Reply to T. Schneider's comment on "Spatio-temporal filling of missing points in geophysical data sets"

First, we thank T. Schneider (TS hereafter) for his positive and constructive comments about Kondrashov and Ghil (2006) (KG hereafter). KG focused on exploiting temporal covariability in geophysical data sets, an idea that Schneider (2001; S01 hereafter) had suggested, but not applied to any data, synthetic or geophysical. Two unfortunate inaccuracies ‐ corrected in comments (iii) and (iv) of TS ‐ did crop up when KG described the expectation-maximization (EM) algorithm and its regularized version used by S01 for filling in missing data. We regret this slip, being thoroughly familiar with the general EM framework, which we used for probability density estimation when studying multiple weather regimes (Smyth et al. 1999; Kondrashov et al. 2004, 2006). We thus agree with TS that the regularized EM algorithm and KG’s method are both based on estimating mean and covariance components of the gappy data set under study [his comment (iii)], and that several gap-filling methods, including regularized EM and our own (multi-channel) singularspectrum analysis (M-)SSA, rely ‐ among many other assumptions ‐ also on the probability of a data point’s absence being independent of the missing value itself [his comment (iv)]. Singular-value decomposition (SVD; Golub and Van Loan, 1989) underlies both regression and principal components analysis, and thus represents a common basis for KG’s M-SSA as well as S01’s regularized EM method. In this reply, we concentrate on discussing several differences between our methods, which might look minor to TS, but lead to differences in computational performance and numerical results in practical applications. We have tried out, before submitting KG, the free gap-filling software kindly provided on TS’s personal website and plan to add KG’s gap-filling feature as soon as feasible to the SSA-MTM Toolkit, available for free at http://www.atmos.ucla.edu/tcd/ssa; see also Ghil et al. (2002). KG aim to fill the gaps with smooth information from an