Articles | Volume 28, issue 1
https://doi.org/10.5194/hess-28-103-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-28-103-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
05 Jan 2024
Research article |
| 05 Jan 2024
| 05 Jan 2024
Exploring the joint probability of precipitation and soil moisture over Europe using copulas
Carmelo Cammalleri
CORRESPONDING AUTHOR
Dipartimento di Ingegneria Civile e Ambientale (DICA), Politecnico di Milano, Milan, 20133, Italy
European Commission, Joint Research Centre (JRC), Ispra, 21027, Italy
Carlo De Michele
Dipartimento di Ingegneria Civile e Ambientale (DICA), Politecnico di Milano, Milan, 20133, Italy
Andrea Toreti
European Commission, Joint Research Centre (JRC), Ispra, 21027, Italy
Related authors
Giorgio Baiamonte, Carmelo Agnese, Carmelo Cammalleri, Elvira Di Nardo, Stefano Ferraris, and Tommaso Martini
Adv. Stat. Clim. Meteorol. Oceanogr., 10, 51–67, https://doi.org/10.5194/ascmo-10-51-2024, https://doi.org/10.5194/ascmo-10-51-2024, 2024
Short summary
Short summary
In hydrology, the probability distributions are used to determine the probability of occurrence of rainfall events. In this study, two different methods for modeling rainfall time characteristics have been applied: a direct method and an indirect method that make it possible to relax the assumptions of the renewal process. The analysis was extended to two additional time variables that may be of great interest for practical hydrological applications: wet chains and dry chains.
Carmelo Cammalleri, Niall McCormick, and Andrea Toreti
Nat. Hazards Earth Syst. Sci., 22, 3737–3750, https://doi.org/10.5194/nhess-22-3737-2022, https://doi.org/10.5194/nhess-22-3737-2022, 2022
Short summary
Short summary
We evaluated the ability of vegetation indices derived from satellite data to capture annual yield variations across Europe. The strength of the relationship varies throughout the year, with March–October representing the optimal period in most cases. Spatial differences were also observed, with the best results obtained in the Mediterranean regions.
Veit Blauhut, Michael Stoelzle, Lauri Ahopelto, Manuela I. Brunner, Claudia Teutschbein, Doris E. Wendt, Vytautas Akstinas, Sigrid J. Bakke, Lucy J. Barker, Lenka Bartošová, Agrita Briede, Carmelo Cammalleri, Ksenija Cindrić Kalin, Lucia De Stefano, Miriam Fendeková, David C. Finger, Marijke Huysmans, Mirjana Ivanov, Jaak Jaagus, Jiří Jakubínský, Svitlana Krakovska, Gregor Laaha, Monika Lakatos, Kiril Manevski, Mathias Neumann Andersen, Nina Nikolova, Marzena Osuch, Pieter van Oel, Kalina Radeva, Renata J. Romanowicz, Elena Toth, Mirek Trnka, Marko Urošev, Julia Urquijo Reguera, Eric Sauquet, Aleksandra Stevkov, Lena M. Tallaksen, Iryna Trofimova, Anne F. Van Loon, Michelle T. H. van Vliet, Jean-Philippe Vidal, Niko Wanders, Micha Werner, Patrick Willems, and Nenad Živković
Nat. Hazards Earth Syst. Sci., 22, 2201–2217, https://doi.org/10.5194/nhess-22-2201-2022, https://doi.org/10.5194/nhess-22-2201-2022, 2022
Short summary
Short summary
Recent drought events caused enormous damage in Europe. We therefore questioned the existence and effect of current drought management strategies on the actual impacts and how drought is perceived by relevant stakeholders. Over 700 participants from 28 European countries provided insights into drought hazard and impact perception and current management strategies. The study concludes with an urgent need to collectively combat drought risk via a European macro-level drought governance approach.
Brunella Bonaccorso, Carmelo Cammalleri, Athanasios Loukas, and Heidi Kreibich
Nat. Hazards Earth Syst. Sci., 22, 1857–1862, https://doi.org/10.5194/nhess-22-1857-2022, https://doi.org/10.5194/nhess-22-1857-2022, 2022
Carmelo Cammalleri, Carolina Arias-Muñoz, Paulo Barbosa, Alfred de Jager, Diego Magni, Dario Masante, Marco Mazzeschi, Niall McCormick, Gustavo Naumann, Jonathan Spinoni, and Jürgen Vogt
Nat. Hazards Earth Syst. Sci., 21, 481–495, https://doi.org/10.5194/nhess-21-481-2021, https://doi.org/10.5194/nhess-21-481-2021, 2021
Short summary
Short summary
Building on almost ten years of expertise and operational application of the Combined Drought Indicator (CDI) for the monitoring of agricultural droughts in Europe within the European Commission's European Drought Observatory (EDO), this paper proposes a revised version of the index. This paper shows that the proposed revised CDI reliably reproduces the evolution of major droughts, outperforming the current version of the indicator, especially for long-lasting events.
Carmelo Cammalleri, Gustavo Naumann, Lorenzo Mentaschi, Bernard Bisselink, Emiliano Gelati, Ad De Roo, and Luc Feyen
Hydrol. Earth Syst. Sci., 24, 5919–5935, https://doi.org/10.5194/hess-24-5919-2020, https://doi.org/10.5194/hess-24-5919-2020, 2020
Short summary
Short summary
Climate change is anticipated to alter the demand and supply of water at the earth's surface. This study shows how hydrological droughts will change across Europe with increasing global warming levels, showing that at 3 K global warming an additional 11 million people and 4.5 ×106 ha of agricultural land will be exposed to droughts every year, on average. These effects are mostly located in the Mediterranean and Atlantic regions of Europe.
Juan C. Acosta Navarro, Alvise Aranyossy, Paolo De Luca, Markus G. Donat, Arthur Hrast Essenfelder, Rashed Mahmood, Andrea Toreti, and Danila Volpi
Earth Syst. Dynam., 16, 1723–1737, https://doi.org/10.5194/esd-16-1723-2025, https://doi.org/10.5194/esd-16-1723-2025, 2025
Short summary
Short summary
A computationally inexpensive climate model analog method yields skillful climate predictions across timescales, from seasons to multiple years, complementing existing climate prediction systems and potentially providing valuable information for sectors like agriculture and energy.
Roland Baatz, Gohar Ghazaryan, Michael Hagenlocher, Claas Nendel, Andrea Toreti, and Ehsan Eyshi Rezaei
Hydrol. Earth Syst. Sci., 29, 1379–1393, https://doi.org/10.5194/hess-29-1379-2025, https://doi.org/10.5194/hess-29-1379-2025, 2025
Short summary
Short summary
Our global review of 130 000 peer-reviewed articles reveals that drought forecasting and plant genetics dominate drought research priorities. Using topic modelling, we traced evolving themes from 1901 to 2022, highlighting a shift from ecology to cutting-edge technologies. By applying unsupervised machine learning, we offer insights into how integrated approaches matter, guiding future priorities to strengthen drought resilience and to safeguard water resources.
Fabiola Banfi, Emanuele Bevacqua, Pauline Rivoire, Sérgio C. Oliveira, Joaquim G. Pinto, Alexandre M. Ramos, and Carlo De Michele
Nat. Hazards Earth Syst. Sci., 24, 2689–2704, https://doi.org/10.5194/nhess-24-2689-2024, https://doi.org/10.5194/nhess-24-2689-2024, 2024
Short summary
Short summary
Landslides are complex phenomena causing important impacts in vulnerable areas, and they are often triggered by rainfall. Here, we develop a new approach that uses information on the temporal clustering of rainfall, i.e. multiple events close in time, to detect landslide events and compare it with the use of classical empirical rainfall thresholds, considering as a case study the region of Lisbon, Portugal. The results could help to improve the prediction of rainfall-triggered landslides.
Giorgio Baiamonte, Carmelo Agnese, Carmelo Cammalleri, Elvira Di Nardo, Stefano Ferraris, and Tommaso Martini
Adv. Stat. Clim. Meteorol. Oceanogr., 10, 51–67, https://doi.org/10.5194/ascmo-10-51-2024, https://doi.org/10.5194/ascmo-10-51-2024, 2024
Short summary
Short summary
In hydrology, the probability distributions are used to determine the probability of occurrence of rainfall events. In this study, two different methods for modeling rainfall time characteristics have been applied: a direct method and an indirect method that make it possible to relax the assumptions of the renewal process. The analysis was extended to two additional time variables that may be of great interest for practical hydrological applications: wet chains and dry chains.
Juan Camilo Acosta Navarro and Andrea Toreti
Weather Clim. Dynam., 4, 823–831, https://doi.org/10.5194/wcd-4-823-2023, https://doi.org/10.5194/wcd-4-823-2023, 2023
Short summary
Short summary
Droughts and heatwaves have become some of the clearest manifestations of a changing climate. Near-term adaptation strategies can benefit from seasonal predictions, but these predictions still have limitations. We found that an intrinsic property of multi-system forecasts can serve to better anticipate extreme high-temperature and low-precipitation events during boreal summer in several regions of the Northern Hemisphere with different levels of predictability.
F. Ioli, E. Bruno, D. Calzolari, M. Galbiati, A. Mannocchi, P. Manzoni, M. Martini, A. Bianchi, A. Cina, C. De Michele, and L. Pinto
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLVIII-M-1-2023, 137–144, https://doi.org/10.5194/isprs-archives-XLVIII-M-1-2023-137-2023, https://doi.org/10.5194/isprs-archives-XLVIII-M-1-2023-137-2023, 2023
Camille Labrousse, Wolfgang Ludwig, Sébastien Pinel, Mahrez Sadaoui, Andrea Toreti, and Guillaume Lacquement
Hydrol. Earth Syst. Sci., 26, 6055–6071, https://doi.org/10.5194/hess-26-6055-2022, https://doi.org/10.5194/hess-26-6055-2022, 2022
Short summary
Short summary
The interest of this study is to demonstrate that we identify two zones in our study area whose hydroclimatic behaviours are uneven. By investigating relationships between the hydroclimatic conditions in both clusters for past observations with the overall atmospheric functioning, we show that the inequalities are mainly driven by a different control of the atmospheric teleconnection patterns over the area.
Carmelo Cammalleri, Niall McCormick, and Andrea Toreti
Nat. Hazards Earth Syst. Sci., 22, 3737–3750, https://doi.org/10.5194/nhess-22-3737-2022, https://doi.org/10.5194/nhess-22-3737-2022, 2022
Short summary
Short summary
We evaluated the ability of vegetation indices derived from satellite data to capture annual yield variations across Europe. The strength of the relationship varies throughout the year, with March–October representing the optimal period in most cases. Spatial differences were also observed, with the best results obtained in the Mediterranean regions.
Veit Blauhut, Michael Stoelzle, Lauri Ahopelto, Manuela I. Brunner, Claudia Teutschbein, Doris E. Wendt, Vytautas Akstinas, Sigrid J. Bakke, Lucy J. Barker, Lenka Bartošová, Agrita Briede, Carmelo Cammalleri, Ksenija Cindrić Kalin, Lucia De Stefano, Miriam Fendeková, David C. Finger, Marijke Huysmans, Mirjana Ivanov, Jaak Jaagus, Jiří Jakubínský, Svitlana Krakovska, Gregor Laaha, Monika Lakatos, Kiril Manevski, Mathias Neumann Andersen, Nina Nikolova, Marzena Osuch, Pieter van Oel, Kalina Radeva, Renata J. Romanowicz, Elena Toth, Mirek Trnka, Marko Urošev, Julia Urquijo Reguera, Eric Sauquet, Aleksandra Stevkov, Lena M. Tallaksen, Iryna Trofimova, Anne F. Van Loon, Michelle T. H. van Vliet, Jean-Philippe Vidal, Niko Wanders, Micha Werner, Patrick Willems, and Nenad Živković
Nat. Hazards Earth Syst. Sci., 22, 2201–2217, https://doi.org/10.5194/nhess-22-2201-2022, https://doi.org/10.5194/nhess-22-2201-2022, 2022
Short summary
Short summary
Recent drought events caused enormous damage in Europe. We therefore questioned the existence and effect of current drought management strategies on the actual impacts and how drought is perceived by relevant stakeholders. Over 700 participants from 28 European countries provided insights into drought hazard and impact perception and current management strategies. The study concludes with an urgent need to collectively combat drought risk via a European macro-level drought governance approach.
Brunella Bonaccorso, Carmelo Cammalleri, Athanasios Loukas, and Heidi Kreibich
Nat. Hazards Earth Syst. Sci., 22, 1857–1862, https://doi.org/10.5194/nhess-22-1857-2022, https://doi.org/10.5194/nhess-22-1857-2022, 2022
Greta Cazzaniga, Carlo De Michele, Michele D'Amico, Cristina Deidda, Antonio Ghezzi, and Roberto Nebuloni
Hydrol. Earth Syst. Sci., 26, 2093–2111, https://doi.org/10.5194/hess-26-2093-2022, https://doi.org/10.5194/hess-26-2093-2022, 2022
Short summary
Short summary
Rainfall estimates are usually obtained from rain gauges, weather radars, or satellites. An alternative is the measurement of the signal loss induced by rainfall on commercial microwave links (CMLs). In this work, we assess the hydrologic response of Lambro Basin when CML-retrieved rainfall is used as model input. CML estimates agree with rain gauge data. CML-driven discharge simulations show performance comparable to that from rain gauges if a CML-based calibration of the model is undertaken.
Fabiola Banfi and Carlo De Michele
The Cryosphere, 16, 1031–1056, https://doi.org/10.5194/tc-16-1031-2022, https://doi.org/10.5194/tc-16-1031-2022, 2022
Short summary
Short summary
Climate changes require a dynamic description of glaciers in hydrological models. In this study we focus on the local modelling of snow and firn. We tested our model at the site of Colle Gnifetti, 4400–4550 m a.s.l. The model shows that wind erodes all the precipitation of the cold months, while snow is in part conserved between April and September since higher temperatures protect snow from erosion. We also compared modelled and observed firn density, obtaining a satisfying agreement.
Roberto Villalobos-Herrera, Emanuele Bevacqua, Andreia F. S. Ribeiro, Graeme Auld, Laura Crocetti, Bilyana Mircheva, Minh Ha, Jakob Zscheischler, and Carlo De Michele
Nat. Hazards Earth Syst. Sci., 21, 1867–1885, https://doi.org/10.5194/nhess-21-1867-2021, https://doi.org/10.5194/nhess-21-1867-2021, 2021
Short summary
Short summary
Climate hazards may be caused by events which have multiple drivers. Here we present a method to break down climate model biases in hazard indicators down to the bias caused by each driving variable. Using simplified fire and heat stress indicators driven by temperature and relative humidity as examples, we show how multivariate indicators may have complex biases and that the relationship between driving variables is a source of bias that must be considered in climate model bias corrections.
Carmelo Cammalleri, Carolina Arias-Muñoz, Paulo Barbosa, Alfred de Jager, Diego Magni, Dario Masante, Marco Mazzeschi, Niall McCormick, Gustavo Naumann, Jonathan Spinoni, and Jürgen Vogt
Nat. Hazards Earth Syst. Sci., 21, 481–495, https://doi.org/10.5194/nhess-21-481-2021, https://doi.org/10.5194/nhess-21-481-2021, 2021
Short summary
Short summary
Building on almost ten years of expertise and operational application of the Combined Drought Indicator (CDI) for the monitoring of agricultural droughts in Europe within the European Commission's European Drought Observatory (EDO), this paper proposes a revised version of the index. This paper shows that the proposed revised CDI reliably reproduces the evolution of major droughts, outperforming the current version of the indicator, especially for long-lasting events.
Marco Bongio, Ali Nadir Arslan, Cemal Melih Tanis, and Carlo De Michele
The Cryosphere, 15, 369–387, https://doi.org/10.5194/tc-15-369-2021, https://doi.org/10.5194/tc-15-369-2021, 2021
Short summary
Short summary
The capability of time-lapse photography to retrieve snow depth time series was tested. We demonstrated that this method can be efficiently used in three different case studies: two in the Italian Alps and one in a forested region of Finland, with an accuracy comparable to the most common methods such as ultrasonic sensors or manual measurements. We hope that this simple method based only on a camera and a graduated stake can enable snow depth measurements in dangerous and inaccessible sites.
Fabiola Banfi and Carlo De Michele
The Cryosphere Discuss., https://doi.org/10.5194/tc-2020-357, https://doi.org/10.5194/tc-2020-357, 2021
Manuscript not accepted for further review
Short summary
Short summary
Climate changes require a dynamic description of glaciers in hydrological models. In this study we focus on the local modeling of snow and firn. We tested our model at the site of Colle Gnifetti, 4400–4550 m a.s.l. The model shows that wind erodes all the precipitation of the cold months, while snow is in part conserved between May and September, since higher temperatures protect snow from erosion. We also compared modeled and observed firn density obtaining a satisfying agreement.
Carmelo Cammalleri, Gustavo Naumann, Lorenzo Mentaschi, Bernard Bisselink, Emiliano Gelati, Ad De Roo, and Luc Feyen
Hydrol. Earth Syst. Sci., 24, 5919–5935, https://doi.org/10.5194/hess-24-5919-2020, https://doi.org/10.5194/hess-24-5919-2020, 2020
Short summary
Short summary
Climate change is anticipated to alter the demand and supply of water at the earth's surface. This study shows how hydrological droughts will change across Europe with increasing global warming levels, showing that at 3 K global warming an additional 11 million people and 4.5 ×106 ha of agricultural land will be exposed to droughts every year, on average. These effects are mostly located in the Mediterranean and Atlantic regions of Europe.
Cited articles
Aas, K., Czado, C., Frigessi, A., and Bakken, H.: Pair-copula constructions of multiple dependence, Ins. Math. Econ., 44, 182–198, https://doi.org/10.1016/j.insmatheco.2007.02.001, 2009.
Aghakouchak, A., Ciach, G., and Habib, E.: Estimation of tail dependence coefficient in rainfall accumulation fields, Adv. Water Resour., 33, 1142–1149, https://doi.org/10.1016/j.advwatres.2010.07.003, 2010.
Almenda-Martín, L., Martínez-Fernández, J., Piles, M., González-Zamora, A., Benito-Verdugo, P., and Gaona, J.: Influence of atmospheric patterns on soil moisture dynamics in Europe, Sci. Total Environ., 846, 157537, https://doi.org/10.1016/j.scitotenv.2022.157537, 2022.
Anderson, M. C., Hain, C., Wardlow, B., Pimstein, A., Mecikalski, J. R., and Kustas, W. P.: Evaluation of drought indices based on thermal remote sensing of evapotranspiration over the continental United States, J. Climate, 24, 2025–2044, https://doi.org/10.1175/2010JCLI3812.1, 2011.
Arnal, L., Asp, S.-S., Baugh, C., de Roo, A., Disperati, J., Dottori, F., Garcia, R., Garcia Padilla, M., Gelati, E., Gomes, G., Kalas, M., Krzeminski, B., Latini, M., Lorini, V., Mazzetti, C., Mikulickova, M., Muraro, D., Prudhomme, C., Rauthe-Schöch, A., Rehfeldt, K., Salamon, P., Schweim, C., Skoien, J. O., Smith, P., Sprokkereef, E., Thiemig, V., Wetterhall, F., and Ziese, M.:. EFAS upgrade for the extended model domain – technical documentation, JRC Technical Reports, EUR 29323 EN, Publications Office of the European Union, Luxembourg, 58 pp., https://doi.org/10.2760/806324, 2019.
Bachmair, S., Tanguy, M., Hannaford, J., and Stahl, K.: How well do meteorological indicators represent agricultural and forest drought across Europe?, Environ. Res. Lett., 13, 034042, https://doi.org/10.1088/1748-9326/aaafda, 2018.
Bateni, M. M., Behmanesh, J., De Michele, C., Bazrafshan, J., and Rezaie, H.: Composite agrometeorological drought index accounting for seasonality and autocorrelation, J. Hydrol. Eng., 23, 04018020, https://doi.org/10.1061/(ASCE)HE.1943-5584.0001654, 2018.
Box, G. E. P. and Jenkins, G. M.: Time Series Analysis, Forecasting and Control, Holden-Day, San Francisco, 64–65, ISBN 978-1-118-67502-1, 1976.
Breiman, L.: Random forests, Machine Learn., 45, 5–32, https://doi.org/10.1023/A:1010933404324, 2001.
Brown, J. F., Wardlow, B. D., Tadesse, T., Hayes, M. J., and Reed, B. C.: The Vegetation Drought Response Index (VegDRI): A new integrated approach for monitoring drought stress in vegetation, GISci. Remote Sens., 45, 16–46, https://doi.org/10.2747/1548-1603.45.1.16, 2008.
Burnham, K. P. and Anderson, D. R.: Model Selection and Multimodel Inference: A practical information-theoretic approach, Springer-Verlag, 488 pp., ISBN 9780387953649, 2002.
Cammalleri, C., Micale, F., and Vogt, J.: On the value of combining different modelled soil moisture products for European drought monitoring, J. Hydrol., 525, 547–558, https://doi.org/10.1016/j.jhydrol.2015.04.021, 2015.
Cammalleri, C., Micale, F., and Vogt, J.: A novel soil moisture-based drought severity index (DSI) combining water deficit magnitude and frequency, Hydrol. Process., 30, 289–301, https://doi.org/10.1002/hyp.10578, 2016.
Cammalleri, C., Vogt, J. V., Bisselink, B., and de Roo, A.: Comparing soil moisture anomalies from multiple independent sources over different regions across the globe, Hydrol. Earth Syst. Sci., 21, 6329–6343, https://doi.org/10.5194/hess-21-6329-2017, 2017.
Cammalleri, C., Arias-Muñoz, C., Barbosa, P., de Jager, A., Magni, D., Masante, D., Mazzeschi, M., McCormick, N., Naumann, G., Spinoni, J., and Vogt, J.: A revision of the Combined Drought Indicator (CDI) used in the European Drought Observatory (EDO), Nat. Hazards Earth Syst. Sci., 21, 481–495, https://doi.org/10.5194/nhess-21-481-2021, 2021a.
Cammalleri, C., Spinoni J., Barbosa, P., Toreti, A., and Vogt, J. V.: The effects of non-stationarity on SPI for operational drought monitoring in Europe, Int. J. Climatol., 21, 1–13, https://doi.org/10.1002/joc.7424, 2021b.
Carrão, H., Russo, S., Sepulcre-Canto, G., and Barbosa, P.: An empirical standardized soil moisture index for agricultural drought assessment from remotely sensed data, Int. J. Appl. Earth Obs., 48, 74–84, https://doi.org/10.1016/j.jag.2015.06.011, 2016.
Chen, L. and Guo, S.: Copulas and Its Application in Hydrology and Water Resources, Springer Water, 290 pp., ISBN 978-981-13-0573-3, 2019.
Dash, S. S., Sahoo, B., and Raghuwanshi, N. S.: A SWAT-Copula based approach for monitoring and assessment of drought propagation in an irrigation command, Ecol. Eng., 127, 417–430, https://doi.org/10.1016/j.ecoleng.2018.11.021, 2019.
De Michele, C. and Salvadori, G.: A generalized Pareto intensity-duration model of storm rainfall exploiting 2-copulas, J. Geophys. Res.-Atmos., 108, 4067, https://doi.org/10.1029/2002JD002534, 2003.
de Roo, A. P. J., Wesseling, C., and Van Deusen, W.: Physically based river basin modelling within a GIS: The LISFLOOD model, Hydrol. Process., 14, 1981–1992, https://doi.org/10.1002/1099-1085(20000815/30)14:11/12<1981::AID-HYP49>3.0.CO;2-F, 2000.
Dißman, J., Brechmann, E. C., Czado, C., and Kurowicka, D.: Selecting and estimating regular vine copulae and application to financial returns, Comput. Stat. Data Anal., 59, 52–69, https://doi.org/10.1016/j.csda.2012.08.010, 2013.
Dixit, S. and Jayakumar, K. V.: Spatio-temporal analysis of copula-based probabilistic multivariate drought index using CMIP6 model, Int. J. Climatol., 42, 4333–4350, https://doi.org/10.1002/joc.7469, 2021.
Dutra, E., Viterbo, P., and Miranda, P. M. A.: ERA-40 reanalysis hydrological applications in the characterization of regional drought, Geophys. Res. Lett., 35, L19402, https://doi.org/10.1029/2008GL035381, 2008.
European Commission, Joint Research Centre (JRC): EDO Soil Moisture Anomaly (SMA) (version 2.1.1), European Commission, Joint Research Centre (JRC) [data set] PID, http://data.europa.eu/89h/882501f9-b783-4b6e-8aca-1875a7c0b372 (last access: 20 December 2023), 2021.
Farahmand, A. and AghaKouchak, A.: A generalized framework for deriving nonparametric standardized drought indicators, Adv. Water Resour., 76, 140–145, https://doi.org/10.1016/j.advwatres.2014.11.012, 2015.
Frahm, G., Junker, M., and Schmidt, R.: Estimating the tail-dependence coefficient: properties and pitfalls, Insur. Math. Econ., 37, 80–100, https://doi.org/10.1016/j.insmatheco.2005.05.008, 2005.
Gaona, J., Quintana-Seguí, P., Escorihuela, M. J., Boone, A., and Llasat, M. C.: Interactions between precipitation, evapotranspiration and soil-moisture-based indices to characterize drought with high-resolution remote sensing and land-surface model data, Nat. Hazards Earth Syst. Sci., 22, 3461–3485, https://doi.org/10.5194/nhess-22-3461-2022, 2022.
Genest, C., Favre, A. C., Béliveau, J., and Jacques, C.: Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data, Water Resour. Res., 43, 1–12, https://doi.org/10.1029/2006WR005275, 2007.
Halwatura, D., McIntyre, N., Lechner, A. M., and Arnold, S.: Capability of meteorological drought indices for detecting soil moisture droughts, J. Hydrol., 12, 396–412, https://doi.org/10.1016/j.ejrh.2017.06.001, 2017.
Hao, Z. and AghaKouchak, A.: Multivariate Standardized Drought Index: A parametric multi-index model, Adv. Water Resour., 57, 12–18, https://doi.org/10.1016/j.advwatres.2013.03.009, 2013.
Hao, Z. and Singh, V. P.: Drought characterization from a multivariate perspective: A review, J. Hydrol., 527, 668–678, https://doi.org/10.1016/j.jhydrol.2015.05.031, 2015.
Ji, L. and Peters, A. J.: Assessing vegetation response to drought in the northern Great Plains using vegetation and drought indices, Remote Sens. Environ., 87, 85–98, https://doi.org/10.1016/S0034-4257(03)00174-3, 2003.
Joe, H.: Dependence Modeling with Copulas, CRC Press, Taylor and Francis, 480 pp., ISBN 9781032477374, 2015.
Kanthavel, P., Saxena, C. K., and Singh, R. K.: Integrated drought index based on vine copula modelling, Int. J. Climatol., 42, 9510–9529, https://doi.org/10.1002/joc.7840, 2022.
Kao, S. C. and Govindaraju, R. S.: A copula-based joint deficit index for droughts, J. Hydrol., 380, 121–134, https://doi.org/10.1016/j.jhydrol.2009.10.029, 2010.
Kwon, M., Kwon, H. -H., and Han, D.: Spatio-temporal drought patterns of multiple drought indices based on precipitation and soil moisture: A case study in South Korea, Int. J. Climatol., 39, 4669-4687, https://doi.org/10.1002/joc.6094, 2019.
Laimighofer, J. and Laaha, G.: How standard are standardized drought indices? Uncertainty components for the SPI & SPEI case, J. Hydrol., 613, 128385, https://doi.org/10.1016/j.jhydrol.2022.128385, 2022.
Manning, C., Widmann, M., Bevacqua, E., van Loon, A. F., Maraun, D., and Vrac, M.: Soil moisture drought in Europe: A compound event of precipitation and potential evapotranspiration on multiple time scales. J. Hydrometeorol., 19, 1255–1271, https://doi.org/10.1175/JHM-D-18-0017.1, 2018.
McKee, T. B., Doesken, N. J., and Kleist, J.: The Relationship of Drought Frequency and Duration to Time Scales, Proceedings of the 8th Conference on Applied Climatology, 17–22 January, Anaheim, CA, American Meteorological Society, https://www.droughtmanagement.info/literature/AMS_Relationship_Drought_Frequency_Duration_Time_Scales_1993.pdf (last access: 2 January 2024), 1993.
Mishra, A. K. and Singh, V. P.: A review of drought concepts, J. Hydrol., 391, 202–216, https://doi.org/10.1016/j.rse.2016.02.064, 2010.
Mo, K. C. and Lettenmaier, D. P.: Objective drought classification using multiple land surface models, J. Hydrometeorol., 15, 990–1010, https://doi.org/10.1175/JHM-D-13-071.1, 2013.
Mo, K. C. and Lyon, B.: Global meteorological drought prediction using the North American multi-model ensemble, J. Hydrometeorol., 16, 1409–1424, https://doi.org/10.1175/JHM-D-14-0192.1, 2015.
Mohammed, S., Alsafadi, K., Enaruvbe, G. O., Bashir, B., Elbeltagi, A., Széles, A., Alsalman, A., and Harsanyi, E.: Assessing the impacts of agricultural drought (SPI/SPEI) on maize and wheat yields across Hungary, Sci. Rep., 12, 8838, https://doi.org/10.1038/s41598-022-12799-w, 2022.
Nelsen, R. G.: An introduction to copulas, Springer Series in Statistics, Springer-Verlag, New York, 272 pp., https://doi.org/10.1007/0-387-28678-0, 2006.
Palmer, W. C.: Meteorological Drought, Office of Climatology Research Paper No. 45, Washington DC, US Weather Bureau, https://www.droughtmanagement.info/literature/USWB_Meteorological_Drought_1965.pdf (last access: 2 January 2024), 1965.
Panu, U. S. and Sharma, T. C.: Challenges in drought research: Some perspectives and future directions, Hydrolog. Sci. J., 47, S19–S30, https://doi.org/10.1080/02626660209493019, 2002.
Pieper, P., Düsterhus, A., and Baehr, J.: A universal Standardized Precipitation Index candidate distribution function for observations and simulations, Hydrol. Earth Syst. Sci., 24, 4541–4565, https://doi.org/10.5194/hess-24-4541-2020, 2020.
Poulin, A., Huard, D., Favre, A. C., and Pugin, S.: Importance of tail dependence in bivariate frequency analysis, J. Hydrol. Eng., 12, 394–403, https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(394), 2007.
Quiring, S. M. and Papakryiakou, T. N.: An evaluation of agricultural drought indices for the Canadian prairies, Agr. Forest Meteorol., 118, 49–62, https://doi.org/10.1016/S0168-1923(03)00072-8, 2003.
Ravelo, A. C. and Decker, W. L.: The probability distribution of a soil moisture index, Agr. Meteorol., 20, 301–312, https://doi.org/10.1016/0002-1571(79)90004-9, 1979.
Rembold, F., Meroni, M., Urbano, F., Csak, G., Kerdiles, H., Perez-Hoyos, A., Lemoine, G., Leo, O., and Negre, T.: ASAP: A new global early warning system to detect anomaly hot spots of agricultural production for food security analysis, Agr. Syst., 168, 247–257, https://doi.org/10.1016/j.agsy.2018.07.002, 2019.
Ribeiro, A. and Pires, C.: Seasonal drought predictability in Portugal using statistical–dynamical techniques, Phys. Chem. Earth, 94, 155–166, https://doi.org/10.1016/j.pce.2015.04.003, 2016.
Sadri, S., Pan, M., Wada, Y., Vergopolan, N., Sheffield, J., Famiglietti, J. S., Kerr, Y., and Wood, E. F.: A global near-real-time soil moisture index monitor for food security using integrated SMOS and SMAP, Remote Sens. Environ., 246, 111864, https://doi.org/10.1016/j.rse.2020.111864, 2020.
Salvadori G. and De Michele C.: Frequency analysis via copulas: Theoretical aspects and applications to hydrological events, Wat. Resour. Res., 40, W12511, https://doi.org/10.1029/2004WR003133, 2004.
Salvadori, G., De Michele, C., Kottegoda, N. T., and Rosso, R.: Extremes in Nature: An approach using Copulas, Water Science and Technology Library Series, vol. 56, Springer, Dordrecht, 292 pp., ISBN 978-1-4020-4415-1, 2007.
Schmidt, R. and Stadtmueller, U.: Non-parametric estimation of tail dependence, Scand. J. Stat., 33, 307–335, https://doi.org/10.1111/j.1467-9469.2005.00483.x, 2006.
Sehler, R., Li, J., Reager, J. T., and Ye, H.: Investigating relationship between soil moisture and precipitation globally using remote sensing observations, J. Cont. Water Res. Edu., 168, 106–118, https://doi.org/10.1111/j.1936-704X.2019.03324.x, 2019.
Seneviratne, S. I., Corti, T., Davin, E. L., Hirschi, M., Jaeger, E. B., Lehner, I., Orlowsky, B., and Teuling, A. J.: Investigating soil moisture–climate interactions in a changing climate: A review, Earth-Sci. Rev., 99, 125–161, https://doi.org/10.1016/j.earscirev.2010.02.004, 2010.
Sepulcre-Canto, G., Horion, S., Singleton, A., Carrao, H., and Vogt, J.: Development of a Combined Drought Indicator to detect agricultural drought in Europe, Nat. Hazards Earth Syst. Sci., 12, 3519–3531, https://doi.org/10.5194/nhess-12-3519-2012, 2012.
Serinaldi, F.: Analysis of inter-gauge dependence by Kendall's τK upper tail dependence coefficient, and 2-copulas with application to rainfall fields, Stoch. Environ. Res. Risk A, 22, 671–688, https://doi.org/10.1007/s00477-007-0176-4, 2008.
Serinaldi, F., Bárdossy, A., and Kilsby, C. G.: Upper tail dependence in rainfall extremes: would we know it if we saw it?, Stoch. Environ. Res. Risk A, 29, 1211–1233, https://doi.org/10.1007/s00477-014-0946-8, 2015.
Sheffield, J. and Wood, E. F.: Characteristics of global and regional drought, 1950–2000: Analysis of soil moisture data from off-line simulation of the terrestrial hydrologic cycle, J. Geophys. Res., 112, D17115, https://doi.org/10.1029/2006JD008288, 2007.
Sheffield, J., Goteti, G., Wen, F., and Wood, E. F.: A simulated soil moisture based drought analysis for the United States, J. Geophys. Res., 109, D24108, https://doi.org/10.1029/2004JD005182, 2004.
Sims, A. P., Niyogi, D. S., and Raman, S.: Adopting drought indices for estimating soil moisture: A North Carolina case study, Geophys. Res. Lett., 29, 24-1–24-4, https://doi.org/10.1029/2001GL013343, 2002.
Sivakumar, M. V. K., Motha, R. P., Wilhite, D. A., and Wood, D. A.: Agricultural Drought Indices, Proceedings of the WMO/UNISDR Expert Group Meeting on Agricultural Drought Indices, 2–4 June 2010, Murcia, Spain: Geneva, Switzerland: World Meteorological Organization, AGM-11, WMO/TD No. 1572, WAOB-2011, 197 pp., https://library.wmo.int/idurl/4/58726 (last access: 2 January 2024), 2011.
Soľáková, T., De Michele, C., and Vezzoli, R.: Comparison between parametric and nonparametric approaches for the calculation of two drought indices: SPI and SSI, J. Hydrol. Eng., 19, 04014010, https://doi.org/10.1061/(ASCE)HE.1943-5584.0000942, 2014.
Stagge, J. H., Tallaksen, L. M., Gudmundsson, L., van Loon, A. F., and Stahl, K.: Candidate distributions for climatological drought indices (SPI and SPEI), Int. J. Climatol., 35, 4027–4040, https://doi.org/10.1002/joc.4267, 2015.
Stoica, P. and Selen, Y.: Model-order selection: a review of information criterion rules, IEEE Signal Proc. Mag., 21, 36–47, https://doi.org/10.1109/MSP.2004.1311138, 2004.
Svoboda, M., LeComte, D., Hayes, M., Heim, R., Gleason, K., Angel, J., Rippey, B., Tinker, R., Palecki, M., and Stooksbury, D.: The drought monitor, B. Am. Meteorol. Soc., 83, 1181–1190, https://doi.org/10.1175/1520-0477-83.8.1181, 2002.
Thielen, J., Bartholmes, J., Ramos, M.-H., and de Roo, A.: The European Flood Alert System – Part 1: Concept and development, Hydrol. Earth Syst. Sci., 13, 125–140, https://doi.org/10.5194/hess-13-125-2009, 2009.
Thieming, V., Gomes, G. N., Skøien, J. O., Ziese, M., Rauthe-Schöch, A., Rustemeier, E., Rehfeldt, K., Walawender, J. P., Kolbe, C., Pichon, D., Schweim, C., and Salamon, P.: EMO-5: a high-resolution multi-variable gridded meteorological dataset for Europe, Earth Syst. Sci. Data, 14, 3249–3272, https://doi.org/10.5194/essd-14-3249-2022, 2022.
Tian, L., Yuan, S., and Quiring, S. M.: Evaluation of six indices for monitoring agricultural drought in the south-central United States, Agr. Forest Meteorol., 249, 107–119, https://doi.org/10.1016/j.agrformet.2017.11.024, 2018.
van der Wiel, K., Batelaan, T. J., and Wanders, N.: Large increases of multi-year droughts in north-western Europe in a warmer climate, Clim. Dynam., 60, 1781–1800, https://doi.org/10.1007/s00382-022-06373-3, 2022.
Vicente-Serrano S. M., Beguería, S., and López-Moreno, J. I.: A Multi-scalar drought index sensitive to global warming: The Standardized Precipitation Evapotranspiration Index – SPEI, J. Climate, 23, 1696–1718, https://doi.org/10.1175/2009JCLI2909.1, 2010.
Wang, H., Rogers, J. C., and Munroe, D. K.: Commonly used drought indices as indicators of soil moisture in China, Hydrometeorol., 16, 1397–1408, https://doi.org/10.1175/JHM-D-14-0076.1, 2015.
Wilhite, D. A. and Glantz, M. H.: Understanding the drought phenomenon: The role of definitions, Water Int., 10, 111–120, 1985.
World Meteorological Organization (WMO): Standardized Precipitation Index User Guide (WMO n. 1090), Geneva, 24 pp., https://library.wmo.int/idurl/4/39629 (last access: 2 January 2024), 2012.
World Meteorological Organization (WMO), Global Water Partnership (GWP): Handbook of Drought Indicators and Indices, edited by: Svoboda, M. and Fuchs, B. A., Integrated Drought Management Programme (IDMP), Integrated Drought Management Tools and Guidelines Series 2, Geneva, 52 pp., ISBN 978-92-63-11173-9, 2016.
Xia, Y., Ek, M. B., Peters-Lidard, C. D., Mocko, D., Svoboda, M., Sheffield, J., and Wood, E. F.: Application of USDM statistics in NLDAS-2: optimal blended NLDAS drought index over the continental United States, J. Geophys. Res.-Atmos., 119, 2947–2965, https://doi.org/10.1002/2013JD020994, 2014.
Yuan, X. and Wood, E. F.: Multimodel seasonal forecasting of global drought onset, Geophys. Res. Lett., 40, 4900–4905, https://doi.org/10.1002/grl.50949, 2013.
Zargar, A., Sadiq, R., Naser, B., Khan, F. I.: A review of drought indices, Environ. Rev., 19, 333–349, https://doi.org/10.1139/A11-013, 2011.
Short summary
Precipitation and soil moisture have the potential to be jointly used for the modeling of drought conditions. In this research, we analysed how their statistical inter-relationship varies across Europe. We found some clear spatial patterns, especially in the so-called tail dependence (which measures the strength of the relationship for the extreme values). The results suggest that the tail dependence needs to be accounted for to correctly assess the value of joint modeling for drought.
Precipitation and soil moisture have the potential to be jointly used for the modeling of...
