Modeling Of Extreme Events Research Articles

Exploring the Dynamic Behavior of Crude Oil Prices in Times of Crisis: Quantifying the Aftershock Sequence of the COVID-19 Pandemic

Crude oil prices crashed and dropped into negative territory at the onset of the COVID-19 pandemic. This extreme event triggered a series of great-magnitude aftershocks. We seek to investigate the cascading dynamics and the characteristics of the series immediately following the oil market crash. Utilizing a robust method named the Omori law, we quantify the correlations of these events. This research presents empirical regularity concerning the number of times that the absolute value of the percentage change in the oil index exceeds a given threshold value. During the COVID-19 crisis, the West Texas Intermediate (WTI) oil prices exhibit greater volatility compared to the Brent oil prices, with higher relaxation values at all threshold levels. This indicates that larger aftershocks decay more rapidly, and the period of turbulence for the WTI is shorter than that of Brent and the stock market indices. We also demonstrate that the power law’s exponent value increases with the threshold value’s magnitude. By proposing this alternative method of modeling extreme events, we add to the current body of literature, and the findings demonstrate its practical use for decision-making authorities—particularly financial traders who model high-volatility products like derivatives.

Extended metric validation of a semi-physical Space Weather Modeling Framework conductance model on field-aligned current estimations

In this study, a detailed metric survey on the “Galaxy 15” (April 2010) space weather event is conducted to validate MAGNetosphere–Ionosphere–Thermosphere (MAGNIT), a semi-physical auroral ionospheric conductance model characterizing four precipitation sources, against AMPERE measurements via field-aligned current (FAC) characteristics. As part of this study, the comparative performance of three ionosphere electrodynamic specifications involving auroral conductance models, MAGNIT, Ridley Legacy Model (RLM) (empirical), and Conductance Model for Extreme Events (CMEE) (empirical), within the Space Weather Modeling Framework (SWMF), is demonstrated. Overall, MAGNIT exhibits marginally improved predictions; root mean square error values in upward and downward FACs of MAGNIT predictions compared to AMPERE data are smaller than those of CMEE and Ridley Ionosphere Model (RIM) by ∼12.7% and ∼6.24% before the storm, ∼4.52% and ∼2.13% better during the main phase, ∼1.98% and ∼1.27% worse during the second minimum, and better by ∼1.84% and ∼1.49% by the beginning of the recovery, respectively. In all three model configurations, the dusk and night magnetic local time (MLT) sectors over-predict throughout the storm, while the day and dawn MLT sectors under-predict in response to interplanetary magnetic field (IMF) conditions. In addition to accuracy and bias, similar results and conclusions are drawn from additional metrics, including in the categories of correlation, precision, extremes, and skill, and recommendations are made for the best-performing model configuration in each metric category. Visual data–model comparisons conducted by studying the FAC location and latitude/MLT spread throughout various phases of the storm suggest that the spatial extent of the FACs is captured relatively well in the night-side auroral oval, unlike in the day-side oval. The spread in latitude of the FACs matches that in the previous literature on other model performances. This information on auroral precipitation sources and their weight on FACs, along with metrics from model–data comparisons, can be used to modify MAGNIT settings to optimize SWMF model performance.

Probabilistic modeling of extreme events involving decaying variables with an application in seismology

Probabilistic modeling of extreme events involving decaying variables with an application in seismology

The role of wave setup on extreme water levels around Australia

Estimates of extreme sea levels have mainly been derived using atmospheric and tidal forcing only, but surface gravity waves are a key process that can cause a substantial elevation of mean sea level at the coast. In this paper a coupled wave-circulation model was used to simulate storm surge and wave setup across a broad range of coastal topographies and storm types around Australia. The main aim was a practical assessment of the benefits and limitations of using a coupled wave-surge model to determine wave effects for extreme sea level studies on the continental scale. The simulations included: tropical cyclones Yasi (2011) and George (2007) on the northeast and northwest coasts of Australia; Cyclone Alby (1978) that underwent extratropical transition in southwest Australia; and a large extratropical winter storm in the Southern Ocean (2016). Predicted wave setup was highly variable both spatially and temporally, with values up to 0.45 m, 35% of maximum storm surge height, and 9% of incident significant wave heights. In general, where storm surge heights were smaller, the relative importance of wave setup increased in the presence of large waves. The model best resolved wave setup in shallow gently sloping coastal areas, whilst unrealistically low values were predicted for steep coastlines. Predictions improved when wave setup was included for most sites and events, however, these wave effects were often secondary to other assumptions implicit in modeling extreme events. This was especially true for tropical cyclones where reliable wind forcing was not available. The results showed similar contributions from wave setup to other studies but highlighted the high temporal and spatial variability of wave setup across a wider variety of storms and coastal morphologies. The results also revealed that the maximum wave setup did not always coincide with the maximum storm surge. Overall, the coupled wave-surge model presented a useful tool to predict extreme water levels including wave setup when accurate depth and atmospheric data are available, however, significant challenges still exist to model this process at the continental scale.

Comparison of some Bayesian estimation methods for type-I generalized extreme value distribution with simulation

The Weibull distribution is considered one of the Type-I Generalized Extreme Value (GEV) distribution, and it plays a crucial role in modeling extreme events in various fields, such as hydrology, finance, and environmental sciences. Bayesian methods play a strong, decisive role in estimating the parameters of the GEV distribution due to their ability to incorporate prior knowledge and handle small sample sizes effectively. In this research, we compare several shrinkage Bayesian estimation methods based on the squared error and the linear exponential loss functions. They were adopted and compared by the Monte Carlo simulation method. The performance of these methods is assessed based on their accuracy and computational efficiency in estimating the scale parameter of the Weibull distribution. To evaluate their performance, we generate simulated datasets with different sample sizes and varying parameter values. A technique for pre-estimation shrinkage is suggested to enhance the precision of estimation. Simulation experiments proved that the Bayesian shrinkage estimator and shrinkage pre-estimation under the squared loss function method are better than the other methods because they give the least mean square error. Overall, our findings highlight the advantages of shrinkage Bayesian estimation methods for the proposed distribution. Researchers and practitioners in fields reliant on extreme value analysis can benefit from these findings when selecting appropriate Bayesian estimation techniques for modeling extreme events accurately and efficiently.

Fast parameter estimation of generalized extreme value distribution using neural networks

AbstractThe heavy‐tailed behavior of the generalized extreme‐value distribution makes it a popular choice for modeling extreme events such as floods, droughts, heatwaves, wildfires and so forth. However, estimating the distribution's parameters using conventional maximum likelihood methods can be computationally intensive, even for moderate‐sized datasets. To overcome this limitation, we propose a computationally efficient, likelihood‐free estimation method utilizing a neural network. Through an extensive simulation study, we demonstrate that the proposed neural network‐based method provides generalized extreme value distribution parameter estimates with comparable accuracy to the conventional maximum likelihood method but with a significant computational speedup. To account for estimation uncertainty, we utilize parametric bootstrapping, which is inherent in the trained network. Finally, we apply this method to 1000‐year annual maximum temperature data from the Community Climate System Model version 3 across North America for three atmospheric concentrations: 289 ppm (pre‐industrial), 700 ppm (future conditions), and 1400 ppm , and compare the results with those obtained using the maximum likelihood approach.

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

The pioneering work in finance by Black, Scholes and Merton during the 1970s led to the emergence of the Black-Scholes (B-S) equation, which offers a concise and transparent formula for determining the theoretical price of an option. The establishment of the B-S equation, however, relies on a set of rigorous assumptions that give rise to several limitations. The non-local property of the fractional derivative (FD) and the identification of fractal characteristics in financial markets have paved the way for the introduction and rapid development of fractional calculus in finance. In comparison to the classical B-S equation, the fractional B-S equations (FBSEs) offer a more flexible representation of market behavior by incorporating long-range dependence, heavy-tailed and leptokurtic distributions, as well as multifractality. This enables better modeling of extreme events and complex market phenomena, The fractional B-S equations can more accurately depict the price fluctuations in actual financial markets, thereby providing a more reliable basis for derivative pricing and risk management. This paper aims to offer a comprehensive review of various FBSEs for pricing European options, including associated solution techniques. It contributes to a deeper understanding of financial model development and its practical implications, thereby assisting researchers in making informed decisions about the most suitable approach for their needs.

Modeling Extreme Events in Time Series and Their Impact on Seasonal Adjustment in the Post-Covid-19 Era

Modeling Extreme Events in Time Series and Their Impact on Seasonal Adjustment in the Post-Covid-19 Era

Attractor Inspired Deep Learning for Modelling Chaotic Systems

Predicting and understanding the behavior of dynamic systems have driven advancements in various approaches, including physics-based models and data-driven techniques like deep neural networks. Chaotic systems, with their stochastic nature and unpredictable behavior, pose challenges for accurate modeling and forecasting, especially during extreme events. In this paper, we propose a novel deep learning framework called Attractor-Inspired Deep Learning (AiDL), which seamlessly integrates actual statistics and mathematical models of system kinetics. AiDL combines the strengths of physics-informed machine learning and data-driven methods, offering a promising solution for modeling nonlinear systems. By leveraging the intricate dynamics of attractors, AiDL bridges the gap between physics-based models and deep neural networks. We demonstrate the effectiveness of AiDL using real-world data from various domains, including catastrophic weather mechanics, El Niño cycles, and disease transmission. Our empirical results showcase AiDL’s ability to substantially enhance the modeling of extreme events. The proposed AiDL paradigm holds promise for advancing research in Time Series Prediction of Extreme Events and has applications in real-world chaotic system transformations.

Data reformation – A novel data processing technique enhancing machine learning applicability for predicting streamflow extremes

Hydrologists have been actively exploring the utility of machine learning (ML) models for predicting streamflow. While ML methods have proven to be as accurate as conventional modeling techniques for streamflows well represented in the training set, they continue to lack satisfactory skills for extreme events. In this study, a novel ‘data reformation’ technique is proposed based on the Relative Strength Index (RSI) – a measure of speed and direction of changes in the time series. RSI homogenizes all observations to a constrained 0–100 range, and all ‘out-of-sample’ data in the testing set fall within the space of the training set. Long Short-Term Memory network with an attention mechanism is used to train three ML models using 55,055 events from the CAMELS dataset (670 basins, 1980–2014). Predictions are made for 12,424 events, of which 3,810 are significantly higher than streamflows in the training set. The ML model based on RSI-reformed data exhibits superior performance, as compared to other advanced ML models without data reformation. Peaks up to 15 times larger than those in the training events are accurately predicted, leading to an outperforming model skill for 433 out of 670 catchments. These findings indicate that incorporating a new data reformation technique into the data pre-processing step in ML modeling can enhance the utility of ML models for extreme events. This research encourages further exploration to identify better data reformation methods to enable confident ML predictions.

A Dynamic Extreme Value Model with Application to Volcanic Eruption Forecasting

Extreme events such as natural and economic disasters leave lasting impacts on society and motivate the analysis of extremes from data. While classical statistical tools based on Gaussian distributions focus on average behaviour and can lead to persistent biases when estimating extremes, extreme value theory (EVT) provides the mathematical foundations to accurately characterise extremes. This motivates the development of extreme value models for extreme event forecasting. In this paper, a dynamic extreme value model is proposed for forecasting volcanic eruptions. This is inspired by one recently introduced for financial risk forecasting with high-frequency data. Using a case study of the Piton de la Fournaise volcano, it is shown that the modelling framework is widely applicable, flexible and holds strong promise for natural hazard forecasting. The value of using EVT-informed thresholds to identify and model extreme events is shown through forecast performance, and considerations to account for the range of observed events are discussed.

Modeling Extreme Events: Time-Varying Extreme Tail Shape

We propose a dynamic semiparametric framework to study time variation in tail parameters. The framework builds on the Generalized Pareto Distribution (GPD) for modeling peaks over thresholds as in Extreme Value Theory, but casts the model in a conditional framework to allow for time-variation in the tail parameters. We establish parameter regions for stationarity and ergodicity and for the existence of (unconditional) moments and consider conditions for consistency and asymptotic normality of the maximum likelihood estimator for the deterministic parameters in the model. Two empirical datasets illustrate the usefulness of the approach: daily U.S. equity returns, and 15-min euro area sovereign bond yield changes.

Extreme value modeling with errors-in-variables in detection and attribution of changes in climate extremes

The generalized extreme value (GEV) regression provides a framework for modeling extreme events across various fields by incorporating covariates into the location parameter of GEV distributions. When the covariates are subject to errors-in-variables (EIV) or measurement error, ignoring the EIVs leads to biased estimation and degraded inferences. This problem arises in detection and attribution analyses of changes in climate extremes because the covariates are estimated with uncertainty. It has not been studied even for the case of independent EIVs, let alone the case of dependent EIVs, due to the complex structure of GEV. Here we propose a general Monte Carlo corrected score method and extend it to address temporally correlated EIVs in GEV modeling with application to the detection and attribution analyses for climate extremes. Through extensive simulation studies, the proposed method provides an unbiased estimator and valid inference. In the application to the detection and attribution analyses of temperature extremes in central regions of China, with the proposed method, the combined anthropogenic and natural signal is detected in the change in the annual minimum of daily maximum and the annual minimum of daily minimum.

Assessment of cloud microphysics and cumulus convection schemes to model extreme rainfall events over the Paraiba do Sul River Basin

Highly urbanized areas with complex terrains and multiple land uses pose challenges to extreme precipitation forecasts. The present study investigates the performance of several cloud microphysics and cumulus convection parameterizations on a severe rainfall event over the Paraiba do Sul River Basin, an area periodically affected by heavy precipitation. The Weather Research and Forecasting (WRF) model was applied to perform high resolution simulations, and the results were compared against ground observations, weather radar data, and satellite-based precipitation estimates. The simulations tend to underestimate precipitation by an average bias of 55%; however, some experiments showed good fittings in terms of time correlations (over 90%). Overall, the radar vertical profile of reflectivity agrees with observations, where the height of the warm and mixed layers was accurately simulated, despite overpredictions of convective depth (by up to 3 km in regions of intense ascending currents). Typically, WRF was more sensitive to distinct microphysics schemes rather than cloud convection ones. Also, urban areas showed greater precipitation and hydrometeor content in comparison with non-urban ones, even under strong synoptic-scale forcing. The framework was able to reproduce convectively active environments, supporting its application on operational runs over urbanized regions for warning issuing and decision-making.

An Insurance Value Modeling Approach That Captures the Wider Value of a Novel Antimicrobial to Health Systems, Patients, and the Population.

Background: Traditional health economic evaluations of antimicrobials currently underestimate their value to wider society. They can be supplemented by additional value elements including insurance value, which captures the value of an antimicrobial in preventing or mitigating impacts of adverse risk events. Despite being commonplace in other sectors, constituents of the impacts and approaches for estimating insurance value have not been investigated. Objectives: This study assessed the insurance value of a novel gram-negative antimicrobial from operational healthcare, wider population health, productivity, and informal care perspectives. Methods: A novel mixed-methods approach was used to model insurance value in the United Kingdom: (1) literature review and multidisciplinary expert workshops to identify risk events for 4 relevant scenarios: ward closures, unavoidable shortage of conventional antimicrobials, viral respiratory pandemics, and catastrophic antimicrobial resistance (AMR); (2) parameterizing mitigable costs and frequencies of risk events across perspectives and scenarios; (3) estimating insurance value through a Monte Carlo simulation model for extreme events and a dynamic disease transmission model. Results: The mean insurance value across all scenarios and perspectives over 10 years in the UK was £718 million, should AMR remain unchanged, where only £134 million related to operational healthcare costs. It would be 50%-70% higher if AMR steadily increased or if a more risk-averse view (1-in-10 year downside) of future events is taken. Discussion: The overall insurance value if AMR remains at current levels (a conservative projection), is over 5 times greater than insurance value from just the operational healthcare costs perspective, traditionally the sole perspective used in health budgeting. Insurance value was generally larger for nationwide or universal (catastrophic AMR, pandemic, and conventional antimicrobial shortages) rather than localized (ward closure) scenarios, across perspectives. Components of this insurance value match previously published estimates of operational costs and mortality impacts. Conclusions: Insurance value of novel antimicrobials can be systematically modeled and substantially augments their traditional health economic value in normal circumstances. These approaches are generalizable to similar health interventions and form a framework for health systems and governments to capture broader value in health technology assessments, improve healthcare access, and increase resilience by planning for adverse scenarios.

An Insurance Value Modeling Approach That Captures the Wider Value of a Novel Antimicrobial to Health Systems, Patients, and the Population

Background: Traditional health economic evaluations of antimicrobials currently underestimate their value to wider society. They can be supplemented by additional value elements including insurance value, which captures the value of an antimicrobial in preventing or mitigating impacts of adverse risk events. Despite being commonplace in other sectors, constituents of the impacts and approaches for estimating insurance value have not been investigated. Objectives: This study assessed the insurance value of a novel gram-negative antimicrobial from operational healthcare, wider population health, productivity, and informal care perspectives. Methods: A novel mixed-methods approach was used to model insurance value in the United Kingdom: (1) literature review and multidisciplinary expert workshops to identify risk events for 4 relevant scenarios: ward closures, unavoidable shortage of conventional antimicrobials, viral respiratory pandemics, and catastrophic antimicrobial resistance (AMR); (2) parameterizing mitigable costs and frequencies of risk events across perspectives and scenarios; (3) estimating insurance value through a Monte Carlo simulation model for extreme events and a dynamic disease transmission model. Results: The mean insurance value across all scenarios and perspectives over 10 years in the UK was £718 million, should AMR remain unchanged, where only £134 million related to operational healthcare costs. It would be 50%-70% higher if AMR steadily increased or if a more risk-averse view (1-in-10 year downside) of future events is taken. Discussion: The overall insurance value if AMR remains at current levels (a conservative projection), is over 5 times greater than insurance value from just the operational healthcare costs perspective, traditionally the sole perspective used in health budgeting. Insurance value was generally larger for nationwide or universal (catastrophic AMR, pandemic, and conventional antimicrobial shortages) rather than localized (ward closure) scenarios, across perspectives. Components of this insurance value match previously published estimates of operational costs and mortality impacts. Conclusions: Insurance value of novel antimicrobials can be systematically modeled and substantially augments their traditional health economic value in normal circumstances. These approaches are generalizable to similar health interventions and form a framework for health systems and governments to capture broader value in health technology assessments, improve healthcare access, and increase resilience by planning for adverse scenarios.

Mixture Probability Models with Covariates: Applications in Estimating Risk of Hydroclimatic Extremes

Modeling of extreme events is important in many scientific fields, including environmental and civil engineering, and impacts and risk assessments. Among available methods, statistical models that allow estimating extremes’ frequency and intensity are regularly used in procedures to anticipate potential changes in extreme events. Extreme value theory provides a theoretical basis for statistical estimation of extreme events using frequency analysis. The challenge in modeling is knowing when to use the block maxima method or the peaks-over-threshold (POT) method. Each has its drawbacks. POT describes the main characteristics of the observed extreme series; the threshold selection is always challenging and might affect the accuracy of the simulated results and the credibility of changes in extreme values. To encompass this challenge, mixture models offer more flexibility to represent samples with nonhomogeneous data. This study presents the gamma generalized Pareto (GGP) mixture model for estimating risk occurrence of hydroclimatic extremes. The model was developed in its general form, whereas the observed hydrometeorological extreme events depend on multidimensional covariates. A maximum likelihood algorithm is proposed to estimate the parameters with a constraint on the shape parameter of the generalized Pareto (GP) distribution. A Monte Carlo (MC) simulation compared the proposed model with the classical POT approach, with a fixed threshold, and the annual maximum series of streamflow. The approach was applied using a daily hydrological data set from an observed station located in the Saint John River at Fort Kent (01AD002), New Brunswick, Canada. The results show a flexibility to model extremes for dependent or nonstationary time series and adequately describes the central part of the observed frequencies, as well as the tails.

Output-weighted and relative entropy loss functions for deep learning precursors of extreme events

Many scientific and engineering problems require accurate models of dynamical systems with rare and extreme events. Such problems present a challenging task for data-driven modeling, with many naive machine learning methods failing to predict or accurately quantify such events. One cause for this difficulty is that systems with extreme events, by definition, yield imbalanced datasets and that standard loss functions easily ignore rare events. That is, metrics for goodness of fit used to train models are not designed to ensure accuracy on rare events. This work seeks to improve the performance of regression models for extreme events by considering loss functions designed to highlight outliers. We propose a novel loss function, the adjusted output weighted loss, and extend the applicability of relative entropy based loss functions to systems with low dimensional output. The proposed functions are tested using several cases of dynamical systems exhibiting extreme events and shown to significantly improve accuracy in predictions of extreme events.

A deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling

The numerical modelling of natural disasters such as landslides presents several challenges for conventional mesh-based methods such as the finite element method (FEM) due to the presence of numerically challenging phenomena such as severe material deformation and fragmentation. In contrast, meshfree methods such as the reproducing kernel particle method (RKPM) possess unique features conducive to modelling extreme events such as the absence of a structured mesh and the ease of adaptive refinement, among others. While the semi-Lagrangian reproducing kernel (SL-RK) shape functions of RKPM defined in the current configuration have proven to be effective in extreme event modelling, the computational cost for the re-evaluation of the shape functions at every time step is costly. In this work, a deformation-dependent coupling of the Lagrangian reproducing kernel (L-RK) and SL-RK approximations is proposed for the solution of a hydro-mechanical formulation for effective simulations of landslides. The ramp function is constructed based on an equivalent plastic strain as a deformation-dependent transition from L-RK shape functions to SL-RK ones as the deformation progresses. The particular focus of the paper will be on modelling seepage-induced landslides with a mixed u–p formulation to couple the solid and fluid phases. Examples are presented to examine the effectiveness of this coupled Lagrangian/semi-Lagrangian reproducing kernel (L–SL RK) formulation and to highlight its performance in landslide modelling.

Assessing the Potential of IMERG and TMPA Satellite Precipitation Products for Flood Simulations and Frequency Analyses over a Typical Humid Basin in South China

The availability of the new generation Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG) V06 products facilitates the utility of long-term higher spatial and temporal resolution precipitation data (0.1° × 0.1° and half-hourly) for monitoring and modeling extreme hydrological events in data-sparse watersheds. This study aims to evaluate the utility of IMERG Final run (IMERG-F), Late run (IMERG-L) and Early run (IMERG-E) products, in flood simulations and frequency analyses over the Mishui basin in Southern China during 2000–2017, in comparison with their predecessors, the Tropical Rainfall Measuring Mission Multi-satellite Precipitation Analysis (TMPA) products (3B42RT and 3B42V7). First, the accuracy of the five satellite precipitation products (SPPs) for daily precipitation and extreme precipitation events estimation was systematically compared by using high-density gauge station observations. Once completed, the modeling capability of the SPPs in daily streamflow simulations and flood event simulations, using a grid-based Xinanjiang model, was assessed. Finally, the flood frequency analysis utility of the SPPs was evaluated. The assessment of the daily precipitation accuracy shows that IMERG-F has the optimum statistical performance, with the highest CC (0.71) and the lowest RMSE (8.7 mm), respectively. In evaluating extreme precipitation events, among the IMERG series, IMERG-E exhibits the most noticeable variation while IMERG-L and IMERG-F display a relatively low variation. The 3B42RT exhibits a severe inaccuracy and the improvement of 3B42V7 over 3B42RT is comparatively limited. Concerning the daily streamflow simulations, IMERG-F demonstrates a superior performance while 3B42V7 tends to seriously underestimate the streamflow. With regards to the simulations of flood events, IMERG-F has performed optimally, with an average DC of 0.83. Among the near-real-time SPPs, IMERG-L outperforms IMERG-E and 3B42RT over most floods, attaining a mean DC of 0.81. Furthermore, IMERG-L performs the best in the flood frequency analyses, where bias is within 15% for return periods ranging from 2–100 years. This study is expected to contribute practical guidance to the new generation of SPPs for extreme precipitation monitoring and flood simulations as well as promoting the hydro-meteorological applications.