Projections of changes in extreme climate are sometimes predicted by multimodel ensemble methods that combine forecasts from individual simulation models using weighted averaging. One method to assign weight to each model is the Bayesian model averaging (BMA) in which posterior probability is used. For the cases of extreme climate, the generalized extreme value distribution (GEVD) is typically used. We applied the approach of GEV-embedded BMA to a series of 35 years of the annual maximum daily precipitation data (both historical data and data gathered from simulation experiments for future periods) over the Korean peninsula as simulated by the models in the Coupled Model Intercomparison Project Phase 5 (CMIP5). Simulation data under two Representative Concentration Pathway (RCP) scenarios, namely RCP4.5 and RCP8.5, were used. Observed data and 17 CMIP5 models for 12 gird cells in Korea have been examined to predict future changes in precipitation extremes. A simple regional frequency analysis of pooling observations from three stations in each cell was employed to reduce the estimation variance and local fluctuations. A bias correction technique using the regression-type transfer function was applied to these simulation data. Return levels spanning over 20 and 50 years, as well as the return periods relative to the reference years , were estimated for two future periods, namely Period 1 (2021-2050) and Period 2 (2066-2095). From these analyses, relative increase observed in the spatially averaged 20-year (50-year) return level was approximately 23% (16%) and 45% (36%) in the RCP4.5 and RCP8.5 experiments, respectively, by the end of the 21st century. We concluded that extreme rainfalls will likely occur two times and four times more frequently in the RCP4.5 and RCP8.5 scenarios, respectively, as compared to in the reference years by the end of the 21st century. K E Y W O R D Sclimatic change, global climate model, heavy rainfall, multimodel simulation, Taylor diagram, weighted averaging

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.

Projections of changes in extreme climate are sometimes predicted by using multi-model ensemble methods such as Bayesian model averaging (BMA) embedded with the generalized extreme value (GEV) distribution. BMA is a popular method for combining the forecasts of individual simulation models by weighted averaging and characterizing the uncertainty induced by simulating the model structure. This method is referred to as the GEV-embedded BMA. It is, however, based on a point-wise analysis of extreme events, which means it overlooks the spatial dependency between nearby grid cells. Instead of a point-wise model, a spatial extreme model such as the max-stable process (MSP) is often employed to improve precision by considering spatial dependency. We propose an approach that integrates the MSP into BMA, which is referred to as the MSP-BMA herein. The superiority of the proposed method over the GEV-embedded BMA is demonstrated by using extreme rainfall intensity data on the Korean peninsula from Coupled Model Intercomparison Project Phase 5 (CMIP5) multi-models. The reanalysis data called APHRODITE (Asian Precipitation Highly-Resolved Observational Data Integration Towards Evaluation, v1101) and 17 CMIP5 models are examined for 10 grid boxes in Korea. In this example, the MSP-BMA achieves a variance reduction over the GEV-embedded BMA. The bias inflation by MSP-BMA over the GEV-embedded BMA is also discussed. A by-product technical advantage of the MSP-BMA is that tedious 'regridding' is not required before and

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.

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.