Dear Authors,



Please find my review in the attached pdf.

Best wishes,

Kevin Hank

This is a review of "Estimation of the state and parameters in ice sheet model using an ensemble Kalman filter and Observing System Simulation Experiments" by Choi et al., submitted for publication to The Cryosphere. This manuscript describes the use of an ensemble-based data assimilation system, the Ensemble Kalman Filter (EnKF), to assimilate data into a 2D large-scale ice sheet models, for the purpose of better estimating parameter values and state variables during the historical period. It follows on other studies that have explored similar methods for 1D ice sheet models, and makes the crucial step of applying such methods to a model widely used for projections. This study also adds a novel "Observing System Simulation Experiment" in which different potential observing system configurations (resolution, track spacing, observational accuracy) are tested to determine their ability to improve accuracy in estimated parameters and state.

Overall, I think this is a pretty straightforward study using well-known tools in a new way with ice sheet models, advancing the state of the art in our field. My main suggestions are to further explore certain DA and modeling choices that are unexamined in the current version of the manuscript. I have detailed these suggestions and more minor ones below.

Major suggestions:

1. The manuscript briefly describes what the EnKF is, and then indicates that the EAKF version is chosen for this study. There are multiple different flavors of the EnKF available in DART, so it is unclear why EAKF is chosen and whether the results would be any different if another filter was chosen. My suggestion is to describe in some more detail what is done in an EnKF and how the EAKF is different from the standard EnKF. Additionally, either some justification for why the EAKF was chosen and some level of justification for why that is the preferred approach when others are available.

2. One thing that is unclear from your study design is the relative importance of assimilation window (e.g. 5 vs 15 vs 30 years) as compared to number of assimilation cycles. You don't change the frequency of observations, which may be sensible given than annual observations are reasonable for current observing platforms. However, it is then hard to understand as a reader whether there is something fundamental about having 20-30 years of observations related to the time scales of ice sheet response to adjustments, or whether it is having 20-30 assimilation cycles to improve. If the observations were more frequent (e.g. an IceSAT2-like 90 days) would it takes less time for the EnKF to improve to the level that you show here?

3. A big difference between your perfect model design and a real scenario where DA might be applied is that only two constant-in-time parameter fields are unknown. In reality, (e.g.) ice viscosity and climate forcing are also likely to be poorly known (though at least climate forcing is directly observable), and climate forcing (and basal friction) may vary in time. Two possibilities that would be helpful to run some experiments to assess are:

(a) if you are mistaken about the values of other parameters, but still only estimate basal friction and topography, will the estimate of basal friction compensate for these other errors (particularly for ice viscosity which trades off quite directly with basal friction in a depth-integrated model) - there is some evidence of such compensation already happening in your estimates, see below

(b) could this DART-ISSM configuration be used to estimate multiple parameters at once (I don't see a reason why not, but the performance may not be the same as what is found for the single parameter estimation experiments explored currently).

I get that the design of these experiments are meant to mimic and compare directly to Gillet-Chaulet 2020, but it would be useful to also push beyond their design to get closer to a realistic case where DA might be used.

4. At more than one point it is suggested that using variational methods is more computationally intensive that ensemble-based DA. However, there is no real direct proof of this as you don't perform a direct comparison and to my knowledge this has not been done in the published literature. Given that ISSM has a variational DA option already implemented, it could be valuable to compare EnKF with ISSM to EnKF with ISSM in terms of core-hours for a simple standardized run. Short of that, it would be useful to have a sense for the DART overhead? If it is negligible then I would expect ensemble-based DA to have n times the computational expense of a conventional ISSM run where n is the number of ensemble members. Additionally, giving a sense for how this ensemble-based approach has (or can be) parallelized would be useful. In theory, ensemble DA is highly amenable to parallelization, but this depends on how covariance matrices are constructed and how shared memory parallelism is handled. More details on all the computational aspects of this new method would be very useful to include.

Minor suggestions:

L16: less numerical model re-development

L26: use a form of variational

L28: realy on observational at a single time to

L30: it often introduces nonphysical artifacts into the

L35: The use of computational techniques such as automatic differentiation in ice sheet models

L69: to my knowledge this is the first ice sheet modeling paper to apply OSSE, so I think you can be more direct about this sentence

L86: an ensemble...for ice sheet model initialization

L88: on model initialization

L92: simulation of ice sheets

L100: explain what the random midpoint displacement method is

L138: model simulations

L143: I am confused here because you don't include velocity in the state vector, but later you say it is part of what is assimilated?

L184: does localization as implemented preserve covariance between different variables at the same location in space or does it simply localize along the diagonal of the covariance matrix? For example, there should be strong correlation between the ice thickness estimate and the bed topography estimate, and so you would be losing a significant amount of your ability to assimilate if covariances between these two variables at the same location in space where zeroed out by localization.

L205: what would happen if you had no velocity observations? How much of the performace is due to velocity observations vs thickness?

L243: I think this should refer to Fig. 5

L259: mean to initialization the deterministics...full ensemble to initialization the ensemble

Fig 4. In the caption you mention that highly localized experiments diverge. It would be helpful to speak to why these experiments diverge in the main text.

Fig. 7: There are artifacts in the bed topography and ice thickness estimates that correspond to the basal friction estimate. Can you speak to this? Is it related to how the localization is performed?

L276: can you quantify this change in spread? by eye it doesn't seem to change much between 20 and 30 years of assimilation

Figure 9: can you add a legend and plot the ensemble mean as well?

L290: It would help to discuss what this sentence means in practice. Is prediction accuracy degraded for this case? Or can you achieve similar reuslts with different localization and inflation parameters?

L325 initial estimates for the model parameters?

L328: correlation between both parameters

L332: what do you mean by "initial ensembles"

L354: need to fill in values for XX

L358: transient changes in model state but not in parameters

L366: can you speak to the limitations on this? would having 100m resolution data be even better or proportionally so?

L370 this is a very important point that is worth highlighting in the abstract