This paper presents some results of fitting to surface drifter and wind stress data an empirical impulse response function assuming linear dynamics for the forcing of the upper ocean. These results form the basis of a model for unsteady wind-driven near-surface ocean current estimates which are distributed as part of the Globcurrent CMEMS MOB-TAC product.

General comments:

I think the text of this article is not very clear in terms of what the authors define as wind-driven currents, and this should be clarified. Various terms are used such as inertial oscillations, oscillations, unsteady Ekman currents, (WOC?) etc and it is not clear what the authors mean in each instance (see my detailed comments as an attached PDF). The impulse response function framework effectively extracts from the data the linearly forced response to the wind stress, in a manner which peaks at the inertial frequency, but it is broadband in frequency. I think that “time-varying wind-driven” currents or perhaps “unsteady Ekman” currents may be appropriate? There is maybe a need to further clarify the difference between the wind-driven currents derived in this study and the ones from “Globcurrent/CMEMS”.

I think the paper is a little bit light on the description of the calculations conducted in sections 3.2 and 3.3. As an example, I am not quite sure how the data were divided in time and in latitude (daily bins? 1 degree latitude bands?). In order for others to try to replicate your study, I believe you could provide more information. In particular, have you conducted any sensitivity on the length of the wind stress time series input? Is T= 10 days an optimal value? Could it depend on latitude and season?

In general, the mathematical notations could be made more rigorous. As an example, some symbols are written sometimes with bold fonts and sometimes without (examples in sections 3.2 and elsewhere). More importantly, I suggest to revise the formulation of the impulse response function in order to make clearly appear the convolution operation and to correctly deal with the bivariate nature of the various quantities. Examples can be found in Chapter 6 of Bendat and Piersol (cited by the authors) as well as in Elipot and Gille (2009) and Lilly and Elipot (2021).

Some more detailed (but not necessarily minor) comments are attached in a separate PDF document.

Once my comments are properly addressed I believe this article is worthy of publication because of its scientific content but also because it documents a product already available.