Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency

•Stochastic modelling reproducing any marginal distribution and linear correlation.•Applicable in univariate, cyclostationary and multivariate cases.•Precise modelling of precipitation, river discharge, wind, etc. at any time scale.•Parametric correlation transformation functions unify and simplify...

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Bibliographic Details
Published in:Advances in water resources Vol. 115; pp. 234 - 252
Main Author: Papalexiou, Simon Michael
Format: Journal Article
Language:English
Published: Oxford Elsevier Ltd 01.05.2018
Elsevier Science Ltd
Subjects:
Computer simulation
Correlation
Distribution
Frameworks
Gaussian process
Generators
Humidity
Hydroclimatic processes
Hydrologic analysis
Hydrological analysis
Hydrology
Intermittency
Modelling
Normal distribution
Parent-Gaussian framework
Precipitation
probability distribution
Probability theory
River discharge
River flow
Rivers
Stationary processes
Statistical analysis
Stochastic modelling
Stochastic models
stochastic processes
stream flow
Structures
Temperature
Transformations
Transformations (mathematics)
water resources
Weather generator
Wind speed
Precipitation
Temperature
Wind speed
Hydroclimatic processes
River discharge
Humidity
Transformations
Stochastic modelling
Parent-Gaussian framework
Weather generator
ISSN:0309-1708, 1872-9657
Online Access:Get full text
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Summary:•Stochastic modelling reproducing any marginal distribution and linear correlation.•Applicable in univariate, cyclostationary and multivariate cases.•Precise modelling of precipitation, river discharge, wind, etc. at any time scale.•Parametric correlation transformation functions unify and simplify the scheme.•Empirical correlation representation through parsimonious parametric functions. Hydroclimatic processes come in all “shapes and sizes”. They are characterized by different spatiotemporal correlation structures and probability distributions that can be continuous, mixed-type, discrete or even binary. Simulating such processes by reproducing precisely their marginal distribution and linear correlation structure, including features like intermittency, can greatly improve hydrological analysis and design. Traditionally, modelling schemes are case specific and typically attempt to preserve few statistical moments providing inadequate and potentially risky distribution approximations. Here, a single framework is proposed that unifies, extends, and improves a general-purpose modelling strategy, based on the assumption that any process can emerge by transforming a specific “parent” Gaussian process. A novel mathematical representation of this scheme, introducing parametric correlation transformation functions, enables straightforward estimation of the parent-Gaussian process yielding the target process after the marginal back transformation, while it provides a general description that supersedes previous specific parameterizations, offering a simple, fast and efficient simulation procedure for every stationary process at any spatiotemporal scale. This framework, also applicable for cyclostationary and multivariate modelling, is augmented with flexible parametric correlation structures that parsimoniously describe observed correlations. Real-world simulations of various hydroclimatic processes with different correlation structures and marginals, such as precipitation, river discharge, wind speed, humidity, extreme events per year, etc., as well as a multivariate example, highlight the flexibility, advantages, and complete generality of the method.
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ISSN:0309-1708
1872-9657
DOI:10.1016/j.advwatres.2018.02.013