Skill of Climate Field Reconstruction Methods in the Context of Optimal

Interpolation Estimates

Alexey Kaplan, Jason Smerdon

Lamont-Doherty Earth Observatory of Columbia University

Michael Evans,Unoversity of Maryland

General Approach

To investigate a possible solution to typical pseudoproxy experiments as an OI problem of reconstructing temperature field T from a ptoxy vector P:

P = H*T+e, where H is a proxy sampling matrix, T ~ N(M,C),

and e ~ N(0,R), whereR=diag(HCH’)*SNR^2

Covariance estimation from available model fields

Canonical decomposition:C=ESE’

The solution in a truncated basis Er:

T=Era, a=SEr’H’(HErSEr’H’+R+)-1P

Q=ErqEr’, q=S-SEr’H’(HErSEr’H’+R+)-1HErS

where R+=R+HEdSEd’H’ includes the effect of discarded modes Ed

Surface temperature annual anomalies from the CCSM 1.4 model run (Amman et al.),

instrumental data mask from Mann et al. PNAS, pseudoproxy locations from MBH98, and generation as in Mann et al. 2005, 2007;

calibration (parameter estimation) period 1856-1980, reconstruction period 850-1855.

A useful comparison: results based on the covariance estimated from the entire model run

(850-1999 period)

Normalized eigenvalues (bottom) and their cumulative sums (top) for

calibration and full model period

Calibration Period EOFs

Full Model Period EOFs

Initial Methods Intercomparison: RMS

error for 850-1855,SNR=1

OI CCA

RegEM-Ridge RegEM-TTLS

Future Work

• Investigation of detail dependence on parameters

• Influence of errors of local proxy model estimation

• Estimation of covariance, its role in the solution, and possible improvement

• Exploring the consistency of theoretical and actual error