Multi-timescale data assimilation for atmosphere–ocean state estimates

Abstract. Paleoclimate proxy data span seasonal to millennial timescales, and Earth's climate system has both high- and low-frequency components. Yet it is currently unclear how best to incorporate multiple timescales of proxy data into a single reconstruction framework and to also capture both high- and low-frequency components of reconstructed variables. Here we present a data assimilation approach that can explicitly incorporate proxy data at arbitrary timescales. The principal advantage of using such an approach is that it allows much more proxy data to inform a climate reconstruction, though there can be additional benefits. Through a series of offline data-assimilation-based pseudoproxy experiments, we find that atmosphere–ocean states are most skillfully reconstructed by incorporating proxies across multiple timescales compared to using proxies at short (annual) or long (∼ decadal) timescales alone. Additionally, reconstructions that incorporate long-timescale pseudoproxies improve the low-frequency components of the reconstructions relative to using only high-resolution pseudoproxies. We argue that this is because time averaging high-resolution observations improves their covariance relationship with the slowly varying components of the coupled-climate system, which the data assimilation algorithm can exploit. These results are consistent across the climate models considered, despite the model variables having very different spectral characteristics. Our results also suggest that it may be possible to reconstruct features of the oceanic meridional overturning circulation based on atmospheric surface temperature proxies, though here we find such reconstructions lack spectral power over a broad range of frequencies.