Modelling extremes of spatial aggregates of precipitation using conditional methods

Richards, J. Ian; Tawn, Jonathan A.; Brown, Simon J.

doi:10.1214/22-aoas1609

Cited by 9 publications

(8 citation statements)

References 41 publications

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“…In fact, it is possible to extend our copula approach to explicitly capture temporal dependence by adapting the kernel parameter according to temporal information. Other improvements particular to the modelling of extreme rainfall events could be made to the JGNM by considering extreme value distributions [Behrens et al, 2004, MacDonald et al, 2011, Ding et al, 2019, Gao et al, 2021, Richards et al, 2022, either entirely or by adding them as a mixture term in the tail. Finally, we acknowledge that imposing a Gaussian covariance structure, while computationally appealing and leading to easy spatial modelling, might be too restrictive, especially for extreme variations in rainfall levels at close-by locations.…”

Section: Discussionmentioning

confidence: 99%

“…Modelling extreme rainfall through a Brown-Resnick process, Richards and Wadsworth [2021] resort to a composite likelihood approach as an alternative to a computationally unfeasible MLE. More recently, in Richards et al [2022] and Richards et al [2023], authors use a censored Gaussian copula model for the dependence of extreme rainfall events, circumventing the unavailable likelihood by adopting a pseudo-likelihood approach with spatially-informed sub-sampling. Outside of rainfall forecasting, Dobra and Lenkoski [2011] model graphical binary and ordinal variables in a Bayesian framework with a latent Gaussian copula, requiring an approximation to the likelihood function with the extended rank likelihood of D. Hoff [2007].…”

Section: Copula Estimation Problemsmentioning

confidence: 99%

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Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

Huk

Adewoyin

Dutta

2023

Preprint

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<p>This work develops a novel method for generating conditional probabilistic rainfall forecasts with temporal and spatial dependence. A two-step procedure is employed. Firstly, marginal location-specific distributions are modelled independently of one another. Secondly, a spatial dependency structure is learned in order to make these marginal distributions spatially coherent. <br />To learn marginal distributions over rainfall values, we propose a class of models termed Joint Generalised Neural Models (JGNMs). These models expand the linear part of generalised linear models with a deep neural network allowing them to take into account non-linear trends of the data while learning the parameters for a distribution over the outcome space.<br />In order to understand the spatial dependency structure of the data, a model based on censored copulas is presented. It is designed for the particularities of rainfall data and incorporates the spatial aspect into our approach. Uniting our two contributions, namely the JGNM and the Censored Spatial Copulas into a single model, we get a probabilistic model capable of generating possible scenarios on short to long-term timescales, able to be evaluated at any given location, seen or unseen. We show an application of it to a precipitation downscaling problem on a large UK rainfall dataset and compare it to existing methods.</p>

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Section: Discussionmentioning

confidence: 99%

Section: Copula Estimation Problemsmentioning

confidence: 99%

Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

Huk

Adewoyin

Dutta

2023

Preprint

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“…Given any i ∈ BA val , we assume all observations in the set BAP N i follow the semiparametric marginal distribution given in [24]. This distribution was proposed for modelling precipitation data, which are similar to wildfire data in the sense that they typically contain a large number of zero observations.…”

Section: A Semi-parametric Approach For Modelling Bapmentioning

confidence: 99%

A marginal modelling approach for predicting wildfire extremes across the contiguous United States

et al. 2023

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This paper details a methodology proposed for the EVA 2021 conference data challenge. The aim of this challenge was to predict the number and size of wildfires over the contiguous US between 1993 and 2015, with more importance placed on extreme events. In the data set provided, over 14% of both wildfire count and burnt area observations are missing; the objective of the data challenge was to estimate a range of marginal probabilities from the distribution functions of these missing observations. To enable this prediction, we make the assumption that the marginal distribution of a missing observation can be informed using non-missing data from neighbouring locations. In our method, we select spatial neighbourhoods for each missing observation and fit marginal models to non-missing observations in these regions. For the wildfire counts, we assume the compiled data sets follow a zero-inflated negative binomial distribution, while for burnt area values, we model the bulk and tail of each compiled data set using non-parametric and parametric techniques, respectively. Cross validation is used to select tuning parameters, and the resulting predictions are shown to significantly outperform the benchmark method proposed in the challenge outline. We conclude with a discussion of our modelling framework, and evaluate ways in which it could be extended.

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“…Figure 1 shows a map of the 28 manual stations analysed. Flood events are mainly determined by aggregations in space and/or time of extreme rainfalls (Richards et al, 2021). A spatio-temporal study of threshold exceedances of the rainfall process, therefore, has important practical implications in evaluating flood risk.…”

Section: Applicationmentioning

confidence: 99%

A model for space-time threshold exceedances with an application to extreme rainfall

Bortot

Gaetan

2022

Statistical Modelling

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In extreme value studies, models for observations exceeding a fixed high threshold have the advantage of exploiting the available extremal information while avoiding bias from low values. In the context of space-time data, the challenge is to develop models for threshold exceedances that account for both spatial and temporal dependence. We address this issue through a modelling approach that embeds spatial dependence within a time series formulation. The model allows for different forms of limiting dependence in the spatial and temporal domains as the threshold level increases. In particular, temporal asymptotic independence is assumed, as this is often supported by empirical evidence, especially in environmental applications, while both asymptotic dependence and asymptotic independence are considered for the spatial domain. Inference from the observed exceedances is carried out through a combination of pairwise likelihood and a censoring mechanism. For those model specifications for which direct maximization of the censored pairwise likelihood is unfeasible, we propose an indirect inference procedure which leads to satisfactory results in a simulation study. The approach is applied to a dataset of rainfall amounts recorded over a set of weather stations in the North Brabant province of the Netherlands. The application shows that the range of extremal patterns that the model can cover is wide and that it has a competitive performance with respect to an alternative existing model for space-time threshold exceedances.

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Modelling extremes of spatial aggregates of precipitation using conditional methods

Cited by 9 publications

References 41 publications

Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

A marginal modelling approach for predicting wildfire extremes across the contiguous United States

A model for space-time threshold exceedances with an application to extreme rainfall

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