NOTES AND CORRESPONDENCE Comments on ‘‘A Surrogate Ensemble Study of Climate Reconstruction Methods: Stochasticity and Robustness’’

In a recent paper, Christiansen et al. compared climate reconstruction methods using surrogate ensembles from a coupled general circulation model and pseudoproxies. Their results using the regularized expectation maximization method with truncated total least squares (RegEM-TTLS) appear inconsistent with previous studies. Results presented here show that the poor performance of RegEM-TTLS in Christiansen et al. is due to 1) their use of the nonhybrid method compared to the hybrid method; 2) a stagnation tolerance that is too large and does not permit the solution to stabilize, which is compounded in another paper by Christiansen et al. by the introduction of an inappropriate measure of stagnation; and 3) their use of a truncation parameter that is too large. Thus, the poor performance of RegEM-TTLS in both Christiansen et al. papers is due to poor implementation of the method rather than to shortcomings inherent to the method. Christiansen et al. (2009) provide a comparison of climate reconstruction methods as applied to surrogate ensembles from the ECHAM4/Ocean Isopycnal Model (OPYC3) coupled general circulation model. Such comparisons are useful and necessary endeavors to understand the relative strengths and weaknesses of climate reconstruction techniques. We wish to address the authors’ use of one technique used in their comparisons, the regularized expectation maximization (RegEM) method using truncated total least squares (TTLS). The RegEM-TTLS reconstructions shown in Christiansen et al. (2009) seem inconsistent with results presented in Mann et al. (2007, hereafter MRWA07) and with those of Lee et al. (2008) and Riedwyl et al. (2009), who both used a different implementation of RegEM than did MRWA07 but showed that RegEM generally performed as well as or better than the other methods they tested. This apparent discrepancy led us to investigate possible causes of these disparate results. We see three main differences between RegEM-TTLS as applied by Christiansen et al. (2009) compared to MRWA07. First, Christiansen et al. (2009) do not employ the hybrid frequency-band approach favored by MRWA07, where both proxies and instrumental data were separated into two frequency bands and each frequency band was reconstructed separately. Second, Christiansen et al. (2009) use a stagnation tolerance (stopping criterion) Corresponding author address: Scott Rutherford, Department of Environmental Science, Roger Williams University, Bristol, RI 02809. E-mail: [email protected] 2832 J O U R N A L O F C L I M A T E VOLUME 23 DOI: 10.1175/2009JCLI3146.1 2010 American Meteorological Society that is large compared to that used in MRWA07, although they do test the impact of varying the stagnation tolerance (in addition, in Christiansen et al. 2010, a problematic measure of stagnation was introduced). Finally, their truncation parameter (i.e., the number of principal components retained in RegEM) is considerably larger than that used in MRWA07. To examine the impact of these differences, we used the annual mean surface temperature field between 708N and 708S from a transient simulation of the Climate System Model (CSM; Ammann et al. 2007) and created white-noise pseudoproxies representing the 104 unique locations of the Mann et al. (1998) network between 708N and 708S. In MRWA07, this is referred to as pseudoproxy network ‘‘A.’’ We use a calibration period of 1900–80, a verification period of 850–1899, and a pseudoproxy signal-to-noise ratio of 0.4 (86% noise). In all cases presented in Fig. 1 and Table 1, we used the same pseudoproxy realization. Although we focus here on the Northern Hemisphere mean as in Christiansen et al. (2009), we include multivariate field scores to demonstrate that the RegEM settings that produce the best hemispheric mean scores also produce good multivariate scores. We will begin with the results achieved using the MRWA07 implementation of RegEM-TTLS and move toward what appears to be the implementation of Christiansen et al. (2009). First, we will address variations in the stagnation tolerance for the low-frequency component of the hybrid frequency-band implementation. Next, we will move from the hybrid to the nonhybrid implementation. Finally, we will examine the effect of stagnation tolerance and truncation parameter on the nonhybrid approach. In these experiments we will focus on reconstructing the Northern Hemisphere mean series, as that is the focus of Christiansen et al. (2009). We use RegEM-TTLS to first reconstruct the field and then spatially average the field to reconstruct the hemispheric mean. If one is only interested in the hemispheric mean, note that it is possible to directly reconstruct the mean FIG. 1. Results of pseudoproxy experiments. (a) Results using the hybrid frequency-band approach. The stagnation tolerance used by Christiansen et al. results in an interim result that is not fully converged (red line). (b) Results of experiments using the nonhybrid RegEM-TTLS approach. Note that all nonhybrid results perform poorly relative to the hybrid, MRWA07 approach (blue line). The magenta line most closely approximates the implementation of Christiansen et al. whereas the red line reflects the MRWA07 nonhybrid approach. 15 MAY 2010 N O T E S A N D C O R R E S P O N D E N C E 2833