skip to main content

Title: Flexible and Fast Spatial Return Level Estimation Via a Spatially Fused Penalty
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.  more » « less
Award ID(s):
1922758 1830312
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Computational and Graphical Statistics
Page Range / eLocation ID:
1 to 19
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    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.

    more » « less
  2. Extreme storm surges can overwhelm many coastal flooding protection measures in place and cause severe damages to private communities, public infrastructure, and natural ecosystems. In the US Mid-Atlantic, a highly developed and commercially active region, coastal flooding is one of the most significant natural hazards and a year-round threat from both tropical and extra-tropical cyclones. Mean sea levels and high-tide flood frequency has increased significantly in recent years, and major storms are projected to increase into the foreseeable future. We estimate extreme surges using hourly water level data and harmonic analysis for 1980–2019 at 12 NOAA tide gauges in and around the Delaware and Chesapeake Bays. Return levels (RLs) are computed for 1.1, 3, 5, 10, 25, 50, and 100-year return periods using stationary extreme value analysis on detrended skew surges. Two traditional approaches are investigated, Block Maxima fit to General Extreme Value distribution and Points-Over-Threshold fit to Generalized Pareto distribution, although with two important enhancements. First, the GEV r -largest order statistics distribution is used; a modified version of the GEV distribution that allows for multiple maximum values per year. Second, a systematic procedure is used to select the optimum value for r (for the BM/GEVr approach) and the threshold (for the POT/GP approach) at each tide gauge separately. RLs have similar magnitudes and spatial patterns from both methods, with BM/GEVr resulting in generally larger 100-year and smaller 1.1-year RLs. Maximum values are found at the Lewes (Delaware Bay) and Sewells Point (Chesapeake Bay) tide gauges, both located in the southwest region of their respective bays. Minimum values are found toward the central bay regions. In the Delaware Bay, the POT/GP approach is consistent and results in narrower uncertainty bands whereas the results are mixed for the Chesapeake. Results from this study aim to increase reliability of projections of extreme water levels due to extreme storms and ultimately help in long-term planning of mitigation and implementation of adaptation measures. 
    more » « less
  3. Geospatio-temporal data are pervasive across numerous application domains.These rich datasets can be harnessed to predict extreme events such as disease outbreaks, flooding, crime spikes, etc.However, since the extreme events are rare, predicting them is a hard problem. Statistical methods based on extreme value theory provide a systematic way for modeling the distribution of extreme values. In particular, the generalized Pareto distribution (GPD) is useful for modeling the distribution of excess values above a certain threshold. However, applying such methods to large-scale geospatio-temporal data is a challenge due to the difficulty in capturing the complex spatial relationships between extreme events at multiple locations. This paper presents a deep learning framework for long-term prediction of the distribution of extreme values at different locations. We highlight its computational challenges and present a novel framework that combines convolutional neural networks with deep set and GPD. We demonstrate the effectiveness of our approach on a real-world dataset for modeling extreme climate events. 
    more » « less
  4. Abstract

    We develop a space‐time Bayesian hierarchical modeling (BHM) framework for two flood risk attributes—seasonal daily maximum flow and the number of events that exceed a threshold during a season (NEETM)—at a suite of gauge locations on a river network. The model uses generalized extreme value (GEV) and Poisson distributions as marginals for these flood attributes with non‐stationary parameters. The rate parameters of the Poisson distribution and location, scale, and shape parameters of the GEV are modeled as linear functions of suitable covariates. Gaussian copulas are applied to capture the spatial dependence. The best covariates are selected using the Watanabe‐Akaike information criterion (WAIC). The modeling framework results in the posterior distribution of the flood attributes at all the gauges and various lead times. We demonstrate the utility of this modeling framework to forecast the flood risk attributes during the summer peak monsoon season (July‐August) at five gauges in the Narmada River basin (NRB) of West‐Central India for several lead times (0–3 months). As potential covariates, we consider climate indices such as El Niño–Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD), and the Pacific Warm Pool Region (PWPR) from antecedent seasons, which have shown strong teleconnections with the Indian monsoon. We also include new indices related to the East Pacific and West Indian Ocean regions depending on the lead times. We show useful long lead skill from this modeling approach which has a strong potential to enable robust risk‐based flood mitigation and adaptation strategies 3 months before flood occurrences.

    more » « less
  5. Storm surges are the most important driver of flooding in many coastal areas. Understanding the spatial extent of storm surge events has important financial and practical implications for flood risk management, reinsurance, infrastructure reliability and emergency response. In this paper, we apply a new tracking algorithm to a high-resolution surge hindcast (CODEC, 1980–2017) to characterize the spatial dependence and temporal evolution of extreme surge events along the coastline of the UK and Ireland. We quantify the severity of each spatial event based on its footprint extremity to select and rank the collection of events. Several surge footprint types are obtained based on the most impacted coastal stretch from each particular event, and these are linked to the driving storm tracks. Using the collection of the extreme surge events, we assess the spatial distribution and interannual variability of the duration, size, severity, and type. We find that the northeast coastline is most impacted by the longest and largest storm surge events, while the English Channel experiences the shortest and smallest storm surge events. The interannual variability indicates that the winter seasons of 1989-90 and 2013–14 were the most serious in terms of the number of events and their severity, based on the return period along the affected coastlines. The most extreme surge event and the highest number of events occurred in the winter season 1989–90, while the proportion of events with larger severities was higher during the winter season 2013–14. This new spatial analysis approach of surge extremes allows us to distinguish several categories of spatial footprints of events around the UK/Ireland coast and link these to distinct storm tracks. The spatial dependence structures detected can improve multivariate statistical methods which are crucial inputs to coastal flooding assessments. 
    more » « less