location by trilateration.  But there are issues.  The military, which originally developed GPS, also wanted to know the elevations as well as horizontal location.

Remember sea level?  Our lumpy egg of a planet drove us to turn that into an abstract surface, where all points on it had the same gravitational potential.  An easy way to think of that is to think of a surface where an object weighs exactly the same, no matter where it is (yes, if you want to lose weight, just climb a mountain).  This surface is called the geoid, and is less lumpy than earth as a whole, but lumpy all the same.  GPS gives you the actual surface of the earth, but you have to adjust that to sea level to get a useful elevation.  Shouldn’t be a problem, right?

Wrong.  Since the geoid is irregular, there’s no easy way to model it for the computers to work with.  The best we could do was a smoothish egg, kinda-sorta where we thought sea level was, but often significantly different.  What to do?  It turns out that traditional ways of measuring elevation, with spirit levels, was very, very good at arriving at the geoid.

Years ago, I worked as a land surveyor when the military was just developing GPS.  The Defense Department sent out memos to surveyors everywhere, requesting us to set up our receivers at known elevation points every chance we got, and report the official elevation along with the what the GPS receiver thought the elevation was.  It wasn’t too long before an accurate model of the geoid was available.

Now you know what that little flat box does when you tell it to go to Grandma’s house, by the mountains or the sea.

The mountains and the sea, Part 1

Rummaging through my closet, I came upon my old professor hat.  Thought I’d put it on, and write a bit about sea level.

If you’re a hiker, you’re familiar with those USGS topo sheets showing, among other things, terrain relief.  You probably also know those numbers you see on the elevation lines are all measurements of the vertical distance to sea level.  Even if you’re not into hiking, you might know the elevation of some mountain, or the highest point in your state, or the levee down by the river; same thing for them, measured above sea level.

You probably also know that the sea level is rising.  What does that do to all those numbers?

Well, nothing, actually.

It might seem that the level of the sea used to be constant, and any change is pretty recent, but there have always been fluctuations, both on a local and a global scale.

Think about something as seemingly simple as determining sea level at any given point on a shoreline.  Do you measure it during high tide or low?  Full moon or new?  What about those little ripples  of waves lapping the shore; is your measurement going to be taken at the maximum encroachment or the minimum?

Okay, fine, you say, measure all those points and use the average.  That, in fact, was originally what was done, which is why the official elevation was always given as distance above mean sea level.  Unfortunately, that doesn’t fix things.  Because, you see, you have to ask yourself, mean sea level exactly where?  The solution was to take means at various points, and average those, and so on.

What developed was a convention in which a statistical mean was taken as sea level, which didn’t correspond to actual sea level anywhere in particular.  At this point, sea level was already an abstraction, but some respect was still given to the original concept, and means were kept as close as possible to actual sea levels.  But it turned out that if you used a global mean, the numbers were too far off.  In the end, we got elevations taken with respect to various regional reference points, or datums, around the world: the North American datum, the European datum, and so on.

Confused?  How can sea level differ so much around the world?

First of all, the earth is not a sphere; it’s more like a lumpy egg.  As a result, early suggestions to use the center of the earth as a reference were useless.  Furthermore, water is not even level with respect to local elevations.  Lake Huron, for example, is 5 centimeters higher at the south end than at the north end.  This is partly due to the direction of water flow, but also in the difference in composition of what’s under it.  The iron-rich substrates in the north are denser, and therefore exert a greater gravitational pull.  These effects are compounded globally.

The result is the so-called equipotential system of sea level.  Rather than using the physical measurement of the distance from a point above another point, mean sea level is now defined as an imaginary surface on which every point measures the same gravitational pull.  The only concession to the actual level of the sea is in the name.

Of course, that used to be a very hard thing to measure.  Thank goodness for GPS satellites.

(to be continued)