A data fusion model for meteorological data using the INLA-SPDE method

We present a data fusion model designed to address the problem of sparse observational data by incorporating numerical forecast models as an additional data source to improve predictions of key variables. This model is applied to two main meteorological data sources in the Philippines. The data fusion approach assumes that different data sources are imperfect representations of a common underlying process. Observations from weather stations follow a classical error model, while numerical weather forecasts involve both a constant multiplicative bias and an additive bias, which is spatially structured and time-varying. To perform inference, we use a Bayesian model averaging technique combined with integrated nested Laplace approximation. The model's performance is evaluated through a simulation study, where it consistently results in better predictions and more accurate parameter estimates than models using only weather stations data or regression calibration, particularly in cases of sparse observational data. In the meteorological data application, the proposed data fusion model also outperforms these benchmark approaches, as demonstrated by leave-group-out cross-validation.