An Assessment of Convergence of Climate Reanalyses from Two Coupled Data Assimilation Systems with Identical High-Efficiency Filtering
Authors: Jiang Yingjing , Lu Lv , Zhang Shaoqing , Zhu Chenyu , Gao Yang , Lin Zikuan , Wan Lingfeng , Li Mingkui , Yu Xiaolin , Wu Lixin , Lin Xiaopei 
Published: May 2024

Abstract
Coupled data assimilation (CDA) uses coupled model dynamics and physics to extract observational information from measured data in multiple Earth system domains to reconstruct historical states of the Earth system, forming a reanalysis of climate variability. Due to imperfect numerical schemes in modeling dynamics and physics, models are usually biased from the real world. Such model bias is a critical obstacle in the reconstruction of historical variability by combining model and observations and, to some degree, causes divergence of CDA results because of individual model behavior in each system. Here, based on a multitime-scale high-efficiency filtering algorithm which includes a deep-ocean bias relaxing scheme, we first develop a high-efficiency online CDA system with the Community Earth System Model (CESM-MSHea-CDA). Then, together with the other previously established CDA system within the Coupled Model, version 2.1 (CM2-MSHea-CDA), that is developed by the Geophysical Fluid Dynamics Laboratory, we conduct climate reanalysis for the past 4 decades (1978–2018). Evaluations show that due to improved representation for multiscale background statistics and effective deep-ocean model bias relaxing, both CDA systems produce convergent estimation of variability for major climate signals such as variability of basin-scale ocean heat content, El Niño–Southern Oscillation (ENSO), and Pacific decadal oscillation (PDO). Particularly, both CDA systems generate similar time mean of global and Atlantic meridional overturning circulations that converge to the geostrophic velocity estimate from climatological temperature and salinity data. The CDA-estimated mass transport at typical measurement sections is mostly consistent with the observations.

Significance Statement
A coupled climate model simulates the interactions of the atmosphere, ocean, sea ice, and land processes and derives change and variations of the climate system by combining these components. Due to imperfect numerical schemes, a model usually has systematic biases to the real world. Coupled data assimilation (CDA) combines coupled model dynamics and physics with atmospheric and oceanic observations to reconstruct the historical states of Earth’s climate system, forming the analysis of climate change and variability. However, because of the existence of model errors and individual data assimilation algorithm behaviors, currently, the ocean variability of reanalysis produced by different numerical systems is basically divergent. Here, we first apply an identical coupled data assimilation algorithm and effective model error relaxing scheme to two widely used IPCC coupled models to establish two CDA systems. Then, we use both CDA systems to assimilate historical atmospheric and oceanic observations to form two sets of climate reanalyses for the past 4 decades. We found, by some degree, that the results of these multimodel coupled climate reanalyses converged to what historical states ought to be in observational estimation. These convergent climate reanalyses are expected to significantly increase our understanding of CDA and climate assessment.