High-resolution models of tropospheric delays and refractivity based on GNSS and numerical weather prediction data for alpine regions in Switzerland

Abstract

The tropospheric delay of a microwave signal affects all space geodetic techniques. One possibility of modeling the delay is by introducing tropospheric models from external data sources. In this study, we present high-resolution models of tropospheric total refractivity and zenith total delay (ZTD) for the alpine area in Switzerland. The troposphere models are based on different combinations of data sources, including numerical weather prediction (NWP) model COSMO-1 with high spatial resolution of 1.1 km × 1.1 km, GNSS data from permanent geodetic stations and GPS L1-only data from low-cost permanent stations. The tropospheric parameters are interpolated to the arbitrary locations by the least-squares collocation method using the in-house developed software package COMEDIE (Collocation of Meteorological Data for Interpretation and Estimation of Tropospheric Pathdelays). The first goal of this study is to validate the obtained models with the reference radiosonde and GNSS data to show the improvement w.r.t. the previous studies that used lower resolution input data. In case of total refractivity, the profiles reconstructed from COSMO-1 model show the best agreement with the reference radiosonde measurements, with an average bias of 1.1 ppm (0.6% of the total refractivity value along a vertical profile) and standard deviation of 2.6 ppm (1.6%) averaged from the whole profile. The radiosondes are assimilated into COSMO-1 model; thus, a high correlation is expected, and this comparison is not independent. In case of ZTD, the GNSS-based model shows the highest agreement with the reference GNSS data, with an average bias of 0.2 mm (0.01%) and standard deviation of 4.3 mm (0.2%). For COSMObased model, the agreement is also very high, especially compared to our previous studies with lower resolution NWPs. The average bias is equal to − 2.5 mm (0.1%) with standard deviation of 9.2 mm (0.5%). The second goal of this study is to test the feasibility of calculating high-resolution troposphere models over a limited area from coarser data sets. We calculate the ZTD models with spatial resolution of 20 m for a test area in Matter Valley. We include the information from the low-cost GPS stations (X-Sense), to also assess the performance and future usability of such stations. We validate the models based on three data sources w.r.t. the reference GNSS data. For the station located inside the area of the study, the models have an agreement of few mm with the reference data. For stations located further away from the study area, the agreement for X-Sense is smaller, but the standard deviations of residuals are still below 15 mm. We consider also another factor of evaluating the high-resolution models, i.e., spatial variability of the data. For designing a GNSS network, also for the tropospheric estimates, the height variability of the network may be as important as the horizontal distribution. The GNSS-based models are built from the coarsest network; thus, their variability is the lowest. The variability of X-Sense-based stations...

Comparison of Tropospheric Path Delay Estimates from GNSS and Space-Borne SAR Interferometry in Alpine Conditions

“…where σ 2 signal is the a-priori variance of the signal, x i , y i , z i , t i are the projected Swiss coordinates, orthometric height, and time of observation i, x j , y j , z j , t j are the coordinates, height and time of observation j, z 0 = 4 km is a parameter modifying the correlation lengths as a function of height, ∆x 0 = 50 km, ∆y 0 = 50 km, ∆z 0 = 1 km, ∆t 0 = 1.7 h are the empirically determined correlation lengths of space and time. These collocation models have already been tested for the interpolation of GNSS data in [34,35]. In [35], the cross-validation was performed for the stations in the similar area as in this study.…”

“…These collocation models have already been tested for the interpolation of GNSS data in [34,35]. In [35], the cross-validation was performed for the stations in the similar area as in this study. The average bias between the reference stations and the interpolation models was close to 0 mm with 4 mm of standard deviation.…”

“…The GNSS-based estimates are interpolated to the locations of PS using the least-squares collocation software COMEDIE (Collocation of Meteorological Data for Interpretation and Estimation of Tropospheric Path delays) developed at ETH Zürich [30][31][32][33][34]. In [35] we have interpolated a sparse data in the alpine area into high-resolution 20 m grid. Three data sources were evaluated, namely NWM, GNSS, and low-cost GPS.…”

“…The GNSS estimates have been proven to provide the interpolations with the highest accuracy regarding the reference data and the low-cost GPS estimates have the highest variability. The research area of this study has been extended from [35] to cover the entire footprint of the ordered SAR images. The GNSS and InSAR estimates are compared for this region for the first time.…”

Performance Evaluation of Troposphere Estimated from Galileo-Only Multi-Frequency Observations

“…Tropospheric delay refers to the refraction of the microwave signal when it passes through the neutral atmosphere. The space-borne microwave techniques, including Global Navigation Satellite Systems (GNSS), Very Long Baseline Interferometry (VLBI), Doppler Orbitography, and Radiopositioning Integrated by Satellite (DORIS), or Synthetic Aperture Radar Interferometry (InSAR), are all subjected to tropospheric delays [1]. GNSS has been proven to be an efficient tool for the retrieval of total tropospheric delays between the observing station and the satellites in view.…”