Forecasting dose-time profiles of solar particle events using a dosimetry-based Bayesian forecasting methodology

A dosimetery-based Bayesian methodology for forecasting astronaut radiation doses in deep space due to radiologically significant solar particle event proton fluences is developed. Three non-linear sigmoidal growth curves (Gompertz, Weibull, logistic) are used with hierarchical, non-linear, regression models to forecast solar particle event dose-time profiles from doses obtained early in the development of the event. Since there are no detailed measurements of dose versus time for actual events, surrogate dose data are provided by calculational methods. Proton fluence data are used as input to the deterministic, coupled neutron-proton space radiation computer code, BRYNTRN, for transporting protons and their reaction products (protons, neutrons, 2H, 3H, ³He, and "He) through aluminum shielding material and water. Calculated doses and dose rates for ten historical solar particle events are used as the input data by grouping similar historical solar particle events, using asymptotic dose and maximum dose rate as the grouping criteria. These historical data are then used to lend strength to predictions of dose and dose rate-time profiles for new solar particle events. Bayesian inference techniques are used to make parameter estimates and predictive forecasts. Due to the difficulty in performing the numerical integrations necessary to calculate posterior parameter distributions and posterior predictive distributions, Markov Chain Monte Carlo (MCMC) methods are used to sample from the posterior distributions.

Hierarchical, non-linear regression models provide useful predictions of asymptotic dose and dose-time profiles for the November 8, 2000 and August 12, 1989 solar particle events. Predicted dose rate-time profiles are adequate for the November 8, 2000 solar particle event. Predicitions of dose rate-time profiles for the August 12, 1989 solar particle event suffer due to a more complex dose rate- time profile. Model assessment indicates adequate fits of the data. Model comparison results clearly indicate preference for the Weibull model for both events.

Forecasts provide a valuable tool to space operations planners when making recommendations concerning operations in which radiological exposure might jeopardize personal safety or mission completion. This work demonstrates that Bayesian inference methods can be used to make forecasts of dose and dose rate-time profiles early in the evolution of solar particle events. Bayesian inference methods provide a coherent methodology for quantifying uncertainty. Hierarchical models provide a natural framework for the prediction of new solar particle event dose and dose rate-time profiles.