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Ensemble Forecast Sensitivity to Observation (EFSO) is a technique that can efficiently identify the beneficial/detrimental impacts of every observation in ensemble‐based data assimilation (DA). While EFSO has been successfully employed on atmospheric DA, it has never been applied to ocean or coupled DA due to the lack of a suitable error norm for oceanic variables. This study introduces a new density‐based error norm incorporating sea temperature and salinity forecast errors, making EFSO applicable to ocean DA for the first time. We implemented the oceanic EFSO on the CFSv2‐LETKF and investigated the impact of ocean observations under a weakly coupled DA framework. By removing the detrimental ocean observations detected by EFSO, the CFSv2 forecasts were significantly improved, showing the validation of impact estimation and the great potential of EFSO to be extended as a data selection criterion. Plain Language Summary: This study introduces a new method to efficiently estimate the beneficial/detrimental impacts of each oceanic observation in the air‐sea coupled data assimilation (CDA) by incorporating the forecast errors for sea temperature and salinity with a novel density norm. For the first time, we implemented this approach onto the operational‐like CDA system and examined the impacts of ocean observations on the National Centers for Environmental Prediction CFSv2 forecasts. Our findings demonstrate that assimilating ocean profiles and satellite‐retrieved sea surface temperature products significantly improves the CFSv2 forecasts. Moreover, after excluding the detrimental ocean observations identified by our new method, we observed significant improvements in the CFSv2 forecasts. This result validates the accuracy of impact estimation and underscores its great potential as a data selection criterion in CDA. Key Points: A new oceanic Ensemble Forecast Sensitivity to Observation (EFSO) is proposed and implemented on the CFSv2 to investigate observation impactsThe 24‐hr CFSv2 forecasts of sea temperature, salinity, and 2‐m air temperature were improved by 1.5%, 0.8%, and 0.4%, respectively, after removing detrimental ocean observations detected by EFSOThe improvements in the CFSv2 forecast can last for at least 5 days for the ocean and 3 days for the low‐level atmosphere [ABSTRACT FROM AUTHOR]

Oscillatory modes of the climate system are among its most predictable features, especially at intraseasonal time scales. These oscillations can be predicted well with data-driven methods, often with better skill than dynamical models. However, since the oscillations only represent a portion of the total variance, a method for beneficially combining oscillation forecasts with dynamical forecasts of the full system was not previously known. We introduce Ensemble Oscillation Correction (EnOC), a general method to correct oscillatory modes in ensemble forecasts from dynamical models. We compute the ensemble mean—or the ensemble probability distribution—with only the best ensemble members, as determined by their discrepancy from a data-driven forecast of the oscillatory modes. We also present an alternate method that uses ensemble data assimilation to combine the oscillation forecasts with an ensemble of dynamical forecasts of the system (EnOC-DA). The oscillatory modes are extracted with a time series analysis method called multichannel singular spectrum analysis (M-SSA), and forecast using an analog method. We test these two methods using chaotic toy models with significant oscillatory components and show that they robustly reduce error compared to the uncorrected ensemble. We discuss the applications of this method to improve prediction of monsoons as well as other parts of the climate system. We also discuss possible extensions of the method to other data-driven forecasts, including machine learning. [ABSTRACT FROM AUTHOR]