Measuring rainfall using microwave links: the influence of temporal sampling

van der Valk, Luuk D.; Coenders-Gerrits, Miriam; Hut, Rolf W.; Overeem, Aart; Walraven, Bas; Uijlenhoet, Remko

doi:https://doi.org/10.5194/egusphere-2023-1971

Preprints

https://doi.org/10.5194/egusphere-2023-1971

Preprints

13 Sep 2023

| 13 Sep 2023

Measuring rainfall using microwave links: the influence of temporal sampling

Luuk D. van der Valk, Miriam Coenders-Gerrits, Rolf W. Hut, Aart Overeem, Bas Walraven, and Remko Uijlenhoet

Abstract. Terrestrial microwave links are increasingly being used to estimate path-averaged precipitation by determining the attenuation caused by rainfall along the link path, mostly with commercial microwave links from cellular telecommunication networks. However, the temporal resolution of and method to derive these rainfall estimates is often determined by the temporal sampling strategy that is employed by the mobile network operators. Currently, the links are most often sampled at a temporal resolution of 15 minutes with a recording of the minimum and maximum values, while more recently also a form of instantaneous sampling with possible intervals up to 1 s has been set up. For rainfall research purposes, often high temporal resolutions in combination with averaged values are preferred. However, it is uncertain how these various temporal sampling strategies affect the estimated rainfall intensity. Here we aim to understand how temporal sampling strategies affect the measured rainfall intensities using microwave links. To do so, we use data from three collocated microwave links, two 38 GHz and one 26 GHz, sampled at 20 Hz and covering a 2.2 km path over the city of Wageningen, the Netherlands. We aggregate the microwave link power levels to multiple time intervals (1 s to 60 min) and use a mean, instantaneous, and minimum and maximum value to characterize the signal. Based on the aggregated data, we compute rainfall intensities and compare these with 20 Hz rainfall estimates, such that we isolate errors and uncertainties caused by the sampling strategies from instrumental effects, such as different biases between instruments and representativeness errors. In general, our results show that for all sampling strategies an increase in sampling time interval reduces the performance of the rainfall estimates, which especially holds for the instantaneous sampling strategy. Even the mean sampling strategy, which generally performs best of all strategies, is sensitive to this reduction in temporal resolution and could lead to significant underestimations. In this, the non-linear relation between attenuation and rainfall intensity seems to play an important role. The min-max sampling strategy is mostly prone to minor underestimations or large overestimations of the path-averaged rainfall intensities. Moreover, our results, including a comparison with theoretical events, show that the attenuation due to wet antennas not only affects the comparison between the rainfall estimates obtained with a microwave link and another reference instrument, but also has a significant influence on the rainfall retrieval algorithm. Overall, this study demonstrates the effect a selected sampling strategy can have on rainfall intensity estimates using (commercial) microwave links.

Received: 29 Aug 2023 – Discussion started: 13 Sep 2023

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Journal article(s) based on this preprint

08 May 2024

Measuring rainfall using microwave links: the influence of temporal sampling

Luuk D. van der Valk, Miriam Coenders-Gerrits, Rolf W. Hut, Aart Overeem, Bas Walraven, and Remko Uijlenhoet

Atmos. Meas. Tech., 17, 2811–2832, https://doi.org/10.5194/amt-17-2811-2024,https://doi.org/10.5194/amt-17-2811-2024, 2024

Short summary

Luuk D. van der Valk, Miriam Coenders-Gerrits, Rolf W. Hut, Aart Overeem, Bas Walraven, and Remko Uijlenhoet

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-1971', Anonymous Referee #1, 18 Oct 2023

The paper presents an overview of the effects of different sampling techniques for microwave links for measurements of rainfall. In general, this paper presents not only the different sampling methodologies, but also gives a good overview how rainfall can be derived from (C)MLs, with the accompanying uncertainties and contains many relevant references. The information is also relevant. While the effects of temporal sampling could be suspected, as also stated by the authors, this paper gives a comprehensive discussion of these effects at different temporal resolutions.
As the paper is now it is fit for publication with some very minor changes.

Minor suggestions/remarks:
Line 45 or 57: One sentence on CML network density and changes over time and location might highlight their relevance
Line 140: Why the decision for 30 seconds? What are the effects of another threshold on your study?
Line 200: As RMSE and MBE are explained it might be good to also explain r²
Line 240: If possible more information on this filter would be beneficial. If not, it would be good to state this.
Line 242: Why more fluctuations?

Minor technical remarks:
Line 112: 'as remnant' seems a bit redundant
Figs. 4 and 5. The color between 1,s, 5min and 60min has low contrast, making it difficult to see, especially for the small figures.
Fig. 7: In the legend move 'mean' to the right column
Line 375: Also, a general

Citation: https://doi.org/10.5194/egusphere-2023-1971-RC1
- AC1: 'Reply on RC1', Luuk van der Valk, 05 Feb 2024
  
  Dear Reviewer,
  In the attachment, you can find our reply to your review.
  Thank you for your time and consideration.
  With kind regards,
  Luuk van der Valk, on behalf of all co-authors
  
  Citation: https://doi.org/10.5194/egusphere-2023-1971-AC1
RC2:
'Comment on egusphere-2023-1971', Anonymous Referee #2, 17 Jan 2024

The authors show an interesting and novel way to study the effect of different sampling strategies based on real microwave link data with a very high sampling rate of 20 Hz. Their approach is well thought out and sound. The paper is mostly nicely written, with the exception of some imprecise writing in several parts. In general the results are interesting and very well suited for AMT. The results and their interpretation do, however, lack focus and will require some restructuring and extension. In addition there might be one issue with the analysis of the theoretical events. In summary, I recommend a major revision, albeit not necessarily a large one.

Main comments:

1. There is a multitude of sampling strategies that are investigated in this manuscript. That results in a bit too many individual results of which not all are equally important. Almost all larger CML datasets do use either 15-minute min-max sampling or instantaneous sampling at 1 minute or faster (10 seconds is also common nowadays). The later does require a dedicated data acquisition system. Thus one very interesting question is, if it is worth to convince CML network operators to upgrade their data collection system to provide 1-minute instantaneous data instead of 15-minute min-max. Hence, I suggest to add a dedicated comparison of these two (or three if including 30sec or 1sec) different sampling strategies in the results and also in the discussion section. Parts of the results section could potentially also be reduced to increase the focus of the manuscript.
2. The result section 3.3 lacks focus or at least lacks structure. I suggest to add sub-subsection or to split up section 3.3. The discussion section would also be much easier to comprehend with some subsections and maybe also increasing the focus of the content.
3. If the temporal alignment of the theoretical events is always fixed with the full hour (which is not clear form the text, but it looks like that in Fig. 3), I strongly suggest to redo this analysis with random starting times of the events because this very likely has an effect, in particular for longer sampling intervals and (I guess) in particular for instantaneous sampling.
4. There is no differentiation between different rain rates for the analysis based on real data. But different sampling strategies might have a higher impact for heavy short duration rainfall events. Hence, it would be good to also see the differences of the sampling strategy for high rain rates. That would also allow to draw conclusion about the performance in other rainfall climates, e.g in the tropics where heavy rainfall is much more common than in Central Europe. Unfortunately, the plots in the supplementary material are cut off at 10 mm/h and are also hard to interpret for the fewer and less visible high rain rates. I suggest to add an analysis for high rain rates or for events that have a high peak rain rate (based on disdrometer data). Maybe this can be accomplished by just subsetting the data for Fig 9 to have the same figure but with data only for high rain rate events. If the authors do not want to add this analysis, they should at least discuss the impact of high rain rate events on the sampling strategies in the discussion section.

Specific comments:
L7: „…averaged values are preferred“. Why is that? Is this a conclusion of this work or from previous work?
L17: Not sure what „In this“ means here. Maybe rephrase.
L22: „…attenuation due to wet antenna not only…but also has a significant influence on the rainfall retrieval algorithm“. It is not clear to me how the wet antenna attenuation has influence on the retrieval algorithm. In what sense? Choice of parameters? Please be a bit more precise here.
L28: What is so special about this old paper Niemczynowicz (1988) that it is added here? I am not saying that it does not belong here. It is indeed impressive to look at the plots in that paper considering the computational resources available 30 years ago. Was this the first paper to do this kind of analysis? Is yes, that could also be highlighted.
L38: One main drawback of satellite products is also the latency at which they become available, in particular if they are merged products.
L48: „when considering aggregation scales that are too large for point measurements“ I find this formulation a bit confusing. Do you mean large spatial or temporal aggregation? And how is that related to points measurements? Please rephrase.
Equation 1: It seems to be more common to write k = aR^b. Hence, the authors might want to change that. But this is of course a matter of definition.
L69: Papua New Guinea is not in Africa!
L82: Why is it not preferred to keep the instantaneous data for high temporal resolution sampling for research purposes? One can always average the data later.
L90: Was one CML part of an operational network during the data collection? (Update: It is clear from text later on that it was formerly an operational CML. Maybe rephrase here.)
L109: What is the cut-off frequency of the filter of the Nokia CML? How does that affect the 20 Hz sampling? A related question is also the effect of the bandwidth of the two systems. Higher bandwidth results in higher noise in the receiver. Can this also be an effect here?
Figure 2 and related text: What is the purpose of the analysis of event duration? It is not clear from this section. If this analysis is just there to give an idea of the rainfall distribution it might also be interesting to show some other quantities (rainfall sum, q99 rain rate, …) in additional subplots (maybe just one in addition) of Fig2.
L217: „The latter two events resemble two individual events…“. I do not get why these two are individual events. Please explain and maybe rephrase in the manuscript. (Update: After reading section 2.3 I know understand. I suggest to write „…resemble the two real rain events that are studied in section 2.3)
L218: Is the noise that you are adding the same kind as the noise in the measurement data (white noise vs. more autocorrelated) and if not, why is it still valid to add the normally distributed white noise.
Section 2.3: The events start and end at the full hour. Did you also randomly adjust the temporal alignment with the full hour? It seems that this alignment could have a relevant influence when using longer aggregation times. Please comment and potentially extend your analysis in that regard.
Section 3.1: I suggest to make it clear in the section title that two individual events are analysed here for better illustration.
L240: „Yet, this does not seem to affect the computed rainfall intensity using the min-max sampling strategy.“ To which plot and which exact feature of the min-max rainfall intensity does this refer? Please explain and maybe also slightly rephrase.
Fig 6: I suggest to write „Nokia 38 GHz H“ and „RAL 26 GHz H“ in the legend so that this is consistent. That also makes it clearer just from the plot that Fig 7 shows something different (noiseless devices)
L276 to L278: I think this statements here should be refined. From Fig 6, I would say the instantaneous sampling is clearly performing worse for the theoretical evens with added noise. That could be stated here.
Fig 6: Why is there such a significantly lower R_squared for instantaneous sampling for the 26 GHz , even for 1 sec data?
Section 3.3: The title is exactly the same as in section 3.1. Please correct.
Fig 8: I suggest to add a selection of the scatter plots that are in the supplementary material to Fig 8. Maybe select the plots that are needed most for the discussion in the text. Given the space an individual scatter plot needs, one can easily fit 4 or 4x3 or maybe 3x3 into one figure. Or, since I suggest to focus on 1-minute instantaneous vs. 15-minute min-max (see my main comment) maybe add these two here.
Fig 9: If I understand correctly, the min-max results that are shown here are the ones with the optimised alpha, correct? If yes, why did you chose to show the optimised min-max results here and not the ones with the default value of alpha?
L303: What is meant with „reducing influence of the power law“ here? Do the authors mean the impact of the non-linearity of the power law, which is smaller for small attenuation values (from averaging) than for larger attenuation values? Please be more precise in this sentence.
L313: It is hard to understand this sentence. After reading it multiple times I now understand that the slope of the regression, which goes thought the origin, is below 1. But please rephrase.
L324 to 326. What is the reason for the fairly good metrics of the RAL link? Is it wet antenna that is still present at the end of the events? This is not clear from the text. (Update: After reading the paragraph starting at L330 this is now clear. The structure of the text is a bit strange here, though. It is not clear to me how the content is distributed to the different paragraphs and how the paragraphs are linked, maybe because the sentence at L330 does not make that clear. I suggest to restructure the text/paragraphs here).
L330: What is „these difference“ referring to? I checked the last sentences before, but could not find a suitable statement. Please make this clearer in the text.
L341: With „the fluctuations around the mean“ do you mean fluctuations caused by noise, or the rain-induced changes of the attenuation? Maybe it would be best to not use the term „fluctuation“ here and in the next two sentences.
L356 to L365: If I understand correctly this describes a shortcoming of the way the maximum power level is treated, in combination with how the baseline is set, resulting in overestimation during low attenuation rain events. This seems to also apply to how CML processing is done e.g. in RAINLINK. Hence, this is a very relevant detail. It is, however, hard to understand the explanation. Having a plot that support the explanation would be good. Rephrasing the text might still be required.
L381: „This shows that the performance of the sampling strategy and rainfall retrieval algorithm is largely dependent on the wet-antenna attenuation and differences in baseline power levels“. This sounds as if the significant temporal undersampling of instantaneous sampling with long intervals has a smaller effect than wet antenna and baseline power levels. Is this really the case?
General statement on Section 3.3: This section is too long and covers too many different details. I suggest to either add sub-subsection (maybe without numbering) or to split the content into more subsections. Since I also suggest (see my main comments) to add an analysis that focuses on the comparison of 15-minute-min-max with 1-minute-instantaneous (maybe in addition 30sec or 1sec), some content could be redistributed.
L421: I do not see why it should be „surprising“ that the instantaneous sampling performs well for shortest time intervals. If the sampling is done fast enough to avoid undersampling of the rain-induced signal changes, it will capture the relevant dynamics very well, albeit being more affected by instrument noise than e.g. mean sampling.
L433: „Our results are in line with Pudashine et al. (2021)…“. From Fig. 9 I conclude that mean sampling is clearly better than min-max at 15-minute sampling for correlation and RMSE (MBE is not a fair comparison because of optimised min-max). Hence, I do not see how your results are in line with their results.
L435: I do not find any analysis of the effect of quantisation in this manuscript. How can your results be in line with Ostrometzky et al. (2017)? Please elaborate also in the manuscript or remove this statement.
L445: „…likely caused by an internal filter“. This filter was mentioned already before. But how do you know that there is such a filter. Maybe the Nokia CML’s hardware is just more sophisticated with better low-noise amplifiers and/or better shielding from external disturbances?
L458: „…we do not expect this mismatch in timescales to have a significant effect“. Since shorter event will have an impact already for sampling with shorter intervals, this could have an effect on your results. You do not sample with spacing longer than 60 minutes. Hence, your theoretical rain events are longer than your longest sampling interval. Please comment and adjust accordingly.
L460: „Additionally, it would create more need to adjust for the instrumental bias.“ I do not understand what this sentence means.
L462: General comment on this paragraph. The most comprehensive and very recent comparison of different wet antenna methods is given by Pastorek et al. (2021) https://doi.org/10.1109/TGRS.2021.3110004 . This paper should be added here.
L470: „…a correction based on rainfall intensity outperformed a method based on the time…“ Graf et al (2020) used the methods that are described in this paragraph, the one from Schleiss et al (2013) and the one from Leijnse et al (2008), but with adjusted parameters.
L483: „…when using the same device as reference data.“ I do not understand what is meant here.
L491: „In general, our efforts allow future studies to focus on estimating the uncertainty of their observed rainfall intensities using microwave links and uncover the instrumental bias of these links“. I do not understand how this should be done. Maybe it is described somehow in the sentences before, but this is not clear (to me). Please rephrase, potentially also the sentences before, or add a more detailed explanation.
L494: The fact that CML lengths can be very different in a real network is mentioned here, but it is not discussed in the text below. Since increasing path length will decrease the variability of the rain-induced path-attenuation, it might have an effect on the time scales at which a sampling strategy starts to show significant decrease of performance. The study from Leijnse et al (2008), albeit using a smaller number of sampling variants, includes CML path length. I suggest to discuss the effect of path length and its interplay with sampling strategy, potentially using the results from Leijnse et al (2008) to estimate an extrapolation of your results to different path lengths.
L567: „…independent of the selected sampling strategy“. But for sampling on short intervals, wet antenna cannot have an effect in your analysis because the drying periods are considered dry based on disdrometer data. Hence, I find this statement a bit confusing. Of course, wet antenna has a „significant influence“ on the „rainfall estimates“ when compared to reference data, but this is not done in this manuscript. Please rephrase.

Technical corrections
L35: I think it would be easier to read with „radars measure…“ instead of „radar measures“.
L42: „… CMLs are deployed, of which…“ I suggest to find a better formulation here. This is hard to understand.
L45: Not sure but a comma might be required after the „thus“
L114: Maybe better write „less prone to“ instead of „prone to less“
L260: not sure, but maybe better to write „from the instruments“
L327: add „is“ after „We except that this“
L458: Better write „the two individual events studied in section 3.1“ to be clearer
L528: Remove one „with“

Citation: https://doi.org/10.5194/egusphere-2023-1971-RC2
- AC2: 'Reply on RC2', Luuk van der Valk, 05 Feb 2024
  
  Dear Reviewer,
  In the attachment, you can find our reply to your review.
  Thank you for your time and consideration.
  With kind regards,
  Luuk van der Valk, on behalf of all co-authors
  
  Citation: https://doi.org/10.5194/egusphere-2023-1971-AC2
RC3:
'Comment on egusphere-2023-1971', Anonymous Referee #3, 19 Jan 2024

The Authors investigate the impact of the temporal sampling method and on the sampling frequency on rainfall intensity estimates from microwave links. They analyse data from three different microwave links, and also set up an experiment in which they apply their retrieval algorithm to simulated rain events, in order to separate the effect of the algorithm and that of instrumental noise. I found the paper very well written, and the explanation detailed and clear. I do not have any major objections on the presented methodology. Just few very minor/editorial comments from my side:
- P2, L52: "complimentary" -> complementary
- P3, L69. Papua New Guinea is actually in Oceania. Do you actually mean Papua New Guinea or some other country (Guinea, Equatorial Guinea, Guinea Bissau) that is actually in Africa?
- P3, L77-78. Consider rephrasing as "minimum and maximum values (and occasionally mean and/or instantaneous values) are most commonly measured with a temporal resolution of 15 minutes"
- P8. L203-204. "This makes that... are different..". Consider rephrasing as "This causes the rain intensities... to be different..."
- P11, L327, "We expect that this caused..." -> "We expect that this is caused..."

Citation: https://doi.org/10.5194/egusphere-2023-1971-RC3
- AC3: 'Reply on RC3', Luuk van der Valk, 05 Feb 2024
  
  Dear Reviewer,
  In the attachment, you can find our reply to your review.
  Thank you for your time and consideration.
  With kind regards,
  Luuk van der Valk, on behalf of all co-authors
  
  Citation: https://doi.org/10.5194/egusphere-2023-1971-AC3

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2023-1971', Anonymous Referee #1, 18 Oct 2023

The paper presents an overview of the effects of different sampling techniques for microwave links for measurements of rainfall. In general, this paper presents not only the different sampling methodologies, but also gives a good overview how rainfall can be derived from (C)MLs, with the accompanying uncertainties and contains many relevant references. The information is also relevant. While the effects of temporal sampling could be suspected, as also stated by the authors, this paper gives a comprehensive discussion of these effects at different temporal resolutions.
As the paper is now it is fit for publication with some very minor changes.

Minor suggestions/remarks:
Line 45 or 57: One sentence on CML network density and changes over time and location might highlight their relevance
Line 140: Why the decision for 30 seconds? What are the effects of another threshold on your study?
Line 200: As RMSE and MBE are explained it might be good to also explain r²
Line 240: If possible more information on this filter would be beneficial. If not, it would be good to state this.
Line 242: Why more fluctuations?

Minor technical remarks:
Line 112: 'as remnant' seems a bit redundant
Figs. 4 and 5. The color between 1,s, 5min and 60min has low contrast, making it difficult to see, especially for the small figures.
Fig. 7: In the legend move 'mean' to the right column
Line 375: Also, a general

Citation: https://doi.org/10.5194/egusphere-2023-1971-RC1
- AC1: 'Reply on RC1', Luuk van der Valk, 05 Feb 2024
  
  Dear Reviewer,
  In the attachment, you can find our reply to your review.
  Thank you for your time and consideration.
  With kind regards,
  Luuk van der Valk, on behalf of all co-authors
  
  Citation: https://doi.org/10.5194/egusphere-2023-1971-AC1
RC2:
'Comment on egusphere-2023-1971', Anonymous Referee #2, 17 Jan 2024

The authors show an interesting and novel way to study the effect of different sampling strategies based on real microwave link data with a very high sampling rate of 20 Hz. Their approach is well thought out and sound. The paper is mostly nicely written, with the exception of some imprecise writing in several parts. In general the results are interesting and very well suited for AMT. The results and their interpretation do, however, lack focus and will require some restructuring and extension. In addition there might be one issue with the analysis of the theoretical events. In summary, I recommend a major revision, albeit not necessarily a large one.

Main comments:

1. There is a multitude of sampling strategies that are investigated in this manuscript. That results in a bit too many individual results of which not all are equally important. Almost all larger CML datasets do use either 15-minute min-max sampling or instantaneous sampling at 1 minute or faster (10 seconds is also common nowadays). The later does require a dedicated data acquisition system. Thus one very interesting question is, if it is worth to convince CML network operators to upgrade their data collection system to provide 1-minute instantaneous data instead of 15-minute min-max. Hence, I suggest to add a dedicated comparison of these two (or three if including 30sec or 1sec) different sampling strategies in the results and also in the discussion section. Parts of the results section could potentially also be reduced to increase the focus of the manuscript.
2. The result section 3.3 lacks focus or at least lacks structure. I suggest to add sub-subsection or to split up section 3.3. The discussion section would also be much easier to comprehend with some subsections and maybe also increasing the focus of the content.
3. If the temporal alignment of the theoretical events is always fixed with the full hour (which is not clear form the text, but it looks like that in Fig. 3), I strongly suggest to redo this analysis with random starting times of the events because this very likely has an effect, in particular for longer sampling intervals and (I guess) in particular for instantaneous sampling.
4. There is no differentiation between different rain rates for the analysis based on real data. But different sampling strategies might have a higher impact for heavy short duration rainfall events. Hence, it would be good to also see the differences of the sampling strategy for high rain rates. That would also allow to draw conclusion about the performance in other rainfall climates, e.g in the tropics where heavy rainfall is much more common than in Central Europe. Unfortunately, the plots in the supplementary material are cut off at 10 mm/h and are also hard to interpret for the fewer and less visible high rain rates. I suggest to add an analysis for high rain rates or for events that have a high peak rain rate (based on disdrometer data). Maybe this can be accomplished by just subsetting the data for Fig 9 to have the same figure but with data only for high rain rate events. If the authors do not want to add this analysis, they should at least discuss the impact of high rain rate events on the sampling strategies in the discussion section.

Specific comments:
L7: „…averaged values are preferred“. Why is that? Is this a conclusion of this work or from previous work?
L17: Not sure what „In this“ means here. Maybe rephrase.
L22: „…attenuation due to wet antenna not only…but also has a significant influence on the rainfall retrieval algorithm“. It is not clear to me how the wet antenna attenuation has influence on the retrieval algorithm. In what sense? Choice of parameters? Please be a bit more precise here.
L28: What is so special about this old paper Niemczynowicz (1988) that it is added here? I am not saying that it does not belong here. It is indeed impressive to look at the plots in that paper considering the computational resources available 30 years ago. Was this the first paper to do this kind of analysis? Is yes, that could also be highlighted.
L38: One main drawback of satellite products is also the latency at which they become available, in particular if they are merged products.
L48: „when considering aggregation scales that are too large for point measurements“ I find this formulation a bit confusing. Do you mean large spatial or temporal aggregation? And how is that related to points measurements? Please rephrase.
Equation 1: It seems to be more common to write k = aR^b. Hence, the authors might want to change that. But this is of course a matter of definition.
L69: Papua New Guinea is not in Africa!
L82: Why is it not preferred to keep the instantaneous data for high temporal resolution sampling for research purposes? One can always average the data later.
L90: Was one CML part of an operational network during the data collection? (Update: It is clear from text later on that it was formerly an operational CML. Maybe rephrase here.)
L109: What is the cut-off frequency of the filter of the Nokia CML? How does that affect the 20 Hz sampling? A related question is also the effect of the bandwidth of the two systems. Higher bandwidth results in higher noise in the receiver. Can this also be an effect here?
Figure 2 and related text: What is the purpose of the analysis of event duration? It is not clear from this section. If this analysis is just there to give an idea of the rainfall distribution it might also be interesting to show some other quantities (rainfall sum, q99 rain rate, …) in additional subplots (maybe just one in addition) of Fig2.
L217: „The latter two events resemble two individual events…“. I do not get why these two are individual events. Please explain and maybe rephrase in the manuscript. (Update: After reading section 2.3 I know understand. I suggest to write „…resemble the two real rain events that are studied in section 2.3)
L218: Is the noise that you are adding the same kind as the noise in the measurement data (white noise vs. more autocorrelated) and if not, why is it still valid to add the normally distributed white noise.
Section 2.3: The events start and end at the full hour. Did you also randomly adjust the temporal alignment with the full hour? It seems that this alignment could have a relevant influence when using longer aggregation times. Please comment and potentially extend your analysis in that regard.
Section 3.1: I suggest to make it clear in the section title that two individual events are analysed here for better illustration.
L240: „Yet, this does not seem to affect the computed rainfall intensity using the min-max sampling strategy.“ To which plot and which exact feature of the min-max rainfall intensity does this refer? Please explain and maybe also slightly rephrase.
Fig 6: I suggest to write „Nokia 38 GHz H“ and „RAL 26 GHz H“ in the legend so that this is consistent. That also makes it clearer just from the plot that Fig 7 shows something different (noiseless devices)
L276 to L278: I think this statements here should be refined. From Fig 6, I would say the instantaneous sampling is clearly performing worse for the theoretical evens with added noise. That could be stated here.
Fig 6: Why is there such a significantly lower R_squared for instantaneous sampling for the 26 GHz , even for 1 sec data?
Section 3.3: The title is exactly the same as in section 3.1. Please correct.
Fig 8: I suggest to add a selection of the scatter plots that are in the supplementary material to Fig 8. Maybe select the plots that are needed most for the discussion in the text. Given the space an individual scatter plot needs, one can easily fit 4 or 4x3 or maybe 3x3 into one figure. Or, since I suggest to focus on 1-minute instantaneous vs. 15-minute min-max (see my main comment) maybe add these two here.
Fig 9: If I understand correctly, the min-max results that are shown here are the ones with the optimised alpha, correct? If yes, why did you chose to show the optimised min-max results here and not the ones with the default value of alpha?
L303: What is meant with „reducing influence of the power law“ here? Do the authors mean the impact of the non-linearity of the power law, which is smaller for small attenuation values (from averaging) than for larger attenuation values? Please be more precise in this sentence.
L313: It is hard to understand this sentence. After reading it multiple times I now understand that the slope of the regression, which goes thought the origin, is below 1. But please rephrase.
L324 to 326. What is the reason for the fairly good metrics of the RAL link? Is it wet antenna that is still present at the end of the events? This is not clear from the text. (Update: After reading the paragraph starting at L330 this is now clear. The structure of the text is a bit strange here, though. It is not clear to me how the content is distributed to the different paragraphs and how the paragraphs are linked, maybe because the sentence at L330 does not make that clear. I suggest to restructure the text/paragraphs here).
L330: What is „these difference“ referring to? I checked the last sentences before, but could not find a suitable statement. Please make this clearer in the text.
L341: With „the fluctuations around the mean“ do you mean fluctuations caused by noise, or the rain-induced changes of the attenuation? Maybe it would be best to not use the term „fluctuation“ here and in the next two sentences.
L356 to L365: If I understand correctly this describes a shortcoming of the way the maximum power level is treated, in combination with how the baseline is set, resulting in overestimation during low attenuation rain events. This seems to also apply to how CML processing is done e.g. in RAINLINK. Hence, this is a very relevant detail. It is, however, hard to understand the explanation. Having a plot that support the explanation would be good. Rephrasing the text might still be required.
L381: „This shows that the performance of the sampling strategy and rainfall retrieval algorithm is largely dependent on the wet-antenna attenuation and differences in baseline power levels“. This sounds as if the significant temporal undersampling of instantaneous sampling with long intervals has a smaller effect than wet antenna and baseline power levels. Is this really the case?
General statement on Section 3.3: This section is too long and covers too many different details. I suggest to either add sub-subsection (maybe without numbering) or to split the content into more subsections. Since I also suggest (see my main comments) to add an analysis that focuses on the comparison of 15-minute-min-max with 1-minute-instantaneous (maybe in addition 30sec or 1sec), some content could be redistributed.
L421: I do not see why it should be „surprising“ that the instantaneous sampling performs well for shortest time intervals. If the sampling is done fast enough to avoid undersampling of the rain-induced signal changes, it will capture the relevant dynamics very well, albeit being more affected by instrument noise than e.g. mean sampling.
L433: „Our results are in line with Pudashine et al. (2021)…“. From Fig. 9 I conclude that mean sampling is clearly better than min-max at 15-minute sampling for correlation and RMSE (MBE is not a fair comparison because of optimised min-max). Hence, I do not see how your results are in line with their results.
L435: I do not find any analysis of the effect of quantisation in this manuscript. How can your results be in line with Ostrometzky et al. (2017)? Please elaborate also in the manuscript or remove this statement.
L445: „…likely caused by an internal filter“. This filter was mentioned already before. But how do you know that there is such a filter. Maybe the Nokia CML’s hardware is just more sophisticated with better low-noise amplifiers and/or better shielding from external disturbances?
L458: „…we do not expect this mismatch in timescales to have a significant effect“. Since shorter event will have an impact already for sampling with shorter intervals, this could have an effect on your results. You do not sample with spacing longer than 60 minutes. Hence, your theoretical rain events are longer than your longest sampling interval. Please comment and adjust accordingly.
L460: „Additionally, it would create more need to adjust for the instrumental bias.“ I do not understand what this sentence means.
L462: General comment on this paragraph. The most comprehensive and very recent comparison of different wet antenna methods is given by Pastorek et al. (2021) https://doi.org/10.1109/TGRS.2021.3110004 . This paper should be added here.
L470: „…a correction based on rainfall intensity outperformed a method based on the time…“ Graf et al (2020) used the methods that are described in this paragraph, the one from Schleiss et al (2013) and the one from Leijnse et al (2008), but with adjusted parameters.
L483: „…when using the same device as reference data.“ I do not understand what is meant here.
L491: „In general, our efforts allow future studies to focus on estimating the uncertainty of their observed rainfall intensities using microwave links and uncover the instrumental bias of these links“. I do not understand how this should be done. Maybe it is described somehow in the sentences before, but this is not clear (to me). Please rephrase, potentially also the sentences before, or add a more detailed explanation.
L494: The fact that CML lengths can be very different in a real network is mentioned here, but it is not discussed in the text below. Since increasing path length will decrease the variability of the rain-induced path-attenuation, it might have an effect on the time scales at which a sampling strategy starts to show significant decrease of performance. The study from Leijnse et al (2008), albeit using a smaller number of sampling variants, includes CML path length. I suggest to discuss the effect of path length and its interplay with sampling strategy, potentially using the results from Leijnse et al (2008) to estimate an extrapolation of your results to different path lengths.
L567: „…independent of the selected sampling strategy“. But for sampling on short intervals, wet antenna cannot have an effect in your analysis because the drying periods are considered dry based on disdrometer data. Hence, I find this statement a bit confusing. Of course, wet antenna has a „significant influence“ on the „rainfall estimates“ when compared to reference data, but this is not done in this manuscript. Please rephrase.

Technical corrections
L35: I think it would be easier to read with „radars measure…“ instead of „radar measures“.
L42: „… CMLs are deployed, of which…“ I suggest to find a better formulation here. This is hard to understand.
L45: Not sure but a comma might be required after the „thus“
L114: Maybe better write „less prone to“ instead of „prone to less“
L260: not sure, but maybe better to write „from the instruments“
L327: add „is“ after „We except that this“
L458: Better write „the two individual events studied in section 3.1“ to be clearer
L528: Remove one „with“

Citation: https://doi.org/10.5194/egusphere-2023-1971-RC2
- AC2: 'Reply on RC2', Luuk van der Valk, 05 Feb 2024
  
  Dear Reviewer,
  In the attachment, you can find our reply to your review.
  Thank you for your time and consideration.
  With kind regards,
  Luuk van der Valk, on behalf of all co-authors
  
  Citation: https://doi.org/10.5194/egusphere-2023-1971-AC2
RC3:
'Comment on egusphere-2023-1971', Anonymous Referee #3, 19 Jan 2024

The Authors investigate the impact of the temporal sampling method and on the sampling frequency on rainfall intensity estimates from microwave links. They analyse data from three different microwave links, and also set up an experiment in which they apply their retrieval algorithm to simulated rain events, in order to separate the effect of the algorithm and that of instrumental noise. I found the paper very well written, and the explanation detailed and clear. I do not have any major objections on the presented methodology. Just few very minor/editorial comments from my side:
- P2, L52: "complimentary" -> complementary
- P3, L69. Papua New Guinea is actually in Oceania. Do you actually mean Papua New Guinea or some other country (Guinea, Equatorial Guinea, Guinea Bissau) that is actually in Africa?
- P3, L77-78. Consider rephrasing as "minimum and maximum values (and occasionally mean and/or instantaneous values) are most commonly measured with a temporal resolution of 15 minutes"
- P8. L203-204. "This makes that... are different..". Consider rephrasing as "This causes the rain intensities... to be different..."
- P11, L327, "We expect that this caused..." -> "We expect that this is caused..."

Citation: https://doi.org/10.5194/egusphere-2023-1971-RC3
- AC3: 'Reply on RC3', Luuk van der Valk, 05 Feb 2024
  
  Dear Reviewer,
  In the attachment, you can find our reply to your review.
  Thank you for your time and consideration.
  With kind regards,
  Luuk van der Valk, on behalf of all co-authors
  
  Citation: https://doi.org/10.5194/egusphere-2023-1971-AC3

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Luuk van der Valk on behalf of the Authors (05 Feb 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (06 Feb 2024) by Gianfranco Vulpiani

RR by Anonymous Referee #2 (26 Feb 2024)

Suggestions for revision or reasons for rejection

The authors have done a thorough revision and have responded to all my comments. Following one of my main comments, they have extended the analysis of the theoretical events. For the cases where the authors did not follow my recommendation, they provided reasonable explanations. I only have some minor comments which I think the authors can address without the need for another round of reviews. Note that my comments are mostly suggestions, which I think would be beneficial for the manuscript, but there is no strict need to follow them.

Line numbers refer to the track-changes version.

General comments:

1. I appreciate that the authors have added markers to certain figures to highlight 1-minute instantaneous and 15-min min-max sampling. I do find the markers a bit too large, though. Maybe there was a reason to use the large crosses as markers. But smaller makers, maybe with a thiner edge and maybe some transparency could mitigate the overplotting that is unavoidable in the figures. Or maybe you could give the individual markers a small horizontal offset. Or maybe use three different maker types?

2. Reading through the paper and looking at the (updated) plots I am again automatically concentrating mostly on a comparison between 1-minute instantaneous and 15-minute min-max. I understand that the authors want to provide, as they wrote in their response letter, a systematic overview of the consequences of different sampling strategies. However, as I already stated in my last review, there is significant importance to the comparison between 1-minutes instantaneous and 15-minutes min-max. There is still not a dedicated discussion on this, even though some figures have now been updated to mark these two different sampling strategies. Since I was again dedicatedly looking for this information, I have two suggestions:
2a: It would be beneficial to have a short (sub-)subsection in section 3 or 4 to discuss the comparison of 1-minute instantaneous and 15-minute min-max.
2b. It would be beneficial to add a version of Fig 5 (and also Fig 4) to the supplementary material that only shows 20 Hz, 1-minute instantaneous and 15-minute min-max, maybe also 1-second instantaneous because some CML data is available at 10-second resolution and higher resolution data might become available the future. If you use separate columns with one line each, you could add the 20 Hz data always in the background.

3. The new results in Fig 8 are interesting and well described. However, I found it complicated to visually compare the results to Fig 7 and Fig 6 to understand how the temporal shift affects performance compared to adding noise. Since the colors are the same but with different meaning in Fig 8, and since the x axis is linear instead of log in Fig 8, it requires some effort to detect differences. I wonder if this could be improved, but I do not have a solution. Maybe an easy fix could be to add data from Fig 6 or Fig 7 with a very light color in the background. But this could also make the plot too busy.

Specific comments:

Fig 6: The updated information in the text clearly explains why R_2 is so low for the low intensity event. But why is this not happening in Fig 10? I assume that most rainfall in the real dataset comes at low intensities, hence R_2 is most likely dominated by these low rainfall intensities. But at 1-minute instantaneous sampling there is only a very small difference between RAL 26 and RAL 38 in Fig 10, even though RAL 26 has a high noise level relative to the rain-induced attenuation (as you describe in your updated text related to Fig 6). It would be good to explain this behavior because, from Fig 6, one concludes that the (relative) noisiness of RAL 26 has a significant impact, while for the statistics from the real dataset in Fig 10 one would not draw that conclusion. Maybe wet antenna increases the attenuation in the real data so that low attenuation during low rainfall is less often smaller than zero (which happens for the theoretical events due to added noise)?

L284: „…instantaneous and min-max sampling strategies seem to be more prone to errors in retrieving high rainfall intensities…“ Some lines below you write that instantaneous sampling is good in capturing the peaks intensities. This is also what I would get from Fig 5, of course not for 60-minute aggregation. But at 5-minute sampling the height of the second peak is, surprisingly, best captured with instantaneous sampling. Maybe this is a general tendency because the mean can easily get biased towards underestimation, as you write elsewhere. But I am not sure if this is the reason here.

L289: What is meant with „signal-to-noise“ ratio here in the context of comparing instantaneous with the other sampling methods?

L290: Which „sensitivity“ increases with larger time intervals?

L587-L591: What about shorter link length? Of course, one expects the opposite of what happens for longer link lengths (which is described in the new text). But given that it has been reported that very short instantaneously sampled CMLs (with lengths of hundreds of meters or even only tens of meters) are prone to overestimation of rain rates, can you make a statement on the question if instantaneous sampling is a potential reason for this overestimation and not (only) the wet antenna estimation (which is undoubtedly a large source of error for very short and thus insensitive CMLs)? If I assume that the positive MBE of instantaneous sampling around 5-minutes in Fig 10 is shifted to the left (maybe to 30-s or below) for very short CMLs, that could be the case.

Hide

ED: Publish subject to minor revisions (review by editor) (29 Feb 2024) by Gianfranco Vulpiani

AR by Luuk van der Valk on behalf of the Authors (14 Mar 2024) Author's response Author's tracked changes Manuscript

ED: Publish as is (25 Mar 2024) by Gianfranco Vulpiani

AR by Luuk van der Valk on behalf of the Authors (25 Mar 2024)

Journal article(s) based on this preprint

08 May 2024

Measuring rainfall using microwave links: the influence of temporal sampling

Luuk D. van der Valk, Miriam Coenders-Gerrits, Rolf W. Hut, Aart Overeem, Bas Walraven, and Remko Uijlenhoet

Atmos. Meas. Tech., 17, 2811–2832, https://doi.org/10.5194/amt-17-2811-2024,https://doi.org/10.5194/amt-17-2811-2024, 2024

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Luuk D. van der Valk, Miriam Coenders-Gerrits, Rolf W. Hut, Aart Overeem, Bas Walraven, and Remko Uijlenhoet

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https://doi.org/10.5194/egusphere-2023-1971-supplement

Luuk D. van der Valk, Miriam Coenders-Gerrits, Rolf W. Hut, Aart Overeem, Bas Walraven, and Remko Uijlenhoet

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Microwave links, often part of mobile phone networks, can be used to measure rainfall along the link path by determining the signal loss caused by rainfall. We use high-frequency data of multiple microwave links to recreate commonly used sampling strategies. For time intervals up to 1 min, the influence of sampling strategies on estimated rainfall intensities is relatively little, while for intervals longer than 5–15 min, the sampling strategy can have significant influences on the estimates.


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