Article Figures & Data
Figures
- FIGURE 1
The GNSS stations in the Alpine region of Valais. Inside the yellow rectangle is the region where COSMO-SkyMed SAR images were acquired (Topo data: swisstopo)
- FIGURE 2
Spatio-temporal characteristics of co-located GNSS and InSAR techniques
- FIGURE 3
Polar plot of the error of the sine mapping function. We simulated total, dry, and wet slant delays using the COSMO-1 model at different elevation angles (2° up to 90°) for every 30° azimuth angles. Therefore, the slant delays (total, dry, and wet) are mapped in the zenith direction and compared to the zenith delays calculated directly from COSMO-1 data. In the plots, the center of the circle is 90° elevation and the edge 2°. The two (light) black circles are at 5° and 10°, respectively
- FIGURE 4
Polar plot of the error of wet delays for the six investigated mapping functions. We simulated slant wet delays using the COSMO-1 model at different elevation angles (2° up to 90°) for every 30° azimuth angles. Therefore, the SWDs are mapped in the zenith direction and compared to the zenith delay. The center of the circle is 90° elevation and the edge 2°. The black circles are at 5° and 10°, respectively
- FIGURE 5
Error of considered mapping functions for different elevation angles. The absolute error is plotted at the top panels, where the impact for elevation angles up to (about) 25° is visualized. The bottom panels display a zoom (i.e., the colorbar is set at lower values such as ≤ 4 mm) where the impact of mapping functions at higher elevation angles (about 25° to 90°) is highlighted
- FIGURE 6
Work flow chart in case of simulated measurements. The work flow consists of 3 steps: 1) Measurement simulation based on COSMO-1 data, 2) Combination of simulated GNSS and InSAR measurements in a collocation approach, and 3) Validation of our results (in a closed-loop work frame), where the combination results are compared with COSMO calculated delays
- FIGURE 7
Standard deviation (plotted over the topography) of the difference of estimated ZTDs at COSMO-1 grid points. The difference is computed between our estimated ZTDs from the GNSS-InSAR combined solution and the ZTDs calculated on the COSMO-1 grid by directly integrating COSMO-1 meteorological parameters
- FIGURE 8
Time series of estimated ZTDs differences using the GNSS-InSAR combination in COMEDIE. The top part is a quantile plot where the whisker corresponds to 99.3% coverage assuming a normal distribution; the red ‘+’ are outliers, and ‘-’ in the box is the median. In the bottom part of the figure, the time series are directly plotted. The difference is computed between our estimated ZTDs from the GNSS-InSAR combined solution and the ZTDs calculated on the COSMO-1 grid by directly integrating COSMO-1 meteorological parameters
- FIGURE 9
Residuals of the used ZTD measurements (top) and their standard deviations (bottom)
- FIGURE 10
Time series of zenith total and wet delays at the GNSS stations over the investigation period
- FIGURE 11
Standard deviation of zenith total and wet delays over the investigated period
- FIGURE 12
Work flow chart for real measurements. The work flow consists of 3 steps: 1) GNSS and InSAR real measurement collection (the processing was performed by third parties), 2) Combination of GNSS and InSAR delays in a collocation approach, and 3) Cross validation (qualitative comparison) of GNSS, InSAR, and GNSS/InSAR combined delays
- FIGURE 13
2D map of ddSTDs computed by InSAR, GNSS, and their combination, when GNSS and InSAR meteorological products have a high level of agreement (top plots) and low level of agreement (bottom plots)
- FIGURE 14
Histograms of estimated ddSTDs using InSAR, GNSS, and their combination. The plot on the left shows the case when GNSS and InSAR individual estimations have a high level of agreement, and the plot on the right shows the case when they have poor agreement
- FIGURE 15
Estimated ddSTDs time series using GNSS, InSAR, and their combination. The top part is a quantile plot where the whisker corresponds to 99.3% coverage in case of a normal distribution (‘+’ and ‘-’ in the box represent the mean and the median, respectively), whilst in the bottom part of the figure are directly plotted the ddSTDs
Tables
- TABLE 1
Investigated mapping functions. In the table: ε - elevation angle, H - height of atmosphere, R - Earth radius, a, b, c - mapping function coefficients, h - station height, aht, bht, cht - mapping function coefficients for height, DOY - day of year, φ - latitude, λ - longitude and HEM - hemisphere
Model Mathematical Form Coef a,b,c Sine 1/sin ε No Geometrical 
No B & E No Niell F(DOY, h, φ) UNB3m F(DOY, h, φ) GMF F(DOY,Hem,φ,λ) - TABLE 2
Statistics of ZTD differences (GNSS/InSAR interpolated ZTDs from COSMO-1-calculated ZTDs) when considering different InSAR PSI points sample spacing
PSI points sample spacing (number of PSI points distributed uniformly) 4125 1064 475 266 130 63 Std.dev (ZTD differences) [mm] 2.1 2.1 2.1 2.2 2.4 2.4 Bias (ZTD differences) [mm] <0.1 0.1 0.1 0.1 0.2 <0.1 - TABLE 3
Statistics of ZTD differences (GNSS/InSAR interpolated ZTDs from COSMO-1-calculated ZTDs) when considering different InSAR footprint size
InSAR footprint size (the PSI points sample spacing remains unchanged) 30 × 22 km2 25 × 18 km2 20 × 14 km2 15 × 10 km2 10 × 6 km2 6 × 3.5 km2 Std.dev (ZTD differences) [mm] 2.1 2.1 2.3 2.5 2.7 2.8 Bias (ZTD differences) [mm] <0.1 0.1 <0.1 –0.2 –0.2 –0.4
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