Sea levels and measurements of the Earth by GPS

[LoneTree1941]

We know the earth’s diameter at the equator is about 25 miles larger than at the poles, therefore about 12.5 miles larger in the radii. Some large part of this phenomenon is due to the spin of the earth on its axis. The Mississippi river flows from an elevation of 1476 above msl at Lake Itasca down to sea level at the Mississippi Delta. A linear equation suggests that the sea at is about 11,200 feet further from the center of the earth at New Orleans than at the source of the Mississippi.

The longitudinal difference is 17.25 deg. or about 19.2 percent of the 90 degrees between the equator and the pole, so 19.2% of r. of 12.5 miles is 2.4 miles or 12,670 feet less the 1,476 slope = roughly 11,200 feet. (is that roughly a valid assumption?)

Before the GPS I'm assuming that the benchmarks for elevations were established empirically by surveyors performing inland surveys/traverses across the Northwest Territory with cross references being made across the great lakes.


My question is how elevations are determined accurately by GPS since, for instance, the delta is further from earth’s center (closer to the GPS for purposes of distance) than the source at Lake Itasca?

Another related item, I read (HERE) is that the sea level is rising at a (3 or for times) faster rate on the east coast of North America than other places around the world. That seems irrational to me, unless that faster rate is accounted for by a movement of some large heavy mass below the earth’s surface, under or centered nearby, and geological changes of that sort are not seen in decades but in hundreds of millennia. Any ideas why there would be isolated regional and relatively rapid in changes in sea levels such as this?

[Ara Pacis]

We know the earth’s diameter at the equator is about 25 miles larger than at the poles, therefore about 12.5 miles larger in the radii. Some large part of this phenomenon is due to the spin of the earth on its axis. The Mississippi river flows from an elevation of 1476 above msl at Lake Itasca down to sea level at the Mississippi Delta. A linear equation suggests that the sea at is about 11,200 feet further from the center of the earth at New Orleans than at the source of the Mississippi.

Wikipedia lists the radii differently, with a difference of 21.3 km or 13.2 mi. An equation is not as useful as actual measurements, as Mark Twain famously quiped about the Mississippi and linear equations.

In the space of one hundred and seventy-six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over one mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oolitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.

Are you confusing a statistical sphere with the Geoid and/or with actual topography?

The longitudinal difference is 17.25 deg. or about 19.2 percent of the 90 degrees between the equator and the pole, so 19.2% of r. of 12.5 miles is 2.4 miles or 12,670 feet less the 1,476 slope = roughly 11,200 feet. (is that roughly a valid assumption?)

Probably not, but I don't know how smooth the oblation of the sphere is.

Before the GPS I'm assuming that the benchmarks for elevations were established empirically by surveyors performing inland surveys/traverses across the Northwest Territory with cross references being made across the great lakes.

Not sure what you mean by cross references with the Great Lakes, which are not at MSL. What era are you referring to? Before GPS they may have used lasers or radar mapping from aircraft or satellites. Prior to that, perhaps trigonometry, perhaps also using stars, sextants and clocks to determine longitude and latitude and using barometers to estimate altitude, but that's a guess.

My question is how elevations are determined accurately by GPS since, for instance, the delta is further from earth’s center (closer to the GPS for purposes of distance) than the source at Lake Itasca?

As mentioned above, Radar and/or Laser mapping. Gravitational mapping also helps determine gravitational anomalies from Mass Concentrations (mascons) which is needed to develop accurate trajectories for all satellites and long range suborbital rocket trajectories (e.g. ICBMs).

Another related item, I read (HERE) is that the sea level is rising at a (3 or for times) faster rate on the east coast of North America than other places around the world. That seems irrational to me, unless that faster rate is accounted for by a movement of some large heavy mass below the earth’s surface, under or centered nearby, and geological changes of that sort are not seen in decades but in hundreds of millennia. Any ideas why there would be isolated regional and relatively rapid in changes in sea levels such as this?

Nope, it's not unexpected or irrational. Continents are comprised of mass, therefore they have more gravity and therefore they cause a distortion of the geoid (see link above). Also, a lot of the sea level changes are from the Greenland Ice Sheet (GIS), which means that the east coast of North America (NA) will see more of an increase first. Also important is that the GIS itself is a mascon, and its melting will also alter the geoid and the sea that was drawn to it will no longer be drawn to it and will be drawn to something else instead, that something else being NA (a large component of eustacy). However, as the GIS melts and calves, the crust beneath it will rise and the mantle will adjust as well in the process of isostacy, specifically post-glacial rebound.

Read those wikipedia links for more detail.

We also discussed it a bit in this thread off and on over the last few years.

[LoneTree1941]

As to my comment about the great lakes, but also the St Lawrence Seaway, those bodies served as great extended (spirit) levels over more than a thousand miles, once their different elevations were allowed for.
I.E. - the level above msl at the eastern end of Lake Eirie is the same as at the western end, 240 miles distant.

[Ara Pacis]

As to my comment about the great lakes, but also the St Lawrence Seaway, those bodies served as great extended (spirit) levels over more than a thousand miles, once their different elevations were allowed for.
I.E. - the level above msl at the eastern end of Lake Eirie is the same as at the western end, 240 miles distant.

Ah, but the lakes follow the geoid and not the reference ellipse, both of which are curved though sometimes in opposite directions (concave v. convex). A spirit level, on the other hand, might be expected to be straight, as in true to a level plane, which might be defined as either tangential to the reference ellipse; or might be defined as conforming to the geoid; or baring a torpedo level that big, a laser or visual sighting that follows the geodesic taken by a photon in Earth's vicinity.

[grapes]

Ah, but the lakes follow the geoid and not the reference ellipse, both of which are curved though sometimes in opposite directions (concave v. convex).

I'm pretty sure neither is ever concave. :)

But yes, there is a difference. The geoid is that (theoretical) equipotential surface that coincides with mean sea level (a few calculations and adjustments)--in regions above sea-level, even more calculations have to be done. But once established, sea-level *by definition* is related to a good fit reference ellipsoid. Using GPS, that calculation is pretty straightforward, given the reference ellipsoid.

In the past, different areas used different best-fit ellipsoids. North America, just a few decades ago, used NAD27, which didn't match the ellipsoids for South America or Europe. Now, with a global standard, the fit to the geoid is poorer, locally, but we can have an international standard that works world-wide (and "meets" at the continental interfaces).

A spirit level, on the other hand, might be expected to be straight, as in true to a level plane, which might be defined as either tangential to the reference ellipse; or might be defined as conforming to the geoid; or baring a torpedo level that big, a laser or visual sighting that follows the geodesic taken by a photon in Earth's vicinity.

Careful there. :)

The geodesic followed by a photon is not a geodesic on the earth's geoid--two different uses of the same term. The geodesic followed by a photon is, for earth geodetic purposes, indistinguishable from a straight line, I'm pretty sure.

[Ara Pacis]

I'm pretty sure neither is ever concave. :)

It looks that way on the graphic on the geoid page, but I have no idea if it every would make that shape in actuality on Earth. I wonder if we could construct a sphere with enough density and structural integrity to create continental rises and deep basins that would actually create a geoid that is concave in places.

But yes, there is a difference. The geoid is that (theoretical) equipotential surface that coincides with mean sea level (a few calculations and adjustments)--in regions above sea-level, even more calculations have to be done. But once established, sea-level *by definition* is related to a good fit reference ellipsoid. Using GPS, that calculation is pretty straightforward, given the reference ellipsoid.

In the past, different areas used different best-fit ellipsoids. North America, just a few decades ago, used NAD27, which didn't match the ellipsoids for South America or Europe. Now, with a global standard, the fit to the geoid is poorer, locally, but we can have an international standard that works world-wide (and "meets" at the continental interfaces).

Ah, I didin't realize that. So MSL equals the geoid except when we decide it equals the reference ellipse for convenience.

Careful there. :)

The geodesic followed by a photon is not a geodesic on the earth's geoid--two different uses of the same term. The geodesic followed by a photon is, for earth geodetic purposes, indistinguishable from a straight line, I'm pretty sure.

That's what I was saying, WRT a geodesic and the straight line. One follows light through curved space and another one is an imaginary plane not fitted to curved space using an external frame of reference.

[kamaz]

My question is how elevations are determined accurately by GPS since, for instance, the delta is further from earth’s center (closer to the GPS for purposes of distance) than the source at Lake Itasca?

The GPS does not report distance from Earth's center. The GPS does not report elevation above the sea level either.

What GPS does report is elevation above the WGS-84 reference ellipsoid. Now, the reference ellipsoid itself is shaped (i.e. flattened) in a way which matches the Earth's curvature. So, if the world ocean surface was perfectly flat (which it isn't) and its level was constant (which it isn't as well) the surface of WGS-84 ellipsoid would correspond to local sea level surface. The elevation above the reference geoid is what is commonly called elevation above the mean sea level (a.m.s.l.).

To account for local differences in sea level, WGS-84 incorporates a gravitometric model. So, the WGS-84 reference ellipsoid is actually not an ellipsoid at all... it does have good fit to the local sea level though

http://en.wikipedia.org/wiki/World_Geodetic_System

[cran]

Another related item, I read (HERE) is that the sea level is rising at a (3 or for times) faster rate on the east coast of North America than other places around the world. That seems irrational to me, unless that faster rate is accounted for by a movement of some large heavy mass below the earth’s surface, under or centered nearby, and geological changes of that sort are not seen in decades but in hundreds of millennia. Any ideas why there would be isolated regional and relatively rapid in changes in sea levels such as this?

There are a few things that affect sea level in different locations around the world, mostly because water is much more responsive to changes when compared to, say, rocks or continents.

If the world were considered as a non-rotating body, then the differences in sea level would be mostly due to water's response to gravity and sub-crustal thermal variations, which in turn lead to submarine topographical variations. A secondary component arises from the water cycle, with a regional lowering of the surface where evaporation dominates, and a regional raising of the surface where influx dominates.

Bringing other bodies into the equation, like the Sun and the Moon, adds variations in sea surface elevation in response to the gravitational attraction of those masses.

Now, add the Earth's own rotation, which is most simply described as moving from West to East. This leads to a Westward shift of water masses relative to the solid Earth, and so water tends to mound up along the Western boundaries of ocean basins, or along the Eastern coastlines of continents.

Why the Eastern coastline of North America in particular?
Because is it the most removed from any Westward marine passage, and it gains influx from one of the Earth's major rivers, as well as contributions from Northern melts. It simply takes longer for water to equilibrate in the Western North Atlantic basin than in any other ocean basin.

[utesfan100]

The longitudinal difference is 17.25 deg. or about 19.2 percent of the 90 degrees between the equator and the pole, so 19.2% of r. of 12.5 miles is 2.4 miles or 12,670 feet less the 1,476 slope = roughly 11,200 feet. (is that roughly a valid assumption?)

Are you measuring the distance from the center of the earth, or the earth's axis? I don't see where the 2.4 miles comes from.

Before the GPS I'm assuming that the benchmarks for elevations were established empirically by surveyors performing inland surveys/traverses across the Northwest Territory with cross references being made across the great lakes.


My question is how elevations are determined accurately by GPS since, for instance, the delta is further from earth’s center (closer to the GPS for purposes of distance) than the source at Lake Itasca?

Well, the geoid is not actually measured by GPS. This surface was measured by making accurate gravity measurements around the world at known elevations. The GRACE mission provided far better data than GPS.

http://en.wikipedia.org/wiki/Geoid
http://en.wikipedia.org/wiki/Gravity...ate_Experiment

Unlike Grapes, I am not sure the geoid is convex off the tip of India. I can not find the reference where I had read that it has a radius of a few thousand miles, nearly at the level of geosyncronous orbits. As such, I leave this as speculation that it could be something like this.

Another related item, I read (HERE) is that the sea level is rising at a (3 or for times) faster rate on the east coast of North America than other places around the world. That seems irrational to me, unless that faster rate is accounted for by a movement of some large heavy mass below the earth’s surface, under or centered nearby, and geological changes of that sort are not seen in decades but in hundreds of millennia. Any ideas why there would be isolated regional and relatively rapid in changes in sea levels such as this?

A significant factor is that the land itself is not fixed, but rises and sinks. The East coast of the US is sinking into the mantle, making the sea level appear to rise faster there.

http://en.wikipedia.org/wiki/Current...e_measurements

[utesfan100]

Unlike Grapes, I am not sure the geoid is convex off the tip of India. I can not find the reference where I had read that it has a radius of a few thousand miles, nearly at the level of geosyncronous orbits. As such, I leave this as speculation that it could be something like this.

If this was my source, it is worth a second look.

http://www.colorado.edu/geography/gc...s/gps/af99.htm

Consider the anomaly from the center to the blue region, a difference of 30 meters. This is roughly a circle with a radius of 2000 kilometers, giving an angle of roughly 1/3 of a radian from the center of the Earth. The change in ellipsoid is then R(1-cos(1/3)), or 350 km.

350 km >> 30 meters.

The geode is convex at this scale.

[cran]

A significant factor is that the land itself is not fixed, but rises and sinks. The East coast of the US is sinking into the mantle, making the sea level appear to rise faster there.

http://en.wikipedia.org/wiki/Current...e_measurements

For example, over the past 100 years, the rate of sea level rise varied from about an increase of 0.36 inches (9.1 mm) per year along the Louisiana Coast (due to land sinking),

[Bold mine] The East coast is not sinking into the mantle - continental rocks don't do that*. Not all land subsidence is tectonic in origin.

ETA: *Well, ordinarily. Relative sinking of continental crust into the Asthenosphere occurs at continent-continent plate convergences (in other words, where continental plates collide and form mountain chains); however the surface expression of this is still a relative uplift.

For the last century, the global level of the sea appears to have risen at an average rate of nearly two mm/yr. However, in any given region, the apparent rate of rise can vary considerably from the long term global value. Geographical and temporal variations from the long-term mean value occur from a variety of causes such as interdecadal fluctuations of ocean density and circulation, continuing isostatic adjustment of the land level from the last deglaciation, subsidence due to the extraction of underground fluids, and others. The middle Atlantic region of the U.S. east coast gives a good illustration of this phenomenon.

-http://www.ngs.noaa.gov/GRD/GPS/Proj.../sealevel.html

But yes, land subsidence is another factor when considering relative sea levels.