Local eigenvalue analysis of CMIP3 climate model errors

Of the two dozen or so global atmosphere—ocean general circulation models (AOGCMs), many share parameterizations, components or numerical schemes, and several are developed by the same institutions. Thus it is natural to suspect that some of the AOGCMs have correlated error patterns. Here we present a local eigenvalue analysis for the AOGCM errors based on statistically quantified correlation matrices for these errors. Our statistical method enables us to assess the significance of the result based on the simulated data under the assumption that all AOGCMs are independent. The result reveals interesting local features of the dependence structure of AOGCM errors. At least for the variable and the timescale considered here, the Coupled Model Intercomparison Project phase 3 (CMIP3) model archive cannot be treated as a collection of independent models.We use multidimensional scaling to visualize the similarity of AOGCMs and all-subsets regression to provide subsets of AOGCMs that are the best approximation to the variation among the full set of models.ISSN:0280-6495ISSN:1600-087

Multiresolution Models for Nonstationary Spatial Covariance Functions

This is the pre-print version of the article found in Statistical Modelling (http://smj.sagepub.com/).Many geophysical and environmental problems depend on estimating a spatial process that has nonstationary structure. A nonstationary model is proposed based on the spatial field being a linear combination of a multiresolution (wavelet) basis functions and random coefficients. The key is to allow for a limited some number of correlations among coefficients and also to use a wavelet basis that is smooth. When approximately 6 % nonzero correlations are enforced, this representation gives a good approximation to a family of Matern covariance functions. This sparseness is important not only for model parsimony but also has implications for the efficient analysis of large spatial data sets. The covariance model is successfully applied to ozone model output and results in a nonstationary but smooth estimate.This work was supported by National Science Foundation grants DMS-93122686 and DMS-9815344.This work was supported by National Science Foundation grants DMS-93122686 and DMS-9815344

Spatio-Temporal Hierarchical Bayesian Modeling: Tropical Ocean Surface Winds

This is the author's version of the article found in the Journal of the American Statistical Association. The publisher's version can be found at http://pubs.amstat.org/loi/jasa.Spatio-temporal processes are ubiquitous in the environmental and physical sciences. This is certainly true of atmospheric and oceanic processes, which typically exhibit many different scales of spatial and temporal variability. The complexity of these processes and large number of observation/prediction locations preclude the use of traditional covariance-based space-time statistical methods. Alternatively, we focus on conditionally-specified (i.e., hierarchical) spatio-temporal models. These methods offer several advantages over traditional approaches. Primarily, physical and dynamical constraints are easily incorporated into the conditional formulation, so that the series of relatively simple, yet physically realistic, conditional models leads to a much more complicated space-time covariance structure than can be specified directly. Furthermore, by making use of the sparse structure inherent in the hierarchical approach, as well as multiresolution (wavelet) bases, the models are computable with very large datasets. This modeling approach was necessitated by a scientifically meaningful problem in the geosciences. Satellite-derived wind estimates have high spatial resolution but are limited in global coverage. In contrast, wind fields provided by the major weather centers provide complete coverage but have low spatial resolution. The goal is to combine these data in a manner that incorporates the space-time dynamics inherent in the surface wind field. This is an essential task to enable meteorological research as no complete high resolution surface wind datasets exist over the world oceans. High resolution datasets of this kind are crucial for improving our understanding of: global air-sea interactions affecting climate, tropical disturbances, and for driving large-scale ocean circulation models.Support for this research was provided for CKW, DN, and LMB by the NCAR Geophysical Statistics Project, sponsored by the National Science Foundation (NSF) under Grant DMS93-12686. Support for RFM and CKW is provided by the NCAR NSCAT Science Working Team cooperative agreement with NASA JPL. NCAR is supported in part by the NSF

Regridding Uncertainty for Statistical Downscaling of Solar Radiation

Initial steps in statistical downscaling involve being able to compare observed data from regional climate models (RCMs). This prediction requires (1) regridding RCM output from their native grids and at differing spatial resolutions to a common grid in order to be comparable to observed data and (2) bias correcting RCM data, via quantile mapping, for example, for future modeling and analysis. The uncertainty associated with (1) is not always considered for downstream operations in (2). This work examines this uncertainty, which is not often made available to the user of a regridded data product. This analysis is applied to RCM solar radiation data from the NA-CORDEX data archive and observed data from the National Solar Radiation Database housed at the National Renewable Energy Lab. A case study of the mentioned methods over California is presented.Comment: 16 pages, 5 figures, submitted to: Advances in Statistical Climatology, Meteorology and Oceanograph

Reduced Basis Kriging for Big Spatial Fields

In spatial statistics, a common method for prediction over a Gaussian random field (GRF) is maximum likelihood estimation combined with kriging. For massive data sets, kriging is computationally intensive, both in terms of CPU time and memory, and so fixed rank kriging has been proposed as a solution. The method however still involves operations on large matrices, so we develop an alteration to this method by utilizing the approximations made in fixed rank kriging combined with restricted maximum likelihood estimation and sparse matrix methodology. Experiments show that our methodology can provide additional gains in computational efficiency over fixed-rank kriging without loss of accuracy in prediction. The methodology is applied to climate data archived by the United States National Climate Data Center, with very good results