the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 28 Jun 2023
Exploring the joint probability of precipitation and soil moisture over Europe using copulas
Carmelo Cammalleri
Carlo De Michele
Andrea Toreti
Abstract. The joint probability of precipitation and soil moisture is here investigated over Europe with the goal to extrapolated meaningful insights on the potential joint use of these variables for the detection of agricultural droughts within a probabilistic modeling framework. The use of copulas is explored as a parametric approach often used in hydrological studies for the analysis of bivariate distributions. The analysis is performed for the period 1996–2020 on the ERA5 precipitation and LISFLOOD soil moisture datasets, both available as part of the Copernicus European Drought Observatory. The results show an overall good correlation between the empirical frequency series derived from the two datasets (Kendall’s τ = 0.42±0.1), but also clear spatial patterns in the tail-dependence derived with both non-parametric and parametric approaches. About half of the domain shows symmetric tail-dependences, well reproduced by the Student-t copula, whereas the rest of the domain is almost equally split between low and high tail-dependences (modeled with the Gumbel family of copulas). These spatial patterns are reasonably reproduced by a random forest classifier, suggesting that this outcome is not driven by chance. This study stresses how a joint use of precipitation and soil moisture for agriculture drought characterization may be more beneficial in areas with strong low tail-dependence, such as southern France, northern UK, northern Germany, and Denmark in this study, and how this behavior should be carefully considered in drought studies.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(1379 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1379 KB) - Metadata XML
- BibTeX
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- Final revised paper
Journal article(s) based on this preprint
Carmelo Cammalleri et al.
Interactive discussion
Status: closed
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CC1: 'Comment on egusphere-2023-1318', Francesco Serinaldi, 29 Jun 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1318/egusphere-2023-1318-CC1-supplement.pdf
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AC1: 'Reply on CC1', Carmelo Cammalleri, 15 Sep 2023
We really welcome your feedback on our manuscript, and the topics of discussion raised by your insightful comments. We would like to clarify that when we were referring to “limited use of upper/lower tail…”, we were specifically discussing about the context of drought and in particular on the development of joint drought indices. We are aware of the extensive literature on the topic in hydro-climate in general, and we will revise the text to better clarify this point, as well as extended the cited literature to give a better and more general context to our study.
Indeed, it is true that large uncertainties and biases may arise from different procedures used to analyse the tail dependence structure, and this is one of the reasons why we adopted different approaches (parametric and non-parametric) to investigate the issue, in an attempt to identify a converge of evidence. It is worth mentioning that in the context of this work, where we are trying to discriminate between grid cells with signs of upper or lower tail dependency, the absolute accuracy in lL estimates may be less demanding.
We get this chance to report that we also applied another method, not dissimilar to the pair wise correlation discussed in Serinaldi et al. (2015), with the goal to provide another test on the outcomes of our simple mapping of the TD. These results were not included in the submitted manuscript, but we will consider adding them in a revised version of the manuscript, since they may further support the converge of evidence principle mentioned above.
Overall, the key message of our study is that considering the tail dependence in precipitation-soil moisture bivariate drought studies may have relevant operational impacts that are often overlooked when a copula is selected without attention on the TD, but that multiple approaches need to be considered due to the large uncertainty of different methodology used to quantify TD. It seems that this second part of the message didn’t pass through as intended, so we will strengthen this message in a revised version of the text, as well as better highlight the bias and uncertainty of some estimators by citing the relevant literature.
As for the shuffling procedure, it is indeed true that a proper cut-off value to identify the TD should be derived with a cell-specific CI estimated from a shuffled dataset that preserve the local tau. However, as you correctly mentioned, the single value derived with our simple shuffling represents a lower boundary conditions, as it is meant at detecting the grid cells for which the presence of asymmetric tail dependence can be almost certainly excluded rather than identifying the grid cells where the TD is certain. Those results were used in combination to the outcome of the copula analysis to then sample the regions with converging outcomes.
Citation: https://doi.org/10.5194/egusphere-2023-1318-AC1
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AC1: 'Reply on CC1', Carmelo Cammalleri, 15 Sep 2023
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RC1: 'Comment on egusphere-2023-1318', Anonymous Referee #1, 27 Jul 2023
In this work, the authors investigated the joint probability of soil moisture and precipitation over Europe in order to derive meaningful insights on the combined usage of these variables for the detection of agricultural droughts within a probabilitic modelling framework. The in-depth analysis of the tail-dependence especially reveals clear spatial patterns, such as identification of regions which may benefit more from the joint use of the two variables due to the observed strong low tail-dependence, over others. The authors also showed that the spatial patterns are significant using a random forest classification. The scientific goal and the findings of the manuscript are of high relevance and are presented in a clear, concise and well structured way. There are only but a few grammatical errors and typos which could be corrected upon a thorough reading of the manuscript.
Citation: https://doi.org/10.5194/egusphere-2023-1318-RC1 -
AC2: 'Reply on RC1', Carmelo Cammalleri, 15 Sep 2023
We would like to thank the reviewer for the positive feedback on our manuscript. We will thoughtfully revise the text to fix typos and grammatical errors.
Citation: https://doi.org/10.5194/egusphere-2023-1318-AC2
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AC2: 'Reply on RC1', Carmelo Cammalleri, 15 Sep 2023
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RC2: 'Comment on egusphere-2023-1318', Anonymous Referee #2, 30 Jul 2023
General Overview:
The manuscript deals with the investigation of the joint probability of precipitation and soil moisture by using different copula functions and a large dataset over Europe. The analysis of the tail-dependence shows clear spatial patterns in non-parametric and parametric approaches. The manuscript is an interesting approach that could be valuable to drought studies and, presented the approach in a clear and well-structured way. However, I have a few concerns which should be resolved before recommending the paper for publication.
Major remarks:
1) The independence is questionable between the 3-month accumulated precipitation and soil moisture which is a requirement in copula-based analysis, but it can be checked using some statistical tests.
2) Is this study looking at the joint probability of precipitation and soil moisture or SPI-3 and SMA? This is not clear to me, and I could not see consistency in the manuscript.
3) I would suggest authors to add some explanations with the justification for the practical use of the results in agriculture drought studies and drought characterization.
Citation: https://doi.org/10.5194/egusphere-2023-1318-RC2 -
AC3: 'Reply on RC2', Carmelo Cammalleri, 15 Sep 2023
We thank the reviewer for highlighting some major points to be clarified in the revised version of the manuscript. We will address these remarks in the new text by: 1) discussing the temporal autocorrelation of the two variables, 2) improve the consistency on the terminology used thought the text to describe the variables analysed, and 3) discuss some examples on the practical impact on agricultural drought studies.
Citation: https://doi.org/10.5194/egusphere-2023-1318-AC3
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AC3: 'Reply on RC2', Carmelo Cammalleri, 15 Sep 2023
Interactive discussion
Status: closed
-
CC1: 'Comment on egusphere-2023-1318', Francesco Serinaldi, 29 Jun 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1318/egusphere-2023-1318-CC1-supplement.pdf
-
AC1: 'Reply on CC1', Carmelo Cammalleri, 15 Sep 2023
We really welcome your feedback on our manuscript, and the topics of discussion raised by your insightful comments. We would like to clarify that when we were referring to “limited use of upper/lower tail…”, we were specifically discussing about the context of drought and in particular on the development of joint drought indices. We are aware of the extensive literature on the topic in hydro-climate in general, and we will revise the text to better clarify this point, as well as extended the cited literature to give a better and more general context to our study.
Indeed, it is true that large uncertainties and biases may arise from different procedures used to analyse the tail dependence structure, and this is one of the reasons why we adopted different approaches (parametric and non-parametric) to investigate the issue, in an attempt to identify a converge of evidence. It is worth mentioning that in the context of this work, where we are trying to discriminate between grid cells with signs of upper or lower tail dependency, the absolute accuracy in lL estimates may be less demanding.
We get this chance to report that we also applied another method, not dissimilar to the pair wise correlation discussed in Serinaldi et al. (2015), with the goal to provide another test on the outcomes of our simple mapping of the TD. These results were not included in the submitted manuscript, but we will consider adding them in a revised version of the manuscript, since they may further support the converge of evidence principle mentioned above.
Overall, the key message of our study is that considering the tail dependence in precipitation-soil moisture bivariate drought studies may have relevant operational impacts that are often overlooked when a copula is selected without attention on the TD, but that multiple approaches need to be considered due to the large uncertainty of different methodology used to quantify TD. It seems that this second part of the message didn’t pass through as intended, so we will strengthen this message in a revised version of the text, as well as better highlight the bias and uncertainty of some estimators by citing the relevant literature.
As for the shuffling procedure, it is indeed true that a proper cut-off value to identify the TD should be derived with a cell-specific CI estimated from a shuffled dataset that preserve the local tau. However, as you correctly mentioned, the single value derived with our simple shuffling represents a lower boundary conditions, as it is meant at detecting the grid cells for which the presence of asymmetric tail dependence can be almost certainly excluded rather than identifying the grid cells where the TD is certain. Those results were used in combination to the outcome of the copula analysis to then sample the regions with converging outcomes.
Citation: https://doi.org/10.5194/egusphere-2023-1318-AC1
-
AC1: 'Reply on CC1', Carmelo Cammalleri, 15 Sep 2023
-
RC1: 'Comment on egusphere-2023-1318', Anonymous Referee #1, 27 Jul 2023
In this work, the authors investigated the joint probability of soil moisture and precipitation over Europe in order to derive meaningful insights on the combined usage of these variables for the detection of agricultural droughts within a probabilitic modelling framework. The in-depth analysis of the tail-dependence especially reveals clear spatial patterns, such as identification of regions which may benefit more from the joint use of the two variables due to the observed strong low tail-dependence, over others. The authors also showed that the spatial patterns are significant using a random forest classification. The scientific goal and the findings of the manuscript are of high relevance and are presented in a clear, concise and well structured way. There are only but a few grammatical errors and typos which could be corrected upon a thorough reading of the manuscript.
Citation: https://doi.org/10.5194/egusphere-2023-1318-RC1 -
AC2: 'Reply on RC1', Carmelo Cammalleri, 15 Sep 2023
We would like to thank the reviewer for the positive feedback on our manuscript. We will thoughtfully revise the text to fix typos and grammatical errors.
Citation: https://doi.org/10.5194/egusphere-2023-1318-AC2
-
AC2: 'Reply on RC1', Carmelo Cammalleri, 15 Sep 2023
-
RC2: 'Comment on egusphere-2023-1318', Anonymous Referee #2, 30 Jul 2023
General Overview:
The manuscript deals with the investigation of the joint probability of precipitation and soil moisture by using different copula functions and a large dataset over Europe. The analysis of the tail-dependence shows clear spatial patterns in non-parametric and parametric approaches. The manuscript is an interesting approach that could be valuable to drought studies and, presented the approach in a clear and well-structured way. However, I have a few concerns which should be resolved before recommending the paper for publication.
Major remarks:
1) The independence is questionable between the 3-month accumulated precipitation and soil moisture which is a requirement in copula-based analysis, but it can be checked using some statistical tests.
2) Is this study looking at the joint probability of precipitation and soil moisture or SPI-3 and SMA? This is not clear to me, and I could not see consistency in the manuscript.
3) I would suggest authors to add some explanations with the justification for the practical use of the results in agriculture drought studies and drought characterization.
Citation: https://doi.org/10.5194/egusphere-2023-1318-RC2 -
AC3: 'Reply on RC2', Carmelo Cammalleri, 15 Sep 2023
We thank the reviewer for highlighting some major points to be clarified in the revised version of the manuscript. We will address these remarks in the new text by: 1) discussing the temporal autocorrelation of the two variables, 2) improve the consistency on the terminology used thought the text to describe the variables analysed, and 3) discuss some examples on the practical impact on agricultural drought studies.
Citation: https://doi.org/10.5194/egusphere-2023-1318-AC3
-
AC3: 'Reply on RC2', Carmelo Cammalleri, 15 Sep 2023
Peer review completion
Journal article(s) based on this preprint
Carmelo Cammalleri et al.
Carmelo Cammalleri et al.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1379 KB) - Metadata XML