Estimation of the state and parameters in ice sheet model using an ensemble Kalman filter and Observing System Simulation Experiments

Choi, Youngmin; Petty, Alek; Felikson, Denis; Poterjoy, Jonathan

doi:https://doi.org/10.5194/egusphere-2025-301

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https://doi.org/10.5194/egusphere-2025-301

Preprints

27 Feb 2025

| 27 Feb 2025

Estimation of the state and parameters in ice sheet model using an ensemble Kalman filter and Observing System Simulation Experiments

Youngmin Choi, Alek Petty, Denis Felikson, and Jonathan Poterjoy

Abstract. Better constraining the current and future evolution of Earth's ice sheets using physical process models is essential for improving our understanding of future sea level rise. Data assimilation is a method that combines models with observations to improve current estimates of model states and parameters, leveraging the information and uncertainties inherent in both models and observations. In this study, we present an ensemble Kalman filter-based data assimilation (DA) framework for ice sheet modeling, aiming to better constrain the model state and key parameters from a single semi-idealized glacier domain. Through a synthetic twin experiment, we show that the ensemble DA method effectively recovers basal conditions and the model state after a few assimilation cycles. Assimilating more observations improves the accuracy of these estimates, thereby improving the model's projection capabilities. We also utilize Observing System Simulation Experiments (OSSEs) to explore the capabilities of the ensemble DA framework to assimilate different types of data and to quantify their impact on the model state and parameter estimation. In our experiments, we assimilate land ice elevation data simulated based on The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) products. These experiments are crucial for identifying observations with the largest impact on state and parameter estimates. Our assimilation results are highly sensitive to design choices for observation networks, such as spatial resolutions and prescribed uncertainties. The ensemble DA framework, capable of assimilating multi-temporal observations, shows promising results for real glacier applications through a continental ice sheet model. Additionally, this framework provides a flexible infrastructure for performing OSSEs aimed at testing various observational settings for future missions, as it requires less numerical development than variational methods.

Received: 23 Jan 2025 – Discussion started: 27 Feb 2025

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Journal article(s) based on this preprint

06 Nov 2025

Estimation of the state and parameters in ice sheet model using an ensemble Kalman filter and Observing System Simulation Experiments

Youngmin Choi, Alek Petty, Denis Felikson, and Jonathan Poterjoy

The Cryosphere, 19, 5423–5444, https://doi.org/10.5194/tc-19-5423-2025,https://doi.org/10.5194/tc-19-5423-2025, 2025

Short summary

Youngmin Choi, Alek Petty, Denis Felikson, and Jonathan Poterjoy

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-301', Kevin Hank, 27 Mar 2025

Dear Authors,

Please find my review in the attached pdf.
Best wishes,
Kevin Hank

Citation: https://doi.org/10.5194/egusphere-2025-301-RC1
- AC1: 'Reply on RC1', Youngmin Choi, 02 May 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-301/egusphere-2025-301-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-301-AC1
RC2:
'Comment on egusphere-2025-301', Alexander Robel, 09 Apr 2025

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

Citation: https://doi.org/10.5194/egusphere-2025-301-RC2
- AC2: 'Reply on RC2', Youngmin Choi, 02 May 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-301/egusphere-2025-301-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-301-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-301', Kevin Hank, 27 Mar 2025

Dear Authors,

Please find my review in the attached pdf.
Best wishes,
Kevin Hank

Citation: https://doi.org/10.5194/egusphere-2025-301-RC1
- AC1: 'Reply on RC1', Youngmin Choi, 02 May 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-301/egusphere-2025-301-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-301-AC1
RC2:
'Comment on egusphere-2025-301', Alexander Robel, 09 Apr 2025

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

Citation: https://doi.org/10.5194/egusphere-2025-301-RC2
- AC2: 'Reply on RC2', Youngmin Choi, 02 May 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-301/egusphere-2025-301-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-301-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Publish subject to revisions (further review by editor and referees) (14 May 2025) by Carlos Martin

AR by Youngmin Choi on behalf of the Authors (12 Aug 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (12 Aug 2025) by Carlos Martin

RR by Alexander Robel (26 Aug 2025)

Suggestions for revision or reasons for rejection

I am satisfied with the substantial changes made by the authors throughout the manuscript in response to my first review. I am happy for the manuscript to proceed to publication if the authors are able to revisit one point.

In my original review, I suggested that if the authors were to claim that EAKF with DART is more computationally tractable than adjoint-based variational DA methods, then this needed to be backed up with computational benchmarking. The authors have since softened this claim and indicate that a direct computational comparison is beyond the scope of this study. I find this to be an acceptable response. However, it is still the case that if this study is meant to provide a proof-of-concept for the utility of using DART and ensemble-based methods more broadly, having some information about the computational resources required for such methods would seem necessary so that readers who might think of using such an approach would know ahead of time what computational resources are required. Specifically, it would be useful if the authors could provide some information about the computational overhead associated with running DART for some of these simulations. In principle, the assembly and computation of the analysis in Kalman-based DA methods can be done with relatively little computational expense compared to the forecast. However, in practice this requires gathering output from difference processes (if the ensemble members are run in parallel, which is what makes ensemble-based methods so promising from a computational perspective) and then calculating information on potentially large arrays. This can prove to be a challenge from an I/O and memory perspective as problems scale in size. I'm not asking for the authors to add a whole new section on this, but simple to use their existing ensemble simulations to estimate the marginal computational cost associated with the analysis step. Even just comparing the total walltime of two cases with the same number of ensemble members run on the same number of processes, but with more assimilation cycles would help to estimate the added computational cost of each analysis cycle. This can be described in a few sentences added in the results or discusison section and shouldn't require running any new simulations assuming that the existing run logs already include information about total run time.

Hide

RR by Kevin Hank (27 Aug 2025)

ED: Publish subject to minor revisions (review by editor) (09 Sep 2025) by Carlos Martin

AR by Youngmin Choi on behalf of the Authors (23 Sep 2025) Author's response Author's tracked changes Manuscript

ED: Publish as is (24 Sep 2025) by Carlos Martin

AR by Youngmin Choi on behalf of the Authors (24 Sep 2025)

Journal article(s) based on this preprint

06 Nov 2025

Estimation of the state and parameters in ice sheet model using an ensemble Kalman filter and Observing System Simulation Experiments

Youngmin Choi, Alek Petty, Denis Felikson, and Jonathan Poterjoy

The Cryosphere, 19, 5423–5444, https://doi.org/10.5194/tc-19-5423-2025,https://doi.org/10.5194/tc-19-5423-2025, 2025

Short summary

Youngmin Choi, Alek Petty, Denis Felikson, and Jonathan Poterjoy

Data sets

Data for "Estimation of the state and parameters in ice sheet model using an ensemble Kalman filter and Observing System Simulation Experiments" Youngmin Choi, Alek Petty, Denis Felikson, and Jonathan Poterjoy https://doi.org/10.5281/zenodo.14722078

Youngmin Choi, Alek Petty, Denis Felikson, and Jonathan Poterjoy

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In this study, we combined numerical models with satellite data using the ensemble Kalman filter to improve predictions of glacier states and their basal conditions. Simulations showed that adding more data enhances prediction accuracy. We also tested the effect of various data types and found that the high-resolution data improve model performance. This method could inform the design of better observation systems and refine future projections of ice sheet behavior.


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