General comments:

This manuscript describes the application of the sweep interpolation with fourth-order accuracy in the GEM. As we all know, the interpolation algorithm for the velocity and tracer densities is vital for the semi-Lagrangian method. The authors proposed an elaborate idea of combining two interpolation stencils to cancel the leading errors. The sweep algorithm is efficient as the third-order one but with higher accuracy as the fourth-order one, and it is easy to implement. The numerical experiment results illustrate the efficacy of the sweep interpolation algorithm. I recommend the publication of this manuscript subject to a minor revision.

Specific comments:

It would be better that some details can be further explained:

• In 2D, there are four possible stencil combinations as shown in Fig. 1 of Mortezazadeh and Wang (2017). Is the selection of forward and backward interpolation stencils related to the parcel characteristic line? Or if the two stencils change according to the backward trajectory?
• The description of the tests is too brief, such as sec. 3.1. Please add more information, such as what the spatial resolution is?
• Why the total mass of sweep scheme is decreasing, while cubic scheme is increasing in Fig. 5.

Technical corrections:

L77: The variable staggering in the vertical direction is the Charney-Phillips grid, so it should not be the Arackawa-C grid in the vertical direction.

L83: “sub grids” to “subgrids”

L116: “ ,on 1D” to “, along the 1D direction”?

This work extends the research conducted by Mortezazadeh and Wang in 2017. In this study, the sweep method is further validated through a series of idealized tests, including 2D vortex simulations and Hadley-like meridional circulation, as well as an Atmospheric methane-like tracer test and global model forecasts. This manuscript demonstrates that the sweep method can significantly reduce computational costs by approximately 15% without compromising accuracy. This improvement is achieved by implementing two 3rd-order backward and forward polynomial interpolation schemes over two consecutive time steps, as opposed to using a 4th-order interpolation method. The results presented in this manuscript are intriguing and robust, supporting its acceptance for publication with only minor revisions.

1. In Figure 3(b) and 4(b), the black dotted line represents the mass error after every two time steps. To enhance clarity, consider changing the label from "Error after two time steps" to "Error every two time steps."
2. It is essential to delve into the motivation behind and the conclusions drawn from the 2D vortex tests. Further discussions are warranted to provide a comprehensive understanding of their significance.
3. Figure 3a illustrates that the error distribution of the 2D vortex simulations is less noisy outside the vortex region when using the sweep method. Is this observed reduction in noise attributed to the method's capability to minimize dispersion and dissipation errors? Additional clarification on this matter would be beneficial.
4. Section 3.3, pertaining to the Atmospheric methane-like tracer experiment, lacks a clear description of the experiment's design. While information on resolution and time steps is provided, it would be beneficial to include more detailed descriptions.