Weighted model calibration with spatial conditional information

TL;DR

This paper introduces a method for calibration that accounts for spatial dependence in environmental data, improving accuracy by weighting observations based on spatial conditional information.

Contribution

It develops a novel weighting approach for model calibration that incorporates spatial conditional information, addressing limitations of traditional methods.

Findings

Weighted inference improves accuracy with increased observation clustering.

Method enhances calibration precision in spatially dependent data.

Application to volcanic tephra data demonstrates real-world effectiveness.

Abstract

Cost functions such as mean square error are often used in environmental model calibration. These treat observations as independent and equally important even though model residuals exhibit spatial dependence and additional observations near existing points do not provide as much information on the system as those elsewhere. To address this issue, we develop a method to derive calibration weights based on spatial conditional information. Using simulation experiments with Gaussian processes and the Tephra2 volcanic tephra dispersion model, we show that the additional accuracy and precision from weighted inference increases with the degree of observation clustering and spatial dependence present. To demonstrate real-world relevance, the methods are applied to tephra load observations from the 2014 eruption of the Kelud volcano in Indonesia.