The trapped radiation specifications, such as AE-8 and AP-8, are based upon a simple and reasonable framework that happens to be insufficient to the modern demands placed upon them. This manuscript outlines an improved framework for the next generation of radiation models. While existing radiation specifications tend to provide mean fluxes on a grid in magnetic coordinates, scientific and engineering users are starting to demand capabilities that are far beyond this simple framework, such as error bars on total mission dose and real-time data assimilation. One framework that can provide these added capabilities while still remaining fairly simple is the joint probability distribution, described here. The joint distribution can describe the behavior of individual fluxes on a grid in magnetic coordinates while also describing how those fluxes vary together. This covariance is a crucial ingredient for data assimilation and for proper error bars and percentiles on composite quantities like dose or fluence to a shielded device. This manuscript describes the core math of the proposed framework, an approach to building the model from in situ observations and/or numerical simulations, how to use the model to calculate error bars and percentiles on composite quantities, how to use the model in data assimilation, and how to make a first estimate of the dependence of worst case fluences on aggregation time.