the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Dec 2024
Least travel time ray tracer, version Two (LTT v2) adapted to the grid geometry of the OpenIFS atmospheric model
Abstract. Electromagnetic signals commonly used in geodetical applications, such as the Global Navigation Satellite System (GNSS), undergo bending and delay in the neutral gas atmosphere of the Earth. The least-travel-time (LTT) concept is one of the approaches to model signal slant delays via a ray tracing (RT) procedure. In this study, we developed an LTT-based RT algorithm (LTT v2), where the 3-dimensional refractivity field of the atmosphere is based on the atmospheric model data. This representation is complete in a sense that the domain of the RT conforms to the native grid geometry of the atmospheric model. In addition, some physical and numerical approximations are improved compared to the previous version (LTT v1). The atmospheric states are generated using a global numerical weather prediction model, the Open Integrated Forecast System of the European Centre for Medium-Range Weather Forecasts. The slant delays of LTT v2 are compared with the products of the original least-travel-time GNSS delay model (LTT v1) and the products of the state-of-the-art VieVS Ray Tracer (RADIATE). The skill of slant delay estimation is assessed using metrics that are indicative of the quality of GNSS products derived using the GROOPS (Gravity Recovery Object Oriented Programming System) orbit solver software toolkit of the Graz University of Technology. Employment of slant delay products of the LTT RT algorithm shows radical improvement in GNSS processing. When using LTT v2 delay estimates, the GNSS orbit midnight discontinuities are reduced by more than 10 % compared to RADIATE, and more than 2 % compared to LTT v1. The residuals of ground station precise positioning are analysed with respect to the IGS14 reference positions. The RMS of residuals (accuracy) and standard deviation (precision) are substantialy reduced compared to RADIATE.
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Status: open (until 26 Mar 2025)
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RC1: 'Comment on gmd-2024-136', Anonymous Referee #1, 16 Jan 2025
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The paper presents a new ray tracing algorithm that can be used to calculate slant tropospheric delays from numerical weather model data. The algorithm is tested by using the slant tropospheric delays derived from LTT v2 in GNSS data analysis and comparing the results to those obtained when using slant tropospheric delays from two other ray tracing programs (LTT v1 and RADIATE). I think the new algorithm seems to be working fine and provide good results. The paper is well writer and interesting to read.
For the evaluation using GNSS data, two metrics are used to check the results: the midnight discontinuities of the orbits and the RMS and standard deviations of the station coordinate offsets. Why were these parameters used as metrics for the evaluations, and not other parameters estimated in the GNSS analysis? It might be nice to motivate this.
I am a bit skeptical about some of the large values in table 1, especially mean the RMS in height for RADIATE which is 23.3 cm. Looking at figure A1, it does not seem that the RMS values in height for RADIATE is not that large, for most stations it is less than 4 cm. Is there a misprint in the table, or do a few stations have huge RMS values (which is not seen in Figure A1 since the x-axis goes only to 10 cm), making the mean RMS large. In the latter case, it would be nice to discuss this in the text and maybe indicate this somehow in the figure. Similarly, from figure A2, it seems that the mean RMS for height should not be as high as 5.26, as given in Table 1.
The fact that the mean RMS for the PPP position estimates are lower by 10.1% for LTT v1 compared to LTT v2. This deserves a bit more discussion, since this would indicate that the older version of LTT is actually better.
Minor comment: when calculating the standard deviation (equations 14b and 16b), normally one ´divides by N-1, not N (to take into account the effect of using the mean value instead of the true value). This has, however, not any significant effect on the results presented in the paper.
Citation: https://doi.org/10.5194/gmd-2024-136-RC1 -
AC1: 'Reply on RC1', Maksym Vasiuta, 18 Feb 2025
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Dear reviewer,
Thank you for your valuable comments. The commentary concerns the evaluation of the ray tracing delay models via GNSS data processing. In the reply to you, we are giving a thorough discussion and minor additions to the manuscript text.
1. The result of GNSS data processing is position and velocity states, as well as clock parameters, ionospheric electron content, integer ambiguities and phase biases. We have selected two types of metrics that represent the stability of the states: one being related to satellite orbits, the second related to station positions. The discussion by Strasser et. al. (2019) suggests that clock parameters are stable over daily processing time, which makes them less informative to analyse. Also, a subjective choice was made to ignore all parameters but orbits and station position, as was done by Zus et. al. (2021) in a similar experiment to analyse atmospheric mismodelling effects. We are adding extra context to the potential readers explaining our choice.
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Regarding the GNSS products, there is no absolute reference. To validate the GNSS processing result, we use two metrics:
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The products of GNSS data processing are position and velocity states, as well as clock parameters, ionospheric electron content, integer ambiguities and phase biases. Since there is no absolute reference, the processing is evaluated by measuring the stability of the solution. Discussions by Strasser et. al. (2019) and Zus et. al. (2021) suggest that among all the most informative are orbit and ground station positions. Hence, we choose two metrics to validate ray tracing models:
2. The report of statistics in the Table 1 is correct. Indeed, the high average value of station height RMS and standard deviation for RADIATE is due to several huge values. The histograms at Figure A1 and A2 are constructed so that values higher than 10 cm are not visible in the figure. We decided not to remove these points as statistical outliers, because the same stations mismodelled in the RADIATE experiment are processed adequately in the LTT v1 and v2 experiments. This notion is hereby explained in the text as following:
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On average, the precise point positioning is significantly more reliable when using the LTT algorithms instead of RADIATE, both for RMS and σ of position residuals.
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PPP residuals are generally smaller when using the LTT algorithms compared to RADIATE. In the RADIATE experiment, the height estimates are very inconsistent for some stations, which leads to high average RMS and σ values. These high values do not appear in Figs. A1 and A2.
3. In the text, we mention that LTT v1 and v2 models demonstrate fairly similar skill. We are not able to draw deeper conclusions. The approach of the processing is to estimate many parameters in the same least squares adjustment. Hence, orbit and station position states are entangled in the fitted solution. The orbit discontinuities and station position offsets (and behavior of other parameters) are indicative of stability of the solution as a whole. To quantify that would require a unified metric, to develop which would be a good idea for future work. Another notion is that between separate experiments the percentage change of orbit metric is lower than for station metric (coloured numbers in Table 1). One might speculate that the station metric is more sensitive to mismodelling than the orbit metric. Again, future sensitivity tests are needed to prove that. Small change to the text:
Lines 379-381 REMOVE
LTT v1 and LTT v2 demonstrate fairly similar skill, which implies that the differences in slant delay estimates induced by the model modifications provide a much smaller effect on PPP results than the improved use of weather model input data.
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LTT v1 and LTT v2 demonstrate comparable skill, with v1 being better at precise point positioning and v2 better at orbit determination. This implies that modifications in ray tracing models from the old to the new version have very minor effect compared to improved use of weather model data.
4. We decided to keep the formula unchanged, since the values of standard deviation are used in comparative manner inside the paper. And, they are not shown against external processing results, such as by operational analysis centers.
References:
Zus, F., Balidakis, K., Dick, G., Wilgan, K., and Wickert, J.: Impact of Tropospheric Mismodelling in GNSS Precise Point Positioning: A Simulation Study Utilizing Ray-Traced Tropospheric Delays from a High-Resolution NWM, Remote Sensing, 13, https://doi.org/10.3390/rs13193944, 2021.
Strasser, S., Mayer-Gürr, T., and Zehentner, N.: Processing of GNSS constellations and ground station networks using the raw observation approach, Journal of Geodesy, 93, 1045–1057, https://doi.org/10.1007/s00190-018-1223-2, 2019.
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AC1: 'Reply on RC1', Maksym Vasiuta, 18 Feb 2025
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Model code and software
Release of Least Travel Time model, version Two (LTT v2) Maksym Vasiuta https://doi.org/10.5281/zenodo.14237335
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