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Climate studies based on global climate models (GCMs) project a steady increase in annual average temperature and severe heat extremes in central North America during the mid-century and beyond. However, the agreement of observed trends with climate model trends varies substantially across the region. The present study focuses on two different locations: Des Moines, IA and Austin, TX. In Des Moines, annual extreme temperatures have not increased over the past three decades unlike the trend of regionally-downscaled GCM data for the Midwest, likely due to a “warming hole” over the area linked to agricultural factors. This warming hole effect is not evident for Austin over the same time period, where extreme temperatures have been higher than projected by regionally-downscaled climate (RDC) forecasts. In consideration of the deviation of such RDC extreme temperature forecasts from observations, this study statistically analyzes RDC data in conjunction with observational data to define for these two cities a 95% prediction interval of heat extreme values by 2040. The statistical model is constructed using a linear combination of RDC ensemble-member annual extreme temperature forecasts with regression coefficients for individual forecasts estimated by optimizing model results against observations over a 52-year training period. 

To help wind turbine reliability analysis with scarce field data, aeroelastic simulators can be used to generate stochastic wind turbine loads with prescribed turbulent wind conditions. However, simulating an extreme load associated with a small load exceedance probability is computationally prohibitive and extreme load estimation from crude Monte Carlo method leads to very large uncertainty. We develop adaptive algorithms based on importance sampling theory to reduce the estimation uncertainty. 

Abstract Quantile is an important quantity in reliability analysis, as it is related to the resistance level for defining failure events. This study develops a computationally efficient sampling method for estimating extreme quantiles using stochastic black box computer models. Importance sampling has been widely employed as a powerful variance reduction technique to reduce estimation uncertainty and improve computational efficiency in many reliability studies. However, when applied to quantile estimation, importance sampling faces challenges, because a good choice of the importance sampling density relies on information about the unknown quantile. We propose an adaptive method that refines the importance sampling density parameter toward the unknown target quantile value along the iterations. The proposed adaptive scheme allows us to use the simulation outcomes obtained in previous iterations for steering the simulation process to focus on important input areas. We prove some convergence properties of the proposed method and show that our approach can achieve variance reduction over crude Monte Carlo sampling. We demonstrate its estimation efficiency through numerical examples and wind turbine case study.