The authors present a numerical solver of the ray equations for surface gravity waves accounting for slowly varying depth and currents. I believe the code should be of value to the community. Below I provide a list with minor suggestions.

Specific comments

Line 5 reads “… spatio-temporal variability much lower than characteristic wave properties”. I suggest being more specific.

8: What data retrieval and transformation are you referring to?

33. The joint effect of current- and depth-induced refraction at intermediate depth was also demonstrated by Romero et al. 2020 (Figure 14d).

57. \chi’ was already defined as \chi

Equation (9) assumes that the currents are stationary (see for example equation 2 of Mathiesen 1987). You should either state that explicitly or account for the current acceleration.

Equations 22-24:  I suggest changing fadv to f_{\bf{x}}. Similarly, I also suggest changing fconc to f_{\bf{k}} in equations 25-27.

119-122: I would remove the comments about the concertina effect referring to the kinematical conservation equation.

265: Kenyon (1971) showed this first.

341-346: Again, Romero et al. 2020 carried out experiments of ray tracing with combined depth and current gradients and without currents.

References

Kenyon, K. E., 1971: Wave refraction in ocean currents. Deep Sea Res., 18, 1023–1034.

Mathiesen, M., 1987: Wave refraction by a current whirl. J. Geophys. Res., 92, 3905–3912.

Romero, L., D. Hypolite, and J. C. McWilliams, 2020: Submesoscale current effects on surface waves. Ocean Model., 153, 101662

This is a short but useful contribution. The paper is well written. I have only one minor comment: the recent paper "Theoretical and applied considerations in depth-integrated currents for third-generation wave models" in AIP Advances (https://doi.org/10.1063/5.0077871) is related to the present note.