Multi-timescale data assimilation for atmosphere–ocean state estimates

Abstract

Abstract. Paleoclimate proxy data span seasonal to millennial timescales, and Earth's climate system has both highand 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.

A pseudoproxy assessment of data assimilation for reconstructing the atmosphere–ocean dynamics of hydroclimate extremes

“…For more mathematical details of the reconstruction methodology and the precise calculation procedure, see the Appendix of Steiger et al (2014). As in previous studies (Steiger et al, 2014Hakim et al, 2016;Steiger and Hakim, 2016;Dee et al, 2016) we use an "offline" DA approach in which the prior distribution is drawn from existing climate model simulations. For this approach, the ensemble members are seasonally or annually averaged climate states instead of an ensemble of independently running model simulations, as in "online" DA.…”

“…In principle, the ensemble members can be drawn from a sin-gle long simulation, multiple simulations, or even from simulations of a collection of climate models; the only important requirement is that the prior be climatologically representative of what one is trying to reconstruct (e.g., to reconstruct a year with a large volcanic eruption, the prior should contain ensemble members that come from simulation years with large volcanic eruptions). Because of how the prior is constructed here, it does not contain year-specific forcings or boundary conditions, information which appears to be superfluous according to many previous reconstructions experiments (Steiger et al, 2014Hakim et al, 2016;Steiger and Hakim, 2016;Dee et al, 2016;Okazaki and Yoshimura, 2017). The reconstruction process is also performed for each year independently such that no information is propagated forward in time.…”

“…As in previous work Steiger and Hakim, 2016;Dee et al, 2016;, we quantify uncertainty in our reconstructions through a combination of Monte Carlo sampling of the proxy network and accounting for the spread in the posterior distribution, x a . Each 1000-year reconstruction is repeated 25 times in a Monte Carlo fashion by sampling 75 % of the pseudoproxy network for each reconstruction iteration (we only perform 25 iterations because the small pseudoproxy errors lead to very similar reconstructions).…”

“…2 are skillful (positive CRPSS) despite the fact that the pseudo-trees are not responsive to the full annual cycle of climate. This is possible because the DA algorithm can exploit climate field covariance information across timescales; see Steiger and Hakim (2016) and note that, for example, ENSO and the approximately 500-day thermal timescale of the global ocean mixed layer (Lintner and Neelin, 2008) are physical features of the climate system that can retain information across seasonal and annual timescales. The skill of the temperature reconstructions in Fig.…”

“…8 together, the pseudoproxy framework indicates that it is possible to skillfully reconstruct the monthly Nino 3.4 index and to potentially do so without coral proxies. The monthly skill associated with the Nino 3.4 reconstruction is likely because monthly values sufficiently covary with the annual proxy observations such that the recon- struction can provide meaningful monthly states for this variable (Tardif et al, 2014;Steiger and Hakim, 2016). The results of the reconstructions using pseudo-trees alone is also particularly important given that coral records are generally short and not extant over more than a few centuries.…”