CORRESPONDENCE Comments on ‘‘Erroneous Model Field Representations in Multiple Pseudoproxy Studies: Corrections and Implications’’

Smerdon et al. report two errors in the climatemodel grid data used in previous pseudoproxy-based climate reconstruction experiments that do not impact the main conclusions of those works. The errors did not occur in subsequent works and therefore have no impact on the results presented therein. Results presented here for the Climate System Model (CSM) using multiple pseudoproxy noise realizations show that the quantitative differences between the incorrect and corrected results are within the expected variability of the noise realizations. It should also be made clear that the climate reconstruction method used in Smerdon et al. to illustrate the nature of the errors, the Regularized ExpectationMaximization method with Ridge Regression (RegEM-Ridge), is known to produce climate reconstructions with considerable variance loss and has been superseded by RegEM-TTLS (TTLS indicates truncated total least squares). Smerdon et al. (2010) describe two technical errors in the model grid data used inMann et al. (2005, 2007a). They are correct in the discovery of these errors.Wewish to confirm that the errors did not occur in subsequent publications and that the main conclusions of Mann et al. (2007a), which supersedes Mann et al. (2005), are not impacted. First, Mann et al. (2005) used the Regularized Expectation Maximization method with Ridge Regression (RegEM-Ridge) as a regularization method. RegEMRidge has been shown to suffer from a loss of variance when reconstructing the hemispheric mean (F. Zwiers and T. Lee 2006, personal communication; Mann et al. 2007a,b; Smerdon and Kaplan 2007; see also Lee et al. 2008), which is not the case with RegEM-TTLS (TTLS stands for truncated total least squares, used for regularization). This ledMann et al. (2007a) and others (e.g., Riedwyl et al. 2009) to abandon RegEM-Ridge in favor of the TTLS implementation of RegEM. This being the case, we will confine our comments toMann et al. (2007a). However, it is important that the reader recognize that Smerdon et al. (2010) used RegEM-Ridge and that the results shown in their Fig. 5a show the expected variance loss of a RegEM-Ridge reconstruction, whereas RegEMTTLS reconstructs the target series with little to no variance loss (Fig. 1; Table 1). Corresponding author address: Scott Rutherford, Department of Environmental Science, Roger Williams University, Bristol, RI 02809. E-mail: [email protected] 3482 JOURNAL OF CL IMATE VOLUME 26 DOI: 10.1175/JCLI-D-12-00065.1 2013 American Meteorological Society Smerdon et al. (2010) address two issues with GCM field data used in Mann et al. (2007a). The first relates to the GKSS model field. In a previous comment/reply sequence (Smerdon et al. 2008; Rutherford et al. 2008), the method used to interpolate the GKSS model field to a resolution commensurate with the instrumental record was changed from that of Mann et al. (2007a) to address an issue with the hemispheric mean. Unbeknownst to us at the time, the changes made to implement the revised interpolation scheme must also have corrected the issue of incorrect longitude orientation of the model field and subsequent pseudoproxy locations raised in Smerdon et al. (2010), as that issue does not exist in the data used in Rutherford et al. (2008). Thus, issues with the GKSS field identified by Smerdon et al. existed inMann et al. (2007a) but not in subsequent works, including Rutherford et al. 2008. The second issue relates to the incorrect longitudes for the interpolated Climate SystemModel (CSM) field. The authors have correctly identified an error that occurred in the process of converting the CSM field into a format consistent with the available instrumental data so that an instrumental-data mask could be applied. As Smerdon et al. point out, this error does not impact the qualitative conclusions drawn from the results and described in Mann et al. 2007a (cf. Fig. 1). The global field was still reasonably sampled with the correct latitudinal distribution of pseudoproxy locations. Comparing the CSM results using the incorrectMann et al. (1998) proxy locations and the corrected locations with the full field (Table 1) indicates that the method produces similar results using different proxy networks as long as the field is adequately sampled. As an additional example, replicate analyses using the full model field to 708N, corrected longitude values, and 30 different pseudoproxy realizations with 104 pseudoproxies coupled with a 1900–80 calibration period and a signal-to-noise ratio of 0.4 produce a NH mean reduction of error (RE) (Cook et al. 1994) score of 0.936 0.06 (mean 6 two standard deviations), a Northern Hemisphere (NH) mean coefficient of efficiency (CE) (Cook et al. 1994) score of 0.456 0.25, a meanmultivariate RE score of 0.33 6 0.08, and a CE score of 20.07 6 0.14. These scores are consistent with the scores reported in FIG. 1. Corrected Northern Hemisphere mean reconstructions for both the (a) GKSS and (b) CSM (Rutherford et al. 2010) model fields, respectively (20-yr smoothed). Note that RegEM-TTLS faithfully reconstructs the target series with little to no variance loss, especially at the important multidecadal and longer time scales. To facilitate comparison, series for both models are calculated over all grid boxes between 08 and 708N. The results shown are for 104 white-noise pseudoproxies with a signal-to-noise ratio of 0.4 and a 1900–80 calibration period. 15 MAY 2013 CORRES PONDENCE 3483