Evaluation of the tail of the probability distribution of daily and sub-daily precipitation in CMIP6 models

Daily and sub-daily precipitation extremes in historical Coupled-Model-Intercomparison-Project-Phase-6 (CMIP6) simulations are evaluated against satellite-based observational estimates. Extremes are defined as the precipitation amount exceeded every x years, ranging from 0.01–10, encompassing the rarest events that are detectable in the observational record without noisy results. With increasing temporal resolution there is an increased discrepancy between models and observations: for daily extremes the multi-model median underestimates the highest percentiles by about a third, and for 3-hourly extremes by about 75% in the tropics. The novelty of the current study is that, to understand the model spread, we evaluate the 3-D structure of the atmosphere when extremes occur. In midlatitudes, where extremes are simulated predominantly explicitly, the intuitive relationship exists whereby higher-resolution models produce larger extremes (r=–0.49), via greater vertical velocity. In the tropics, the convective fraction (the fraction of precipitation simulated directly from the convective scheme) is more relevant. For models below 60% convective fraction, precipitation amount decreases with convective fraction (r=–0.63), but above 75% convective fraction, this relationship breaks down. In the lower-convective-fraction models, there is more moisture in the lower troposphere, closer to saturation. In the higher-convective-fraction models, there is deeper convection and higher cloud tops, which appears to be more physical. Thus, the low-convective models are mostly closer to the observations of extreme precipitation in the tropics, but likely for the wrong reasons. These inter-model differences in the environment in which extremes are simulated hold clues into how parameterizations could be modified in general circulation models to produce more credible 21st-Century projections.

Bayesian cure fraction models with measurement error in the scale mixture of normal distribution

Cure fraction models have been widely used to model time-to-event data when part of the individuals survives long-term after disease and are considered cured. Most cure fraction models neglect the measurement error that some covariates may experience which leads to poor estimates for the cure fraction. We introduce a Bayesian promotion time cure model that accounts for both mismeasured covariates and atypical measurement errors. This is attained by assuming a scale mixture of the normal distribution to describe the uncertainty about the measurement error. Extending previous works, we also assume that the measurement error variance is unknown and should be estimated. Three classes of prior distributions are assumed to model the uncertainty about the measurement error variance. Simulation studies are performed evaluating the proposed model in different scenarios and comparing it to the standard promotion time cure fraction model. Results show that the proposed models are competitive ones. The proposed model is fitted to analyze a dataset from a melanoma clinical trial assuming that the Breslow depth is mismeasured.