The paper by Ide, Courtier, Ghil, and Lorenc proposes a unified notation for data assimilation methods in atmospheric and oceanic sciences. The authors aim to bridge the gap between sequential and variational methods, which have often used different notations, hindering mutual understanding and practical applications. They introduce a consistent set of symbols to facilitate the mastery and development of advanced data assimilation methods. The paper covers basic concepts, definitions, and detailed formulations of sequential methods (extended Kalman filter and optimal interpolation) and variational methods (four-dimensional variational assimilation and incremental 4D-Var). The unified notation is designed to be flexible and adaptable to future methodological advancements. The authors also provide an appendix with recommendations for continuous space-and-time notation, reflecting the field's rapid theoretical expansion.The paper by Ide, Courtier, Ghil, and Lorenc proposes a unified notation for data assimilation methods in atmospheric and oceanic sciences. The authors aim to bridge the gap between sequential and variational methods, which have often used different notations, hindering mutual understanding and practical applications. They introduce a consistent set of symbols to facilitate the mastery and development of advanced data assimilation methods. The paper covers basic concepts, definitions, and detailed formulations of sequential methods (extended Kalman filter and optimal interpolation) and variational methods (four-dimensional variational assimilation and incremental 4D-Var). The unified notation is designed to be flexible and adaptable to future methodological advancements. The authors also provide an appendix with recommendations for continuous space-and-time notation, reflecting the field's rapid theoretical expansion.