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: 

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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.

Dear reviewer,

Thank you for your valuable comments. This commentary concerns the strategies when comparing ray tracing models, and specifically, implementation and validation of the RADIATE model. In the reply to you, we discuss our vision on the role of ray tracing models. Also, we have modified the manuscript text to reflect our way of thinking.

1. The true atmospheric state is always unknown, while numerical models attempt to reconstruct the state closest to reality and to known physical laws. The same applies for the delay model, since such a model is based purely upon the atmospheric representation. In that sense, there is no ground truth to delay estimates. Thus, we avoid deeper analysis in comparing the delay products. However, we have made Figures 5a and 5b (Figures 5 and 7 in the updated manuscript) more informative by adding mean and std.dev. of delay differences for 1-degree zenith angle in the text. One of the challenges with artificial stations creation is station’s model height, i.e. the height with respect to the lowest level in the model atmosphere. The models we use employ different definitions of this lowest level, with LTT v2 definition being the only correct one. Again, the “no-ground-truth” principle dictates that we can assess correctness only with analysis of real GNSS observations.

2. We have purposely omitted using mapping with VMF3 in this study. Also, we do not estimate tropospheric parameters; instead we use only a priori estimates from the ray tracing models. The reason being that previously some of us conducted a study (https://gmd.copernicus.org/articles/15/2763/2022/) of utilizing a priori estimates, and concluded that this approach shows better performance. Thus, we carry on with this approach.

3. We emphasize the development of a signal delay model which is closely connected with numerical weather prediction systems. The main focus here is communication about our vision, while comparing LTT-based models. However, we also need an external reference to make sanity tests of our approach. Therefore, one of our goals is to try incorporating the RADIATE model into this coupled approach. We have performed various adjustments both to RADIATE and atmospheric data, just to make a common processing setup as with LTT-based models. We believe, modifications inside RADIATE are possible for proper contemporary atmospheric data input. Yet, this development is a subject of future studies. We have reflected that by restructuring Section 5 (Results), with LTT and RADIATE analysis reported separately. Table 1 is split into two tables, and extra hints are added to the reader.

Also, we have rerun our GNSS processing experiments after the submission of the manuscript. We found a small but important technical issue in our computation. The issue being usage of different ground stations list in processing and metrics computation. Thus, the values presented in Table 1 (now Tables 1 and 2) have slightly changed. This change is rather minor, thus the conclusions we made in the original submission are not affected.