Bayesian hierarchical models for climate field reconstruction

Edward Cook1, M.P. Tingley2, E. Wahl3 and E. Zorita4

1Lamont-Doherty Earth Observatory, New York, USA; This email address is being protected from spambots. You need JavaScript enabled to view it.

2National Center for Atmospheric Research, Boulder, USA; 3National Oceanic and Atmospheric Administration, National Climatic Data Center (NOAA-NCDC), Paleoclimatology Branch/World Data Center for Paleoclimatology, Boulder, USA; 4Helmholtz-Zentrum Geesthacht Centre for Materials and Coastal Research, Germany

Lamont Doherty Earth Observatory of Columbia University, USA, 8-11 February 2011

Bayesian Hierarchical Models (BHMs) have emerged as a powerful new method for inferring spatially complete climate fields from sparse and noisy proxy time series. BHMs have a potential theoretical advantage over "traditional" linear subspace-based (EOF) methods for inferring climate fields, because the Bayesian "posterior" distribution of the reconstructed climate, once estimated, can be directly sampled to yield complete uncertainty estimates of the reconstructions, along with a point estimate of the expected value. The Bayesian estimates of the climate field encapsulate the uncertainties involved in the estimation of all model parameters, which cannot readily be done using traditional linear subspace methods.

A primary goal of the workshop was to bring together reconstruction experts who currently employ reduced-space multivariate regression models for climate field reconstruction, and provide an in-depth exposure to the theory and application of BHMs for climate reconstruction. Dr. Andrew Gelman of Columbia University gave the opening keynote address, and Drs. Martin Tingley of NCAR, Bo Li of Purdue University, Johannes Werner of the University of Giessen, Matthew Schofield of the University of Kentucky, and Naresh Devineni of Columbia University led the workshop with regard to the use and implementation of BHMs for spatially explicit climate reconstruction.

BHM_Fig1_final.psd

Figure 1: Results of a pseudo-proxy reconstruction experiment comparing Bayesian estimates from BARCAST (upper row; Tingley and Huybers, 2010) with frequentist estimates from RegEM (lower row; Schneider, 2001), an important "state-of-the-art" approach to climate field reconstruction. The left column shows point estimates of the temperature field, while the right column gives the width of 90% uncertainty estimates and indicates the locations of the pseudo-proxies. Results are for the year 1890 of the “medium” experiment described in Tingley and Huybers (2010). The additional assumptions made by BARCAST allow for spatially complete inference, while RegEM does not provide inference at locations where there are no instrumental observations during the calibration interval (indicated by the green shading)

A second important purpose of the workshop was to explore how the more established multivariate regression based methods performed in comparison to BHMs, and to examine the extent to which the traditional methods could offer equally or near-equally valid ways to characterize reconstruction uncertainties in practice (see Fig. 1). This latter goal is important due to the additional complexity and computational expense of BHM approaches, and the more formal and complete treatment of uncertainties afforded by BHMs.

A strong focus was also put on separating model building, per se, from inference of model parameters. It was noted that climate scientists sometimes mix these two concepts, which can result in significant attention being paid to inference issues and comparisons of performance within a closely-related set of models (such as "flavors" of regression, cf., Bürger et al., 2006), rather than to the more general issue of developing conceptually appropriate yet computationally tractable models. In this regard, the key shift in thinking is not to Bayesian methods but to models—which would likely be hierarchical in nature. Inference can then be conducted using a range of tools, but as models become more involved, Bayesian inference strategies may be the (conceptually) simplest option.

Several presenters stressed that BHMs are not “one size fits all”. A given model, such as BARCAST (Tingley and Huybers, 2010), may be appropriate for inferring a particular target process from a particular data set, in the sense that all diagnostics indicate the modeling assumptions are suitable, the Markov Chain Monte Carlo (MCMC) estimation process converges, and the resulting ensemble of draws has reasonable properties. However, the same model may produce results that are physically unreasonable or otherwise problematic if applied to a different data set, or used to infer a different target process examples of which were presented and discussed in the workshop. Such results can often be interpreted as an indication of model misspecification, and it was stressed that model building is an iterative process. Akin to the residual analysis that follows standard linear regression, BHMs allow for posterior checks of the suitability of the model assumptions for the data under analysis.

Bayesian Hierarchical Modeling is still in its infancy in the context of paleoclimate field reconstructions. A key goal of this workshop was to develop a common language, and to focus on formalizing scientific understanding through collaboration between paleoclimate scientists and statisticians. This first (and hopefully not last) workshop took significant steps towards enabling this necessary collaboration to proceed.

References

Bürger, G., Fast, I. and Cubasch, U., 2006: Climate reconstruction by regression-32 variations on a theme, Tellus, 58A: 227–235

Schneider, T., 2001: Analysis of Incomplete Climate Data: Estimation of Mean Values and Covariance Matrices and Imputation of Missing Values, Journal of Climate, 14(5): 853–871.

Tingley, M.P. and Huybers, P., 2010: A Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time, Part I: Development and Applications to Paleoclimate Reconstruction Problems, Journal of Climate, 23: 2759–2781.

 

Category: Workshop Reports | PAGES Magazine articles


Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License.