>From a friend: =====
> Any guess as to how accurate these are? 1. They vary. You have to look up the info on the particular benchmark. Some benchmarks and geodetic monuments (see below) receive a lot of attention and are known as "First Order" points. Many more receive less attention and are known as "Second Order" points. _Most_ receive _little_ attention and are known as "Third Order" points. Basically, the positions/heights of third order points are determined with respect to nearby second order points; and second order points are determined with respect to the nearest first order points. First order points are few and far between, but great care is devoted to determining their relative positions/heights. 2. Traditionally, only the _height_ of a "benchmark" with respect to a "vertical datum" (approximating mean sea level) has been determined accurately. Within the USA, the US Geological Survey (USGS) is legally responsible for determining heights of benchmarks. Height differences are determined by means of "leveling." Level surfaces are determined by liquids in stationary tubes, and by tide gauges. A tide gauge senses the constantly varying height of open water. Of course much time-averaging must be done with tide-gauge data. My point is that the reference surface is an equipotential in the combined gravitational and centrifugal (due to the rotation of the Earth with respect to an inertial frame) field of the Earth. The reference surface has lumps and bumps because the Earth's mass distribution is not uniform or symmetrical. The reference surface is _not_ a regular mathematical-geometric figure such as an ellipsoid. Whereas, only "horizontal" position coordinates (basically, latitude & longitude) have been determined accurately for "geodetic" monuments. Within the USA, the National Geodetic Survey (NGS) is legally responsible for determining horizontal positions. Lat. & long. are determined with respect to a "geodetic datum," by means of geometric measurements such as distances and "horizontal" angles. The datum, or reference coordinate system, is defined geometrically, by means of monuments planted in hopefully stable ground, and mathematical formulas that attempt to account for known systematic motions such as continental drift and solid-earth tides. Benchmarks are much more abundant than geodetic monuments, basically because height differences determine drainage, and drainage problems are more common than horizontal-position problems. It is significant that the USGS is part of the US Dept. of the Interior, whereas the NGS is part of the US Dept. of Commerce. To determine how this plays out in practice is left as an exercise for the student. :-) 3. The advent of GPS has changed the game greatly in practice, although not so much in theory. GPS-based geodetic measurements are three-dimensional, and they are geometric; that is, they do not determine position with respect to an equipotential surface. The fundamental measurements are of double-differences between the times of arrival of radio signals transmitted by different satellites and received at different points on Earth. The origin of the fundamental reference frame is the center of mass of the Earth, about which the satellites orbit; and the directions of the coordinate axes are determined by the average spin angular velocity vector of the Earth, and an artifact that marks the "prime meridian" or origin of longitude. This artifact is not a single marker but an internationally agreed set of markers distributed around the world. These markers are rocks and/or concrete set into hopefully stable ground. Their relative positions have been well-established by great numbers of observations by many people and organizations. One might call these markers "Zero Order" points, although I don't believe that this terminology is official. GPS does not determine height with respect to an equipotential surface or "vertical datum." However, its 3-D geometrical position determinations include determinations of "height" with respect to a mathematically-geometrically defined ellipsoid whose center is at the origin of the GPS coordinate system. "Ellipsoidal height" determinations by GPS are good enough for most practical purposes. A good GPS geodetic surveyor utilizing good equipment and techniques can determine the ellipsoidal-height differences between points a few kilometers apart within a few millimeters. A _very_ good GPS geodetic surveyor utilizing very good equipment and techniques can determine the ellipsoidal-height differences between points 100 kilometers apart within a few millimeters. An excellent GPS geodetic surveyor utilizing excellent equipment and techniques can determine the ellipsoidal-height differences between points 1000 kilometers apart within a few millimeters. The uncertainties of GPS determinations of ellipsoidal-height differences are typically three times greater than the uncertainties of GPS determinations of horizontal-coordinate differences, for two main reasons: (1) A GPS receiver cannot observe satellites below the horizon, although it can observe satellites in both the northern and southern sky, and it can observe satellites in both the eastern and western sky. (2) Uncertainty in the radio-signal propagation time-delay added by the troposphere, especially by the water vapor in the troposphere, affects mainly the height determination, because the troposphere is entirely above a ground-based receiver and, to first order, the troposphere is horizontally stratified. 4. You can probably find your local benchmark in a USGS database on the Web. (Your state or county may also list your benchmark in a database.) See how your benchmark is classified, as first-, second-, or third-order; and look at the accuracy standards in the definitions of these orders. If you're lucky, your benchmark has been visited by GPS receivers and has been incorporated into the NGS database of geodetic monuments. So look at the NGS' website(s), too. (Your state or county may have made GPS observations, and these may or may not have made it into a national database.) ===== Best, -John ==================== >> I hear that there is a hobby where people photograph these and collect >> the photos. Seems pointless in the city but many are on mountain >> peaks and other places with good views. The hobby is more reasonable >> if you find them without using GPS. The USGS maps are good enough o >> put you within 10 to 20 feet of the BM without using a GPS. >> >> Chris Albertson >> Redondo Beach, California _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
