Technical Comments

Response to Comment on “Multiyear Prediction of Monthly Mean Atlantic Meridional Overturning Circulation at 26.5°N”

Science  02 Nov 2012:
Vol. 338, Issue 6107, pp. 604
DOI: 10.1126/science.1223200


Vecchi et al. question the skill of our initialized multiyear predictions of Atlantic Meridional Overturning Circulation (AMOC), arguing that our predictions do not outperform their suggested climatological reference forecast—using a single measure of skill. We show that our initialized AMOC predictions do outperform the climatological reference forecast, using both measures of hindcast performance that were presented in our original paper.

In Matei et al. (1), we demonstrated multiyear predictability of monthly mean strength of Atlantic Meridional Overturning Circulation (AMOC). We established the skill of our initialized AMOC predictions not only from high anomaly correlation (COR) but also from a more realistic amplitude of AMOC variations quantified by root-mean-square (RMS) variability. We diagnosed the skill improvement from the initialization by testing hindcast simulations against a persistence forecast based on observations (2, 3) and against a forecast with the uninitialized coupled model for the same forecast period (4).

Vecchi et al. (5) now propose a reference forecast based on a repeated seasonal cycle of the uninitialized coupled model (CLIMREF hereafter) (6). Vecchi et al. find that our initialized AMOC predictions outperform CLIMREF in only 5 of 13 cases, using COR as the sole skill measure (their figure 1) (7). However, a high COR skill just indicates a substantial phase coherence between the observed and hindcasted AMOC variations.

Here, we reply to Vecchi et al. by showing for CLIMREF both measures of hindcast performance presented in (1). In (1), we analyzed, in addition to COR, RMS variability. We used RMS variability, even though it is not strictly a skill score, because the original submission combined the correlation and RMS analysis by showing Taylor diagrams (8). In an attempt to simplify the presentation, we switched in the review process to a representation of COR and RMS analysis in separate plots [(1), figure 2 and fig. S2, respectively]. As already discussed in (1) concerning individual hindcasts and ensemble mean, there appears to be a tension between obtaining high correlation skill and high enough RMS variability.

Because correlation and RMS variability combine geometrically to RMS error (RMSE) with an overall bias removed (8), we now summarize the two measures of hindcast performance used in (1) to RMSE. Specifically, we compute the RMSE skill score (9) using CLIMREF as a reference forecast. With the RMSE skill score, our initialized AMOC predictions outperform CLIMREF in 8 of 13 cases (Fig. 1). With this demonstration that the model initialization leads to a substantial reduction in forecast error, we maintain that the conclusions about AMOC predictive skill as stated in (1) are justified.

Fig. 1

RMSE skill scores of AMOC with respect to the CLIMREF forecast. RMSE skill scores for the ensemble mean hindcasts started in January 2004, January 2005, January 2006, and January 2007 are shown by black, violet, blue, and yellow filled symbols, respectively, connected by solid lines.

We also test CLIMREF against the updated observational record (Table 1), verifying the AMOC predictions that we made in (1). Using COR, our initialized AMOC predictions outperform CLIMREF in 14 of 22 cases. Using the RMSE skill score, our initialized AMOC predictions outperform CLIMREF in 16 of 22 cases. Hence, with a larger sample size, our initialized AMOC predictions clearly outperform CLIMREF more often than not, using the RMSE skill score and even using COR as a sole measure of skill.

Table 1

Comparison of COR and RMSE skill scores of AMOC against CLIMREF for different lengths of the RAPID time series [4/2004 to 12/2008 as used in (1), and an extension until 12/2010].

View this table:

In conclusion, we have shown that with a combination of correlation and root-mean-square skill measure, as in (1), our ocean initialization results in AMOC prediction skill enhancement over the alternative reference forecast proposed by Vecchi et al. Also, as we showed in (1), we do understand where the skill enhancement arises from: It is the initialization of the upper-ocean zonal density difference. Therefore, we maintain that the conclusions about AMOC predictive skill as stated in (1) are robust.

References and Notes

  1. Because our model underwent some technical changes since the Coupled Model Intercomparison Project phase 3 (CMIP3), we constructed and used in (1) a different 20th-century realization from that in the CMIP3 archive (10).
  2. Vecchi et al. motivate their alternative reference forecast by arguing that the reference forecasts used in (1) ignored the issue of a repeating annual cycle. Although both reference forecasts used in (1) do include baseline knowledge of seasonality, we stand by our discussion in (1) that the limitation of observational record to half a decade does not allow a robust estimation of the seasonal cycle from the observations (11, 12); we therefore decided to keep the seasonal cycle in both modeled and observed AMOC time series and investigated the predictability of the full AMOC signal using monthly means. As already discussed in (1), the observed AMOC seasonal cycle with a maximum in October and a minimum in April has highly nontrivial causes (11, 12). The representation of the AMOC seasonal cycle in the model, and the improvement of monthly mean predictions of the AMOC strength through initialization, should therefore not be considered straightforward.
  3. Figure 1 in (5), and the associated note 14, prompted us to revisit the computation of the significance level. In (1), we have computed the significance level using a single-sided t test taking into account the serial autocorrelation of both time series. However, because the determination of the effective number of degrees of freedom (df) in short time series is associated with uncertainty (13), we have repeated our significance test by constructing an empirical probability density function of correlations. We have calculated the correlations of each year of monthly means of the observed AMOC with the 350 years of uninitialized runs of our model. The 10% significance level now lies at a correlation value of 0.61, compared with 0.55 in the paper. In a similar way, we have reestimated the 10% significance level for the correlation skill of upper-mid-ocean transport and upper-ocean zonal density difference to be 0.65 and 0.67, instead of 0.6 used in the original paper. Hence, we should have been slightly more conservative, but this modification does not change the conclusions drawn from both figures 2 and 3 of (1).
  4. The RMSE skill score (14) is defined as RMSEskill=1RMSEhindcastRMSECLIMREF.
  5. Acknowledgments: This work was supported by the Bundesministerium für Bildung und Forschung North Atlantic project (D.M.) and the Deutsche Forschungsgemeinschaft–funded Cluster of Excellence CliSAP (J.B. and W.A.M.). All model simulations were performed at the German Climate Computing Centre (DKRZ). Data from the RAPID-WATCH MOC monitoring project are funded by the Natural Environment Research Council and are freely available from
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