General Comment

This manuscript examines forecasting experiments where radiosonde and GPS delay observations are assimilated before a significant precipitation event. The main goal being pursued is to establish whether increased model and/or observation resolution can bring significant improvements to the forecasts.

Various combination of model resolutions and observations are tested. The performance of these forecast is mostly assessed from the resulting precipitation compared against observations. The overall conclusion is that the assimilation of operational radiosonde data is important but assimilating extra high resolution observations is not. Deficiencies in modeled moist processes and lack of vertical information in GPS observations are given as factors that could explain the results obtained.

With their heterogeneous distributions and difficult statistical properties, physical state variables such as moisture and precipitation remain challenging to data assimilation and verification. As such, this manuscript takes place in the context of an active topic of research. While the experiments and analyses presented are not fundamentally novel, they contribute to a better understanding of data assimilation for moist processes. The topic is interesting and within the scope of the Weather and Climate Dynamics journal.

The manuscript is well organized and generally easy to follow. The indepth examination of the meteorological impacts (i.e. changes in moisture) brought by the assimilation process is interesting.

We would like to thank Dr. Dominik Jaques for his valuable comments and corrections. We have accepted most of the remarks. In the following, we provide detailed answers to his questions/requests.  

Perhaps the area that needs the most improvement is the description of results related to figure 5. As discussed in major comment 1 below, the description of certain scores is missing or unclear. There is also a labeling error in figure 5.

A detailed review of the changes carried out related to Fig. 5 is included later in this document in the Major Comments section.

Only one precipitation case is presented in this study. On the one hand, this allows for an in depth analysis of the factors contributing to this precipitation event. On the other hand, this imposes a strong limitation on the generalization of conclusions drawn from the various analyses. Luck (good or bad) cannot be ruled out of the many factors influencing the forecasts. Interestingly, the analysis reveals that the assimilation of one radiosonde in the operational network has a significant impact on the forecasts being performed. One can wonder if the conclusions of the manuscript would have been different had this radiosonde been part of the extra high resolution observations being tested. The examination of only one precipitation event should not prevent the publication of this manuscript. However, the limitations that come from this should be emphasized in the concluding statements. Special care should be taken with respect to the models treatment of moist processes (section 5a) which seem to be supported by other studies but which may only be applicable to this one case.

The reason for using just one case study was to be able to focus on the different impacts of each observation type. With a total number of 21 simulations, 3 observation types (and  their combinations) in 3 different resolutions, considering several cases would have been challenging.

We planned these experiments as an illustrative means of assessing the improvement potential of each observation type. Indeed, these experiments belong to a series of GPS assimilation experiments reproducing the whole 2012 Autumn period, where we got further insights on the model biases, regarding water vapour and precipitation. Analysing the impact of the different observation types on all cases of the 3-month period, would have not allowed such an in-depth assessment. This is why we simulated IOP6 separately.

Nevertheless, as pointed out, the manuscript should clearly state that the findings relate to this one case study, and that generalisation of the results is therefore constrained. Several modifications have ben included to clearly stress this point in the new version of the manuscript. 

Major comment

Figure 5 is problematic as it presents results that are not consistent with the verification metrics presented in sections 2.4. Addressing

this issue is important as this figure is the basis for most of the discussion later in the manuscript.

Figure 5 has been completely reworked, together with the supporting text description, which needed, as mentioned in the reviewers’ comments, more readability and suppression of redundant information. In the following the different changes and improvements of Fig.5 are described.

For example, it is not clear what the percentile presented in this figure are or where they come from. Section 2.4 gives a good summary of the verification metrics used in the rest of the study. The percentiles appearing in figure 5 should be introduced there. Also, there appears to be a labeling mistake for the y-axes of panel c.

We have added a new subsection (2.4.1) to introduce how the percentiles are calculated, within section 2.4 Verification metrics. In a nutshell, we obtain 3-hourly precipitation aggregates for the grid points within the investigation area. The 99-percentile is obtained from the sample of all 3-hourly precipitation intensities at each grid point during the day of precipitation i.e., for eight time steps during 24 September 2012. More detailes will be provided in the new version of the manuscript.

The Fraction Skill Score is in the range [0,1] but the y-axis of panel c) goes from 5 to 35. Because of this, most of the discussion on lines ~350-380 is difficult to follow and/or interpret. It is believed that this part of the text and figure 5 should be reworked before

publication of the manuscript.

Panels b) and c) in Fig. 5 were wrongly interchanged. This has been corrected in the new version of the manuscript and the text has been reworked

Still on the topic of verification, the use of anomaly correlation for the verification of precipitation in a day-to-day forecasting context is unusual and somewhat confusing. If the concept of anomalies makes sense in a climatological context, it is more difficult to apply in a weather context. In my understanding, the anomalies should refer to some departure from a preferred mode for the model solution. Because the mode of high-dimensional pdfs are generally difficult to estimate, they are often replaced by the average of a large number of such solutions. Many seasons are averaged for climate forecasts, many ensemble members may be averaged for ensemble forecasts. In the present case, for a single weather event in a deterministic context it does not seem possible to know the normal mode about which the anomalies could be estimated. In particular, the daily average precipitation for one case cannot be thought of as normal baseline against which anomalies can be estimated.

That said, the correlation coefficient between two fields can be used in the context of verification. To avoid the confusion that arise from the concept of anomalies, it is suggested that correlations be estimated from the fields themselves. Just remove the \overbar{mod} and \overbar{obs} from eq. 5. The results previously obtained will be unchanged since the Pearsons's correlation coefficient is invariant to such offsets by constant values. As a final note, one should remember that due to its non-linear response, Pearson's correlation coefficient is difficult to interpret in the context of verification. This problem is discussed in the appendix of

https://doi.org/10.1175/MWR-D-18-0118.1.

We agree with the reviewer that treating the precipitation average of one case cannot be understood as the normal baseline of the event and changed this to a full timeseries correlations .

We have computed the correlation coefficient as suggested by the reviewer, removing the subtraction of the timely means, with an invariant result.

However, the formulation of Eq. 5 remains the same, as it is the formulation of Pearson’s correlation coefficient. We have adapted the text to better explain that in Eq. 5, obs and mod and  stand for the spatially averaged precipitation for time step t=i measured by MSWEP and simulated by COSMO, respectively. With out subtraction of the period mean, as suggested by the reviewer. The corresponding explanations will be included in the revised version of the manuscript. 

Minor comments

Table 1 Table 1 summarizes the description of the different experiments performed in this study. The current titles for the panels of this table make its interpretation difficult. It is believed that small adjustments to the labeling would help.

Table 1 has been adapted, following the indications of the reviewer.

Most description of results repeat a lot of information that can be read from the figures. This makes these description quite lengthy and somewhat difficult to read. For example, the beginning of section 4.2 is especially hard to follow. The paragraph ~445-450 also repeats a lot of information accessible in the table being discussed. It is suggested that the description of results be shortened or summarized wherever possible.

We have shortened the description of the results wherever it was possible, aiming at providing  clearer descriptions of the findings.  

References to supplementary material Often figures found in the supplementary material will be referred to alongside the other figures. For example on line 377 we find "... western side of the Alps (Figs. 4b, S1b ans S2b)." If the  supplementary material will not be immediately available to the readers of the manuscript it is suggested that the supplementary figures not be referred to directly. If these figures are necessary to the comprehension of the text, they should be included in the manuscript.

We have adapted the manuscript not to refer to the SM repeatedly. Only needed graphs are included in the manuscript that are sufficient to comprehend and validate the expressed results.

Minor comments 

If any minor comments posted by the reviewer are not anered here in our reply, it is because we have accepted all corrections. Only minor comments that need further explaining are replied here.  

Line 133: Because of image compression, the red squares in figure 1b look a lot like circles.

It is true, still thanks to the colour difference between operational soundings (blue triangles) and the high-resolution (red squares), we believe these two observation types are readily distinguishable by eye. Additionally, we have changed, in line 133, the word “squares” for “markers”.

Equation 3: Out of curiosity, what is the value of "s" being used? Does it change with the resolution of the model or the observations being assimilated? Should it?

“s” is defined as correlation scale and provides a factor for attenuation of assimilation impact when spreading the information horizontally. “s” varies with altitude and is a parameter pre-defined in the model. For example, for humidity (q) and temperature (T) the correlation scale parameter in km is as follows for pressure levels between 1000 hPa and 50 hPa. The values of s can be found in the model documentation (Schraff and Hess, 2012) but for illustration: applying a  for humidity at a 500 hPa implies that the weight of the observation for the horizontal spreading  is halved at a distance of 135 km from the observation’s location.

We did not perform supplementary experiments varying this parameter as our main goal was to assess the added value of the observation types and their impact on model variables rather than assessing how model parameters could be fine-tuned. We believe such experiments would fall out the scope of the paper. Nevertheless, our interpretation is that adapting the values for s,  is more sensible for different observation types than for model resolution, not to harm the information of too close neighbouring observations (as in the case of GPS due to its larger coverage). However, reasonable conflicts could arise from the use of a too large correlation scale for observations close to the surface in different resolutions. The better representation of the model’s orography in a 2.8 km and a 500 m resolution could impose orographic boundaries that should be considered to truncate the too large horizontal spreading.  This aspect is discussed briefly in the revision in Sect. 2.2.1 The COSMO Model, the nudging scheme.

In figure 4d) we can clearly see artifacts caused by the inflow through the model boundaries. Visibly, it takes some time for the model's parametrizations to generate precipitation from the inflow through the boundaries. Presumably, some of the microphysical species being modeled are initialized at zero at the boundaries. While this does not seem to affect the main areas of interests for this study, this illustrates the difficulties associated with such high resolution forecasts. This phenomenon would probably be worth mentioning.

We have included this observation in the revision, in the description of Fig.4.

Line 334 : "no dynamic impacts" In the Canadian system, the assimilation of radar-inferred precipitation through latent heat nudging is shown (see paper references above) to reduce RMSE for upper-level winds by a few percent on average over a twomonth verification period (~110 forecasts). One would not expect to be able to observe such a small signal on the model dynamics for only one precipitation event.

This information has been included in the manuscript to provide further insights on how the nudging of thermodynamic profiles brought a low impact on wind components for ourcase study.  

Line 421 Altitude-based corrections can sometimes be significant, especially in mountainous terrain where the difference between the model terrain and observation height can be large. Do we know if this is the case here?

We follow the procedure suggested by Bock and Parracho (2019), where stations with height differences (station altitude vs. altitude of selected grid point) larger than 500 m are dismissed from the calculations. The IWV corrections applied to the remainder stations (dIWV/IWV=-4*10^-4*dh) bring corrections that averaged in time and space are no larger than 0.2 %. For a specific date, after spatially averaging to all stations (within investigation domain RhoAlps) are of 1 % and for particular stations can be as large as ±20 %. These corrections are necessary, especially over complex terrain to consider  the height differences. However, for the results presented in Fig. 7 and Tab. 2 bring a marginal impact (~ 1 %), since the values presented are spatially and timely averaged. 

Figure 7 The black line for GPS is difficult to distinguish in this figure. Maybe use a thicker/dashed linestyle?

We acknowledge that the GPS black line is hard to see, precisely because of the good performance of the runs with assimilated observations, that overlay the black line of the GPS. We have added a note “underneath the coloured lines” in Sect. 4.2 to make clear to the reader that the simulations with assimilated observations is underneath all the rest.

Line 532: In other instances of the text, the great heterogeneity of the moisture field is mentioned as a source of complications. It seems reasonable to assume that this likely explains why high moisture content was measured by only one sounding. 

We have adapted the corresponding paragraph to clearly state that the large spatio-temporal hetergoneity and variability of atompsheric moisture might have played a decisive role in this measurement. 

Section 4.3.1: The box plots shown in figure 10 show no obvious differences that would be statistically different between the various experiments. Since this section is quite detailed and the manuscript already long, it is suggested that this section be moved to the supplementary materials. If it is believed that the section should remain in the manuscript, lines ~560-575 should be reworked to improve readability.

We have shortened the text to improve the readability. However, we believe that the explanation on the impact of the sounding on precipitation processes is relevant for the study

References

Beck, H. E., van Dijk, A. I. J. M., Levizzani, V., Schellekens, J., Miralles, D. G., Martens, B. and de Roo, A.: MSWEP: 3-hourly 0.25global gridded precipitation (1979–2015) by merging gauge, satellite, and reanalysis data, Hydrology and Earth System Sciences, 21(1), 589–615, doi:10.5194/hess-21-589-2017, 2017.

Bock, O. and Parracho, A. C.: Consistency and representativeness of integrated water vapour from ground-based GPS observations and ERA-Interim reanalysis, Atmospheric Chemistry and Physics, 19(14), 9453–9468, doi:10.5194/acp-19-9453-2019, 2019.

Hodam, S., Sarkar, S., Marak, A. G. R., Bandyopadhyay, A. and Bhadra, A.: Spatial Interpolation of Reference Evapotranspiration in India: Comparison of IDW and Kriging Methods, Journal of The Institution of Engineers (India): Series A, 98(4), 511–524, doi:10.1007/s40030-017-0241-z, 2017.

Jacques, D., Michelson, D., Caron, J.-F. and Fillion, L.: Latent Heat Nudging in the Canadian Regional Deterministic Prediction System, Monthly Weather Review, 146(12), 3995–4014, doi:10.1175/mwr-d-18-0118.1, 2018.

Khodayar, S., Czajka, B., Caldas-Alvarez, A., Helgert, S., Flamant, C., Girolamo, P. D., Bock, O. and Chazette, P.: Multi-scale observations of atmospheric moisture variability in relation to heavy precipitating systems in the northwestern Mediterranean during HyMeX IOP12, Quarterly Journal of the Royal Meteorological Society, 144(717), 2761–2780, doi:10.1002/qj.3402, 2018.

Schraff, C. and Hess, R.: A Description of the Nonhydrostatic Regional COSMO-Model Part III: Data Assimilation, German Weather Service (DWD), P.O. Box 100465, 63004 Offenbach., 2012.

General Comment

In this paper, the impact of assimilating GPS-ZTD data and sounding observations at low and high vertical resolution is evaluated on a case study of heavy precipitation. The COSMO model is employed at 3 different resolutions over 3 domains and observations are assimilated by a nudging technique. Verification of experiments is performed using several metrics, especially regarding precipitation. Regardless of the model resolution, only the assimilation of operational low vertical resolution radiosondes improves precipitation accuracy, while both high-resolution soundings and GPS observations have a negative impact. This is probably due to deficiencies in model physics and, for GPS, to lack of vertical information.

In my opinion, the topic is relevant and the experiments presented by the authors are interesting. The paper is well written and results are discussed in detail. However, I think that some aspects of the manuscript need to be improved, as reported in the following comments.

We would like to thank the anonymous reviewer for her/his valuable comments and corrections. We have accepted most of the remarks. In the following, we  provide detailed answers to the questions/requests. In case the corrections need no further explaining and are straight-forward, they will be directly included in the new version of the manuscript.   

References

Beck, H. E., van Dijk, A. I. J. M., Levizzani, V., Schellekens, J., Miralles, D. G., Martens, B. and de Roo, A.: MSWEP: 3-hourly 0.25global gridded precipitation (1979–2015) by merging gauge, satellite, and reanalysis data, Hydrology and Earth System Sciences, 21(1), 589–615, doi:10.5194/hess-21-589-2017, 2017.

Hodam, S., Sarkar, S., Marak, A. G. R., Bandyopadhyay, A. and Bhadra, A.: Spatial Interpolation of Reference Evapotranspiration in India: Comparison of IDW and Kriging Methods, Journal of The Institution of Engineers (India): Series A, 98(4), 511–524, doi:10.1007/s40030-017-0241-z, 2017.

Roberts, N. M. and Lean, H. W.: Scale-Selective Verification of Rainfall Accumulations from High-Resolution Forecasts of Convective Events, Monthly Weather Review, 136(1), 78–97, doi:10.1175/2007mwr2123.1, 2008.

Skok, G. and Roberts, N.: Analysis of Fractions Skill Score properties for random precipitation fields and ECMWF forecasts, Quarterly Journal of the Royal Meteorological Society, 142(700), 2599–2610, doi:10.1002/qj.2849, 2016.

Major Comments

High vertical resolution radiosondes (HR) are assimilated without performing any thinning or data reduction. As far as I understand, since HR vertical levels are much more than model levels (700 compared to 40-80), this means that HR observations are overweighted. I think that this point should be reported and discussed in the manuscript.

We agree that this aspect should be discussed in the manuscript.

The nudging procedure of the COSMO model reads radiosonde reports as they are made available, and after quality and consistency checks, observations are either averaged over each model layer (temperature, wind) or vertically interpolated to the height of the mid model layer (humidity). This is done both for operational soundings (RAD) and high-resolution (HR). The improvement gained from the DA comes therefore from how the larger number of levels impacts the layer averages (wind, temperature) or vertical interpolations to the mid model layer (humidity). This aspect will be more relevant as the number of vertical levels is increased with finer model resolutions (40 levels in a 7 km set-up, 50 in 2.8 km and 80 for 500 m).

To bring this discussion in the manuscript the following changes will be introduced in Sect. “Nudging of GPS and radiosondes” within section 2.2.1.

Figure 5 is crucial to quantitatively assess the impact of the various experiments on precipitation accuracy. However, some aspects are not clear and should be discussed further. First of all, it should be explained how the 99th percentile of 3h precipitation is

computed.

We acknowledge that the manuscript needs further explanation on how the 99^th percentile of the 3h precipitation aggregates are computed. To this end, we have extended Sect. 2.4 (Verification Metrics). In a nutshell the 99-percentile of 3h precipitation aggregates are obtained as follows: We obtain 3-hourly precipitation aggregates for the grid points within the investigation area. Then the 99-percentiles are obtained from the sample of all 3-hourly intensities at each grid point during the day of precipitation, i.e. for eight time steps during 24 September 2012.

Moreover, how are the raingauges treated? For example, for the domain average, are they aggregated to the same grid of MSWEP to take into account spatial variability?

We used the values of RG 24hly and 3hly precipitation aggregates at each station to obtain the spatial average (Fig.5a) and the 99-perc percentile (Fig.5b). Hence, in the old version of the manuscript, no interpolation to a common grid (0.1° from MSWEP) was carried out for RG. This, as pointed out, can pose problems regarding comparability between the different data sets. 

We have performed supplementary analyses for this review, trying interpolating the RG 24hly and 3hly to the 0.1° MSWEP native grid by means of an Inverse Distance Weighting Method (Hodam et al., 2017). The analysis has revealed spurious artifacts around the point stations and unrealistic precipitation gradients with no agreement with the original RG distribution. This illustrate the complications of interpolating station, information. Therefore we have decided to restrict the verification to the MSWEP product to avoid the artifacts produced by the gridding of RG data.

More inforamtion and supplementary plots will be provided in the detailed answers to the reviewers. 

Finally note that the title of subplot “b” has to be swapped with that of subplot “c”.

Indeed, panels b) and c) within Fig. 5 were interchanged. This has been corrected in the new version of the manuscript.

Minor comments

L56-58. In contrast to GPS, satellite and radar are claimed to not be all-weather observations. Regarding radar reflectivity, even if it is particularly useful in case of precipitation, it can be gainfully assimilated also in no-precipitating conditions to suppress spurious model rainfall (see for example Bick et al. (2016) and Gastaldo et al. (2021) for COSMO-LETKF, but the same holds for nudging schemes). About satellite observations, clear-sky observations have been assimilated for many years, but there are several

studies dealing with the all-sky assimilation (see for example Geer et al. (2018) for a review). So, please explain more in detail what you mean.

This statement was incorrect. Satellite and ground radars also measure atmospheric variables in cloud-precipitation situations. The intention was highlighting the advantages of GPS in measuring IWV as opposite to satellite products for the same variable. For example, IWV measurements from MODIS only provide IWV estimates in clear conditions, or cloudy areas, above the cloud tops. As opposite to GPS, that also in the presence of clouds can provide information of the IWV. The statement in the introduction has been rephrased.

L61-62. I am not sure that Davolio et al. (2017) restrict the correction to boundary layer. Looking at their Table 3, the moisture correction is smoothed in the boundary layer.

Yes, this is correct. In the Davolio et al., (2017) paper it is explained: “The main role of the parameter  is to limit the specific humidity adjustment in the boundary layer, in order to avoid too unstable profiles that can produce excessive convective activity”.

Indeed, the correction is not restricted in the boundary layer, and it is truncated only at a height of 8 km. The information will be corrected in the manuscript.

L190-231 Several symbols employed in the equations and in the text are not explicitly defined like, for instance, F, x, t, xk in eq 1, all variables in eq 2, ps and Tm at line 220. It is true that most symbols are easy to interpret, but I think it would be more clear to

define all of them.

The variables will be defined for each equation in the new version of the manuscript 

L275-280. Some aspect are not clear to me. Are you computing FSS employing moving boxes consisting of 18 grid points? Why 18 is the maximum number o grid points in the RhoAlps domain? Please rephrase these lines.

L282. I suggest to make clear that FSS=1 when there is a perfect agreement between observations and forecast, in terms of FSS.

We compute FSS using moving boxes of neighbour length (N=20), not 18. This will be corrected in the manuscript. This means that the fractions of precipitation (f=n_precip/n_tot) for the model (f_mod) and the observations (f_obs) are computed using 2*20+1 grid points in both directions (a total of n_tot=1681 grid points). This choice of neighbour length N is selected given the fact that the largest skill of the forecast is given when N is the largest possible. Provided the shortest dimension of the investigation area RhoAlps is , N=20 is the maximum neighbour length possible, to comply with n=2N+1. This is what is defined in Roberts and Lean (2008) as Asymptotic Fractions Skill Score (AFSS), that theoretically would have value of 1 in the case of no bias between the model and the observations. This is the upper limit of the forecast skill. 

This explanation has been reworked to provide a better explanation on how the FSS is computed.  It now shows as follows:

L311-312. MSWEP clearly underestimates precipitation over Liguria region compared to RG, This should be reported. Moreover, this may also be taken into account for the subsequent qualitative verification (Fig. 3 and 4).

The underestimation over Liguria will be noted in the new version of the manuscript in Sect. 3.