Inference for Complex Computer Models and Large Multivariate Spatial Data with Applications to Climate Science

Open Access
Bhat, Kabekode
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
August 26, 2010
Committee Members:
  • Murali Haran, Dissertation Advisor
  • Murali Haran, Committee Chair
  • Klaus Keller, Committee Chair
  • Donald Richards, Committee Member
  • Rana Arnold, Committee Member
  • James Samuel Shortle, Committee Member
  • computer experiments
  • Gaussian process
  • multivariate spatial data
  • spatiotemporal data
  • hierarchical Bayesian modeling
  • climate change
Computer model calibration involves combining information from simulations of a complex computer model with observations of the process being simulated by the model. Increasingly, computer model output is in the form of multiple spatial fields, particularly in climate science. We develop several new approaches for computer model calibration for multivariate spatial data. We first describe an inferential approach using Gaussian processes to emulate the computer model, thereby establishing a connection between the calibration parameters and the multiple spatial fields. We carry out statistical inference for the climate parameters using a Bayesian approach, accounting for spatial dependence, model discrepancy and other sources of uncertainty. We conduct a study of the merits of including a model discrepancy term in the statistical model. One flexible model we develop allows for non-linear relationships among the spatial fields by modeling the spatial fields using a conditional hierarchical approach. Further, we develop a new flexible computationally tractable approach for calibration combining three or more multiple spatial fields using a Linear Model of Coregionalization (LMC) allowing for a non-separable covariance, reducing data-specific modeling decisions, and for a more flexible construction of model discrepancy. We demonstrate an application of our approach to infer vertical diffusivity, a climate parameter that plays a key role in obtaining probabilistic projections of the Atlantic Meridional Overturning Circulation (MOC). As changes in the MOC may result in major disruptions to the climate, MOC projections are of great interest to climate scientists and policy makers. We utilize kernel mixing and matrix identities in our Gaussian process model in order to make computations tractable for large spatial data sets. In addition, we may have hindcasts and historical data from multiple computer climate models. We introduce and apply an new approach using Bayesian Model Averaging (BMA) to an ensemble of Global Circulation Models (GCM) model output from the IPCC Fourth Assessment Report (AR4) of surface temperature at selected spatiotemporal locations. Our approach results in improved projections and more complete uncertainty estimates while incorporating spatial and temporal dependence using Gaussian processes.