the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Number and sizecontrolled rainfall regimes in the Netherlands: physical reality or statistical mirage?
Abstract. An experimental study aimed at identifying special rainfall regimes with the help of colocated disdrometers is performed. Eight potentially special events (i.e., 4 numbercontrolled events and 4 sizecontrolled events) are identified and examined. However, the crosscheck with additional, independent radar measurements reveals no clear evidence of such regimes. The research underscores the difficulty in confirming seemingly straightforward questions about rainfall patterns and dynamics that have been theorized in the literature for several decades. It also questions the reliability of previous claims and serves as a reminder to approach such problems with more caution, emphasizing the need for rigorous uncertainty analysis and multiple crosschecks between sensors to avoid misinterpretation.
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Status: closed

RC1: 'Comment on egusphere20232807', Anonymous Referee #1, 25 Jan 2024
This is a well written manuscript describing the analysis of Parsivel disdrometer data and micro rain radar (MRR) data to identify and characterize rain regimes known as “numbercontrolled” or “size controlled”. I found the manuscript easy to read and the analysis steps clearly described.
I have one question and one recommendation before publishing this manuscript.
1. Page 14, Figure 7. What are the vertical lines in Figure 7? Is that another dataset? If it is a dashed line connecting the individual circles, the dashed line is not needed (and is distracting).
2. A reviewer pointed out to me many years ago that since analysis of disdrometer data involves discrete measurements with quantized values, the equations should not contain integrals but summations. The integrals are not correct because the drop diameters reach a maximum measured value of Dmax and are not infinite. Thus, I recommend changing the integrals in lines 13 and 14, and in equations (2) and (3) to summations. This would also allow the addition of quantized data into the discussion of error sources.
Citation: https://doi.org/10.5194/egusphere20232807RC1 
AC1: 'Reply on RC1', Marc Schleiss, 28 Mar 2024
1. Page 14, Figure 7. What are the vertical lines in Figure 7? Is that another dataset? If it is a dashed line connecting the individual circles, the dashed line is not needed (and is distracting).
Response: The lines are used to connect the data points over time. They are not really needed and I can remove them during the revision.
2. Disdrometer data involve discrete measurements with quantized values. Therefore, the equations should not contain integrals but summations. The integrals are not correct because the drop diameters reach a maximum measured value of Dmax and are not infinite. Thus, I recommend changing the integrals in lines 13 and 14, and in equations (2) and (3) to summations. This would also allow the addition of quantized data into the discussion of error sources.
Response: Good point. Indeed, the paper currently does not distinguish between the theoretical quantities expressed as integrals and the sample estimates calculated from discretized disdrometer data. I will add some information about this in the revised paper (in the Methodology), and provide the equations for explaining how the sample estimates of Nt, Dm and R are derived (using sums rather than integrals). I will also and some sentences in the results and discussion sections to mention that these quantization issues are part of what I call the “overall sampling uncertainty”.
Citation: https://doi.org/10.5194/egusphere20232807AC1

AC1: 'Reply on RC1', Marc Schleiss, 28 Mar 2024

RC2: 'Comment on egusphere20232807', Anonymous Referee #2, 12 Feb 2024
The Authors proposed a new method to identify special rainfall regimes (i.e. numbercontrolled and sizecontrolled regimes). The paper is well written however I have some major issues:
 It is not clear the importance/scope of identifying these kind of rainfall regimes. Or in order words, why this study has been performed? Please clarify better in the introduction.
 The obtained results show that within the considered dataset the proposed method is not able to identify clearly numbercontrolled or sizecontrolled regimes. The latter can be highly due to the fact that the considered precipitation intensities are too low (as stated also by the Author) but can be also highly influenced by the adopted method (section 3.5). The adopted criteria are based on some kind of assumption/considerations? How can the Author be sure that adopting different threshold the results are the same? This can be the key of the problem.
 In section 4.6 the Author stated that also the drop fall velocity (v(D)) can have an influence on the results. Which fall velocity has been used to compute the DSD (i.e. measured or theoretical)? Probably the use of experimental/theoretical v(D) relation can help in limit the effect of the fall velocity on the results.
MINOR COMMENTS
 Table 1: explain the meaning of Ta, Td, Wa
 Section 4.3: The ZR relations can be obtained also from disdrometer data in order to see if these results are in agreement with the ones obtained by the method proposed in the paper.
Citation: https://doi.org/10.5194/egusphere20232807RC2 
AC2: 'Reply on RC2', Marc Schleiss, 28 Mar 2024
 The importance/scope of identifying these kind of rainfall regimes is not clear. In other words, why was this study performed? Please clarify better in the introduction.
Response: Section 1.2 (page 3) already clearly explains why this study has been performed but I agree with the reviewer that the importance/scope of these regimes could still be explained in more detail. I will add a short paragraph in the Introduction to explain why number and sizecontrolled regimes are interesting. From a theoretical point of view, these regimes are important for a) understanding rainfall microphysics, b) formulating DSD models and scaling laws between rainfallintegral parameters, and c) studying the spacetime variability of DSDs in rain. From a practical point of view, the ability to identify and diagnose special regimes could be useful to 1) improve quantitative precipitation estimation algorithms by constraining the prefactor and exponent in the ZR relationship, 2) reduce the number of independent parameters in DSD parameters retrievals from weather radar and 3) improve the statistical modeling of the cofluctuations between raindrop number concentrations and raindrop size distributions in stochastic rainfall simulators.
 The obtained results show that within the considered dataset the proposed method is not able to identify clearly numbercontrolled or sizecontrolled regimes. The latter can be highly due to the fact that the considered precipitation intensities are too low (as stated also by the Author) but can be also highly influenced by the adopted method (section 3.5). The adopted criteria are based on some kind of assumption/considerations? How can the Author be sure that adopting different threshold the results are the same? This can be the key of the problem.
Response: All of the assumptions/choices underlying the methodology are critically discussed in Sections 4.4, 4.5 and 4.6. In addition to the presented work, I also clearly state that other thresholds, time windows and statistical metrics were considered. However, in all of these additional experiments, the main conclusion remained the same: there was no compelling evidence of a pure number or sizecontrolled rainfall regime in the considered dataset. Obviously, this does not mean that special regimes do not exist. Special meteorological conditions that do not occur in the Netherlands may be required for them to occur. Or perhaps, the data record is not long enough. On the other hand, the study also shows that it would still be very hard to experimentally confirm such regimes with the help of disdrometers, especially if they are very short.
 In section 4.6 the Author stated that also the drop fall velocity v(D) can have an influence on the results. Which fall velocity has been used to compute the DSD (i.e. measured or theoretical)? Probably the use of experimental/theoretical v(D) relation can help in limit the effect of the fall velocity on the results.
Response: Yes, the fall velocity of the raindrops is a problem. The definition of number and sizecontrolled regimes implicitly assumes a deterministic relationship between the size and velocity of a raindrop. However, this is hardly the case in reality. Due to turbulence, collisions and breakup, it is better to represent the fall velocity of a raindrop by a random variable. Experimental data shows that the spread of this random variable can be rather large, especially for small drops or in convective events. This is a problem because it means that even if the drop size distribution would be stationary, the rainfall rate could still fluctuate over time due to random changes in the fall velocities of raindrops. To mitigate this effect, I used a theoretical, deterministic fall velocity model proposed by Beard (1976) to calculate the rainfall rates. This will be explained in more detail in the revised text. Also, a new equation for how to estimate R from discretized disdrometer data will be added (see comment 2, reviewer 1).
 Table 1: explain the meaning of Ta, Td, Ws
Response: No problem. They are the air temperature, dew point temperature and wind speed. I’ll add the information to the caption during revision.
 Section 4.3: The ZR relations can be obtained also from disdrometer data in order to see if these results are in agreement with the ones obtained by the method proposed in the paper.
Response: I could calculate them but unfortunately the 1min sampling resolution of the disdrometer makes it impossible to reliably estimate the ZR relationship over such short time windows. I can get some estimates but the confidence intervals would be enormous, and it wouldn't add much to the discussion.
Citation: https://doi.org/10.5194/egusphere20232807AC2
Status: closed

RC1: 'Comment on egusphere20232807', Anonymous Referee #1, 25 Jan 2024
This is a well written manuscript describing the analysis of Parsivel disdrometer data and micro rain radar (MRR) data to identify and characterize rain regimes known as “numbercontrolled” or “size controlled”. I found the manuscript easy to read and the analysis steps clearly described.
I have one question and one recommendation before publishing this manuscript.
1. Page 14, Figure 7. What are the vertical lines in Figure 7? Is that another dataset? If it is a dashed line connecting the individual circles, the dashed line is not needed (and is distracting).
2. A reviewer pointed out to me many years ago that since analysis of disdrometer data involves discrete measurements with quantized values, the equations should not contain integrals but summations. The integrals are not correct because the drop diameters reach a maximum measured value of Dmax and are not infinite. Thus, I recommend changing the integrals in lines 13 and 14, and in equations (2) and (3) to summations. This would also allow the addition of quantized data into the discussion of error sources.
Citation: https://doi.org/10.5194/egusphere20232807RC1 
AC1: 'Reply on RC1', Marc Schleiss, 28 Mar 2024
1. Page 14, Figure 7. What are the vertical lines in Figure 7? Is that another dataset? If it is a dashed line connecting the individual circles, the dashed line is not needed (and is distracting).
Response: The lines are used to connect the data points over time. They are not really needed and I can remove them during the revision.
2. Disdrometer data involve discrete measurements with quantized values. Therefore, the equations should not contain integrals but summations. The integrals are not correct because the drop diameters reach a maximum measured value of Dmax and are not infinite. Thus, I recommend changing the integrals in lines 13 and 14, and in equations (2) and (3) to summations. This would also allow the addition of quantized data into the discussion of error sources.
Response: Good point. Indeed, the paper currently does not distinguish between the theoretical quantities expressed as integrals and the sample estimates calculated from discretized disdrometer data. I will add some information about this in the revised paper (in the Methodology), and provide the equations for explaining how the sample estimates of Nt, Dm and R are derived (using sums rather than integrals). I will also and some sentences in the results and discussion sections to mention that these quantization issues are part of what I call the “overall sampling uncertainty”.
Citation: https://doi.org/10.5194/egusphere20232807AC1

AC1: 'Reply on RC1', Marc Schleiss, 28 Mar 2024

RC2: 'Comment on egusphere20232807', Anonymous Referee #2, 12 Feb 2024
The Authors proposed a new method to identify special rainfall regimes (i.e. numbercontrolled and sizecontrolled regimes). The paper is well written however I have some major issues:
 It is not clear the importance/scope of identifying these kind of rainfall regimes. Or in order words, why this study has been performed? Please clarify better in the introduction.
 The obtained results show that within the considered dataset the proposed method is not able to identify clearly numbercontrolled or sizecontrolled regimes. The latter can be highly due to the fact that the considered precipitation intensities are too low (as stated also by the Author) but can be also highly influenced by the adopted method (section 3.5). The adopted criteria are based on some kind of assumption/considerations? How can the Author be sure that adopting different threshold the results are the same? This can be the key of the problem.
 In section 4.6 the Author stated that also the drop fall velocity (v(D)) can have an influence on the results. Which fall velocity has been used to compute the DSD (i.e. measured or theoretical)? Probably the use of experimental/theoretical v(D) relation can help in limit the effect of the fall velocity on the results.
MINOR COMMENTS
 Table 1: explain the meaning of Ta, Td, Wa
 Section 4.3: The ZR relations can be obtained also from disdrometer data in order to see if these results are in agreement with the ones obtained by the method proposed in the paper.
Citation: https://doi.org/10.5194/egusphere20232807RC2 
AC2: 'Reply on RC2', Marc Schleiss, 28 Mar 2024
 The importance/scope of identifying these kind of rainfall regimes is not clear. In other words, why was this study performed? Please clarify better in the introduction.
Response: Section 1.2 (page 3) already clearly explains why this study has been performed but I agree with the reviewer that the importance/scope of these regimes could still be explained in more detail. I will add a short paragraph in the Introduction to explain why number and sizecontrolled regimes are interesting. From a theoretical point of view, these regimes are important for a) understanding rainfall microphysics, b) formulating DSD models and scaling laws between rainfallintegral parameters, and c) studying the spacetime variability of DSDs in rain. From a practical point of view, the ability to identify and diagnose special regimes could be useful to 1) improve quantitative precipitation estimation algorithms by constraining the prefactor and exponent in the ZR relationship, 2) reduce the number of independent parameters in DSD parameters retrievals from weather radar and 3) improve the statistical modeling of the cofluctuations between raindrop number concentrations and raindrop size distributions in stochastic rainfall simulators.
 The obtained results show that within the considered dataset the proposed method is not able to identify clearly numbercontrolled or sizecontrolled regimes. The latter can be highly due to the fact that the considered precipitation intensities are too low (as stated also by the Author) but can be also highly influenced by the adopted method (section 3.5). The adopted criteria are based on some kind of assumption/considerations? How can the Author be sure that adopting different threshold the results are the same? This can be the key of the problem.
Response: All of the assumptions/choices underlying the methodology are critically discussed in Sections 4.4, 4.5 and 4.6. In addition to the presented work, I also clearly state that other thresholds, time windows and statistical metrics were considered. However, in all of these additional experiments, the main conclusion remained the same: there was no compelling evidence of a pure number or sizecontrolled rainfall regime in the considered dataset. Obviously, this does not mean that special regimes do not exist. Special meteorological conditions that do not occur in the Netherlands may be required for them to occur. Or perhaps, the data record is not long enough. On the other hand, the study also shows that it would still be very hard to experimentally confirm such regimes with the help of disdrometers, especially if they are very short.
 In section 4.6 the Author stated that also the drop fall velocity v(D) can have an influence on the results. Which fall velocity has been used to compute the DSD (i.e. measured or theoretical)? Probably the use of experimental/theoretical v(D) relation can help in limit the effect of the fall velocity on the results.
Response: Yes, the fall velocity of the raindrops is a problem. The definition of number and sizecontrolled regimes implicitly assumes a deterministic relationship between the size and velocity of a raindrop. However, this is hardly the case in reality. Due to turbulence, collisions and breakup, it is better to represent the fall velocity of a raindrop by a random variable. Experimental data shows that the spread of this random variable can be rather large, especially for small drops or in convective events. This is a problem because it means that even if the drop size distribution would be stationary, the rainfall rate could still fluctuate over time due to random changes in the fall velocities of raindrops. To mitigate this effect, I used a theoretical, deterministic fall velocity model proposed by Beard (1976) to calculate the rainfall rates. This will be explained in more detail in the revised text. Also, a new equation for how to estimate R from discretized disdrometer data will be added (see comment 2, reviewer 1).
 Table 1: explain the meaning of Ta, Td, Ws
Response: No problem. They are the air temperature, dew point temperature and wind speed. I’ll add the information to the caption during revision.
 Section 4.3: The ZR relations can be obtained also from disdrometer data in order to see if these results are in agreement with the ones obtained by the method proposed in the paper.
Response: I could calculate them but unfortunately the 1min sampling resolution of the disdrometer makes it impossible to reliably estimate the ZR relationship over such short time windows. I can get some estimates but the confidence intervals would be enormous, and it wouldn't add much to the discussion.
Citation: https://doi.org/10.5194/egusphere20232807AC2
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