Model Calibration via Deformation & Equivalent Kriging

Abstract: This is a two part talk.  

Part I: 
Dynamical computer models often exhibit space-time features that are partially misaligned or 
misshapen when compared to observational data.  Whether due to approximate numerical 
schemes, incomplete physics or estimated boundary conditions, the goal of calibrating these 
models to field data involves optimally aligning model output with observed features.  
Especially for dynamical models, systematic bias may be viewed as feature-based.  Borrowing 
ideas from the image warping literature, we develop a nonlinear deformation of the 
geophysical model that emphasizes calibration settings replicating important scientific 
features.  The method is illustrated on a complex magnetospheric-ionospheric model for 
geomagnetic storms.

Part II: 
Most modern spatial datasets are very large, often involving tens of thousands to millions 
of spatial locations.  Spatial analysis usually focuses on kriging, i.e., spatial smoothing, 
which operationally requires inversion of a dense and unstructured covariance matrix whose 
dimension can be upwards of millions.  We introduce an approach to kriging in the presence 
of large datasets called equivalent kriging, which relies on approximating the kriging 
weight function using an equivalent kernel.  Resulting kriging calculations are extremely 
fast and feasible in the presence of massive spatial datasets.  No likelihood assumptions 
are required apart from existence of first and second moments, and estimation can proceed by 
either cross validation or generalized cross validation.  We derive explicit kriging 
approximations for multiresolution classes of spatial processes, as well as under common 
stationary models such as the Matern.