  This work aims to combine two primary meteorological data sources in the
Philippines: data from a sparse network of weather stations and outcomes of a
numerical weather prediction model. To this end, we propose a data fusion model
which is primarily motivated by the problem of sparsity in the observational
data and the use of a numerical prediction model as an additional data source
in order to obtain better predictions for the variables of interest. The
proposed data fusion model assumes that the different data sources are
error-prone realizations of a common latent process. The outcomes from the
weather stations follow the classical error model while the outcomes of the
numerical weather prediction model involves a constant multiplicative bias
parameter and an additive bias which is spatially-structured and time-varying.
We use a Bayesian model averaging approach with the integrated nested Laplace
approximation (INLA) for doing inference. The proposed data fusion model
outperforms the stations-only model and the regression calibration approach,
when assessed using leave-group-out cross-validation (LGOCV). We assess the
benefits of data fusion and evaluate the accuracy of predictions and parameter
estimation through a simulation study. The results show that the proposed data
fusion model generally gives better predictions compared to the stations-only
approach especially with sparse observational data.
