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Retraction Note: Ocean dynamic equations with the real gravity

The Original Article was published on 05 February 2021

Retraction of: Scientific Reports, published online: 05 February 2021

The Editors have retracted this Article.

After publication of this study concerns were raised that the study is based on a flawed premise that a horizontal component of gravity is neglected in oceanographic calculations. In practice, this component can be taken to be zero, because the errors associated with this neglect are smaller than the error of assuming the resting ocean surface appears locally level, as shown by Chang and Wolfe1. This is further expanded upon in Stewart and McWilliams2, who also show that even in a model formulated in absolute spherical coordinates, the horizontal component of gravity has a negligible impact on ocean circulation.

The Editors no longer stand by the conclusions of this Article.

Peter Chu disagrees with this retraction.


  1. Chang, E. K. M. & Wolfe, C. L. P. The “horizontal” components of the real gravity are not relevant to ocean dynamics. Sci. Rep. 12, 6027. (2022).

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  2. Stewart, A. L. & McWilliams, J. C. Gravity is vertical in Geophysical Fluid Dynamics. Sci. Rep. 12, 6029. (2022).

    ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

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Correspondence to Peter C. Chu.

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Chu, P.C. Retraction Note: Ocean dynamic equations with the real gravity. Sci Rep 12, 6773 (2022).

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