Abstract
Continuous hydrological simulation is a powerful approach for generating long-term series of river discharges used for hydrological analyses. This approach requires as inputs precipitation time series generated by a stochastic weather generator (WGEN) to simulate discharge time series. For small catchments where a lumped hydrological model is suitable, the weather generator needs to generate time series of mean areal precipitation (MAP). Here we assess the ability of an at-site hybrid WGEN to generate time series of MAP for a set of test areas ranging from 9 to 1,089 km\(^2\). The generator is composed of a model based on a Markov chain model used to generate time series of daily MAP, and a multiplicative random cascade used to disaggregate them to an hourly resolution. The work is carried out at several test locations in Switzerland with different precipitation regimes. The parameters of the model are estimated on the observed MAP time series extracted from CombiPrecip, a 1 km\(^2\) resolution radar-gauge product of precipitation assimilating rain gauges and radar data. For each test location and each test area, 100-year time series are generated and compared with the observed MAP time series. Whatever the location and spatial scale considered, the performance of the WGEN is satisfactory. The model reproduces the observed standard statistics and extreme precipitation of observed MAP very well. At an hourly resolution, better results are obtained at larger spatial scales, while no difference is noticed at a daily resolution. The study shows that using this hybrid WGEN is possible to model and generate MAP for areas ranging from 9 to 1,089 km\(^2\). Moreover, this particular WGEN is easy to implement for end-user applications. The modelling approach is even more promising as high-resolution gridded precipitation data are expected to become increasingly available worldwide, offering a source of data to calibrate the hybrid model.










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References
Ailliot P, Allard D, Monbet V, Naveau P (2015) Stochastic weather generators: an overview of weather type models. J Société Française Stat 156(1):101–113
Andres N, Lieberherr G, Sideris IV, Jordan F, Zappa M (2016) From calibration to real-time operations: an assessment of three precipitation bench marks for a Swiss river system. Meteorol Appl 23(3):448–461. https://doi.org/10.1002/met.1569
Antonetti M, Horat C, Sideris IV, Zappa M (2019) Ensemble flood forecasting considering dominant runoff processes—part 1: set-up and application to nested basins (Emme, Switzerland). Nat Hazards Earth Syst Sci 19(1):19–40. https://doi.org/10.5194/nhess-19-19-2019
Barton Y, Sideris IV, Raupach TH, Gabella M, Germann U, Martius O (2020) A multi-year assessment of sub-hourly gridded precipitation for Switzer676 land based on a blended radar-Rain-gauge dataset. Int J Climatol 40(12):5208–5222. https://doi.org/10.1002/joc.6514
Benoit L, Sichoix L, Nugent AD, Lucas MP, Giambelluca TW (2022) Stochas680 tic daily rainfall generation on tropical islands with complex topography. Hydrol Earth Syst Sci 26(8):2113–2129. https://doi.org/10.5194/hess-26-2113-2022
Berg P, Moseley C, Haerter JO (2013) Strong increase in convective precipitation in response to higher temperatures. Nat Geosci 6(3):181–185. https://doi.org/10.1038/ngeo1731
Blanchet J, Mélèse V (2020) A Bayesian framework for the multiscale assessment of storm severity and related uncertainties. J Hydrometeorol 21(1):109–122. https://doi.org/10.1175/JHM-D-18-0254.1
Boughton W, Droop O (2003) Continuous simulation for design flood estimation–a review. Environ Model Softw 18(4):309–318. https://doi.org/10.1016/S1364-8152(03)00004-5
Breinl K (2016) Driving a lumped hydrological model with precipitation output from weather generators of different complexity. Hydrol Sci J 61(8):1395–1414. https://doi.org/10.1080/02626667.2015.1036755
Breinl K, Di Baldassarre G, Girons Lopez M, Hagenlocher M, Vico G, Rutgers son A (2017) Can weather generation capture precipitation patterns across different climates, spatial scales and under data scarcity? Sci Rep 7(1):5449. https://doi.org/10.1038/s41598-017-05822-y
Buishand TA, Brandsma T (2001) Multisite simulation of daily precipitation and temperature in the Rhine Basin by nearest-neighbor resampling. Water Resour Res 37(11):2761–2776. https://doi.org/10.1029/2001WR000291
Bárdossy A, Pegram GGS (2009) Copula based multisite model for daily precipitation simulation. Hydrol Earth Syst Sci 13(12):2299–2314. https://doi.org/10.5194/hess-13-2299-2009
Bürger G, Heistermann M, Bronstert A (2014) Towards subdaily rainfall disaggregation via Clausius-Clapeyron. J Hydrometeorol 15(3):1303–1311. https://doi.org/10.1175/JHM-D-13-0161.1
Callau Poduje A, Haberlandt U (2017) Short time step continuous rainfall modeling and simulation of extreme events. J Hydrol 552:182–197. https://doi.org/10.1016/j.jhydrol.2017.06.036
Chardon J, Favre A-C, Hingray B (2016) Effects of spatial aggregation on the accuracy of statistically downscaled precipitation predictions. J Hydrometeorol 17(5):1561–1578. https://doi.org/10.1175/JHM-D-15-0031.1
Chen J, Brissette FP, Leconte R (2010) A daily stochastic weather generator for preserving low-frequency of climate variability. J Hydrol 388(3):480–490. https://doi.org/10.1016/j.jhydrol.2010.05.032
Chen J, Brissette FP, Zhang XJ (2015) Hydrological modeling using a multisite stochastic weather generator. J Hydrol Eng 21(2):04015060. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001288
Evin G, Blanchet J, Paquet E, Garavaglia F, Penot D (2016) A regional model for extreme rainfall based on weather patterns subsampling. J Hydrol 541:1185–1198. https://doi.org/10.1016/j.jhydrol.2016.08.024
Evin G, Favre A-C, Hingray B (2018) Stochastic generation of multi-site daily precipitation focusing on extreme events. Hydrol Earth Syst Sci 22(1):655–672. https://doi.org/10.5194/hess-22-655-2018
Frei C, Schär C (1998) A precipitation climatology of the Alps from high resolution rain-gauge observations. Int J Climatol 18(8):873–900. https://doi.org/10.1002/(SICI)1097-0088(19980630)18:8.873::AID-JOC255.3.0.CO;2-9
Furrer E, Katz R (2007) Generalized linear modeling approach to stochastic weather generators. Clim Res 34:129–144. https://doi.org/10.3354/cr034129
Gangopadhyay S, Clark M, Werner K, Brandon D, Rajagopalan B (2004) Effects of spatial and temporal aggregation on the accuracy of statistically downscaled precipitation estimates in the upper colorado river basin. J Hydrometeorol 5(6):1192–1206. https://doi.org/10.1175/JHM-391.1
Germann U, Boscacci M, Clementi L, Gabella M, Hering A, Sartori M, Calpini B (2022) Weather radar in complex orography. Remote Sens 14(3):503. https://doi.org/10.3390/rs14030503
Grimaldi S, Volpi E, Langousis A, Michael Papalexiou S, Luciano De Luca D, Piscopia R, Petroselli A (2022) Continuous hydrologic modelling for small and ungauged basins: a comparison of eight rainfall models for sub-daily runoff simulations. J Hydrol 610:127866. https://doi.org/10.1016/j.jhydrol.2022.127866
Gringorten II (1963) A plotting rule for extreme probability paper. J Geophys Res 68(3):813–814. https://doi.org/10.1029/JZ068i003p00813
Gugerli R, Gabella M, Huss M, Salzmann N (2020) CanWeather Radars be used to estimate snow accumulation on Alpine Glaciers? An evaluation based on glaciological surveys. J Hydrometeorol 21(12):2943–2962. https://doi.org/10.1175/JHM-D-20-0112.1
Gyasi-Agyei Y (2011) Copula-based daily rainfall disaggregation model. Water Resour Res 47(7):W07535. https://doi.org/10.1029/2011WR010519
Güntner A, Olsson J, Calver A, Gannon B (2001) Cascade-based disaggregation of continuous rainfall time series: the influence of climate. Hydrol Earth Syst Sci 5(2):145–164. https://doi.org/10.5194/hess-5-145-2001
Haberlandt U, Ebner von Eschenbach A-D, Buchwald I (2008) A space-time hybrid hourly rainfall model for derived flood frequency analysis. Hydrol Earth Syst Sci 12(6):1353–1367. https://doi.org/10.5194/hess-12-1353-2008
Hapuarachchi HAP, Wang QJ, Pagano TC (2011) A review of advances in flash flood forecasting. Hydrol Process 25(18):2771–2784. https://doi.org/10.1002/hyp.8040
Haruna A, Blanchet J, Favre A-C (2023) Modeling intensity-duration-frequency curves for the whole range of non-zero precipitation: a comparison of models. Water Resour Res 59(6):e2022WR033362. https://doi.org/10.1029/2022WR033362
Hingray B, Ben Haha M (2005) Statistical performances of various deterministic and stochastic models for rainfall series disaggregation. Atmos Res 77(1–4):152–175. https://doi.org/10.1016/j.atmosres.2004.10.023
Jothityangkoon C, Sivapalan M, Viney NR (2000) Tests of a space-time model of daily rainfall in southwestern Australia based on nonhomogeneous random cascades. Water Resour Res 36(1):267–284. https://doi.org/10.1029/1999WR900253
Khalili M, Brissette F, Leconte R (2011) Effectiveness of multi-site weather generator for hydrological modeling1. J Am Water Resour Assoc 47(2):303–314. https://doi.org/10.1111/j.1752-1688.2010.00514.x
Kim D, Olivera F, Cho H, Socolofsky SA (2013) Regionalization of the mModified Bartlett-Lewis rectangular pulse stochastic rainfall model. Terr Atmos Ocean Sci 24(3):421. https://doi.org/10.3319/TAO.2012.11.12.01(Hy)
Kim D, Onof C (2020) A stochastic rainfall model that can reproduce important rainfall properties across the timescales from several minutes to a decade. J Hydrol 589:125150. https://doi.org/10.1016/j.jhydrol.2020.125150
Koutsoyiannis D, Onof C (2001) Rainfall disaggregation using adjusting procedures on a Poisson cluster model. J Hydrol 246(1–4):109–122. https://doi.org/10.1016/S0022-1694(01)00363-8
Lamb R, Faulkner D, Wass P, Cameron D (2016) Have applications of continuous rainfall-runoff simulation realized the vision for process-based flood frequency analysis? Hydrol Process 30(14):2463–2481. https://doi.org/10.1002/hyp.10882
Leblois E, Creutin J-D (2013) Space-time simulation of intermittent rainfall with prescribed advection field: adaptation of the turning band method. Water Resour Res 49(6):3375–3387. https://doi.org/10.1002/wrcr.20190
Legrand C, Hingray B, Wilhelm B, Ménégoz M (2024) Assessing downscaling methods to simulate hydrologically relevant weather scenarios from a global atmospheric reanalysis: case study of the upper Rhône River (1902–2009). Hydrol Earth Syst Sci 28(9):2139–2166. https://doi.org/10.5194/hess-28-2139-2024
Li Z, Brissette F, Chen J (2013) Finding the most appropriate precipitation probability distribution for stochastic weather generation and hydrological modelling in Nordic watersheds: applicability of precipitation probability distributions. Hydrol Process 27(25):3718–3729. https://doi.org/10.1002/hyp.9499
Maloku K (2023) disaggMRC: temporal disaggregation of precipitation time series with microcanonical Random Cascade method (v1.0.0). Zenodo [code]. Accessed from https://doi.org/10.5281/zenodo.8435607
Maloku K, Hingray B, Evin G (2023) Accounting for precipitation asymmetry in a multiplicative random cascade disaggregation model. Hydrol Earth Syst Sci 27(20):3643–3661. https://doi.org/10.5194/hess-27-3643-2023
McIntyre N, Shi M, Onof C (2016) Incorporating parameter dependencies into temporal downscaling of extreme rainfall using a random cascade approach. J Hydrol 542:896–912. https://doi.org/10.1016/j.jhydrol.2016.09.057
Menabde M, Sivapalan M (2000) Modeling of rainfall time series and extremes using bounded random cascades and levy-stable distributions. Water Resour Res 36(11):3293–3300. https://doi.org/10.1029/2000WR900197
Mezghani A, Hingray B (2009) A combined downscaling-disaggregation weather generator for stochastic generation of multisite hourly weather variables over complex terrain: Development and multi-scale validation for the Upper Rhone River basin. J Hydrol 377(3):245–260. https://doi.org/10.1016/j.jhydrol.2009.08.033
Müller H, Haberlandt U (2018) 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
Müller-Thomy H, Sikorska-Senoner AE (2019) Does the complexity in temporal precipitation disaggregation matter for a lumped hydrological model? Hydrol Sci J 64(12):1453–1471. https://doi.org/10.1080/02626667.2019.1638926
Naveau P, Huser R, Ribereau P, Hannart A (2016) Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection. Water Resour Res 52(4):2753–2769. https://doi.org/10.1002/2015WR018552
Obled C, Wendling J, Beven K (1994) The sensitivity of hydrological models to spatial rainfall patterns: an evaluation using observed data. J Hydrol 159(1–4):305–333. https://doi.org/10.1016/0022-1694(94)90263-1
Olsson J (1998) Evaluation of a scaling cascade model for temporal rain-fall disaggregation. Hydrol Earth Syst Sci 2(1):19–30. https://doi.org/10.5194/hess-2-19-1998
Onof C, Chandler RE, Kakou A, Northrop P, Wheater HS, Isham V (2000) Rainfall modelling using Poisson-cluster processes: a review of developments. Stoch Environ Res Risk Assess 14(6):384–411. https://doi.org/10.1007/s004770000043
Ormsbee LE (1989) Rainfall disaggregation model for continuous hydrologic modeling. J Hydraul Eng 115(4):507–525. https://doi.org/10.1061/(ASCE)0733-9429(1989)115:4(507)
Panziera L, Gabella M, Germann U, Martius O (2018) A 12-year radar-based climatology of daily and sub-daily extreme precipitation over the Swiss Alps. Int J Climatol 38(10):3749–3769. https://doi.org/10.1002/joc.5528
Paschalis A, Molnar P, Fatichi S, Burlando P (2014) On temporal stochastic modeling of precipitation, nesting models across scales. Adv Water Resour 63:152–166. https://doi.org/10.1016/j.advwatres.2013.11.006
Peleg N, Fatichi S, Paschalis A, Molnar P, Burlando P (2017) An advanced stochastic weather generator for simulating 2-D high-resolution climate variables. J Adv Model Earth Syst 9(3):1595–1627. https://doi.org/10.1002/2016MS000854
Pidoto R, Haberlandt U (2023) A semi-parametric hourly space-time weather generator. Hydrol Earth Syst Sci 27(21):3957–3975. https://doi.org/10.5194/hess-27-3957-2023
Pohle I, Niebisch M, Müller H, Schümberg S, Zha T, Maurer T, Hinz C (2018) Coupling Poisson rectangular pulse and multiplicative microcanonical random cascade models to generate sub-daily precipitation timeseries. J Hydrol 562:50–70. https://doi.org/10.1016/j.jhydrol.2018.04.063
Richardson CW (1981) Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour Res 17(1):182–190. https://doi.org/10.1029/WR017i001p00182
Schertzer D, Lovejoy S (1987) Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. J Geophys Res 92(D8):9693–9714. https://doi.org/10.1029/JD092iD08p09693
Serinaldi F (2009) A multisite daily rainfall generator driven by bivariate copula based mixed distributions. J Geophys Res 114:D10103. https://doi.org/10.1029/2008JD011258
Sideris IV, Gabella M, Erdin R, Germann U (2014) Real-time radar-rain-gauge merging using spatio-temporal co-kriging with external drift in the alpine terrain of Switzerland. Q J R Meteorol Soc 140(680):1097–1111. https://doi.org/10.1002/qj.2188
Srikanthan R, McMahon TA (2001) Stochastic generation of annual, monthly and daily climate data: a review. Hydrol Earth Syst Sci 5(4):653–670. https://doi.org/10.5194/hess-5-653-2001
Tarek M, Brissette FP, Arsenault R (2020) Evaluation of the ERA5 reanalysis as a potential reference dataset for hydrological modelling over North America. Hydrol Earth Syst Sci 24(5):2527–2544. https://doi.org/10.5194/hess-24-2527-2020
Tseng S, Chen C, Senarath SUS (2020) Evaluation of multi-site precipitation generators across scales. Int J Climatol 40(10):4622–4637. https://doi.org/10.1002/joc.6480
Vaittinada Ayar P, Blanchet J, Paquet E, Penot D (2020) Space-time simulation of precipitation based on weather pattern sub-sampling and meta-Gaussian model. J Hydrol 581:124451. https://doi.org/10.1016/j.jhydrol.2019.124451
Viviroli D, Sikorska-Senoner AE, Evin G, Staudinger M, Kauzlaric M, Chardon J, Whealton C (2022) Comprehensive space-time hydrometeorological simulations for estimating very rare floods at multiple sites in a large river basin. Nat Hazards Earth Syst Sci 22(9):2891–2920. https://doi.org/10.5194/nhess-22-2891-2022
Vorobevskii I, Park J, Kim D, Barfus K, Kronenberg R (2024) 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(2):391–416. https://doi.org/10.5194/hess-28-391-2024
Westra S, Mehrotra R, Mehrotra R, Sharma A, Srikanthan R (2012) Continuous rainfall simulation: 1. A regionalized subdaily disaggregation approach. Water Resour Res 48:W01535. https://doi.org/10.1029/2011wr010489
Wilks DS (1998) Multisite generalization of a daily stochastic precipitation generation model. J Hydrol 210(1–4):178–191. https://doi.org/10.1016/S0022-1694(98)00186-3
Wilks DS, Wilby RL (1999) The weather generation game: a review of stochastic weather models. Prog Phys Geogr Earth Environ 23(3):329–357. https://doi.org/10.1177/030913339902300302
Zhao Y, Nearing MA, Guertin DP (2022) Modeling hydrologic responses using multi-site and single-site rainfall generators in a semi-arid watershed. Int Soil Water Conserv Res 10(2):177–187. https://doi.org/10.1016/j.iswcr.2021.09.003
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Funding acquisition: BH. Experimental design: KM, BH and GE. Script development: KM and GE. Model calibration, simulations and analyses: KM. Figure preparation: KM. Paper redaction: KM, GE and BH.
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Maloku, K., Evin, G. & Hingray, B. Generating hourly mean areal precipitation times series with an at-site weather generator in Switzerland. Stoch Environ Res Risk Assess 38, 3737–3754 (2024). https://doi.org/10.1007/s00477-024-02757-5
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DOI: https://doi.org/10.1007/s00477-024-02757-5


