Reply to comment by V. Lesur et al. on “Can core‐surface flow models be used to improve the forecast of the Earth's main magnetic field”

[1] In their comment, Lesur and Wardinski [2009] question two different aspects of our original work [Maus et al., 2008]. [2] They first claim that ‘‘The accuracy of the used magnetic field is not such that the time variation of the flow can be reasonably estimated.’’ [3] The way we look into the time variations of core flows of Maus et al. [2008] is different than in previous studies. In particular, rather than computing a suite of instantaneous estimates of the core flow at successive epochs (such as had been done by, e.g., Pais and Hulot [2000], which in fact led to satisfying predictions of the length of day variations), we decided to simultaneously estimate the core flow and its acceleration from estimates of the core field (the main field, MF), its first time derivative (the secular variation, SV) and its second time derivative (the secular acceleration, SA), at a single central epoch (2003.0). Those estimates have been taken from the POMME-3 model of Maus et al. [2006], which provides a degree-2 Taylor expansion, best fitting magnetic observations between 2000.6 and 2005.7. Deciding how much of the corresponding SVand of the SA should be accounted for by the core flow and acceleration computed in this way is indeed an important issue. Lesur and Wardinski argue that our results are not ‘‘reasonable’’ because we try to fit the POMME-3 model, and especially its SA, too closely. Moreover, they more generally claim that ‘‘the POMME-3 SA model cannot be used to robustly estimate the flow temporal variation.’’ Is that so? [4] It is first important that we briefly recall how we estimated the level of misfit we requested for a set of core flow and flow acceleration to correctly account for the POMME-3 SV and SA. As shown by Eymin and Hulot [2005], what matters most in the case of the SV, is not so much the intrinsic quality of the SV model (which is very high for all recent SV models [see, e.g., Hulot et al., 2007]), but the unmodeled contribution of SV produced by the unknown (not modeled) small-scale core flows interacting with the MF (including its unknown small scales). This contribution can be viewed as a source of error and sets a much larger threshold of the SV misfit we should aim at. Estimating the effects of small-scale field and flow interactions guided us in deciding how much of the observed SV should be accounted for by our truncated flow model (as illustrated in Figures 7a and 7b ofMaus et al. [2008]). In the same way, interaction between the unknown (not modeled) small-scale core flows interacting with the SV, and between the unknown (not modeled) small-scale core flow acceleration interacting with the MF, will produce significant un-modeled SA signal. This must also be considered as a source of noise. The way we chose the level of SA misfit was again guided by these considerations (as is illustrated in Figures 7c and 7d of our original paper). What we did not verify, though, is that this misfit is also compatible with the intrinsic error in the SA coefficients provided by POMME-3, which might indeed be larger than the un-modeled SA signal (note again that as shown by Eymin and Hulot [2005], this is already known not to be an issue in the case of the SV). How large is this error in the SA coefficients of the POMME-3 model really? [5] In their comment, Lesur and Wardinski argue that this error can be assessed by comparing coefficients from POMME-3 and the CHAOS model of Olsen et al. [2006, Figure 1] for epoch 2003.0. This indeed leads to very high, and therefore worrying, estimates. To further make their case, they also compared POMME-3 to several other models (the GRIMM model of Lesur et al. [2008], the xCHAOS model of Olsen and Mandea [2008], and one (unspecified) version of the POMME-4 model (available at http://www.geomag.org/models/pomme4.html), none of which, we note, were available at the time of the study reported by Maus et al. [2008]). All of those models, they argue, provide ‘‘more consistent SA’’ than POMME-3. This leads them to conclude that in their opinion, ‘‘the POMME-3 SA model cannot be used to robustly estimate the flow temporal variations.’’ This, however, is an unfair statement because, as we shall now show, the way they carried out the comparison between POMME-3 and CHAOS is inappropriate. [6] The reason is that POMME-3 and CHAOS provide different representations of the SA. As already recalled, POMME-3 provides a degree-2 Taylor expansion of the MF, best fitting magnetic observations between 2000.6 and 2005.7. It has been optimized to provide the best estimate of the average SA over that period of time. In contrast, CHAOS provides a cubic B-spline temporal description of JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, B04105, doi:10.1029/2008JB006242, 2009 Click Here for Full Article