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), where R=diag(HCH’)*SNR ^2

Covariance estimation from available model fields Canonical decomposition: C=ESE’ The solution in a truncated basis E r : T=E r a, a=SE r ’H’(HE r SE r ’H’+R + ) -1 P Q=E r qE r ’, q=S-SE r ’H’(HE r SE r ’H’+R + ) -1 HE r S where R + =R+HE d SE d ’H’ includes the effect of discarded modes E d

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 , reconstruction period A useful comparison: results based on the covariance estimated from the entire model run ( 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 , 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