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Strongly coupled data assimilation (SCDA) views the Earth as one unified system. This allows observations to have an instantaneous impact across boundaries such as the air-sea interface when estimating the state of each individual component. Operational prediction centers are moving toward Earth system modeling for all forecast timescales, ranging from days to months. However, there have been few studies that examine fundamental aspects of SCDA and the transition from traditional approaches that apply data assimilation only to a single component, whether forecasts were derived from a coupled model or an uncoupled forced model. The SCDA approach is examined here in detail using numerical experiments with a simple coupled atmosphere-ocean quasi-geostrophic model. The impact of coupling is explored with respect to its impact on the Lyapunov spectrum and on data assimilation system stability. Different data assimilation methods are compared within the context of SCDA, including the 3-D and 4-D Variational methods, the ensemble Kalman filter, and the hybrid gain method. The impact of observing system coverage is also investigated. We find that SCDA is generally superior to weakly coupled or uncoupled approaches. Dynamically defined background error covariance estimates are essential for SCDA to achieve an accurate coupled state estimate as the observing system becomes sparser. As a clarification of seemingly contradictory findings from previous studies, it is shown that ocean observations can adequately constrain atmospheric state estimates provided that the analysis-observing frequency is sufficiently high and the ensemble size determining the background error covariance is sufficiently large.

Plain Language Summary To make accurate predictions of weather and climate, scientists develop complex computer models of the Earth that couple smaller models of the atmosphere, oceans, land, etc. Measurements from satellites, ground stations, and ocean buoys are limited, so these give an incomplete picture. Forecasters combine past predictions with new observations to make an informed guess about what the entire Earth looks like at any instant. This guess is used to initialize computer model forecasts. However, since the atmosphere is a chaotic system, small inaccuracies in this initial guess can lead to wildly diverging forecasts further out in time. This study investigates a new method for initializing the Earth models. In the past, physical inconsistencies between the atmosphere and ocean arose because each was initialized independently. We use atmospheric observations to improve our best guess of the ocean conditions, and vice versa, to improve this consistency. This may improve daily weather forecasts and seasonal guidance when adopted by operational weather prediction centers. Given the growing urgency to respond to near-term climate change risks, improved methods to initialize Earth system models provide the potential to generate accurately initialized climate predictions that can better anticipate the coming changes over the next decade.