Trend-Surface Models with Regional and Local Scales of Variation with an Application to Aerial Survey Data

This article specifies a trend-surface model with spatially correlated errors as a model for spatial variation with three scale components, site, local, and regional scales. An iterative scheme is proposed to estimate parameters, and three different ways of modeling the spatially correlated error component are considered, including maximum likelihood. The article evaluates the three approaches and brings together some recent developments in spatial statistics for parameter estimation and inference. There is discussion of an example to describe spatial variation in marine pollution levels monitored from an aerial survey.