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1. Flexible and Fast Spatial Return Level Estimation Via a Spatially Fused Penalty

   https://doi.org/10.1080/10618600.2021.1938584  

   Sass, Danielle ; Li, Bo ; Reich, Brian J. ( July 2021 , Journal of Computational and Graphical Statistics)

   null (Ed.)

   Spatial extremes are common for climate data as the observations are usually referenced by geographic locations and dependent when they are nearby. An important goal of extremes modeling is to estimate the T-year return level. Among the methods suitable for modeling spatial extremes, perhaps the simplest and fastest approach is the spatial generalized extreme value (GEV) distribution and the spatial generalized Pareto distribution (GPD) that assume marginal independence and only account for dependence through the parameters. Despite the simplicity, simulations have shown that return level estimation using the spatial GEV and spatial GPD still provides satisfactory results compared to max-stable processes, which are asymptotically justified models capable of representing spatial dependence among extremes. However, the linear functions used to model the spatially varying coefficients are restrictive and may be violated.We propose a flexible and fast approach based on the spatial GEV and spatial GPD by introducing fused lasso and fused ridge penalty for parameter regularization. This enables improved return level estimation for large spatial extremes compared to the existing methods. Supplemental files for this article are available online. 

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2. Assessing models for estimation and methods for uncertainty quantification for spatial return levels

   https://doi.org/10.1002/env.2508  

   Cao, Yi ; Li, Bo ( July 2018 , Environmetrics)

   The return level estimation is an essential topic in studying spatial extremes for environmental data. Recently, various models for spatial extremes have emerged, which generally yield different estimates for return levels, given the same data. In the meantime, several approaches that obtain confidence intervals (CIs) for return levels have arisen, and the results from different approaches can also largely disagree. These pose natural questions for assessing different return level estimation methods and different CI derivation approaches. In this article, we compare an array of popular models for spatial extremes in return level estimation, as well as three approaches in CI derivation, through extensive Monte Carlo simulations. Our results show that in general, max‐stable models yield return level estimates with similar mean squared error, and the spatial generalized extreme value model also provides comparable estimates. The bootstrap method is recommended for max‐stable models to compute the CI, and the profile likelihood CI works well for spatial generalized extreme value. We also evaluate the methods for return level interpolation at unknown spatial locations and find that kriging of marginal return level estimates performs as well as max‐stable models.

    

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3. Transformed‐Linear Models for Time Series Extremes

   https://doi.org/10.1111/jtsa.12732  

   Mhatre, Nehali ; Cooley, Daniel ( February 2024 , Journal of Time Series Analysis)

   To capture the dependence in the upper tail of a time series, we develop non‐negative regularly varying time series models that are constructed similarly to classical non‐extreme ARMA models. Rather than fully characterizing tail dependence of the time series, we define the concept of weak tail stationarity which allows us to describe a regularly varying time series via a measure of pairwise extremal dependencies, the tail pairwise dependence function (TPDF). We state consistency requirements among the finite‐dimensional collections of the elements of a regularly varying time series and show that the TPDF's value does not depend on the dimension of the random vector being considered. So that our models take non‐negative values, we use transformed‐linear operations. We show existence and stationarity of these models, and develop their properties such as the model TPDFs. We fit models to hourly windspeed and daily fire weather index data, and we find that the fitted transformed‐linear models produce better estimates of upper tail quantities than a traditional ARMA model, classical linear regularly varying models, a max‐ARMA model, and a Markov model.

    

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4. A generalized Spatio-Temporal Threshold Clustering method for identification of extreme event patterns

   https://doi.org/10.5194/ascmo-7-35-2021  

   Kholodovsky, Vitaly ; Liang, Xin-Zhong ( January 2021 , Advances in Statistical Climatology, Meteorology and Oceanography)

   null (Ed.)

   Abstract. Extreme weather and climate events such as floods, droughts, and heat waves can cause extensive societal damages. While various statistical and climate models have been developed for the purpose of simulating extremes, a consistent definition of extreme events is still lacking. Furthermore, to better assess the performance of the climate models, a variety of spatial forecast verification measures have been developed. However, in most cases, the spatial verification measures that are widely used to compare mean states do not have sufficient theoretical justification to benchmark extreme events. In order to alleviate inconsistencies when defining extreme events within different scientific communities, we propose a new generalized Spatio-Temporal Threshold Clustering method for the identification of extreme event episodes, which uses machine learning techniques to couple existing pattern recognition indices with high or low threshold choices. The method consists of five main steps: (1) construction of essential field quantities; (2) dimension reduction; (3) spatial domain mapping; (4) time series clustering; and (5) threshold selection. We develop and apply this method using a gridded daily precipitation dataset derived from rain gauge stations over the contiguous United States. We observe changes in the distribution of conditional frequency of extreme precipitation from large-scale well-connected spatial patterns to smaller-scale more isolated rainfall clusters, possibly leading to more localized droughts and heat waves, especially during the summer months. The proposed method automates the threshold selection process through a clustering algorithm and can be directly applicable in conjunction with modeling and spatial forecast verification of extremes. Additionally, it allows for the identification of synoptic-scale spatial patterns that can be directly traced to the individual extreme episodes, and it offers users the flexibility to select an extreme threshold that is linked to the desired geometrical properties. The approach can be applied to broad scientific disciplines. 

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5. Attribution of Seasonal Wildfire Risk to Changes in Climate: A Statistical Extremes Approach

   https://doi.org/10.1175/JAMC-D-23-0072.1  

   Wixson, Troy P. ; Cooley, Daniel ( November 2023 , Journal of Applied Meteorology and Climatology)

   Wildfire risk is greatest during high winds after sustained periods of dry and hot conditions. This paper is a statistical extreme-event risk attribution study that aims to answer whether extreme wildfire seasons are more likely now than under past climate. This requires modeling temporal dependence at extreme levels. We propose the use of transformed-linear time series models, which are constructed similarly to traditional autoregressive–moving-average (ARMA) models while having a dependence structure that is tied to a widely used framework for extremes (regular variation). We fit the models to the extreme values of the seasonally adjusted fire weather index (FWI) time series to capture the dependence in the upper tail for past and present climate. We simulate 10 000 fire seasons from each fitted model and compare the proportion of simulated high-risk fire seasons to quantify the increase in risk. Our method suggests that the risk of experiencing an extreme wildfire season in Grand Lake, Colorado, under current climate has increased dramatically relative to the risk under the climate of the mid-twentieth century. Our method also finds some evidence of increased risk of extreme wildfire seasons in Quincy, California, but large uncertainties do not allow us to reject a null hypothesis of no change.

    

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