Combining Spatial Information Sources While Accounting for Systematic Errors in Proxies

Abstract

SummaryEnvironmental research increasingly uses high dimensional remote sensing and numerical model output to help to fill space–time gaps between traditional observations. Such output is often a noisy proxy for the process of interest. Thus we need to separate and assess the signal and noise (often called discrepancy) in the proxy given complicated spatiotemporal dependences. Here I extend a popular two-likelihood hierarchical model by using a more flexible representation for the discrepancy. I employ the little-used Markov random-field approximation to a thin plate spline, which can capture small-scale discrepancy in a computationally efficient manner while better modelling smooth processes than standard conditional auto-regressive models. The increased flexibility reduces identifiability, but the lack of identifiability is inherent in the scientific context. I model particulate matter air pollution by using satellite aerosol and atmospheric model output proxies. The estimated discrepancies occur at a variety of spatial scales, with small-scale discrepancy particularly important. The examples indicate little predictive improvement over modelling the observations alone. Similarly, in simulations with an informative proxy, the presence of discrepancy and resulting identifiability issues prevent improvement in prediction. The results highlight but do not resolve the critical question of how best to use proxy information while minimizing the potential for proxy-induced error.