The paper entitled “Improving weather radar rainfall estimates by merging with commercial microwave link data: a fully reproducible, large-scale method intercomparison” by Erlend Oydvin and co-authors investigates the contribution of commercial microwave link data to mitigate observation errors and biases in weather radar rainfall data through data fusion. The idea is potentially interesting but the current version of the study includes a major methodological error that in my opinion should prevent publication in the present form.

The authors propose to skip the variogram estimation step of Kriging, which is missing the point of Geostatistics that are based on estimating the spatial variability of the process at hand from data through variogram estimation (e.g., Chilès and Delfiner, 2012). To justify their choice the authors mention their own sensitivity analysis without sharing any result, and cite two papers: Haberlandt (2007) and Goudenhoofdt and Delobbe (2009). But I red these papers and they do not support the idea of not estimating the parameters of the variogram from data. In Haberlandt (2007) the hypothesis is tested, but the author clearly states that “the use of an assumed linear variogram is not recommended, because this shows by far the largest RMSE values for both interpolation methods (p 151)”. And in Goudenhoofdt and Delobbe (2009) the parameters of the variogram are estimated from data. In my opinion what one can conclude from Haberlandt (2007) and Goudenhoofdt and Delobbe (2009) is that the choice of a complex model of variogram is unnecessary in Kriging when a local neighborhood is used for interpolation, and that in this setting a linear model of variogram is good enough. But the idea of using a spherical model of variogram with arbitrary parameters is not at all supported by these references.

Another misleading use of a reference is the way the authors cite van de Beek et al. (2012) to justify the choice of the variogram parameters they use. The main point of van de Beek et al. (2012) is to show that variogram parameters vary a lot (in this case in time) depending on rainfall characteristics (cf Fig. 3 in van de Beek et al. (2012)). But in the paper in review the authors pick one single value for the variogram parameters, which is in contradiction with acknowledging the variability of variogram parameters. In addition, the way they derive this value from the work of van de Beek et al. (2012) is totally unknown and not justified. Finally, I would like to point out that van de Beek et al. (2012) focuses on the Netherlands, while the present paper investigates rainfall in Sweeden and Italy, where one can expect that rainfall spatial variability is different.

The problem of variogram estimation is also likely to impair block Kriging. The authors acknowledge that former studies estimated the point covariance from block averaged data (Graf et al. (2021); Goovaerts (2008)), but they renounce to this approach without any justification and prefer to use an arbitrary model of variogram with arbitrary parameters. This is very surprising since two of the co-authors of the present paper are also part of Graf et al. (2021), in which point variogram parameters are estimated in a sound way.

References:

Chilès, J. P., and Delfiner, P. (2012). Geostatistics: modeling spatial uncertainty (Vol. 713). John Wiley and Sons.

Goudenhoofdt, E. and Delobbe, L.: Evaluation of radar-gauge merging methods for quantitative precipitation estimates, Hydrology and Earth System Sciences, 13, 195–203, https://doi.org/10.5194/hess-13-195-2009, 2009.

Goovaerts, P.: Kriging and Semivariogram Deconvolution in the Presence of Irregular Geographical Units, Mathematical Geosciences, 40, 101–128, https://doi.org/10.1007/s11004-007-9129-1, 2008.

Graf, M., Hachem, A. E., Eisele, M., Seidel, J., Chwala, C., Kunstmann, H., and Bardossy, A.: Rainfall estimates from opportunistic sensors in Germany across spatio-temporal scales, Journal of Hydrology: Regional Studies, 37, 100 883, https://doi.org/10.1016/j.ejrh.2021.100883, 2021.

Haberlandt, U.: Geostatistical interpolation of hourly precipitation from rain gauges and radar for a large-scale extreme rainfall event, Journal of Hydrology, 332, 144–157, https://doi.org/10.1016/j.jhydrol.2006.06.028, 2007.

van de Beek, C., Leijnse, H., Torfs, 625 P., and Uijlenhoet, R.: Seasonal semi-variance of Dutch rainfall at hourly to daily scales, Advances in Water Resources, 45, 76–85, https://doi.org/10.1016/j.advwatres.2012.03.023, 2012.

This paper introduces the Python package mergeplg, and demonstrates its value by applying it to two publicly available commercial microwave link (CML) datasets. Several of the merging algorithms in this package are tested, and some sensitivity analyses are carried out. I think the paper is interesting, well-written, and a valuable contribution to the field. The paper needs some clarifications and I think there are some important things missing in the discussion. However, I don’t think any new analyses are needed. I therefore recommend minor revisions. Specific comments are listed below.

1. On lines 56-57, I think it would be good to explicitly name mergeplg. I think it is a very valuable contribution to this field, and deserves a bit more attention in the paper.
2. Section 2: are the signals rounded/truncated (e.g. 1 dB r 0.1 dB), or do they have a precision that high enough to not be relevant?
3. Line 91: do you mean 30 dB? Please specify the units.
4. Line 92: can “excessively noisy” be quantified?
5. On line 100, radar-CML pairs are introduced. How is the radar rainfall estimate R defined? Is it the path-averaged radar rainfall estimate or is it the rainfall at the pixel over the center of the link? And are these definitions different for KED than for other methods? It would be good to also include a discussion about the implication of this choice on the results.
6. On line 112, the ratio between CML and radar rainfall estimates is introduced. It would seem logical to me to log-transform this variable to make it symmetric (i.e., underestimation by a given factor would deviate as much from 0 as overestimation by the same factor). What is the reason for not using such a transform?
7. On line 115, please include units (I assume them to be mm/h).
8. On line 116, why is this condition assymetric? I would expect the lower boundary to be the reciprocal of the upper boundary, which is not the case here (0.1 is not equal to 1/15).
9. On lines 110-120, I suggest using different symbols for the differences and ratios, and for the values of these differences and ratios on the one hand and their interpolated fields on the other. Now all four of these are called Z(v), and this can be confusing.
10. In Eq. (6) the covariance function C is introduced. However, the same symbol is used for CML rainfall estimates. This is confusing. Please select a different symbol for one of these variables.
11. On lines 140-141, it is mentioned that the results do not depend too much on the variogram that is used. I think this would only hold if the distance between the points to be interpolated is (much) smaller than the range of the variogram. This could affect the results of the OpenRainER dataset.
12. On lines 141-143, the variogram parameters are introduced. The nugget and sill are expressed in (mm/h)², so I’m assuming these are the parameters for the additive method. What are the parameter values for the multiplicative method?
13. On lines 145-154, KED is explained. It would be good to include here that the CML rainfall estimates are directly interpolated, and not a difference or ratio of CML and radar estimates.
14. On lines 156-166, it is unclear what the meaning of a block is in this context. Is it the path of a link? If so, it would be good to state that. And with that, it would be good to more precisely define the “average point covariance between blocks” and the “average point covariance within each block”.
15. In Fig. 2, it is unclear to me what the gray-scale colors in the background of the third columns are. Can this be added to the caption?
16. In Fig. 5, I have trouble telling the different lines apart because of slight color-blindness. Is there a way to make the graph easier to read, for example by using different symbols/line types?
17. On line 259, I think “near rain gauges” should be “near CMLs”.
18. On lines 261-274, the sensitivity to the range checks is discussed. How many samples were removed (percentage of the total amount of samples) by the different range checks? I think it would be valuable information to include in the paper.
19. On lines 261-274, a sensitivity analysis is presented of the range checks. Was it considered to also carry out a sensitivity analysis on the variogram parameters?
20. On line 264, please include units (mm/h).
21. On line 270, the difference between the two datasets in terms of their response to the range checks is mentioned. What could be the cause of this. Are the CML estimates worse for the OpenRainER dataset?
22. On lines 297-320, the effects of the dataset characteristics on the results are discussed. What I’m missing here is a discussion of the uncertainties or errors in CML rainfall estimates and how they affect the results. I think this should be included in the paper.
23. On lines 340-341 and on line 348, it is mentioned that the path-averaging effect of the CMLs could play a role in dampening rainfall extremes in the interpolated product. If that would be the case I would expect to see a large effect of block Kriging versus point Kriging, but that’s not visible in the results.
24. On line 344 it is mentioned that KED has the tendency to produce smoother rainfall fields. Is this generally the case, or is this specific for these datasets (or only the examples shown in Fig. 2)? I would expect that KED would result in a smoother field only if the radar data are smooth to begin with. Please elaborate on this in the paper. This is important because this apparent smoothing character of KED is repeated throughout the discussion.
25. On lines 346-348, the potential effect of non-linearity of the relation between CML rainfall and radar rainfall is discussed. What could cause such non-linearity, and how severe could it be? If there’s no reason to expect non-linearity, I suggest removing this statement from the paper because it would then not be relevant.
26. On line 349, it is stated that path-averaging of the CMLs combined with possible nonlinearity of the relation between CML and radar rainfall can lead to a smoothed drift surface. Is this really the case? And if so, please explain more clearly in the paper what the mechanism behind this is.
27. On line 353, I think “from rain gauges” should be “from CMLs”.
28. On lines 361-366, multiplicative methods are discussed. I think it would be good here to mention that most errors in radar rainfall estimation are multiplicative, and that from that perspective, it would make sense to use a multiplicative method for merging. The fact that the multiplicative methods actually perform worse makes these conclusions even more relevant.
29. On line 404, I think “performed on pair” should be “performed on par”.
30. On line 406, what is meant by “rainfall simulators”? Does this refer to the correlation or variogram functions?
31. On lines 410-412, and important characteristic of Kriging is discussed that wasn’t discussed before: the interpolation uncertainty estimates. I think it would be good to mention this in the introduction of the paper. And I think that the claim that is made about the improved uncertainty representation of block Kriging cannot be made based on the results presented in this paper (uncertainties are not studied here). So I suggest to reformulate this part.
32. It would be interesting to also discuss the effect of the particluar characteristic of Kriging that it will give more weight to isolated observations. For example, if there are 10 links to the south of the point where I would like to have an estimate and there is only one link to the north, the link to the north will have more weight than, e.g., IDW (where all links would get equal weights if they are all at the same distance from the point of interest). This could be an advantage when dealing with a network that has a very heterogeneous distribution in space like the OpenRainER dataset.
33. I’m missing a discussion about the use of the 12 nearest links. For IDW this makes perfect sense. However, for Kriging, you could miss information that would have received a large weight depending on the link topology. Please include a discusison on this in the paper.