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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| Published in: | Advances in water resources Vol. 115; pp. 234 - 252 |
|---|---|
| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford
Elsevier Ltd
01.05.2018
Elsevier Science Ltd |
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| ISSN: | 0309-1708, 1872-9657 |
| Online Access: | Get full text |
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| Abstract | •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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| AbstractList | 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. •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. |
| Author | Papalexiou, Simon Michael |
| Author_xml | – sequence: 1 givenname: Simon Michael orcidid: 0000-0001-5633-0154 surname: Papalexiou fullname: Papalexiou, Simon Michael email: simon@uci.edu organization: Department of Civil and Environmental Engineering, University of California, Irvine, CA, USA |
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| Keywords | Precipitation Temperature Wind speed Hydroclimatic processes River discharge Humidity Transformations Stochastic modelling Parent-Gaussian framework Weather generator |
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| SubjectTerms | 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 |
| Title | Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency |
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