Chakravarti, N.: Isotonic median regression: a linear programming approach, Math. Oper. Res., 14, 303–308, https://doi.org/10.1287/moor.14.2.303, 1989.
Chowdhury, D. P., Roy, D., and Saha, U.: Incorporation of weather parameters in MMRC-K model for rainfal
l disaggregation, Stoch. Env. Res. Risk A., 39, 289–308, https://doi.org/10.1007/s00477-024-02863-4, 2025.
Correa, C.: pyqcoda: v1.0.4, Zenodo [software], https://doi.org/10.5281/zenodo.19819042, 2026a.
Correa, C.: Dataset and scripts to reproduce the results presented in the paper ”Capturing the extremes: a quasi-comonotonicity-based algorithm for disaggregating daily to hourly rainfall”, Zenodo [data set], https://doi.org/10.5281/zenodo.20926916, 2026b.
De Leeuw, J.: Correctness of Kruskal's algorithms for monotone regression with ties, Psychometrika, 42, 141–144, https://doi.org/10.1007/BF02293750, 1977.
Delong, Ł. and Wüthrich, M. V.: Isotonic regression for variance estimation and its role in mean estimation and model validation, North Am. Actuar. J., 1–29, https://doi.org/10.1080/10920277.2024.2421221, 2024.
Ebers, N., Schröter, K., and Müller-Thomy, H.: Estimation of future rainfall extreme values by temperature-dependent disaggregation of climate model data, Nat. Hazards Earth Syst. Sci., 24, 2025–2043, https://doi.org/10.5194/nhess-24-2025-2024, 2024.
Förster, K., Hanzer, F., Winter, B., Marke, T., and Strasser, U.: An open-source MEteoroLOgical observation time series DISaggregation Tool (MELODIST v0.1.1), Geosci. Model Dev., 9, 2315–2333, https://doi.org/10.5194/gmd-9-2315-2016, 2016.
Fowler, H. J., Wasko, C., and Prein, A. F.: Intensification of short-duration rainfall extremes and implications for flood risk: Current state of the art and future directions, Philos. T. Roy. Soc. A, 379, 20190541, https://doi.org/10.1098/rsta.2019.0541, 2021.
Gong, F., Dai, L., Benchawattananon, R., Foong, S. Y., Cheng, Z., and Weng, C.: Modern pollen–environment calibrations in Thailand–Malaysia: Normalised Difference Vegetation Index (NDVI) and precipitation as quantitative constraints for vegetation reconstruction, J. Biogeogr., 53, e70191, https://doi.org/10.1111/jbi.70191, 2026.
Görner, C., Franke, J., Kronenberg, R., Hellmuth, O., and Bernhofer, C.: Multivariate non-parametric Euclidean distance model for hourly disaggregation of daily climate data, Theor. Appl. Climatol., 143, 241–265, https://doi.org/10.1007/s00704-020-03426-7, 2021.
Gutiérrez, J. M., Maraun, D., Widmann, M., Huth, R., Hertig, E., Benestad, R., Roessler, O., Wibig, J., Wilcke, R., Kotlarski, S., San Martín, D., Herrera, S., Bedia, J., Casanueva, A., Manzanas, R., Iturbide, M., Vrac, M., Dubrovsky, M., Ribalaygua, J., Pórtoles, J., Räty, O., Räisänen, J., Hingray, B., Raynaud, D., Casado, M. J., Ramos, P., Zerenner, T., Turco, M., Bosshard, T., Štěpánek, P., Bartholy, J., Pongracz, R., Keller, D. E., Fisher, A. M., Cardoso, P. M., Soares, P. M. M., Czernecki, B., and Pagé, C.: An intercomparison of a large ensemble of statistical downscaling methods over Europe: Results from the VALUE perfect predictor cross-validation experiment, Int. J. Climatol., 39, 3750–3785, https://doi.org/10.1002/joc.5462, 2019.
Hasan, M. M., Strong, C., Brooks, P. D., Burian, S. J., and Barber, M. E.: Quantifying climate change impacts on low flows of small high mountain watersheds: A nonstationary approach, J. Hydrol. Reg. Stud., 48, 101463, https://doi.org/10.1016/j.ejrh.2023.101463, 2023.
Haslinger, K., Breinl, K., Pavlin, L., Pistotnik, G., Bertola, M., Olefs, M., Greilinger, M., Schöner, W., and Blöschl, G.: Increasing hourly heavy rainfall in Austria reflected in flood changes, Nature, 639, 667–672, https://doi.org/10.1038/s41586-025-08647-2, 2025.
Hernanz, A., Garcia-Valero, J. A., Domínguez, M., Ramos-Calzado, P., Pastor-Saavedra, M. A., and Rodriguez-Camino, E.: Evaluation of statistical downscaling methods for climate change projections over Spain: Present conditions with perfect predictors, Int. J. Climatol., 42, 762–776, https://doi.org/10.1002/joc.7271, 2022.
Joe, H.: Asymptotic efficiency of the two-stage estimation method for copula-based models, J. Multivariate Anal., 94, 401–419, https://doi.org/10.1016/j.jmva.2004.06.003, 2005.
Lee, J., Kim, U., Kim, S., and Kim, J.: Development and application of a rainfall temporal disaggregation method to project design rainfalls, Water-Sui, 14, 1401, https://doi.org/10.3390/w14091401, 2022.
Li, X., Meshgi, A., Wang, X., Zhang, J., Tay, S. H. X., Pijcke, G., and Babovic, V.: Three resampling approaches based on method of fragments for daily-to-subdaily precipitation disaggregation, Int. J. Climatol., 38, e1119–e1138, https://doi.org/10.1002/joc.5438, 2018.
Lopez-Gomez, I., McGovern, A., Agrawal, S., and Hickey, J.: Global extreme heat forecasting using neural weather models, Artif. Intell. Earth Syst., 2, e220035, https://doi.org/10.1175/AIES-D-22-0035.1, 2023.
Maloku, K., Hingray, B., and Evin, G.: Accounting for precipitation asymmetry in a multiplicative random cascade disaggregation model, Hydrol. Earth Syst. Sci., 27, 3643–3661, https://doi.org/10.5194/hess-27-3643-2023, 2023.
Mayer, S., Hendrick, M., Michel, A., Richter, B., Schweizer, J., Wernli, H., and van Herwijnen, A.: Impact of climate change on snow avalanche activity in the Swiss Alps, The Cryosphere, 18, 5495–5517, https://doi.org/10.5194/tc-18-5495-2024, 2024.
Moradzadeh Rahmatabadi, S., Irandoust, M., and Mirabbasi, R.: Multivariate analysis of rainfall–runoff characteristics using copulas, J. Earth Syst. Sci., 132, 93, https://doi.org/10.1007/s12040-023-02105-1, 2023.
Müller, H. and Haberlandt, U.: Temporal rainfall disaggregation using a multiplicative cascade model for spatial application in urban hydrology, J. Hydrol., 556, 847–864, https://doi.org/10.1016/j.jhydrol.2016.01.031, 2018.
Müller-Thomy, H.: Temporal rainfall disaggregation using a micro-canonical cascade model: possibilities to improve the autocorrelation, Hydrol. Earth Syst. Sci., 24, 169–188, https://doi.org/10.5194/hess-24-169-2020, 2020.
Naderi, K., Moghaddasi, M., and Shokri, A.: Drought occurrence probability analysis using multivariate standardized drought index and copula function under climate change, Water Resour. Manag., 36, 2865–2888, https://doi.org/10.1007/s11269-022-03186-1, 2022.
Oates, H., Arora, N., Oh, H. G., and Lee, T.: A long short-term memory model for sub-hourly temporal disaggregation of precipitation, Stoch. Env. Res. Risk A., 1–14, https://doi.org/10.1007/s00477-025-02996-0, 2025.
Olsson, J.: Evaluation of a scaling cascade model for temporal rainfall disaggregation, Hydrol. Earth Syst. Sci., 2, 19–30, https://doi.org/10.5194/hess-2-19-1998, 1998.
Onof, C., Chandler, R. E., Kakou, A., Northrop, P., Wheater, H. S., and Isham, V.: Rainfall modelling using Poisson-cluster processes: a review of developments, Stoch. Env. Res. Risk A., 14, 384–411, https://doi.org/10.1007/s004770000043, 2000.
Pui, A., Sharma, A., Mehrotra, R., Sivakumar, B., and Jeremiah, E.: A comparison of alternatives for daily to sub-daily rainfall disaggregation, J. Hydrol., 470, 138–157, https://doi.org/10.1016/j.jhydrol.2012.08.041, 2012.
Qin, X. and Dai, C.: Investigation of rainfall disaggregation with flexible timescales based on point process models, J. Hydrol., 634, 131101, https://doi.org/10.1016/j.jhydrol.2024.131101, 2024.
Rodriguez-Iturbe, I., Cox, D. R., and Isham, V.: Some models for rainfall based on stochastic point processes, P. Roy. Soc. Lond. A Mat., 410, 269–288, https://doi.org/10.1098/rspa.1987.0039, 1987.
Rousseeuw, P. J.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis, J. Comput. Appl. Math., 20, 53–65, https://doi.org/10.1016/0377-0427(87)90125-7, 1987.
Scher, S. and Peßenteiner, S.: Technical Note: Temporal disaggregation of spatial rainfall fields with generative adversarial networks, Hydrol. Earth Syst. Sci., 25, 3207–3225, https://doi.org/10.5194/hess-25-3207-2021, 2021.
Schilling, W.: Rainfall data for urban hydrology: what do we need?, Atmos. Res., 27, 5–21, https://doi.org/10.1016/0169-8095(91)90003-F, 1991.
Sklar, A.: Random variables, distribution functions, and copulas – a personal look backward and forward, in Distributions with Fixed Marginals and Related Topics (Seattle, WA, 1993), IMS Lecture Notes Monogr. Ser., 28, Inst. Math. Statist., Hayward, CA, 1–14, https://doi.org/10.1214/lnms/1215452606, 1996.
Stoner, O. and Economou, T.: An advanced hidden Markov model for hourly rainfall time series, Comput. Stat. Data An., 152, 107045, https://doi.org/10.1016/j.csda.2020.107045, 2020.
Takhellambam, B. S., Srivastava, P., Lamba, J., McGehee, R. P., Kumar, H., and Tian, S.: Temporal disaggregation of hourly precipitation under changing climate over the Southeast United States, Sci. Data, 9, 211, https://doi.org/10.1038/s41597-022-01304-7, 2022.
Vicente-Serrano, S. M., Beguería, S., Reig, F., Royo, A., Arretxea, M., Gil, M., Latorre, B., El Kenawy, A., Franquesa, M., Halifa-Marin, A., Adell-Michavila, M., Crespillo, A., Pérez-Pajuelo, D., Domínguez-Castro, F., Barriopedro, D., Gutiérrez, J. M., Azorin-Molina, C., Gimeno, L., and Nieto, R.: Developing science-informed maps and climate services for extreme rainfall in Spain, Nat. Hazards, 1–22, https://doi.org/10.1007/s11069-025-07731-0, 2025.
Vorobevskii, I., Park, J., Kim, D., Barfus, K., and Kronenberg, R.: Simulating sub-hourly rainfall data for current and future periods using two statistical disaggregation models: case studies from Germany and South Korea, Hydrol. Earth Syst. Sci., 28, 391–416, https://doi.org/10.5194/hess-28-391-2024, 2024.
Wuertz, D., Lawrimore, J., and Korzeniewski, B.: NOAA Cooperative Observer Program (COOP) precipitation data – hourly, version 2 [COOP Hourly Precip. (1950s-present)], NOAA National Centers for Environmental Information, https://doi.org/10.25921/p7j8-2170, 2018.
