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# Correction: Wind stress curl as a driving force of annual waves in the upper ocean for interpreting energetics at all latitudes

The Original Article was published on 16 May 2024

## 1 Correction to: Progress in Earth and Planetary Science (2024) 11:29 https://doi.org/10.1186/s40645-024-00630-1

After publication of the article [1], it was brought to our attention that there are some equations and reference need to be corrected:

In Eq. 9a, it should be "u^2 + v^2" under the root symbol, the correct Eq. 9a is:

$$\overline{\sqrt{{u }^{2}+{v}^{2}}}\overline{\sqrt{{{\tau }_{wind}^{x}}^{2}+{{\tau }_{wind}^{y}}^{2}}}$$

In Eq. 15, the integration symbol should be 3 times taller, the correct Eq. 15 is:

$${\tau }_{wind}^{x}{U}^{ekm}+{\tau }_{wind}^{y}{V}^{ekm}={\rho }_{0}{\int }_{-\infty }^{0}A\left({{U}_{z}^{ekm}}^{2}+{{V}_{z}^{ekm}}^{2}\right)dz$$

In Eqs. 16a, 16b, 16c, 16d, the angle brackets which indicates a vector in the horizontal direction were not added, the correct Eq. 16a is:

$$\left\langle {H}_{1}{\rho }_{0}up , {H}_{1}{\rho }_{0}vp\right\rangle$$

Equation 16b:

$$\left\langle {H}_{1}{\rho }_{0}\left[up+{\left(\frac{{p}^{2}}{2f}\right)}_{y}\right] , {H}_{1}{\rho }_{0}\left[vp-{\left(\frac{{p}^{2}}{2f}\right)}_{x}\right]\right\rangle$$

Equation 16c:

$$\left\langle {H}_{1}{\rho }_{0}\left[up+{\left(\frac{p\varphi }{2}\right)}_{y}\right] , {H}_{1}{\rho }_{0}\left[vp-{\left(\frac{p\varphi }{2}\right)}_{x}\right]\right\rangle$$

Equation 16d:

$$\left\langle {H}_{1}{\rho }_{0}\left[up+{\left(\frac{p\varphi }{2}\right)}_{y}\right]-\varphi {\tau }_{wind}^{y} , {H}_{1}{\rho }_{0}\left[vp-{\left(\frac{p\varphi }{2}\right)}_{x}\right]+\varphi {\tau }_{wind}^{x}\right\rangle$$

In the first reference, the name ‘Swadhin KB, Toshio Y’ should be replaced by ‘Behera SK, Yamagata T’, the correct reference is:

Aiki H, Zhai X, Greatbatch RJ (2016) Energetics of the global ocean: the role of mesoscale eddies. In: Behera SK, Yamagata T (eds) Indo-Pacific climate variability and predictability. World scientific series on Asia–Pacific weather and climate, vol 7. World Scientific, Singapore, pp. 109–134. https://doi.org/10.1142/97898.14696.623_0004.

Besides, some minor grammar related errors are also corrected. The height of equation 6b and equation 6c are adjusted.

The original paper has been updated.

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Correspondence to Kaiwen Ye.

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Ye, K., Aiki, H. Correction: Wind stress curl as a driving force of annual waves in the upper ocean for interpreting energetics at all latitudes. Prog Earth Planet Sci 11, 43 (2024). https://doi.org/10.1186/s40645-024-00640-z

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• DOI: https://doi.org/10.1186/s40645-024-00640-z