Estimation of extreme precipitations in Estonia and Italy using dual-pol weather radar QPEs

Cremonini, Roberto; Voormansik, Tanel; Post, Piia; Moisseev, Dmitri

doi:https://doi.org/10.5194/amt-2022-220

Preprints

https://doi.org/10.5194/amt-2022-220

Preprints

05 Aug 2022

| 05 Aug 2022

Status: a revised version of this preprint was accepted for the journal AMT and is expected to appear here in due course.

Estimation of extreme precipitations in Estonia and Italy using dual-pol weather radar QPEs

Roberto Cremonini, Tanel Voormansik, Piia Post, and Dmitri Moisseev

Abstract. Climatology of extreme rainfalls for a certain location is commonly taken into account designing stormwater management systems. Rain gauge data have often been used to estimate rainfall intensity for a given return period. However, the poor spatial and temporal resolution of operational gauges is the main limiting factor. Several studies have used rainfall estimates based on weather radar horizontal reflectivity (Z_h), but they come with a significant caveat: while proven reliable on low or moderate rainfall rates, they are subject to major errors in extreme rainfall and convective cases. It is widely known that C-band weather radar can both underestimate precipitation intensity due to signal attenuation or overestimate it due to hail and clutter contamination. This study circumvents these shortcomings by using specific differential phase (K_dp) data from dual-polarization C-band weather radars. The rain intensity estimates based on specific differential phase are immune to attenuation and affected less by hail contamination.

This study aims to estimate depth-duration-frequency (DDF) curves computed using polarimetric weather radar data using quantitative precipitation estimations (QPEs) based on K_dp data and to compare the results with the DDF curves derived using rain-gauge data. Only the warm period of the year is here considered, as most of the extreme precipitation events take place at this time. Limiting the dataset to warm period also allows us to use the radar-based rainfall quantitative precipitation estimates, which are more reliable than the snowfall ones. Single C-band polarimetric weather radar site data are used both from Italy and Estonia. This study demonstrates that polarimetric weather radar observations can provide reliable QPEs compared to rain gauges and, that even relatively short time series can provide a reliable estimation of the rainfall return periods in climatological homogeneous areas.

Received: 23 Jul 2022 – Discussion started: 05 Aug 2022

Roberto Cremonini et al.

Status: closed

RC1:
'Comment on amt-2022-220', Anonymous Referee #1, 19 Sep 2022
This paper presents the first application of extreme value statistics to precipitation estimates based on dual polarisation (dual-pol) weather radar. The topic is relevant to the community and to the readers of this journal, and the contribution is timely because dual-pol technology have been shown to improve radar precipitation estimates but extreme value statistics from such data were so far limited by the lack of sufficiently long records of dual-pol observations.

However, I highlight some aspects that need revisions before this study is considered for publication. These revisions may alter the overall results and conclusions of the study.

Major comments:

The study makes use of strong assumptions on the homogeneity of the extreme precipitation statistics field: all the three parameters of the GEV distribution used to represent the annual maxima are assumed to be uniform within the examined areas. This clearly helps with the problem of parameter estimation. However, while the authors carefully address the issue of independence in the used data, they completely neglect the homogeneity assumption. This homogeneity assumption is quite strong for today’s research and practice standards and is not supported by specific tests/analyses. Spatial variations of precipitation statistics at scales smaller than the examined domains are known and reported in a number of previous studies based on both rain gauge and weather radar data (e.g., https://doi.org/10.1088/1748-9326/ab98b4; https://doi.org/10.5194/hess-26-1659-2022; https://doi.org/10.5194/hess-26-1439-2022). Neglecting the presence of spatial variations in the extreme precipitation statistics violates the identical distribution assumption of the extreme value theorem which underlies the adopted approach. Ultimately, this may lead to erroneous estimates of the parameters (samples from different distributions are mixed) and misleading evaluations of their uncertainty (the large number of data points will lead to small uncertainties, as shown in table 1). Alternative approaches in which only some of the parameters are homogeneous and the others are location-dependent (often referred to as regionalisation approaches) are available (e.g., https://doi.org/10.1080/0262666910949251) and are expected to provide results with comparable levels of uncertainty but higher accuracy. Studies based on weather radar or satellite data using such approaches are available in literature (e.g., see https://doi.org/10.1016/j.jhydrol.2019.04.081).

A proper benchmarking of the results of this study with respect to results based on single-pol measurements is missing. Many studies about the analysis of extreme precipitation statistics from single-pol weather radars are not discussed in the introduction. As a consequence the key scientific questions underpinning this study are not well presented and leave the reader with questions like: why do we need to use dual-pol technology for these applications? what are the expected advantages over single-pol? what kind of uncertainties/errors were found in previous results based on single-pol? is dual-pol able to reduce such uncertainties/errors?

Although some concepts about extreme value theory are presented in a reasonable way in lines 219-225, the manuscript misrepresents many key concepts. Section 2.1.1 in particular should be rewritten

The manuscript is not optimally organised. The results section contains large parts with methodological aspects and the discussion section contains main results rather than discussion.

The main objectives and results should be better stated in the abstract and text. The last sentence of the abstract lists two main results reached by the study as (a) “weather radar observations can provide a reliable QPEs compared to rain gauges” and (b) “even relatively short time series can provide reliable estimation of the rainfall return periods in climatological homogeneous areas”. However, point (a) is a result already addressed by previous literature (also listed in the introduction) and is not actually directly presented as a main result of this paper. Additionally, the study comes short at addressing point (b), because of an improper application of methods for extreme value analyses (see comment 1) and because it lacks a benchmarking of the results against single-polarisation data, neither from the radars used in this study nor from previous studies based on single polarisation technology (see comment 2). The natural question raised by the title and abstract of the paper “can dual-pol estimates improve our quantification of extreme precipitation probability with respect to single-pol estimates?” is not answered by the study.

Minor comments:

line 14-15: “Single C-band polarimetric…” this sentence is not clear

line 19-27: it is weird to start the manuscript with text about climate change when the study assumes stationarity and does not provide any further result or discussion about changes

lines 32 and line 41: the reference to Peleg et al 2016 is a bit misplaced as these authors only focused on one radar pixel. Other more relevant studies could help detailing the state of the art (see above some suggestions among many). Also note that the correct citation is Peleg et al. 2018

lines 37-48: this part is a bit confusing, please rephrase it

Figures 1 and 2: I think these two figures could be merged. The quality of the figure should be improved, for instance using similar graphics and symbols

The division of the Italian domain into two areas tries to address the homogeneity issue described above. It definitely help is some way (although it is in my opinion insufficient), but should be better motivated and explained. Currently it is mentioned in lines 93-95, but no details are presented

line 197-225: this part would better fit the methods section

Figure 4: it is not fully clear what is the difference between the second and third panel of the first row and between the second and the third panels of the second row. The term model-simulated data only appears here and in line 229 of the text.

Figure 5: some quantitative information on the results presented in this figure should be added, also in relation to the biases of the radar-estimated values with respect to rain gauges and with respect to non-polarimetric radar estimates.

lines 285-287: this conclusion is underpinned by crucial assumptions (see above). These assumptions should be clearly mentioned
Citation: https://doi.org/10.5194/amt-2022-220-RC1
- AC1:
  'Reply on RC1', Roberto Cremonini, 02 Nov 2022
  
  Dear reviewer,
  first of all, the authors wish to thank you for the valuable remarks. To provide a precise reply and to improve the paper, we kindly ask for the mentioned reference https://doi.org/10.1080/0262666910949251 as we are not able to find it.
  best regards
  
  Citation: https://doi.org/10.5194/amt-2022-220-AC1
  - EC1: 'Reply on AC1', Gianfranco Vulpiani, 03 Nov 2022
    
    Dear Authors,
    on behalf of the Anonymous Referee #1 who cannont reply, the interactive discussion being closed, I provide through the following link the correct reference you've asked for:
    https://www.tandfonline.com/doi/abs/10.1080/02626669109492519
    Kind regards
    Gianfranco Vulpiani
    
    Citation: https://doi.org/10.5194/amt-2022-220-EC1
- AC2: 'Reply on RC1', Roberto Cremonini, 23 Nov 2022
  
  RC1: 'Comment on amt-2022-220', Anonymous Referee #1
  
  This paper presents the first application of extreme value statistics to precipitation estimates based on dual polarisation (dual-pol) weather radar. The topic is relevant to the community and to the readers of this journal, and the contribution is timely because dual-pol technology have been shown to improve radar precipitation estimates but extreme value statistics from such data were so far limited by the lack of sufficiently long records of dual-pol observations.
  However, I highlight some aspects that need revisions before this study is considered for publication. These revisions may alter the overall results and conclusions of the study.
  Major comments:
  The study makes use of strong assumptions on the homogeneity of the extreme precipitation statistics field: all the three parameters of the GEV distribution used to represent the annual maxima are assumed to be uniform within the examined areas. This clearly helps with the problem of parameter estimation. However, while the authors carefully address the issue of independence in the used data, they completely neglect the homogeneity assumption. This homogeneity assumption is quite strong for today’s research and practice standards and is not supported by specific tests/analyses. Spatial variations of precipitation statistics at scales smaller than the examined domains are known and reported in a number of previous studies based on both rain gauge and weather radar data (e.g., https://doi.org/10.1088/1748-9326/ab98b4; https://doi.org/10.5194/hess-26-1659-2022; https://doi.org/10.5194/hess-26-1439-2022). Neglecting the presence of spatial variations in the extreme precipitation statistics violates the identical distribution assumption of the extreme value theorem which underlies the adopted approach. Ultimately, this may lead to erroneous estimates of the parameters (samples from different distributions are mixed) and misleading evaluations of their uncertainty (the large number of data points will lead to small uncertainties, as shown in table 1). Alternative approaches in which only some of the parameters are homogeneous and the others are location-dependent (often referred to as regionalisation approaches) are available (e.g., https://doi.org/10.1080/0262666910949251) and are expected to provide results with comparable levels of uncertainty but higher accuracy. Studies based on weather radar or satellite data using such approaches are available in literature (e.g., see https://doi.org/10.1016/j.jhydrol.2019.04.081).
  
  The authors wish to thank the reviewer for the valuable comments. The authors improved the paper by addressing the above-mentioned key points. Regarding Italy, careful gauges data quality leads to the removal of some gauges. Then, the application of some regional homogeneity tests (L-moment homogeneity test and the Anderson-Darling (ADAD) rank test) supported the assumption of regional homogeneity. For Estonia, the recent work by Olsson (2022) confirms homogeneity for 1-hour rainfall total maxima. The spatial independence of the samples is assured by the short duration considered in this study. Future studies dealing with longer durations will need to face also the spatial independence of the samples.
  Finally, being critical estimations of the shape parameter on the basis of short time-series data (5-year weather data), it has been assumed equal to zero. Future works analyzing longer datasets could face this problem. Moreover, early warning systems are based on low return periods (typically 10-20 yr), and the shape parameter affects the tail of the distributions, i.e. for longer return periods.
  
  A proper benchmarking of the results of this study with respect to results based on single-pol measurements is missing. Many studies about the analysis of extreme precipitation statistics from single-pol weather radars are not discussed in the introduction. As a consequence the key scientific questions underpinning this study are not well presented and leave the reader with questions like: why do we need to use dual-pol technology for these applications? what are the expected advantages over single-pol? what kind of uncertainties/errors were found in previous results based on single-pol? is dual-pol able to reduce such uncertainties/errors?
  The authors addressed this point by comparing the results with R(Zh) estimations. The description has been completely revised, trying to clarify the questions arisen by the reviewer. Given the assumptions, the study demonstrates that for convective precipitations during the warm season, R(Zh, Kdp) estimations are more reliable and they can be used for rainfall maxima estimations.
  
  Although some concepts about extreme value theory are presented in a reasonable way in lines 219-225, the manuscript misrepresents many key concepts. Section 2.1.1 in particular should be rewritten
  The manuscript is not optimally organised. The results section contains large parts with methodological aspects and the discussion section contains main results rather than discussion.
  Thank you for the valuable comment. The manuscript has been revised with a better organization of the Sections.
  
  The main objectives and results should be better stated in the abstract and text. The last sentence of the abstract lists two main results reached by the study as (a) “weather radar observations can provide a reliable QPEs compared to rain gauges” and (b) “even relatively short time series can provide reliable estimation of the rainfall return periods in climatological homogeneous areas”. However, point (a) is a result already addressed by previous literature (also listed in the introduction) and is not actually directly presented as a main result of this paper. Additionally, the study comes short at addressing point (b), because of an improper application of methods for extreme value analyses (see comment 1) and because it lacks a benchmarking of the results against single-polarisation data, neither from the radars used in this study nor from previous studies based on single polarisation technology (see comment 2). The natural question raised by the title and abstract of the paper “can dual-pol estimates improve our quantification of extreme precipitation probability with respect to single-pol estimates?” is not answered by the study.
  Benchmarking against single polarization QPEs has been reported, comparing results for all three areas for R(Zh, Kdp) and R(Zh) resect raingauges. The study demonstrates for 1-hour rainfall accumulation maxima that QPEs based on Zh-Kdp have a better agreement with rain gauges estimate of rainfall maxima.
  
  Minor comments:
  line 14-15: “Single C-band polarimetric…” this sentence is not clear
  line 19-27: it is weird to start the manuscript with text about climate change when the study assumes stationarity and does not provide any further results or discussion about changes
  The text has been re-phrased. Obviously, a climatological study is beyond this work. The authors wish to underlay that given more heavy precipitation in the next years due to global warming, there is an increased interest in rainfall total maxima.
  
  lines 32 and line 41: the reference to Peleg et al 2016 is a bit misplaced as these authors only focused on one radar pixel. Other more relevant studies could help detailing the state of the art (see above some suggestions among many). Also note that the correct citation is Peleg et al. 2018
  The reference has been removed and other relevant studies added.
  
  lines 37-48: this part is a bit confusing, please rephrase it
  Done
  Figures 1 and 2: I think these two figures could be merged. The quality of the figure should be improved, for instance using similar graphics and symbols
  Done
  The division of the Italian domain into two areas tries to address the homogeneity issue described above. It definitely help is some way (although it is in my opinion insufficient), but should be better motivated and explained. Currently it is mentioned in lines 93-95, but no details are presented
  
  Description and motivation for study areas in Italy have been improved. Some statistical analyses have been performed to support the regional homogeneity hypothesis.
  
  line 197-225: this part would better fit the methods section
  Done
  Figure 4: it is not fully clear what is the difference between the second and third panel of the first row and between the second and the third panels of the second row. The term model-simulated data only appears here and in line 229 of the text.
  The second QQ plot does not add additional information. It has been removed.
  Figure 5: some quantitative information on the results presented in this figure should be added, also in relation to the biases of the radar-estimated values with respect to rain gauges and with respect to non-polarimetric radar estimates.
  
  Quantitative information has been provided and discussed by adding Table 2, which shows 1-hour rainfall maxima for several return periods.
  
  lines 285-287: this conclusion is underpinned by crucial assumptions (see above). These assumptions should be clearly mentioned
  
  Conclusions have been re-phrased and improved on the basis of the additional analysis and with the aim to increase clarity.
  
  Citation: https://doi.org/10.5194/amt-2022-220-AC2
RC2:
'Comment on amt-2022-220', Anonymous Referee #2, 24 Sep 2022

The manuscript by Cremonini et al. presents an interesting application of radar dual polarization QPE to analyze extrema of precipitation to compute return times. Most of existing studies are based on raingauge rainfall measurements or reflectivity-based radar rainfall estimation. Kdp is instead used and expected advantage in estimating maxima is related to the better performance in QPE, especially at C-band and for intense precipitation, with respect to the Z-R based estimation. I recommend publication, after revision.

Major comments:

After reading abstract and the introductive parts of the manuscript, I was expecting some comparisons with Zh or Zh-Kdp rain algorithms, not in terms of QPE, but in term of impact on the GEV analysis in order to pointed out the need or the benefits of using a dual-pol radar approach. Such evidence is not made clear by the manuscript. Maybe a comparison with a single-pol approach could be helpful.

Radar QPE is affected by the choice of parameters of radar rainfall algorithms. Even the performance of the R-Kdp estimator, which, theoretically is marginally affected by the DSD variability, can be influenced by such parameterization. If I am not wrong, authors have use relationships from literature. Also, the Kdp estimation method (different methods are used for the two study areas) can have an impact on results. Could the manuscript discuss this point ?

Minor issues:

Line 32: Zh is more precisely the equivalent reflectivity factor at horizontal polarization. Please specify that authors prefer using a shorter language.

Line 60: “…rainfall intensity estimations based on R(Zh,Kdp)”, why not R(Kdp?)

Line 141: Is the 3-dB variation of bias resulting from self-consistency consistent with technical issues occurred ?

Line 149: About R(Zh,Kdp): Is Zh corrected for attenuation ?

Line 205: It is not clear to me what is “z” in the formula and “Z” mentioned in the caption of Fig- 3.

Figure 4. Please define units of axes.

Figure 5. please specify in the caption the meaning of dash lines.

Citation: https://doi.org/10.5194/amt-2022-220-RC2
- AC3: 'Reply on RC2', Roberto Cremonini, 23 Nov 2022
  
  RC2: 'Comment on amt-2022-220', Anonymous Referee #2
  
  The manuscript by Cremonini et al. presents an interesting application of radar dual polarization QPE to analyze extrema of precipitation to compute return times. Most of existing studies are based on raingauge rainfall measurements or reflectivity-based radar rainfall estimation. Kdp is instead used and expected advantage in estimating maxima is related to the better performance in QPE, especially at C-band and for intense precipitation, with respect to the Z-R based estimation. I recommend publication, after revision.
  Major comments:
  After reading abstract and the introductive parts of the manuscript, I was expecting some comparisons with Zh or Zh-Kdp rain algorithms, not in terms of QPE, but in term of impact on the GEV analysis in order to pointed out the need or the benefits of using a dual-pol radar approach. Such evidence is not made clear by the manuscript. Maybe a comparison with a single-pol approach could be helpful.
  Benchmarking against single polarization QPEs has been reported, comparing results for all three areas for R(Zh, Kdp) and R(Zh) resect raingauges. The study demonstrates for 1-hour rainfall accumulation maxima that QPEs based on Zh-Kdp have a better agreement with rain gauges estimate of rainfall maxima.
  Radar QPE is affected by the choice of parameters of radar rainfall algorithms. Even the performance of the R-Kdp estimator, which, theoretically is marginally affected by the DSD variability, can be influenced by such parameterization. If I am not wrong, authors have use relationships from literature. Also, the Kdp estimation method (different methods are used for the two study areas) can have an impact on results. Could the manuscript discuss this point ?
  The agreement between weather radar-based retrieval has been deeply investigated by Voormansik et al., 2021. The work evaluated algorithms' performances.
  Minor issues:
  Line 32: Zh is more precisely the equivalent reflectivity factor at horizontal polarization. Please specify that authors prefer using a shorter language.
  Corrected with improvement in description at line 32
  Line 60: “…rainfall intensity estimations based on R(Zh,Kdp)”, why not R(Kdp?)
  R(Kdp) derived from C-band weather radar for low rain rates is insensitive and then, affected by large errors. The algorithm R(Zh, Kdp) allows for overcoming these large errors by relying on Zh for precipitation regimes where rain attenuation at C-band is negligible.
  
  Line 141: Is the 3-dB variation of bias resulting from self-consistency consistent with technical issues occurred ?
  Some miscalibration occurred during some device failures. The Zh bias is generally related to the miscalibration of the radar.
  Line 149: About R(Zh,Kdp): Is Zh corrected for attenuation ?
  No, attenuation correction is not needed as Zh attenuation at C-band is negligible for low rain rates (< 25 dBZ).
  Line 205: It is not clear to me what is “z” in the formula and “Z” mentioned in the caption of Fig- 3.
  The semi-variograms have been derived from R(Zh, Kdp) rainfall estimations. Corrected both text and caption.
  Figure 4. Please define units of axes.
  Added units for x-axis of the leftmost plot (mm/h). The other plots show dimensionless quantities like sample numbers and quantiles.
  Figure 5. please specify in the caption the meaning of dash lines.
  Added to the Figure’s caption.
  
  Citation: https://doi.org/10.5194/amt-2022-220-AC3

Status: closed

RC1:
'Comment on amt-2022-220', Anonymous Referee #1, 19 Sep 2022
This paper presents the first application of extreme value statistics to precipitation estimates based on dual polarisation (dual-pol) weather radar. The topic is relevant to the community and to the readers of this journal, and the contribution is timely because dual-pol technology have been shown to improve radar precipitation estimates but extreme value statistics from such data were so far limited by the lack of sufficiently long records of dual-pol observations.

However, I highlight some aspects that need revisions before this study is considered for publication. These revisions may alter the overall results and conclusions of the study.

Major comments:

The study makes use of strong assumptions on the homogeneity of the extreme precipitation statistics field: all the three parameters of the GEV distribution used to represent the annual maxima are assumed to be uniform within the examined areas. This clearly helps with the problem of parameter estimation. However, while the authors carefully address the issue of independence in the used data, they completely neglect the homogeneity assumption. This homogeneity assumption is quite strong for today’s research and practice standards and is not supported by specific tests/analyses. Spatial variations of precipitation statistics at scales smaller than the examined domains are known and reported in a number of previous studies based on both rain gauge and weather radar data (e.g., https://doi.org/10.1088/1748-9326/ab98b4; https://doi.org/10.5194/hess-26-1659-2022; https://doi.org/10.5194/hess-26-1439-2022). Neglecting the presence of spatial variations in the extreme precipitation statistics violates the identical distribution assumption of the extreme value theorem which underlies the adopted approach. Ultimately, this may lead to erroneous estimates of the parameters (samples from different distributions are mixed) and misleading evaluations of their uncertainty (the large number of data points will lead to small uncertainties, as shown in table 1). Alternative approaches in which only some of the parameters are homogeneous and the others are location-dependent (often referred to as regionalisation approaches) are available (e.g., https://doi.org/10.1080/0262666910949251) and are expected to provide results with comparable levels of uncertainty but higher accuracy. Studies based on weather radar or satellite data using such approaches are available in literature (e.g., see https://doi.org/10.1016/j.jhydrol.2019.04.081).

A proper benchmarking of the results of this study with respect to results based on single-pol measurements is missing. Many studies about the analysis of extreme precipitation statistics from single-pol weather radars are not discussed in the introduction. As a consequence the key scientific questions underpinning this study are not well presented and leave the reader with questions like: why do we need to use dual-pol technology for these applications? what are the expected advantages over single-pol? what kind of uncertainties/errors were found in previous results based on single-pol? is dual-pol able to reduce such uncertainties/errors?

Although some concepts about extreme value theory are presented in a reasonable way in lines 219-225, the manuscript misrepresents many key concepts. Section 2.1.1 in particular should be rewritten

The manuscript is not optimally organised. The results section contains large parts with methodological aspects and the discussion section contains main results rather than discussion.

The main objectives and results should be better stated in the abstract and text. The last sentence of the abstract lists two main results reached by the study as (a) “weather radar observations can provide a reliable QPEs compared to rain gauges” and (b) “even relatively short time series can provide reliable estimation of the rainfall return periods in climatological homogeneous areas”. However, point (a) is a result already addressed by previous literature (also listed in the introduction) and is not actually directly presented as a main result of this paper. Additionally, the study comes short at addressing point (b), because of an improper application of methods for extreme value analyses (see comment 1) and because it lacks a benchmarking of the results against single-polarisation data, neither from the radars used in this study nor from previous studies based on single polarisation technology (see comment 2). The natural question raised by the title and abstract of the paper “can dual-pol estimates improve our quantification of extreme precipitation probability with respect to single-pol estimates?” is not answered by the study.

Minor comments:

line 14-15: “Single C-band polarimetric…” this sentence is not clear

line 19-27: it is weird to start the manuscript with text about climate change when the study assumes stationarity and does not provide any further result or discussion about changes

lines 32 and line 41: the reference to Peleg et al 2016 is a bit misplaced as these authors only focused on one radar pixel. Other more relevant studies could help detailing the state of the art (see above some suggestions among many). Also note that the correct citation is Peleg et al. 2018

lines 37-48: this part is a bit confusing, please rephrase it

Figures 1 and 2: I think these two figures could be merged. The quality of the figure should be improved, for instance using similar graphics and symbols

The division of the Italian domain into two areas tries to address the homogeneity issue described above. It definitely help is some way (although it is in my opinion insufficient), but should be better motivated and explained. Currently it is mentioned in lines 93-95, but no details are presented

line 197-225: this part would better fit the methods section

Figure 4: it is not fully clear what is the difference between the second and third panel of the first row and between the second and the third panels of the second row. The term model-simulated data only appears here and in line 229 of the text.

Figure 5: some quantitative information on the results presented in this figure should be added, also in relation to the biases of the radar-estimated values with respect to rain gauges and with respect to non-polarimetric radar estimates.

lines 285-287: this conclusion is underpinned by crucial assumptions (see above). These assumptions should be clearly mentioned
Citation: https://doi.org/10.5194/amt-2022-220-RC1
- AC1:
  'Reply on RC1', Roberto Cremonini, 02 Nov 2022
  
  Dear reviewer,
  first of all, the authors wish to thank you for the valuable remarks. To provide a precise reply and to improve the paper, we kindly ask for the mentioned reference https://doi.org/10.1080/0262666910949251 as we are not able to find it.
  best regards
  
  Citation: https://doi.org/10.5194/amt-2022-220-AC1
  - EC1: 'Reply on AC1', Gianfranco Vulpiani, 03 Nov 2022
    
    Dear Authors,
    on behalf of the Anonymous Referee #1 who cannont reply, the interactive discussion being closed, I provide through the following link the correct reference you've asked for:
    https://www.tandfonline.com/doi/abs/10.1080/02626669109492519
    Kind regards
    Gianfranco Vulpiani
    
    Citation: https://doi.org/10.5194/amt-2022-220-EC1
- AC2: 'Reply on RC1', Roberto Cremonini, 23 Nov 2022
  
  RC1: 'Comment on amt-2022-220', Anonymous Referee #1
  
  This paper presents the first application of extreme value statistics to precipitation estimates based on dual polarisation (dual-pol) weather radar. The topic is relevant to the community and to the readers of this journal, and the contribution is timely because dual-pol technology have been shown to improve radar precipitation estimates but extreme value statistics from such data were so far limited by the lack of sufficiently long records of dual-pol observations.
  However, I highlight some aspects that need revisions before this study is considered for publication. These revisions may alter the overall results and conclusions of the study.
  Major comments:
  The study makes use of strong assumptions on the homogeneity of the extreme precipitation statistics field: all the three parameters of the GEV distribution used to represent the annual maxima are assumed to be uniform within the examined areas. This clearly helps with the problem of parameter estimation. However, while the authors carefully address the issue of independence in the used data, they completely neglect the homogeneity assumption. This homogeneity assumption is quite strong for today’s research and practice standards and is not supported by specific tests/analyses. Spatial variations of precipitation statistics at scales smaller than the examined domains are known and reported in a number of previous studies based on both rain gauge and weather radar data (e.g., https://doi.org/10.1088/1748-9326/ab98b4; https://doi.org/10.5194/hess-26-1659-2022; https://doi.org/10.5194/hess-26-1439-2022). Neglecting the presence of spatial variations in the extreme precipitation statistics violates the identical distribution assumption of the extreme value theorem which underlies the adopted approach. Ultimately, this may lead to erroneous estimates of the parameters (samples from different distributions are mixed) and misleading evaluations of their uncertainty (the large number of data points will lead to small uncertainties, as shown in table 1). Alternative approaches in which only some of the parameters are homogeneous and the others are location-dependent (often referred to as regionalisation approaches) are available (e.g., https://doi.org/10.1080/0262666910949251) and are expected to provide results with comparable levels of uncertainty but higher accuracy. Studies based on weather radar or satellite data using such approaches are available in literature (e.g., see https://doi.org/10.1016/j.jhydrol.2019.04.081).
  
  The authors wish to thank the reviewer for the valuable comments. The authors improved the paper by addressing the above-mentioned key points. Regarding Italy, careful gauges data quality leads to the removal of some gauges. Then, the application of some regional homogeneity tests (L-moment homogeneity test and the Anderson-Darling (ADAD) rank test) supported the assumption of regional homogeneity. For Estonia, the recent work by Olsson (2022) confirms homogeneity for 1-hour rainfall total maxima. The spatial independence of the samples is assured by the short duration considered in this study. Future studies dealing with longer durations will need to face also the spatial independence of the samples.
  Finally, being critical estimations of the shape parameter on the basis of short time-series data (5-year weather data), it has been assumed equal to zero. Future works analyzing longer datasets could face this problem. Moreover, early warning systems are based on low return periods (typically 10-20 yr), and the shape parameter affects the tail of the distributions, i.e. for longer return periods.
  
  A proper benchmarking of the results of this study with respect to results based on single-pol measurements is missing. Many studies about the analysis of extreme precipitation statistics from single-pol weather radars are not discussed in the introduction. As a consequence the key scientific questions underpinning this study are not well presented and leave the reader with questions like: why do we need to use dual-pol technology for these applications? what are the expected advantages over single-pol? what kind of uncertainties/errors were found in previous results based on single-pol? is dual-pol able to reduce such uncertainties/errors?
  The authors addressed this point by comparing the results with R(Zh) estimations. The description has been completely revised, trying to clarify the questions arisen by the reviewer. Given the assumptions, the study demonstrates that for convective precipitations during the warm season, R(Zh, Kdp) estimations are more reliable and they can be used for rainfall maxima estimations.
  
  Although some concepts about extreme value theory are presented in a reasonable way in lines 219-225, the manuscript misrepresents many key concepts. Section 2.1.1 in particular should be rewritten
  The manuscript is not optimally organised. The results section contains large parts with methodological aspects and the discussion section contains main results rather than discussion.
  Thank you for the valuable comment. The manuscript has been revised with a better organization of the Sections.
  
  The main objectives and results should be better stated in the abstract and text. The last sentence of the abstract lists two main results reached by the study as (a) “weather radar observations can provide a reliable QPEs compared to rain gauges” and (b) “even relatively short time series can provide reliable estimation of the rainfall return periods in climatological homogeneous areas”. However, point (a) is a result already addressed by previous literature (also listed in the introduction) and is not actually directly presented as a main result of this paper. Additionally, the study comes short at addressing point (b), because of an improper application of methods for extreme value analyses (see comment 1) and because it lacks a benchmarking of the results against single-polarisation data, neither from the radars used in this study nor from previous studies based on single polarisation technology (see comment 2). The natural question raised by the title and abstract of the paper “can dual-pol estimates improve our quantification of extreme precipitation probability with respect to single-pol estimates?” is not answered by the study.
  Benchmarking against single polarization QPEs has been reported, comparing results for all three areas for R(Zh, Kdp) and R(Zh) resect raingauges. The study demonstrates for 1-hour rainfall accumulation maxima that QPEs based on Zh-Kdp have a better agreement with rain gauges estimate of rainfall maxima.
  
  Minor comments:
  line 14-15: “Single C-band polarimetric…” this sentence is not clear
  line 19-27: it is weird to start the manuscript with text about climate change when the study assumes stationarity and does not provide any further results or discussion about changes
  The text has been re-phrased. Obviously, a climatological study is beyond this work. The authors wish to underlay that given more heavy precipitation in the next years due to global warming, there is an increased interest in rainfall total maxima.
  
  lines 32 and line 41: the reference to Peleg et al 2016 is a bit misplaced as these authors only focused on one radar pixel. Other more relevant studies could help detailing the state of the art (see above some suggestions among many). Also note that the correct citation is Peleg et al. 2018
  The reference has been removed and other relevant studies added.
  
  lines 37-48: this part is a bit confusing, please rephrase it
  Done
  Figures 1 and 2: I think these two figures could be merged. The quality of the figure should be improved, for instance using similar graphics and symbols
  Done
  The division of the Italian domain into two areas tries to address the homogeneity issue described above. It definitely help is some way (although it is in my opinion insufficient), but should be better motivated and explained. Currently it is mentioned in lines 93-95, but no details are presented
  
  Description and motivation for study areas in Italy have been improved. Some statistical analyses have been performed to support the regional homogeneity hypothesis.
  
  line 197-225: this part would better fit the methods section
  Done
  Figure 4: it is not fully clear what is the difference between the second and third panel of the first row and between the second and the third panels of the second row. The term model-simulated data only appears here and in line 229 of the text.
  The second QQ plot does not add additional information. It has been removed.
  Figure 5: some quantitative information on the results presented in this figure should be added, also in relation to the biases of the radar-estimated values with respect to rain gauges and with respect to non-polarimetric radar estimates.
  
  Quantitative information has been provided and discussed by adding Table 2, which shows 1-hour rainfall maxima for several return periods.
  
  lines 285-287: this conclusion is underpinned by crucial assumptions (see above). These assumptions should be clearly mentioned
  
  Conclusions have been re-phrased and improved on the basis of the additional analysis and with the aim to increase clarity.
  
  Citation: https://doi.org/10.5194/amt-2022-220-AC2
RC2:
'Comment on amt-2022-220', Anonymous Referee #2, 24 Sep 2022

The manuscript by Cremonini et al. presents an interesting application of radar dual polarization QPE to analyze extrema of precipitation to compute return times. Most of existing studies are based on raingauge rainfall measurements or reflectivity-based radar rainfall estimation. Kdp is instead used and expected advantage in estimating maxima is related to the better performance in QPE, especially at C-band and for intense precipitation, with respect to the Z-R based estimation. I recommend publication, after revision.

Major comments:

After reading abstract and the introductive parts of the manuscript, I was expecting some comparisons with Zh or Zh-Kdp rain algorithms, not in terms of QPE, but in term of impact on the GEV analysis in order to pointed out the need or the benefits of using a dual-pol radar approach. Such evidence is not made clear by the manuscript. Maybe a comparison with a single-pol approach could be helpful.

Radar QPE is affected by the choice of parameters of radar rainfall algorithms. Even the performance of the R-Kdp estimator, which, theoretically is marginally affected by the DSD variability, can be influenced by such parameterization. If I am not wrong, authors have use relationships from literature. Also, the Kdp estimation method (different methods are used for the two study areas) can have an impact on results. Could the manuscript discuss this point ?

Minor issues:

Line 32: Zh is more precisely the equivalent reflectivity factor at horizontal polarization. Please specify that authors prefer using a shorter language.

Line 60: “…rainfall intensity estimations based on R(Zh,Kdp)”, why not R(Kdp?)

Line 141: Is the 3-dB variation of bias resulting from self-consistency consistent with technical issues occurred ?

Line 149: About R(Zh,Kdp): Is Zh corrected for attenuation ?

Line 205: It is not clear to me what is “z” in the formula and “Z” mentioned in the caption of Fig- 3.

Figure 4. Please define units of axes.

Figure 5. please specify in the caption the meaning of dash lines.

Citation: https://doi.org/10.5194/amt-2022-220-RC2
- AC3: 'Reply on RC2', Roberto Cremonini, 23 Nov 2022
  
  RC2: 'Comment on amt-2022-220', Anonymous Referee #2
  
  The manuscript by Cremonini et al. presents an interesting application of radar dual polarization QPE to analyze extrema of precipitation to compute return times. Most of existing studies are based on raingauge rainfall measurements or reflectivity-based radar rainfall estimation. Kdp is instead used and expected advantage in estimating maxima is related to the better performance in QPE, especially at C-band and for intense precipitation, with respect to the Z-R based estimation. I recommend publication, after revision.
  Major comments:
  After reading abstract and the introductive parts of the manuscript, I was expecting some comparisons with Zh or Zh-Kdp rain algorithms, not in terms of QPE, but in term of impact on the GEV analysis in order to pointed out the need or the benefits of using a dual-pol radar approach. Such evidence is not made clear by the manuscript. Maybe a comparison with a single-pol approach could be helpful.
  Benchmarking against single polarization QPEs has been reported, comparing results for all three areas for R(Zh, Kdp) and R(Zh) resect raingauges. The study demonstrates for 1-hour rainfall accumulation maxima that QPEs based on Zh-Kdp have a better agreement with rain gauges estimate of rainfall maxima.
  Radar QPE is affected by the choice of parameters of radar rainfall algorithms. Even the performance of the R-Kdp estimator, which, theoretically is marginally affected by the DSD variability, can be influenced by such parameterization. If I am not wrong, authors have use relationships from literature. Also, the Kdp estimation method (different methods are used for the two study areas) can have an impact on results. Could the manuscript discuss this point ?
  The agreement between weather radar-based retrieval has been deeply investigated by Voormansik et al., 2021. The work evaluated algorithms' performances.
  Minor issues:
  Line 32: Zh is more precisely the equivalent reflectivity factor at horizontal polarization. Please specify that authors prefer using a shorter language.
  Corrected with improvement in description at line 32
  Line 60: “…rainfall intensity estimations based on R(Zh,Kdp)”, why not R(Kdp?)
  R(Kdp) derived from C-band weather radar for low rain rates is insensitive and then, affected by large errors. The algorithm R(Zh, Kdp) allows for overcoming these large errors by relying on Zh for precipitation regimes where rain attenuation at C-band is negligible.
  
  Line 141: Is the 3-dB variation of bias resulting from self-consistency consistent with technical issues occurred ?
  Some miscalibration occurred during some device failures. The Zh bias is generally related to the miscalibration of the radar.
  Line 149: About R(Zh,Kdp): Is Zh corrected for attenuation ?
  No, attenuation correction is not needed as Zh attenuation at C-band is negligible for low rain rates (< 25 dBZ).
  Line 205: It is not clear to me what is “z” in the formula and “Z” mentioned in the caption of Fig- 3.
  The semi-variograms have been derived from R(Zh, Kdp) rainfall estimations. Corrected both text and caption.
  Figure 4. Please define units of axes.
  Added units for x-axis of the leftmost plot (mm/h). The other plots show dimensionless quantities like sample numbers and quantiles.
  Figure 5. please specify in the caption the meaning of dash lines.
  Added to the Figure’s caption.
  
  Citation: https://doi.org/10.5194/amt-2022-220-AC3

Roberto Cremonini et al.

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Short summary

Climatology of extreme rainfalls for a certain location is crucial for several applications. This study investigates the use of weather polarimetric data to estimate annual hourly maxima in Italy and Estonia. The results demonstrate that thanks to weather radar's high spatial resolution, even a limited-time series of polarimetric weather radar observations can provide reliable estimations of extreme values distribution parameters for rainfall maxima in climatological homogeneous regions.


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