Using modelderived pseudoproxies to test reconstruction methods

As discussed above there are primarily two distinct methods that have been used in proxy-based climate reconstruction: the CPS method, and the CFR method. Experiments using synthetic proxies or "pseudo-proxies" derived from climate model simulations have been used to test the performance of both the CPS (Mann et al. 2005b) and CFR methods (Mann and Rutherford 2002; Rutherford et al. 2003; Zorita et al. 2003; von Storch et al. 2004; Mann et al. 2005b; Wahl et al. 2006). Since our primary interest here is on regional and spatial patterns of change, we will focus on the CFR approach, which provides spatial patterns as well as hemispheric mean reconstructions.

Most of the studies described above have found that CFR-based reconstructions for past centuries are likely to be skilful, given the spatial distributions and estimated signal-to-noise characteristics of available proxy records. Von Storch et al. (2004) argue that proxy-based CFR reconstructions are likely to underestimate low-frequency variability, based on experiments using pseudoproxy networks derived from a millennial simulation of the GKSS ECHO-G coupled model. Wahl et al. (2006) have challenged the von Storch et al. (2004) calculations, arguing that they suffer from an artefact of an originally undisclosed procedure in which data were detrended by von Storch et al. (2004) prior to calibration. Wahl et al. (2006) note that such a procedure a priori removes the primary pattern of low-frequency variability from the surface temperature data.

Von Storch et al. (2004) considered only the more primitive EOF-based CFR method of Mann et al. (1998), and not the RegEM CFR approach used in recent work by Mann and collaborators (e.g. Mann and Rutherford 2002; Rutherford et al. 2003, 2005). Mann et al. (2005b) tested the "RegEM" CFR method using a simulation of the climate of the past millennium using the NCAR CSM 1.4 coupled ocean-atmosphere model driven by estimated long-term natural and anthropogenic radiative forcing histories. The simulated Northern Hemisphere mean surface temperature history indicates modestly greater variability than most other simulations (cf. Figure 7.3), providing a challenging test for CFR methods. "Pseudo-proxy" data were constructed from the model surface temperature field to have signal-to-noise attributes similar to actual proxy data networks used in reconstructing past climates (e.g. as in Mann et al. 1998). Application of the RegEM method to the calibration of the surface temperature field against the pseudo-proxy networks produced skilful reconstructions of the actual surface temperature history, underscoring that CFR methods are likely to yield reliable reconstructions of past variations given realistic assumptions regarding the statistical attributes of actual proxy data networks.

Zorita et al. (2007) have, in turn, argued that the skilful results demonstrated by Mann et al. (2005b) may represent an artefact of the use of a long combined 19th-20th century (1856-1980) rather than a short, 20th century only (1900-1980) calibration interval. They also suggest that the skilful results demonstrated by Mann et al. (2005b) might be peculiar to the specific (NCAR CSM 1.4) model simulation used and not possible in other simulations such as the GKSS ECHO-G simulation used in their analyses. Finally, Zorita et al. (2007) and von Storch et al. (2006) argue that the results presented by Mann et al. (2005b) may represent an artefact of an inappropriate model for the proxy noise, and that poorer results would be achieved if proxy noise was assumed to be spectrally "red" rather than, as assumed in previous studies such as Mann et al. 2005b and von Storch et al. (2004), "white".

We investigate these issues based on more recent experiments by Mann et al. (2007a,b) wherein the RegEM approach was applied to surface temperature reconstructions using pseudo-proxy networks diagnosed from two different model simulations: the NCAR CSM 1.4 coupled simulation used by Mann et al. 2005b, and the GKSS ECHO-G "ERIK" simulation used by von Storch et al. (2004) and Zorita et al. (2007). The pseudo-proxy networks, as in Mann et al. 2005b, von Storch et al. (2004), and Zorita et al. (2007), have the spatial distribution of the full Mann et al. (1998) proxy network. Reconstructions were performed based on the "short" (1900-1980) calibration interval, and a lower signal-to-noise ratio ("SNR") than used by Zorita et al. (2007; the proxy signal-to-noise amplitude ratio was 0.4 whereas Zorita et al. (2007) used SNR = 0.5). The proxy noise was specified to be spectrally "red" as in Zorita et al. (2007), using the average noise autocorrelation coefficient p = 0.32 estimated from the actual Mann et al. (1998) network (see Mann et al. (2007a) for details). The resulting RegEM reconstructions are observed to track closely the actual model temperature histories for both the NCAR and GKSS simulations, and the Northern Hemisphere mean reconstructions lie entirely within the self-consistently estimated uncertainties of the true respective model histories (Figure 7.5). The most pronounced feature in the simulations - the cold temperatures of the 15th-19th centuries associated with anomalous negative radiative forcing by a combination of solar irradi-ance reduction and active explosive volcanic aerosol forcing - is well captured in both simulations, even with the short calibration interval and "red" proxy noise employed.

As discussed earlier the anomalous initial warmth and much of the subsequent long-term cooling trend in the GKSS "ERIK" simulation is an artefact of the model initialization procedures used. Mann et al. 2005b speculated that the unphysical drift resulting from this initialization might degrade CFR performance in tests using the "ERIK" simulation, since the drift pattern might not be captured over the modern training intervals used for calibration. The above test using the ERIK simulation (i.e. Figure 7.5b), however, demonstrates that this drift does not in fact pose an obstacle for the RegEM CFR method. In conclusion, the RegEM CFR approach should provide reliable reconstructions of past surface temperature histories over the past millennium within estimated uncertainties, given available proxy data networks.

Figure 7.5 Reconstruction of Northern Hemisphere (NH) mean temperature based on RegEM CFR reconstructions using "pseudo-proxy" networks taken from

(b) GKSS ECHO-G "ERIK" simulations. In both cases, the pseudo-proxy network locations correspond to the 104 unique locations used by Mann et al. (1998), a proxy signal-to-noise ratio SNR = 0.4, red proxy noise with noise autocorrelation p = 0.32, and a 1900-1980 calibration interval is used. Self-consistent uncertainties in the reconstructions are estimated from the unresolved residual variance during an 1856-1899 "validation" interval, and are indicated by shading (95% uncertainty region). Actual model NH series is shown for comparison (black). All series are decadally smoothed. (From Mann et al. 2007a, ©American Meteorological Society.)

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