Issues in generating stochastic observables for hydrological models

Abstract

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.

Impacts of observational uncertainty on analysis and modelling of hydrological processes: Preface

“…In our special issue, all three papers dealing with input uncertainty similarly focus largely on precipitation uncertainty. The papers investigate input (precipitation) uncertainty and its impact on parameter identification in hydrological models (Liu et al, 2021), input uncertainty in observed and generated variables for hydrological models and process representation (Beven, 2021b), and precipitation uncertainty impact on the rainfall‐triggered landslide events (Culler et al, 2021). Beven (2021b) also discusses uncertainties in other input variables, that is, temperature and evapotranspiration.…”

Spatial Hurst–Kolmogorov Clustering

“…The HK dynamics are also linked to the entropy maximization principle, and thus, to robust physical justification [8]. It is worth noting that the stochastic simulation of the HK dynamics is still a mathematical challenge [9] since it requires the explicit preservation of high-order moments in a vast range of scales [10,11], affecting both the intermittent (fractal) behavior in small scales [12] and the dependence in extremes [13].…”

“…of high-order moments in a vast range of scales [10,11], affecting both the intermittent (fractal) behavior in small scales [12] and the dependence in extremes [13]. Hurst-Kolmogorov (HK) dynamics present in the annual minimum water level of the Nile River as a result of the perpetual change of Earth's climate, and as compared to a roulette timeseries resembling a white noise process.…”

“…The 2D spatial clustering behavior has also been explored in many fields such as hydrology (e.g., [18][19][20], and references therein), biology and ecosystems (e.g., [21,22]), life sciences (e.g., [23][24][25][26]), networks (e.g., [27][28][29]), urban structures (e.g., [30,31]), rock formation (e.g., [32]), turbulence (e.g., [7,33]), art (e.g., [34][35][36]), landscape analysis (e.g., [37,38]), simulated evolution of the universe [39] and many others (e.g., [40]). A unified approach for the quantification of the 2D spatio-temporal clustering in terms of variability in the scale domain (instead of in the common lag and frequency domains) can be of high-order moments in a vast range of scales [10,11], affecting both the intermittent (fractal) behavior in small scales [12] and the dependence in extremes [13]. Hurst-Kolmogorov (HK) dynamics present in the annual minimum water level of the Nile River as a result of the perpetual change of Earth's climate, and as compared to a roulette timeseries resembling a white noise process.…”

Random fractional partial differential equations and solutions for water movement in soils: Theory and applications

“…Stochastic modelling and issues in surface hydrology were provided by Yevjevich (1974), Klemeš (1978), Yevjevich (1987), Wright et al (2020) and Beven (2021). A futuristic opinion on hydrological modelling, including stochastic approaches, was discussed by Yevjevich (1991).…”