Figures 7-10 above illustrate the level of inversion error computed for three major sources of error: (1) phase measurement noise, (2) orbit position and velocity error, and (3) residual ionospheric correction errors. For presentation purposes, all of the refractivity inversion errors are shown as equivalent temperature errors. The refractivity errors were converted to equivalent temperature errors using Equation (5). For comparison, a best case "perfect" inversion (with no errors added) is shown in Figures 7-10. The "No Error" case is indicative of the residual "raytrace/inversion error" at this early stage of software development, and will probably improve in time.
Figure 7 shows the effect of measurement phase noise on the inversion process. Two phase noise magnitudes are shown in the figure: (1) a 1 mm case which is representative of non Anti-Spoof (A/S) P-code tracking, and (2) a 10 mm case representative of codeless L2 tracking in the presence of A/S . The curves shown in Figure 7 are rms errors of 10 different realizations of phase noise error. The 1 mm curve maintains an accuracy of 1 degree up to ~ 41 km. The 1 degree accuracy cut off for the 10 mm curve occurs at ~ 25 km.
Figure 8 illustrates the effect of LEO satellite orbit error on the inversion process for both a best and worst case expected orbit error. The best case orbit contained radial, transverse, and normal (RTN) errors of 0.5, 1.0, 0.5 meters, respectively. The worst case RTN orbit error consisted of 2, 20 and 2 meters, respectively. Figure 8 shows that orbit error is not likely to be a dominant source of error.
The effect of residual ionospheric error on the inversion process is shown in
Figure 9. Two methods of ionospheric correction were used for both
maximum electron density (solar maximum, day-time) and minimum electron density
(solar minimum, night-time) specifications. The first method, commonly used in
conventional GPS applications, uses a linear combination of the L1 and L2 GPS
phase measurements, and is labeled "LC
" in Figure 9. The
second method uses a linear combination of L1 and L2 bending angles, and
is labeled "LC
". Figure 9 shows that both methods
perform adequately for solar minimum conditions. However, for solar maximum
day-time conditions, the LC method performs much better than
the LC method. The LC method maintains an
accuracy of 1 degree up to nearly 40 km altitude, while the LC
method provides 1 degree accuracy only below ~ 27 km.
Figure 10 repeats the worst case errors from the phase noise, orbit error and ionosphere curves in Figures 7-9. From this figure, one can see that, when it is on, it is likely that A/S caused phase noise will dominate the recovered inversion error (for the types of noise studied so far).[22]
Preliminary Observing Systems Simulation Experiments (OSSE) conducted by NCAR/MMM indicate that refractivity profiles of the type that will be available from GPS/MET may have a significant positive impact on forecasts, particularly moisture fields. Figures 11-14 below illustrate the level of improvement possible. For these experiments, high resolution model data (60 km/5 min.), derived from actual measured data on March 8, 1992, was used to generate simulated observations of wind, temperature and refractivity profiles. Figure 11 shows the relative humidity (RH) at the 700 mb level without data assimilation. Figure 12 shows the result after assimilating temperature and wind observations. Figure 13 shows the result from assimilating temperature, wind, and refractivity data. Figure 14, which was derived from the high resolution control run, shows the true distribution of RH at 700 mb. Note how well Figure 13 correlates with Figure 14.
