Elevation angle and phase residuals for single satellite Epochs 20 0 mm -20 To help you visualize the measurements, I’ve shown the phase recorded for a single satellite at a stations after removing everything we know about the propagation medium and the motion of the station wrt the satellites. 30s samples. Overall rms here is .04 cycles, 8 mm in equivalent path length. At for high elevation angles, the rms is about 2 mm; for low elevation angles about 15 mm. Low elevation angles increase both multipathing and atmospheric delays. Note temporal correlations of 10-20 minutes, suggesting that we have oversampled by a factor of 20-40, and that we should expect the formal errors, propagated from the scatter in the phases, to be too small by a factor of 5 or so. These are due to multipathing and variations in water vapor along the path. 1 2 3 4 5 Hours Elevation angle and phase residuals for single satellite

Simple geometry for incidence of a direct and reflected signal The most common and dominant source of high-frequency multipath is reflection from the horizontal surface beneath the antenna. If this surface is far enough away from the antenna (1-2 m) to be outside the fresnel zone (no interaction with the antenna itself), then geometric optics allows us to model the signal well enough to predict the frequency. For an antenna mounted 1-2 m above the surface, the variations will be of the order of minutes, and tend to have low, though still significant correlatations with the signature of the station’s coordinates and the atmopheric delay. Once you get within a half-meter, though, the longer period variations are a real problem. And this is even without taking into account the interaction with the antenna structure. Multipath contributions to observed phase for an antenna at heights (a) 0.15 m, (b) 0.6 m, and (c ) 1 m. [From Elosegui et al, 1995]

Now we’ve taken the phase vs time residuals and projected them onto the sky. Same 12-hr period for the same stations on two successive days. North to the right!! This is the pattern you see on the sky at mid-latitudes and shows a mixture of N-S and E-W motion, with N-S dominating. At the equator, all the satellites move nearly N-S on the sky, and at the poles more E-W. The dominant motion determines whether the N-S or E-W component of the station position is better determined. You see again the largest fluctuations at low elevation angles, and much of this noise repeats from day to day—signal multipathing. Where you see differences, as near 90 degrees between 20-24 hours, the likely cause is water vapor.

Antenna Phase Patterns The first problem we have is that the phase-response pattern of any physical antenna is not spherical. So the effective phase center ---the point to which you want to refer the location of the ground monument---varies as a function of elevation angle, and hence changes if you use a different minimum cutoff—which can happen when you change receivers or cables because of the change in SNR. Sometimes, the patterns also vary with azimuth, as with the Leica and Rascal antennas here, but most of the antennas used for high precision work have symmetric patterns. L1 phase variations for antennas tested by UNAVCO. Zenith values at the center and values for 10 degrees elevation at the edges. 10 deg L1 phase = 5 mm. From Rocken et a. ???? Antenna Phase Patterns

Top: PBO station near Lind, Washington. Bottom: BARD station CMBB at Columbia College, California We now routinely create phase vs elevation plots in all of our processing. Here are two examples from continuous stations used in my processing of this summer’s PNW survey. The top one is a new PBO station in Eastern Washington. Except for the thin rods supporting the antenna, the support and the area around the antenna is “clean”, and the phase pattern quite flat. An older continuous station, mounted on a pillar, I think.

Left: Phase residuals versus elevation for Westford pillar, without (top) and with (bottom) microwave absorber. Right: Change in height estimate as a function of minimum elevation angle of observations; solid line is with the unmodified pillar, dashed with microwave absorber added To see how sensitive this problem can be, I’ll show first the results of a controlled experiment performed by the Harvard GPS group. They noticed a high dependence of their height estimates for the continuous tracker near the Westford VLBI antenna at Haystack, which they hypothesized was from the metal plate imbedded in the concrete of the pillar supporting the antenna. [From Elosequi et al.,1995]

Correlation between estimates of height and zenith delay as function of minimum elevation angle observed (VLBI, from Davis [1986])

The problem with estimating the zenith delay is that it is highly correlated with estimates of the vertical component of position. With VLBI, we can break this correlation somewhat by observing to very low elevation angles, but with GPS we can’t go this low. You can see from this curve that estimating the zenith delay with a cutoff of 15 degrees increases the vertical uncertainty by over a factor of 5. Uncertainty in estimated height as function of minimum elevation angle observed (VLBI, from Davis [1986]; dotted line with no zenith delay estimated)

The atmospheric delay can vary by decimeters, and though the surface pressure provides an adequate calibration of the the gases in hydrostatic equilibrium, there is no reliable and economical way to remove the contribution of water vapor. So we estimate that portion, parameterized by a delay at the zenith and a mapping function that is reliable to 15 degree elevation angle, the usual lower limit for GPS observations. This slide shows the estimates at 2-hr intervals for two stations used in our analysis of PNW data from last summer. GPS adjustments to atmospheric zenith delay for 29 June, 2003; southern Vancouver Island (ALBH) and northern coastal California (ALEN). Estimates at 2-hr intervals.