Multi-time scale data assimilation for atmosphere–ocean state estimates
Abstract. Paleoclimate proxy data span seasonal to millennial time scales, and Earth's climate system has both high- and low-frequency components. Yet it is currently unclear how best to incorporate multiple time scales 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 algorithm that can explicitly incorporate proxy data at arbitrary time scales. Through a series of pseudoproxy experiments, we find that atmosphere–ocean states are most skilfully reconstructed by incorporating proxies across multiple time scales compared to using proxies at short (annual) or long (~ decadal) time scales alone. Additionally, reconstructions that incorporate long time-scale 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 insensitive to the choice of climate model, 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 solely on atmospheric surface temperature proxies.