This study present a so called 2.5D inverse model for simulating the age–depth relationships along a flow line from Dome C to Little Dome C in Antarctica. This is an important topic in glaciology, e.g., finding a location of an old ice core, which matchs the scope of The Cryosphere. However, I find it is very difficult for me to understand this manuscript, and at some places I feel not much senses to me.

The main reason is that the authors do not even put some basic explanations of their model. I do not undertand why “a full description of the forward model will be available in a separate subsequent article” is possible if they do not make it clear in this paper? For example, Eqn 1 gives the vertical velocity profile, but what does the horizontal ice velocity (flux) look like? Both horizontal and vertical ice velocity are critical in determing the shapes of age-depth profiles. The authors also do not explain basically the inverse model, e.g., what is p_prior and why they need to use a term “mechanical ice thickess” since they have already the observed ice thickness data - this do not make much sense not using the observed data!

Actually, the age-depth modeling is not new. If the authors can dig a bit in past literatures, they can easily find some nice and important papers, like Greve et al. (2002) and Rybak and Huybrechts (2003). Based on ice flow models and the Eulerian or Lagrangian methods, we can determine the age-depth relationships in a more physical way. I do not see the authors even mention these previous work in the Introduction section. I am not sure what the “forward model” is about if they do not use a physical ice flow model. If I am not convinced the velocity field is correct, it is also hard for me to believe the inversed age-depth profiles are correct either. The inverse model is then just an optimization approach to find the numbers that match the radar chronology record, but without much physics inside.

The writings also make me confused often. For example,

L13, “the 2.5D model predicts a basal layer 200–250 m thick at the base of the ice sheet”, what is “basal layer 200-250 thick”?

L68, “There is no direct thermal representation in the forward model as we use an inferred mechanical ice thickness to determine a basal melt rate”, this sentence comes from no where, and has no references and no explanations.

L80: what is the form of “horizontal flux shape function”?

L97: no definitions for p and Hw

L110: What is delta q and delta x?

Table 1: what is the spatial locations for these 19 IRHs?

These kind of major and minor issues make me feel very difficult to read and understand this manuscript. Thus, I suggest the authors take another careful round of modifications and re-submit the manuscript after they add the necessary inputs.

References:

Ralf Greve, Yongqi Wang, and Bernd Mügge. Comparison of numerical schemes for the solution of the advective age equation in ice sheets. Annals of Glaciology, 35:487–494, 2002.

Oleg Rybak and Philippe Huybrechts. A comparison of eulerian and lagrangian methods for dating in numerical ice-sheet models. Annals of Glaciology, 37:150–158, 2003.

Chung et al. use a 2.5D flowband model and dated internal layers to estimate the age of basal ice along a flowline from Dome C to the Beyond EPICA drill site of Little Dome C. The model finds the best fit spatial pattern of accumulation rate, velocity shape function, and mechanical ice thickness, which can then be translated to either stagnant ice thickness or basal melt rate. The primary result is that the age of basal ice (for Little Dome C this is just above the layer of stagnant ice) is younger than previously suggested, which has implications for the Beyond EPICA ice core.

The modeling is novel and well described. The manuscript is clearly written with a clear and well supported conclusion. There is acknowledgement of the unknown basal process which adds to the excitement of what Beyond EPICA will find when the drilling is completed this season (assuming good fortune). The discussion of ice cores having younger ages than the model predicts is interesting and useful component. The paper is ready for publication, but I hope the authors will consider the including the points below.

The one area that I suggest more of is a discussion of the age results with Lilien et al., 2021. While Lilien et al., 2021 is mentioned in multiple places, it is not clear how this age scale differs. Lilien et al. suggested that a 1.5Ma age, rather than a 1.1Ma age, is likely to be reached, but I think this is not so much a difference in the depth-age relationship as in the definition of "interpretable ice", with this paper using a value of 20 ka/m while Lilien et al. find 14 ka/m. It is a bit difficult for people outside of Beyond EPICA to keep the differences straight, so providing discussions and summaries of the differences more clearly is quite helpful.

A few other minor comments:

- The discussion of ice fabric is appreciated and not including ice fabric in your model is understandable. However, it seems like the effects of fabric could be parameterized through constraints on the shape of the velocity, i.e. the p value. This is obviously future work, but I think considerable progress could be made without trying to model fabric evolution.

- The last sentence of the abstract is frustrating. Why end on such a sour note? Can you finish instead with a concluding note about the progress you have made?