Reinhard Furrer's Projects

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Statistical evaluation of climate model output

Spatial Hierarchical Bayes Model for AOGCM Climate Projections
In collaboration with R. Knutti, EPFL, G. A. Meehl, NCAR, D. Nychka, NCAR, and S. R. Sain, NCAR.

Numerical experiments based on atmospheric-ocean general circulation models (AOGCMs) are one of the primary tools in deriving projections for future climate change. However, each model has its strengths and weaknesses within local and global scales. This motivates climate projections synthesized from results of several AOGCMs' output, combining present day observations, present day and future climate projections in a single hierarchical Bayes model for which the posterior climate change distributions are obtained with computer-intensive MCMC simulations.

We propose to extend the above idea and develop a Bayesian statistical model serving two purposes: quantifying uncertainty and attributing it to different factors. We use spatial statistical models that borrow strength across adjacent spatial regions of the globe in order to provide an statistically accurate assessment of (climate) model bias and inter-model variability. An additional feature of the methodology is the ability to synthesize climate change projections across the different models and then to down-scale to almost arbitrary regions providing a coherent uncertainty estimate.

This project is linked to my NSF DMS grant.

Statistics for large datasets

Fitting Large-Scale Spatial Models with Applications to Microarray Data Analysis
In collaboration with S. R. Sain, University of Colorado, Denver.

A single microarray includes over 400,000 individual observations, too much data for classical analysis techniques. We apply covariance tapering to a very general type of mixed model that has a random spatial component. Then, taking advantage of the sparse nature of such tapered covariance matrices, backfitting is used to estimate the fixed and random model parameters. Results are demonstrated on an experiment using microarrays to build a profile of differentially expressed genes relating to cerebral vascular malformations, an important cause of hemorrhagic stroke and seizures.

The taper technique is of general nature and can be applied to many other problems in the environmental and biological sciences. This requires more flexibility in the tapering technique. A potential approach is to taper directly the Cholesky factor instead of the covariance matrix itself.

Combining observations and models

Quantitative Assessment of the Difference between Aerosol Measurements and Off-line Transport Models
In collaboration with G. Feingold, NOAA, J. A. Ogren, NOAA.

Aerosols, particle matter or simply water vapor can be measured with many different techniques, based on, for example, LIDAR, satellites, surface and airborne in-situ devices. Although these various instruments have different sampling times, volumes/footprints and measurement errors it is commonly accepted that they agree to a certain extent. Despite the large diversity of measurement types, sampling is often very sparse in space and/or time and it is almost impossible to quantify large scale behavior. The latter is often studied with off-line transport models or even fully coupled atmosphere-ocean models.

This project aims to relate the modeled and observed aerosol values. We need to formalize a statistical model taking into account the different scales and uncertainties.