Quantifying uncertainty for temperature maps derived from computer models

Computer models are often deterministic simulators used to predict several environmental phenomena. Such models do not associate any measure of uncertainty with their output since they are derived from deterministic specifications. However, many sources of uncertainty exist in constructing and employing numerical models. We are motivated by temperature maps arising from the Rapid Update Cycle (RUC) model, a regional short-term weather forecast model for the continental United States (US) which provides forecast maps without associated uncertainty. Despite a rapidly growing literature on uncertainty quantification, there is little regarding statistical methods for attaching uncertainty to model output without information about how deterministic predictions are created. Although numerical models produce deterministic surfaces, the output is not the ‘true’ value of the process and, given the true value and the model output, the associated error is not stochastic. However, under suitable stochastic modeling, this error can be interpreted as a random unknown. Then, we infer about this error using a Bayesian specification within a data fusion setting, fusing the computer model data with some external validation data collected independently over the same spatial domain. Illustratively, we apply our modeling approach to obtain an uncertainty map associated with RUC forecasts over the northeastern US.