I congratulate the authors on a nicely written, interesting article on

the assimilation of GNSS ZTDs and ZTD gradients into WRF using a fast

observation operator, avoiding time consuming ray tracing.

It has high value for the GNSS meteorological community. Being a first

test one can always ask for more details and work, but I advocate

publication with just minor adjustments in order to make it quickly

available for others to use.

It will be interesting to see in the future whether higher resolution

NWP shows improved impact, and whether the benefit is still clear in NWP

using more types of standard meteorological observations.

Detailed comments:

Don't use dots as a sign for multiplication, like in equation 3. When

you have defined \phi as a function, it is clear that \phi \delta z

means multiplication.

You use a limited set of standard meteorological observations in your

DA. SYNOP will be available at all 4 assimilation times, but

radiosondings are more rare at 06 and 18 UTC, than 00 and 12 UTC. Please

specifiy how large the difference is in your area.

In figure 2, what does the shorter and shorter vertical green, blue and

red lines indicate?

Specify explicitly whether the 3 simulations run independently, ie.

the ZTD and ZTD+gradients are assimilated in first guesses based on

ZTD only and ZTD+gradients, not into the control first guess.

In figure 4, what is the location of the "lobes" where you obtain

the profiles (is it for example a certain distance from the location of

the GNSS sites?

What is shown in figure 18?  Is it the average rmse of the mixing ratio

up through the radiosonde profile? That might be dominated by mixing

ratios at certain heights. Or is it rmse at a certain level?

Review of GMD-2023-202

Assimilation of GNSS Tropospheric Gradients into the Weather Research and Forecasting Model Version 4.4.1 

By Rohith Thundathil, Florian Zus, Galina Dick, and Jens Wickert

General Comment:

The authors have implemented the GNSS tropospheric gradient operator into WRFDA version 4.4.1 and conducted single observation tests with ZTD data and tropospheric gradients. Three experiments, employing a rapid-update cycle throughout June and July 2021, were carried out to investigate the impact of assimilating tropospheric gradients. The analyses and simulations have been verified against GNSS data from 100 stations, ERA5 reanalysis, and radiosondes. It is nice that the authors integrated the new operator into the WRFDA data assimilation system, and the manuscript is well-written.

However, it is noted that the comparisons are primarily based on the control run with limited observations involved. Therefore, the impacts of additional observations overlaid on the control run could be overestimated. Specific comments are provided as follows.

Specific comments:

This study implemented the tropospheric gradient operator atop the GNSS ZTD modules in the WRFDA system. While the authors stated that the manuscript aims to test the functionality of the operator and assess the relative impact of tropospheric gradients, it is noted that the control run assimilated with surface stations and radiosondes only is limited and insufficient for the impact study. The comparing experiments (ZTD and ZTDGRA) added ZTD and tropospheric gradient data on top of the two types of observations in the control run, which could potentially enlarge the data impacts of ZTD and tropospheric gradient. A suggestion is to incorporate most of the observations adopted in the operational model for the control run. This aligns with the goal of the EGMAP, as mentioned in lines 97-98.

In addition, incorporating more observations into the data assimilation usually benefits the model's initial analysis. The study conducted a long period of cycling data assimilation within a model domain that covered a larger region than the assimilated observations’ coverage. Is there a specific reason for not utilizing all the observations within the model domain? 

To evaluate the impact of tropospheric gradient data, the study compares the difference between ZTD and ZTDGRA rather than comparing the assimilation without ZTD data (i.e., only the conventional observations and tropospheric gradient) with the control run. On the other hand, section 4.3.1 discussed that the ZTD run adjusted not only the ZTDs but also the tropospheric gradients. When assimilating both ZTD and tropospheric gradient observations, would it be overweighting the effects of the tropospheric gradient? Could you further elaborate on the interaction and influence as both data are assimilated simultaneously?

Figures 9-11 indicate similar information. Merge the three figures into one would be clearer for comparison. For example, display the RMSE of ZTD for the control run, ZTD run, and ZTDGRA run by three curves on one panel. Similar processes for RMSEs of the North and East components on the second and third panels. The same suggestion is for Figures 12-14. 

In WRFDA, it has converted geometric height to the geopotential height for GNSS refractivity, not as the description in the manuscript to ignore the conversion. It can be found in da_fill_obs_structures.inc. Ignoring the conversion could result in some errors, particularly at higher altitudes (Scherlllin-Pirscher et al. 2017).

Scherllin-Pirscher, B., A. K. Steiner, G. Kirchengast, M. Schwärz, and S. S. Leroy (2017), The power of vertical geolocation of atmospheric profiles from GNSS radio occultation, J. Geophys. Res. Atmos., 122, 1595–1616, doi:10.1002/2016JD025902.

Typos:

Line 241. The NMC method is widely used for generating B by … --> Please revise B to bold B.

Figure 6. A real …. component equals0.099 mm. --> Please add a blank between equals and 0.099 mm.