On-line and off-line data assimilation in palaeoclimatology: a case study

Abstract

Abstract. Different ensemble-based data assimilation (DA) approaches for palaeoclimate reconstructions have been recently undertaken, but no systematic comparison among them has been attempted. We compare an off-line and an online ensemble-based method, with the testing period being the 17th century, which led into the Maunder Minimum. We use a low-resolution version of Max Planck Institute for Meteorology Earth System Model (MPI-ESM) to assimilate the Past Global Changes (PAGES) 2k continental temperature reconstructions. In the off-line approach, the ensemble for the entire simulation period is generated first and then the ensemble is used in combination with the empirical information to produce the analysis. In contrast, in the on-line approach, the ensembles are generated sequentially for sub-periods based on the analysis of previous sub-periods. Both schemes perform better than the simulations without DA. The on-line method would be expected to perform better if the assimilation led to states of the slow components of the climate system that are close to reality and the system had sufficient memory to propagate this information forward in time. In our comparison, which is based on analysing correlations and differences between the analysis and the proxy-based reconstructions, we find similar skill for both methods on the continental and hemispheric scales. This indicates either a lack of control of the slow components in our setup or a lack of skill in the information propagation on decadal timescales. Additional experiments are however needed to check whether the conclusions reached in this particular setup are valid in other cases. Although the performance of the two schemes is similar and the on-line method is more difficult to implement, the temporal consistency of the analysis in the on-line method makes it in general preferable.

Assimilation of pseudo-tree-ring-width observations into an atmospheric general circulation model

“…546 W. Acevedo et al: Assimilation of pseudo-tree-ring-width observations the previous analysis state. This phenomenon, currently referred to as an "off-line regime", has been observed in several paleo-DA studies (Huntley and Hakim, 2010;Bhend et al, 2012;Pendergrass et al, 2012;Matsikaris et al, 2015). Furthermore, some recent studies have assumed the presence of the off-line condition and accordingly have removed the reinitialization step after assimilation altogether (Steiger et al, 2014;Dee et al, 2016;Hakim et al, 2016).…”

“…Furthermore, they observed that this loss of skill may be ameliorated by means of a fuzzy logic (FL)-based extension of the VSL model. Matsikaris et al (2015) compared the offline and online implementations of a "degenerate particle filter" applied to a low-resolution Earth system model. They found similar skill for both methods on the continental and hemispheric scales.…”

“…So far, several very diverse paleo-DA schemes have been investigated, including pattern nudging (von Storch et al, 2000), forcing singular vectors (Barkmeijer et al, 2003;van der Schrier and Barkmeijer, 2005), 4D-Var (Paul and Schäfer-Neth, 2005;Kurahashi-Nakamura et al, 2014), particle filters (Annan and Hargreaves, 2012;Dubinkina et al, 2011;Dubinkina and Goosse, 2013;Mathiot et al, 2013;Matsikaris et al, 2015) and ensemble Kalman filter techniques (EnKF; Huntley and Hakim, 2010;Bhend et al, 2012;Pendergrass et al, 2012;Steiger et al, 2014; see Hughes and Ammann, 2009;Widmann et al, 2010;Hakim et al, 2013 for further references).…”

Multi-timescale data assimilation for atmosphere–ocean state estimates

“…It is also advantageous to use an offline approach when the predictability time limit of the model is shorter than the timescale of the observations: for example, if observations are only available at annual resolution yet the model cannot skilfully forecast the climate state a year into the future, then no useful information is gained by cycling the model. Matsikaris et al (2015) recently compared online and offline approaches to paleoclimate DA with a fully coupled Earth system model and found no improvement with the online method, suggesting that the model was unable to provide useful information at analysis times. Nevertheless, one way the approach outlined here can generalize to the online approach is by cycling on the shortest timescale (e.g., annual or seasonal) and updating longer timescales at the end of the appropriate interval without cycling.…”

On the utility of proxy system models for estimating climate states over the common era

“…Briefly, it uses an off-line approach, wherein the prior ensemble, x b , consists of annually averaged climate states drawn from a climate model simulation; the ensemble is not integrated forward in time because of the massive computational constraints involved and because online DA for paleoclimate reconstructions appears to provide little improvement in skill over off-line DA, at least for atmospheric variables [Matsikaris et al, 2015]. The most important difference from Steiger et al [2014] is that we use PSMs for generating y and for computing Hðx b Þ (in most cases).…”