A model weighting scheme is important in multi-model climate ensembles for projecting future changes. The climate model output typically needs to be bias corrected before it can be used. When a bias-correction (BC) is applied, equal model weights are usually derived because some BC methods cause the observations and historical simulation to match perfectly. This equal weighting is sometimes criticized because it does not take into account the model performance. Unequal weights reflecting model performance may be obtained from raw data before BC is applied. However, we have observed that certain models produce excessively high weights, while the weights generated in all other models are extremely low. This phenomenon may be partly due to the fact that some models are more fit or calibrated to the observations for a given applications. To address these problems, we consider, in this study, a hybrid weighting scheme including both equal and unequal weights. The proposed approach applies an “imperfect” correction to the historical data in computing their weights, while it applies ordinary BC to the future data in computing the ensemble prediction. We employ a quantile mapping method for the BC and a Bayesian model averaging for performance-based weighting. Furthermore, techniques for selecting the optimal correction rate based on the chi-square test statistic and the continuous ranked probability score are examined. Comparisons with ordinary ensembles are provided using a perfect model test. The usefulness of the proposed method is illustrated using the annual maximum daily precipitation as observed in the Korean peninsula and simulated by 21 models from the Coupled Model Intercomparison Project Phase 6.

Scientists who want to know future climate can use multimodel ensemble (MME) methods that combine projections from individual simulation models. To predict the future changes of extreme rainfall in Iran, we examined the observations and 24 models of the Coupled Model Inter-Comparison Project Phase 6 (CMIP6) over the Middle East. We applied generalized extreme value (GEV) distribution to series of annual maximum daily precipitation (AMP1) data obtained from both of models and the observations. We also employed multivariate bias-correction under three shared socioeconomic pathway (SSP) scenarios (namely, SSP2-4.5, SSP3-7.0, and SSP5-8.5). We used a model averaging method that takes both performance and independence of model into account, which is called PI-weighting. Return levels for 20 and 50 years, as well as the return periods of the AMP1 relative to the reference years (1971–2014), were estimated for three future periods. These are period 1 (2021–2050), period 2 (2046–2075), and period 3 (2071–2100). From this study, we predict that over Iran the relative increases of 20-year return level of the AMP1 in the spatial median from the past observations to the year 2100 will be approximately 15.6% in the SSP2-4.5, 23.2% in the SSP3-7.0, and 28.7% in the SSP5-8.5 scenarios, respectively. We also realized that a 1-in-20 year (or 1-in-50 year) AMP1 observed in the reference years in Iran will likely become a 1-in-12 (1-in-26) year, a 1-in-10 (1-in-22) year, and a 1-in-9 (1-in-20) year event by 2100 under the SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios, respectively. We project that heavy rainfall will be more prominent in the western and southwestern parts of Iran.

Non‐stationarity in heavy rainfall time series is often apparent in the form of trends because of long‐term climate changes. We have built non‐stationary (NS) models for annual maximum daily (AMP1) and 2‐day precipitation (AMP2) data observed between 1984 and 2020 years by 71 stations and between 1960 and 2020 by eight stations over Thailand. The generalized extreme value (GEV) models are used. Totally, 16 time‐dependent functions of the location and scale parameters of the GEV model are considered. On each station, a model is selected by using Bayesian and Akaike information criteria among these candidates. The return levels corresponding to some years are calculated and predicted for the future. The stations with the highest return levels are Trad, Samui, and Narathiwat, for both AMP1 and AMP2 data. We found some evidence of increasing (decreasing) trends in maximum precipitation for 22 (10) stations in Thailand, based on NS GEV models.

Scientists occasionally predict projected changes in extreme climate using multi-model ensemble methods that combine predictions from individual simulation models. To predict future changes in precipitation extremes in the Korean peninsula, we examined the observed data and 21 models of the Coupled Model Inter-Comparison Project Phase 6 (CMIP6) over East Asia. We applied generalized extreme value distribution (GEVD) to a series of annual maximum daily precipitation (AMP1) data. Multivariate bias-corrected simulation data under three shared socioeconomic pathway (SSP) scenarios—namely, SSP2-4.5, SSP3-7.0, and SSP5-8.5—were used. We employed a model weighting method that accounts for both performance and independence (PI-weighting). In calculating the PI-weights, two shape parameters should be determined, but usually, a perfect model test method requires a considerable amount of computing time. To address this problem, we suggest simple ways for selecting two shape parameters based on the chi-square statistic and entropy. Variance decomposition was applied to quantify the uncertainty of projecting the future AMP1. Return levels spanning over 20 and 50 years, as well as the return periods relative to the reference years (1973–2010), were estimated for three overlapping periods in the future, namely, period 1 (2021–2050), period 2 (2046–2075), and period 3 (2071–2100). From these analyses, we estimated that the relative increases in the observations for the spatial median 20-year return level will be approximately 18.4% in the SSP2-4.5, 25.9% in the SSP3-7.0, and 41.7% in the SSP5-8.5 scenarios, respectively, by the end of the 21st century. We predict that severe rainfall will be more prominent in the southern and central parts of the Korean peninsula.

Background: The purpose of the current study was (1) to analyze various factors that may be associated with the outcomes of Legg-Calvé-Perthes disease (LCPD), and (2) to develop and internally validate machine learning algorithms capable of providing patient-specific predictions of which patients with LCPD will achieve relevant improvement in radiologic outcomes after proximal femoral varus osteotomy (PFVO). We examined several variables, previously identified as factors, that may influence the outcome of LCPD and developed a machine learning algorithm based on them. Methods: In this retrospective study, we analyzed patients aged older than 6 years at the time of LCPD diagnosis who underwent PFVO at our institution between 1979 and 2015. Univariate and multivariate logistic regression analyses were used to examine the effects of variables on the sphericity of the femoral head at skeletal maturity, including age at onset, sex, stage at operation, extent of epiphyseal involvement and collapse, presence of specific epiphyseal, metaphyseal, and acetabular changes, and postoperative neck shaft angle (NSA). Recursive feature selection was used to identify the combination of variables from an initial pool of 13 features that optimized the model performance. Five machine learning algorithms [extreme gradient boosting (XGBoost), multilayer perception, support vector machine, elastic-net penalized logistic regression, and random forest) were trained using 5-fold cross-validation 3 times and applied to an independent testing set of patients. Results: Ninety patients with LCPD who underwent PFVO were included in this study. The mean age at diagnosis was 7.93 (range, 6.0 to 12.33) years. The average follow-up period was 10.11 (range, 5.25 to 22.92) years. A combination of 8 variables, optimized algorithm performance, and specific cutoffs were found to decrease the likelihood of achieving the 1 or 2 Stulberg classification: age at onset ≤ 8.06, lateral classification ≤ B, 12.40 < preoperative migration percentage (MP) ≤ 22.85, Catterall classification ≤ 2, 117.4 < postoperative NSA ≤ 122.90, −10.8 < postoperative MP ≤ 6.5, 139.65 < preoperative NSA ≤ 144.67, and operation at stage 1. The XGBoost model demonstrated the best performance (F1 score: 0.78; area under the curve: 0.84). Conclusions: The XGBoost machine learning algorithm achieved the best performance in predicting the postoperative radiologic outcomes in patients with LCPD who underwent PFVO. In our population, age at onset ≤ 8.06, lateral classification ≤ B, 12.40 < preoperative MP ≤ 22.85, Catterall classification ≤ 2, 117.4 < postoperative NSA ≤ 122.90, −10.8 < postoperative MP ≤ 6.5, 139.65 < preoperative NSA ≤ 144.67, and operation at an early stage had the likelihood of achieving the spherical femoral head for the patients with LCPD that underwent PFVO. After external validation, the online application of this model may enhance shared decision-making. Level of Evidence: Level III—retrospective cohort study.