Issues in generating stochastic observables for hydrological models

Beven, K. (2021) Issues in generating stochastic observables for hydrological models. Hydrological Processes, 35 (6). ISSN 0885-6087

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This paper provides a historical review and critique of stochastic generating models for hydrological observables, from early generation of monthly discharge series, through flood frequency estimation by continuous simulation, to current weather generators. There are a number of issues that arise in such models, from uncertainties in the observational data on which such models must be based, to the potential persistence effects in hydroclimatic systems, the proper representation of tail behaviour in the underlying distributions, and the interpretation of future scenarios.

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Journal Article
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Hydrological Processes
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Funding details: Natural Environment Research Council, NERC, NE/R004722/1 Funding text 1: Work on this paper has been supported by the NERC Q‐NFM project led by Dr. Nick Chappell (grant no. NE/R004722/1). The paper has greatly benefitted from an excellent review and the recent work of Demetris Koutsoyiannis for which I am most grateful. References: Benson, M.A., Thoughts on the design of design floods (1973) Floods and droughts, Proceedings of the 2nd international symposium in hydrology, pp. 27-33. , Water Resour. Publ; Bertoni, G., Daemen, J., Peeters, M., Van Assche, G., Sponge-based pseudo-random number generators (2010) International workshop on cryptographic hardware and embedded systems, pp. 33-47. , Springer; Betson, R.P., What is watershed runoff (1964) Journal of Geophysical Research, 69, pp. 1541-1552; Beven, K.J., Hillslope runoff processes and flood frequency characteristics (1986) Hillslope processes, pp. 187-202. , A. D. Abrahams, (Ed.),, Allen and Unwin; Beven, K.J., Runoff production and flood frequency in catchments of order n: An alternative approach (1986) Scale problems in hydrology, pp. 107-131. , V. K. Gupta, I. Rodriguez-Iturbe, E. F. Wood, (Eds.),, Reidel; Beven, K.J., Towards the use of catchment geomorphology in flood frequency predictions (1987) Earth Surface Processes and Landforms, V12 (1), pp. 69-82; Beven, K.J., Hydrograph separation? (1991) Proc.BHS third National Hydrology Symposium, pp. 3.1-3.8. , Institute of Hydrology; Beven, K.J., (2009) Environmental modelling: An uncertain future?, , Routledge; Beven, K.J., I believe in climate change but how precautionary do we need to be in planning for the future? (2011) Hydrological Processes, 25, pp. 1517-1520. ,; Beven, K.J., (2012) Rainfall-Runoiff modelling: The primer, , 2nd ed., Wiley-Blackwell; Beven, K.J., On hypothesis testing in hydrology: Why falsification of models is still a really good idea (2018) WIREs Water, 5 (3). ,; Beven, K.J., Towards a methodology for testing models as hypotheses in the inexact sciences (2019) Proceedings Royal Society A, 475 (2224), p. 20180862. ,; Beven, K.J., A history of the concept of time of concentration (2020) Hydrology and Earth System Sciences, 24, pp. 2655-2670. ,; Beven, K.J., Deep learning, hydrological processes and the uniqueness of place (2020) Hydrological Processes, 34 (16), pp. 3608-3613. ,; Beven, K.J., The era of infiltration (2021) Hydrology and Earth System Sciences, 25 (2), pp. 851-866. ,; Beven, K.J., An epistemically uncertain walk through the rather fuzzy subject of observation and model uncertainties (2021) Hydrological Processes, 35. ,; Beven, K.J., Buytaert, W., Smith, L.A., On virtual observatories and modeled realities (or why discharge must be treated as a virtual variable) (2012) Hydrological Processes (HPToday), 26 (12), pp. 1905-1908. ,; Beven, K.J., Lamb, R., The uncertainty cascade in model fusion (2014) Integrated environmental modelling to solve real world problems: Methods, vision and challenges. Special Publications, 408, pp. 255-266. ,, A. T. Riddick, H. Kessler, J. R. A. Giles, (Eds.),, London, Geological Society; Beven, K.J., Lane, S., nvalidation of models and fitness-for-purpose: A rejectionist approach, Chapter 6 (2019) Computer simulation validation—Fundamental concepts, methodological frameworks, and philosophical perspectives, pp. 145-171. , I, Beisbart, C., &, Saam, N. J, (eds.),, Springer; Blazkova, S., Beven, K., A limits of acceptability approach to model evaluation and uncertainty estimation in flood frequency estimation by continuous simulation: Skalka catchment, Czech Republic (2009) Water Resources Research, 45. ,; Bordoy, R., Burlando, P., Stochastic downscaling of precipitation to high-resolution scenarios in orographically complex regions: Model evaluation (2014) Water Resources Research, 50, pp. 540-561. ,; Bowman, R.L., Evaluating pseudo-random number generators (1995) Computers & Graphics, 19 (2), pp. 315-324; Brittan, M.R., (1961) Probability analysis applied to the development of synthetic hydrology for the Colorado River, Rep.4, p. 99. , (p., Bureau of Economic Research; Burton, A., Kilsby, C.G., Fowler, H.J., Cowpertwait, P.S.P., O'Connell, P.E., RainSim: A spatial–temporal stochastic rainfall modelling system (2008) Environmental Modelling & Software, 23 (12), pp. 1356-1369; Calder, I.R., Harding, R.J., Rosier, P.T.W., An objective assessment of soil moisture deficit models, J (1983) Hydrology, 60, pp. 329-355; Cameron, D., Beven, K.J., Tawn, J., An evaluation of three stochastic rainfall models (2000) Journal of Hydrology, 228, pp. 130-149; Cameron, D., Beven, K.J., Tawn, J., Modelling extreme rainfalls using a modified random pulse Bartlett-Lewis stochastic rainfall model (with uncertainty) (2001) Advances in Water Resources, 24, pp. 203-211; Cameron, D., Beven, K.J., Tawn, J., Blazkova, S., Naden, P., Flood frequency estimation by continuous simulation for a gauged upland catchment (with uncertainty) (1999) Journal of Hydrology, 219, pp. 169-187; Chandler, R.E., Multisite, multivariate weather generation based on generalised linear models (2020) Environmental Modelling & Software, 134; Chandler, R.E., Isham, V., Bellone, E., Yang, C., Northrop, P., Space-time modelling of rainfall for continuous simulation (2006) Statistical methods for spatiotemporal systems, monographs on statistics and applied probability, 107, pp. 177-216. , B. Finkenstädt, L. Held, V. Isham, (Eds.),, Chapman and Hall/CRC Press; Claps, P., Giordano, A., Laio, F., Advances in shot noise modeling of daily streamflows (2005) Advances in Water Resources, 28 (9), pp. 992-1000; Clark, M.P., Slater, A.G., Probabilistic quantitative precipitation estimation in complex terrain (2006) Journal of Hydrometeorology, 7 (1), pp. 3-22; Colston, N.V., Wiggert, J.M., A technique of generating a synthetic flow record to estimate the variability of dependable flows for a fixed reservoir capacity (1970) Water Resources Research, 6 (1), pp. 310-315; Cowpertwait, P.S.P., Kilsby, C.G., O'Connell, P.E., A space-time Neyman-Scott model of rainfall: Empirical analysis of extremes (2002) Water Resources Research, 38 (8), pp. 1-6; Cowpertwait, P.S.P., O'Connell, P.E., A Neyman-Scott shot noise model for the generation of daily streamflow time series (1992) Advances in Theoretical Hydrology, pp. 75-94. ,, &, J. P. O'Kane, (Ed.),, European Geophysical Society Series on Hydrological Sciences, Amsterdam, Elsevier; Cox, D.R., Isham, V., A simple spatial-temporal model of rainfall (1988) Proceedings of the Royal Society of London, A415 (1849), pp. 317-328; Coxon, G., Freer, J., Westerberg, I.K., Wagener, T., Woods, R., Smith, P.J., A novel framework for discharge uncertainty quantification applied to 500 UKgauging stations (2015) Water Resources Research, 51 (7), pp. 5531-5546; De Michele, C., Salvadori, G., On the derived flood frequency distribution: Analytical formulation and the influence of antecedent soil moisture condition (2002) Journal of Hydrology, 262 (1-4), pp. 245-258; Diaz-Granados, M.A., Valdes, J.B., Bras, R.L., A physically based flood frequency distribution (1984) Water Resources Research, 20 (7), pp. 995-1002; Dimitriadis, P., Koutsoyiannis, D., Stochastic synthesis approximating any process dependence and distribution (2018) Stochastic Environmental Research and Risk Assessment, 32 (6), pp. 1493-1515; Eagleson, P.S., Dynamics of flood frequency (1972) Water Resources Research, 8 (4), pp. 878-898; Eagleson, P.S., Climate, soil and vegetation (7 papers) (1978) Water Resources Research, 14 (5), pp. 705-776; Entekhabi, D., Rodriguez-Iturbe, I., Eagleson, P.S., Probabilistic representation of the temporal rainfall process by a modified Neyman-Scott rectangular pulses model: Parameter estimation and validation (1989) Water Resources Research, 25 (2), pp. 295-302; Favre, A.C., Musy, A., Morgenthaler, S., Unbiased parameter estimation of the Neyman–Scott model for rainfall simulation with related confidence interval (2004) Journal of Hydrology, 286 (1-4), pp. 168-178; Fiering, M.B., (1967) Streamflow synthesis, , Harvard University Press; Fildes, R., Kourentzes, N., Validation and forecasting accuracy in models of climate change (2011) International Journal of Forecasting, 27 (4), pp. 968-995; Fleming, G., Franz, D.D., Flood frequency estimating techniques for small watersheds (1971) Journal of the Hydraulics Division, 97 (9), pp. 1441-1460; Ghotbi, S., Wang, D., Singh, A., Blöschl, G., Sivapalan, M., A new framework for exploring process controls of flow duration curves (2020) Water Resources Research, 56 (1); Gubernatis, J.E., Marshall Rosenbluth and the Metropolis algorithm (2005) Physics of Plasmas, 12 (5); Gupta, V.K., Waymire, E.C., A statistical analysis of mesoscale rainfall as a random cascade (1993) Journal of Applied Meteorology and Climatology, 32 (2), pp. 251-267; Gupta, V.K., Waymire, E.D., On the formulation of an analytical approach to hydrologic response and similarity at the basin scale (1983) Journal of Hydrology, 65 (1-3), pp. 95-123; Harms, A.A., Campbell, T.H., An extension to the Thomas-Fiering Model for the sequential generation of streamflow (1967) Water Resources Research, 3 (3), pp. 653-661; Hastings, W.K., Monte Carlo sampling methods using Markov chains and their applications (1970) Biometrika, 57 (1), pp. 97-109; Hebson, C., Wood, E.F., A derived flood frequency distribution using Horton order ratios (1982) Water Resources Research, 18 (5), pp. 1509-1518; Hershfield, D.M., Estimating the probable maximum precipitation (1961) Journal of the Hydraulics Division [American Society of Civil Engineers], 87 (HY5), pp. 99-106; Hollaway, M.J., Beven, K.J., Collins, A.L., Evans, R., Falloon, P.D., Forber, K.J., Hiscock, K.M., Haygarth, P.M., Evaluating a processed based water quality model on a UKheadwater catchment: What can we learn from a ‘limits of acceptability’ uncertainty framework? (2018) Journal of Hydrology, 558, pp. 607-624. ,, Benskin, C.McW.H; Hubert, P., Tessier, Y., Lovejoy, S., Schertzer, D., Schmitt, F., Ladoy, P., Carbonnel, J.P., Desurosne, I., Multifractals and extreme rainfall events (1993) Geophysical Research Letters, 20 (10), pp. 931-934; Hurst, H.E., A suggested statistical model of some time series which occur in nature (1957) Nature, 180, p. 494. ,; Hutchinson, P., A note on random raingauge errors (1969) Journal of Hydrology (New Zealand), 8 (1), pp. 8-10. , 1969; Kiang, J.E., Gazoorian, C., McMillan, H., Coxon, G., Le Coz, J., Westerberg, I.K., Belleville, A., Reitan, T., A comparison of methods for streamflow uncertainty estimation (2018) Water Resources Research, 54 (10), pp. 7149-7176; Kirchner, J.W., A double paradox in catchment hydrology and geochemistry (2003) Hydrological Processes, 17 (4), pp. 871-874; Klemeš, V., The Hurst phenomenon: A puzzle? (1974) Water Resources Research, 10 (4), pp. 675-688; Klemeš, V., Physically based stochastic hydrologic analysis (1978) Advances in Hydroscience, 11, pp. 285-356; Klemeš, V., Bulu, A., Limited confidence in confidence limits derived by operational stochastic hydrological models (1979) Journal of Hydrology, 42, pp. 9-22; Koutsoyiannis, D., A probabilistic view of Hershfield's method for estimating probable maximum precipitation (1999) Water Resources Research, 35 (4), pp. 1313-1322; Koutsoyiannis, D., Statistics of extremes and estimation of extreme rainfall: II. Empirical investigation of long rainfall records (2004) Hydrological Sciences Journal, 49 (4), pp. 591-610. ,; Koutsoyiannis, D., Nonstationarity versus scaling in hydrology (2006) Journal of Hydrology, 324 (1-4), pp. 239-254; Koutsoyiannis, D., Hurst-Kolmogorov dynamics and uncertainty (2011) JAWRA Journal of the American Water Resources Association, 47 (3), pp. 481-495; Koutsoyiannis, D., Hydrology and change (2013) Hydrological Sciences Journal, 58 (6), pp. 1177-1197; Koutsoyiannis, D., Simple stochastic simulation of time irreversible and reversible processes (2020) Hydrological Sciences Journal, 65 (4), pp. 536-551. ,; Koutsoyiannis, D., (2021) Stochastics of hydroclimatic extremes—A cool look at risk, p. 333. ,, (p., Kallipos, open source book, Retrieved from; Koutsoyiannis, D., Rethinking climate, climate change, and their relationship with water (2021) Water, 13, p. 849. ,; Koutsoyiannis, D., Dimitriadis, P., Lombardo, F., Stevens, S., From fractals to stochastics: Seeking theoretical consistency in analysis of geophysical data (2018) Advances in Nonlinear Geosciences, pp. 237-278. ,, A.A. Tsonis, &, A. A. Tsonis, (eds.), (, Cham, Springer, Springer; Koutsoyiannis, D., Efstratiadis, A., Mamassis, N., Christofides, A., On the credibility of climate predictions (2008) Hydrological Sciences Journal, 53, pp. 671-684. ,; Koutsoyiannis, D., Montanari, A., Negligent killing of scientific concepts: The stationarity case (2015) Hydrological Sciences Journal, 60 (7-8), pp. 1174-1183; Kratzert, F., Klotz, D., Shalev, G., Klambauer, G., Hochreiter, S., Nearing, G., Towards learning universal, regional, and local hydrological behaviors via machine learning applied to large-sample datasets (2019) Hydrology and Earth System Sciences, 23 (12), pp. 5089-5110; Lamb, R., Kay, A.L., Confidence intervals for a spatially generalized, continuous simulation flood frequency model for Great Britain (2004) Water Resources Research, 40. ,; LeCam, L., A stochastic description of precipitation (1961) Proc. 4th Berkeley Symposium on Mathematical Statistics and Probability, pp. 165-186. , J. Neyman, (Ed.),, Berkeley, CA, University of California Press; Leonard, M., Lambert, M.F., Metcalfe, A.V., Cowpertwait, P.S.P., A space-time Neyman–Scott rainfall model with defined storm extent (2008) Water Resources Research, 44 (9), p. W09402. ,; Leopold, L.B., Probability analysis applied to a water supply problem (1959) U.S. Geological Survey Circular, 410, p. 18; Li, Z., Lü, Z., Li, J., Shi, X., Links between the spatial structure of weather generator and hydrological modeling (2017) Theoretical and Applied Climatology, 128 (1-2), pp. 103-111; Maass, A., (1962) Design of water resource systems, p. 602. , A. Maass, (Ed.),, (p., Harvard University Press; Mandelbrot, B.B., A fast fractional Gaussian noise generator (1971) Water Resources Research, 7 (3), pp. 543-553; Mandelbrot, B.B., Wallis, J.R., Noah, Joseph, and operational hydrology (1968) Water Resources Research, 4 (5), pp. 909-918; Maskey, M.L., Puente, C.E., Sivakumar, B., Temporal downscaling rainfall and streamflow records through a deterministic fractal geometric approach (2019) Journal of Hydrology, 568, pp. 447-461; McMillan, H.K., Westerberg, I.K., Krueger, T., Hydrological data uncertainty and its implications (2018) Wiley Interdisciplinary Reviews: Water, 5 (6). ,; Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E., Equation of state calculations by fast computing machines (1953) Journal of Chemical Physics., 21 (6), pp. 1087-1092; Metropolis, N., Ulam, S., The Monte Carlo method (1949) Journal of the American Statistical Association, 44 (247), pp. 335-341; Micovic, Z., Schaefer, M.G., Taylor, G.H., Uncertainty analysis for probable maximum precipitation estimates (2015) Journal of Hydrology, 521, pp. 360-373; Montanari, A., Koutsoyiannis, D., Modeling and mitigating natural hazards: Stationarity is immortal! (2014) Water Resources Research, 50 (12), pp. 9748-9756; Nearing, G.S., Kratzert, F., Sampson, A.K., Pelissier, C.S., Klotz, D., Frame, J.M., Prieto, C., Gupta, H.V., What role does hydrological science play in the age of machine learning? (2021) Water Resources Research, 57 (3). ,; Nearing, G.S., Mocko, D.M., Peters-Lidard, C.D., Kumar, S.V., Xia, Y., Benchmarking NLDAS-2 soil moisture and evapotranspiration to separate uncertainty contributions (2016) Journal of Hydrometeorology, 17, pp. 745-759; Obregon, N., Puente, C.E., Sivakumar, B., Modeling high-resolution rain rates via a deterministic fractal-multifractal approach (2002) Fractals, 10 (3), pp. 387-394; O'Connell, P.E., A simple stochastic modelling of Hurst's law (1971) Proceedings of International Symposium on Mathematical Models in Hydrology, IAHS Warsaw Symposium, Vol. 1, pp. 169-187. , Wallingford, UK, IAHS Press; O'Connell, P.E., Shot noise models in synthetic hydrology (1977) Mathematical models for surface water hydrology, pp. 19-26. , T. A. Ciriani, V. Maione, &, J.R. Wallis, (Eds.),, New York, Wiley InterScience; Onof, C., Wheater, H.S., Modelling of British rainfall using a random parameter Bartlett-Lewis rectangular pulse model (1993) Journal of Hydrology, 149 (1-4), pp. 67-95; Onof, C., Wheater, H.S., Improvements to the modelling of British rainfall using a modified random parameter Bartlett–Lewis rectangular pulse model (1994) Journal of Hydrology, 157, pp. 177-195; Page, T., Beven, K.J., Freer, J., Modelling the chloride signal at the Plynlimon catchments, Wales using a modified dynamic TOPMODEL (2007) Hydrological Processes, 21, pp. 292-307; Papalexiou, S.M., Koutsoyiannis, D., A probabilistic approach to the concept of probable maximum precipitation (2006) Advances in Geosciences, 7, pp. 51-54; Peleg, N., Fatichi, S., Paschalis, A., Molnar, P., Burlando, P., An advanced stochastic weather generator for simulating 2-D high-resolution climate variables (2017) Journal of Advances in Modeling Earth Systems, 9 (3), pp. 1595-1627; Peleg, N., Molnar, P., Burlando, P., Fatichi, S., Exploring stochastic climate uncertainty in space and time using a gridded hourly weather generator (2019) Journal of Hydrology, 571, pp. 627-641; Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., (2007) Numerical recipes: The art of scientific computing, , 3rd ed., Cambridge University Press; Puente, C.E., Obregón, N., A deterministic geometric representation of temporal rainfall: Results for a storm in Boston (1996) Water Resources Research, 32 (9), pp. 2825-2839; Restrepo-Posada, P.J., Eagleson, P.S., Identification of independent rainstorms (1982) Journal of Hydrology, 55 (1-4), pp. 303-319; Reuss, M., Is it time to resurrect the Harvard water program? (2003) Journal of Water Resources Planning and Management, 129 (5), pp. 357-360; Rodriguez-Iturbe, I., Cox, D.R., Isham, V., Some models for rainfall based on stochastic point processes (1987) Proceedings of the Royal Society of London A, 410, pp. 269-288; Salas, J.D., Smith, R.A., Physical basis of stochastic models of annual flows (1981) Water Resources Research, 17 (2), pp. 428-430; Scheidegger, A.E., Stochastic models in hydrology (1970) Water Resources Research, 6 (3), pp. 750-755; Schertzer, D., Lovejoy, S., Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes (1987) Journal of Geophysical Research: Atmospheres, 92 (D8), pp. 9693-9714; Semenov, M.A., Brooks, R.J., Barrow, E.M., Richardson, C.W., Comparison of WGEN and LARS-WG stochastic weather generators for diverse climates (1998) Climate Research, 10, pp. 95-107; Serinaldi, F., Kilsby, C.G., Lombardo, F., Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology (2018) Advances in Water Resources, 111, pp. 132-155; Sivapalan, M., Wood, E.F., Beven, K.J., On hydrologic similarity, 3. A dimensionless flood frequency distribution (1990) Water Resources Research, 26, pp. 43-58; Srikanthan, R., McMahon, T.A., Stochastic generation of monthly flows for ephemeral streams (1980) Journal of Hydrology, 47 (1-2), pp. 19-40; Suckling, E.B., Smith, L.A., An evaluation of decadal probability forecasts from state of-the-art climate models (2013) Journal of Climate, 26 (23), pp. 9334-9347; Szczepanski, J., Wajnryb, E., Amigó, J.M., Sanchez-Vives, M.V., Slater, M., Biometric random number generators (2004) Computers & Security, 23 (1), pp. 77-84; Thomas, I.A., Fiering, M., Mathematical synthesis of stream flow sequences for the analysis of river basins by simulation, Ch. 12 (1962) Design of water resource systems, , A. Maass, (Ed.),, Harvard University Press; Thompson, E.A., Smith, L.A., Escape from model-land (2019) Economics, 13 (2019-40), pp. 1-15. ,; Tyralis, H., Koutsoyiannis, D., On the prediction of persistent processes using the output of deterministic models (2017) Hydrological Sciences Journal, 62, pp. 2083-2102. ,; Velghe, T., Troch, P.A., de Troch, F.P., van de Velde, J., Evaluation of cluster-based rectangular pulses point process models for rainfall (1994) Water Resources Research, 30 (10), pp. 2847-2857; Veneziano, D., Furcolo, P., Iacobellis, V., Imperfect scaling of time and space-time rainfall (2006) Journal of Hydrology, 322, pp. 105-119. ,; Venugopal, V., Roux, S.G., Foufoula-Georgiou, E., Arneodo, A., Revisiting multifractality of high-resolution temporal rainfall using a wavelet-based formalism (2006) Water Resources Research, 42 (6). ,; Verhoest, N., Vandenberghe, S., Cabus, P., Onof, C., Meca-Figueras, T., Jameleddine, S., Are stochastic point rainfall models able to preserve extreme flood statistics? (2010) Hydrological Processes, 24 (23), pp. 3439-3445; Wallis, J.R., Wood, E.F., Relative accuracy of log Pearson III procedures (1985) Journal of Hydraulic Engineering, 111 (7), pp. 1043-1056; Waymire, E.D., Gupta, V.K., Rodriguez-Iturbe, I., A spectral theory of rainfall intensity at the meso-β scale (1984) Water Resources Research, 20 (10), pp. 1453-1465; Waymire, E.D., Gupta, V.K., The mathematical structure of rainfall representations: 1. A review of the stochastic rainfall models (1981) Water Resources Research, 17 (5), pp. 1261-1272; Weiss, G., Shot noise models for the generation of synthetic streamflow data (1977) Water Resources Research, 13 (1), pp. 101-108; Westerberg, I., Guerrero, J.-L., Seibert, J., Beven, K.J., Halldin, S., Stage-discharge uncertainty derived with a non-stationary rating curve in the Choluteca River, Honduras (2011) Hydrological Processes, 25, pp. 603-613. ,; Wheater, H.S., Isham, V.S., Cox, D.R., Chandler, R.E., Kakou, A., Northrop, P.J., Oh, L., Rodriguez-Iturbe, I., Spatial-temporal rainfall fields: Modelling and statistical aspects (2000) Hydrology and Earth System Sciences, 4 (4), pp. 581-601; (1986) Intercomparison of models of snowmelt runoff. Operational Hydrology Report no. 23, , WMO; Yagil, S., Generation of input data for simulation (1963) IBM System Journal, 2, pp. 288-296; Yang, C., Chandler, R.E., Isham, V.S., Wheater, H.S., Spatial-temporal rainfall simulation using generalized linear models (2005) Water Resources Research, 41. ,; Yevjevich, V., Stochastic models in hydrology (1987) Stochastic Hydrology and Hydraulics, 1 (1), pp. 17-36; Yevjevich, V.M., (1961) Some General Aspects of Fluctuations of Annual Runoff in the Upper Colorado River Basin, Rep. 3, p. 48. , Department of Engineering Research, Colorado State University, Fort Collins; Yevjevich, V.M., (1964) Fluctuation of wet and dry years, part 2, analysis by serial correlation, hydrology papers no. 4, , Colorado State University; Young, P.C., Hypothetico-inductive data-based mechanistic modeling of hydrological systems (2013) Water Resources Research, 49 (2), pp. 915-935; Young, P.C., Data-based mechanistic modelling and forecasting globally averaged surface temperature (2018) International Journal of Forecasting, 34 (2), pp. 314-335. ,; Young, P.C., Allen, G.P., Bruun, J.T., A re-evaluation of the Earth's surface temperature response to radiative forcing (2021) Environmental Research Letters, ,, in press; Yu, F., Li, L., Tang, Q., Cai, S., Song, Y., Xu, Q., A survey on true random number generators based on chaos (2019) Discrete Dynamics in Nature and Society, 2019, p. 2545123. ,
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