Bacci, M., Sukys, J., Reichert, P., Ulzega, S., and Albert, C.: A Comparison of Numerical Approaches for Statistical Inference with Stochastic Models,
Stoch. Environ. Res. Risk A., 37, 3041–3061,
https://doi.org/10.1007/s00477-023-02434-z, 2023.
a
Cowpertwait, P. S. P., O’Connell, P. E., Metcalfe, A. V., and Mawdsley,
J. A.: Stochastic point process modelling of rainfall. I. Single-site fitting
and validation, J. Hydrol., 175, 17–46,
https://doi.org/10.1016/S0022-1694(96)80004-7, 1996.
a
Deidda, R., Benzi, R., and Siccardi, F.: Multifractal modeling of anomalous
scaling laws in rainfall, Water Resour. Res., 35, 1853–1867,
https://doi.org/10.1029/1999WR900036, 1999.
a
Del Giudice, D., Löwe, R., Madsen, H., Mikkelsen, P. S., and Rieckermann,
J.: Comparison of two stochastic techniques for reliable urban runoff
predictions by modeling systematic errors, Water Resour. Res., 51, 5004–5022,
https://doi.org/10.1002/2014WR016678, 2015.
a
Del Giudice, D., Albert, C., Rieckermann, J., and Reichert, P.: Describing the catchment-averaged precipitation as a stochastic process improves parameter and input estimation, Water Resour. Res., 52, 3162–3186,
https://doi.org/10.1002/2015WR017871, 2016.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j,
k,
l,
m,
n,
o,
p
Duane, S., Kennedy, A. D., Pendleton, B. J., and Roweth, D.: Hybrid Monte
Carlo, Phys. Lett. B, 195, 216–222,
https://doi.org/10.1016/0370-2693(87)91197-X, 1987.
a
Earl, D. J. and Deem, M. W.: Parallel tempering: Theory, applications, and new perspectives, Phys. Chem. Chem. Phys., 7, 3910–3916,
https://doi.org/10.1039/B509983H, 2005.
a
Hartmann, M., Girolami, M., and Klami, A.: Lagrangian manifold Monte Carlo on
Monge patches, in: Proceedings of The 25th International Conference on
Artificial Intelligence and Statistics, vol. 151 of Proceedings of Machine Learning Research, edited by: Camps-Valls, G., Ruiz, F. J. R., and Valera, I., PMLR, 4764–4781,
https://proceedings.mlr.press/v151/hartmann22a.html (last access: 9 August 2023), 2022. a
Hoffman, M. D. and Gelman, A.: The No-U-Turn Sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo, J. Mach. Learn. Res., 15, 1351–1381, 2014. a
Hogan, R. J.: Fast reverse-mode automatic differentiation using expression
templates in C
, ACM Trans. Math. Softw., 40, 1–16,
https://doi.org/10.1145/2560359, 2014.
a
Honti, M., Stamm, C., and Reichert, P.: Integrated uncertainty assessment of
discharge predictions with a statistical error model, Water Resour. Res., 49,
4866–4884,
https://doi.org/10.1002/wrcr.20374, 2013.
a,
b
Kavetski, D., Kuczera, G., and Franks, S. W.: Bayesian analysis of input
uncertainty in hydrological modeling: 1. Theory, Water Resour. Res., 42,
W03407,
https://doi.org/10.1029/2005WR004368, 2006.
a,
b,
c
Laio, A. and Gervasio, F. L.: Metadynamics: a method to simulate rare events
and reconstruct the free energy in biophysics, chemistry and material
science, Rep. Prog. Phys., 71, 126601,
https://doi.org/10.1088/0034-4885/71/12/126601, 2008.
a
Langousis, A. and Kaleris, V.: Statistical framework to simulate daily rainfall series conditional on upper-air predictor variables, Water Resour. Res., 50, 3907–3932,
https://doi.org/10.1002/2013WR014936, 2014.
a
McMillan, H., Jackson, B., Clark, M., Kavetski, D., and Woods, R.: Rainfall
uncertainty in hydrological modelling: An evaluation of multiplicative error
models, J. Hydrol., 400, 83–94,
https://doi.org/10.1016/j.jhydrol.2011.01.026, 2011.
a
Neal, R. M.: MCMC Using Hamiltonian Dynamics, in: Handbook of Markov Chain Monte Carlo, edited by: Brooks, S., Gelman, A., Jones, G. L., and Meng, X.-L., Chapman and Hall/CRC, 113–162,
https://doi.org/10.1201/b10905, 2011.
a
Ochoa-Rodriguez, S., Wang, L.-P., Gires, A., Pina, R. D., Reinoso-Rondinel, R., Bruni, G., A., I., Gaitan, S., Cristiano, E., van Assel, J., Kroll, S.,
Murlà-Tuyls, D., Tisserand, B., Schertzer, D., Tchiguirinskaia, I., Onof,
C., Willems, P., and ten Veldhuis, M.-C.: Impact of spatial and temporal
resolution of rainfall inputs on urban hydrodynamic modelling outputs: A
multi-catchment investigation, J. Hydrol., 531, 389–407,
https://doi.org/10.1016/j.jhydrol.2015.05.035, 2015.
a
Paschalis, A., P., M., Fatichi, S., and Burlando, P.: A stochastic model for
high-resolution space-time precipitation simulation, Water Resour. Res., 49,
8400–8417,
https://doi.org/10.1002/2013WR014437, 2013.
a
Reichert, P. and Mieleitner, J.: Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time-dependent parameters, Water
Resour. Res., 459, W10402,
https://doi.org/10.1029/2009WR007814, 2009.
a
Reichert, P., Ammann, L., and Fenicia, F.: Potential and challenges of
investigating intrinsic uncertainty of hydrological models with stochastic,
time-dependent parameters, Water Resour. Res., 57, e2020WR028400,
https://doi.org/10.1029/2020WR028400, 2021.
a
Renard, B., Kavetski, D., Leblois, E., Thyer, M., Kuczera, G., and Franks,
S. W.: Toward a reliable decomposition of predictive uncertainty in
hydrological modeling: Characterizing rainfall errors using conditional
simulation, Water Resour. Res., 47, W11516,
https://doi.org/10.1029/2011WR010643, 2011.
a,
b,
c
Rodriguez-Iturbe, I., Cox, D. R., and Isham, V.: Some models for rainfall based on stochastic point processes, P. Roy. Soc. Lond. A, 410, 269–298,
https://doi.org/10.1098/rspa.1987.0039, 1987.
a
Sikorska, A., Scheidegger, A., Banasik, K., and Rieckermann, J.: Bayesian
uncertainty assessment of flood predictions in ungauged urban basins for
conceptual rainfall-runoff models, Hydrol. Earth Syst. Sci., 16, 1221–1236,
https://doi.org/10.5194/hess-16-1221-2012, 2012.
a,
b
Sun, S. and Bertrand-Krajewski, J.: Separately accounting for uncertainties in rainfall and runoff: Calibration of event-based conceptual hydrological
models in small urban catchments using Bayesian method, Water Resour. Res.,
49, 5381–5394,
https://doi.org/10.1002/wrcr.20444, 2013.
a
Tomassini, L., Reichert, P., Künsch, H. R., Buser, C., Knutti, R., and
Borsuk, M. E.: A Smoothing Algorithm for Estimating Stochastic Continuous
Time Model Parameters and Its Application to a Simple Climate Model, J. Roy. Stat. Soc. C, 58, 679–704, 2009. a
Tuckerman, M., Berne, B. J., and Martyna, G. J.: Reversible multiple time scale molecular dynamics, J. Chem. Phys., 97, 1990–2001,
https://doi.org/10.1063/1.463137, 1992.
a
Tuckerman, M. E., Berne, B. J., Martyna, G. J., and Klein, M. L.: Efficient
molecular dynamics and hybrid Monte Carlo algorithms for path integrals,
J. Chem. Phys., 99, 2796–2808,
https://doi.org/10.1063/1.465188, 1993.
a
ulzegasi: HMC_SIP, GitHub [code and data set],
https://github.com/ulzegasi/HMC_SIP.git (last access: 8 August 2023), 2023. a
Yang, J., Reichert, P., Abbaspour, K. C., Xia, J., and Yang, H.: Comparing
uncertainty analysis techniques for a SWAT application to the Chaohe Basin in
China, J. Hydrol., 358, 1–23,
https://doi.org/10.1016/j.jhydrol.2008.05.012, 2008.
a