Review for NPG-2024-21 “Simulation and Data Assimilation in an Idealized Coupled Atmosphere-Ocean-Sea Ice Floe Model with Cloud Effects” by Changhong Mou et al.

The authors propose a coupled atmosphere-ocean-sea ice system that accounts for the effects of clouds and precipitation. The atmospheric and oceanic components are based on quasi-geostrophic (QG) model configurations while the sea-ice model is a Discrete Element Method based implementation with which they focus on the marginal ice zone (MIZ) dynamics. The atmospheric QG model employs a saturated precipitating version that allows to study the impact of the clouds and precipitation on the ice floes and on MIZ under different ice floe regime. Furthermore, the coupled modelling system is interfaced to a Local Ensemble Transform Kalman Filter (LETKF) data assimilation (DA) scheme to study the impact of observations.

General comments

The manuscript is well written, model equations are documented well. I found Section 3 a bit hard to follow since the majority of it describes surrogate models not DA. But it is fine since those are used only in the ensemble DA experiments. However, the DA system description is left limited; this may make the manuscript hard to follow for non-expert readers on DA while looking at the experiments in Section 5. 

Furthermore, the validation of the experiments can be done in a more quantitative way. The skill of the posterior mean is documented in Tables 6-8 but they can be extended to prior mean to see how much the DA improves with respect to the forecast. Another way of doing it is using the non-assimilative experiments in Section 4 as a baseline to see how the sparse and plenty observation cases improve when observations are incorporated. Another interesting diagnostic can be to look at the spread of the prior and posterior ensemble to see the uncertainty before and after the assimilation.

Finally, conclusions can be extended considering my specific comments below. Overall, I would expect a more quantitative assessment of the results. I would be happy to see a revised version.

Specific Comments

Introduction: The data assimilation literature related to the work should be extended to give the reader a view of which studies have been done in line with the investigation presented in Section 5.

Section 2:  Sections 2.2.4 and 2.2.4 can be subsections of 2.2.2. Similarly, 2.2.6 and 2.27 can be subsections of 2.2.5.

Section 3: how costly is the coupled system? Can you be a bit precise in terms of cpu time? Is the code parallelized? What is the gain with the reduced-order models in this case?

Section 3.2 it is not clear to me how the total water content is linked to the ice floe area?

• Using “q” in the equations for both the PV and water content is confusing from time to time. 

Section 3.3.2 describes directly the data assimilation scheme (LETKF) not the localizations. This can be the introduction to Section 3.3. You don’t detail the scheme, no KF equations for example, but you allocate a dedicated section to localization. What is the reason that you prefer to discuss localization explicitly for your application? How does your analysis benefit from it? 

Section 4.1 Is the time step equal for all the components? If so, what are the implications for resolved scales for the supposedly fast evolving atmosphere and relatively slow ocean and sea ice? By the way, is there a specific reason that you choose the timestep as a decimal number in seconds? It is 58.2 seconds in line 399 while 1.2941 hours in Table 1. Not clear to me why they are different.

Section 4.3 The trajectory of the large floes seems to me more unpredictable including returns and changing directions. Is there a way to quantify this behavior? 

Section 5.1 Returning back to my comment on Section 3, did you try running an experiment with smaller ensemble size (instead of 300) using the full models (instead of surrogates)? 

• What are the state variables, all model variables? 

Section 5.2 It would be useful to provide the prior mean and spread of both the analysis and forecast to assess the improvements via DA. The posterior mean compared to truth is fine but doesn’t show how much the state and the trajectory improved. 

Technical corrections

Format of the citations are not adequate and should be corrected all over the text. e.g. Cámara-Mor et al. (2010); Kwok (2018) → (Cámara-Mor et al. 2010; Kwok 2018)

The authors present an original study on idealized modeling of coupled atmosphere-ocean-sea ice dynamics that incorporates the effects of clouds and precipitation. Ocean component is modeled using a two-layer quasi-geostrophic (QG) model. Atmosphere is modeled using a two-layer saturated precipitating QG model that explicitly includes water content and precipitation. Sea-ice is modeled using Discrete Element Method (DEM), which simulates circular ice floes in different distributions, representative of the Marginal Ice Zone (MIZ).

In addition, the authors implement data assimilation (DA) using the Local Ensemble Transform Kalman Filter (LETKF) applied to reduced-order stochastic surrogate models. A particular focus is placed on observational uncertainty and sparsity due to cloud cover, which affects the accessibility of atmospheric observations.

The manuscript is generally well organized and provides a novel contribution to the field. However, several aspects of the methodology, assumptions, and presentation require further clarification or justification. I provide below a list of comments and questions aimed at helping the authors strengthen the manuscript.

• The governing equations for sea ice floes do not appear to include the Coriolis force. Please clarify whether this was omitted intentionally and, if so, provide a justification.
• Are the background velocities of ocean and atmosphere considered for the computation of drag forces and torques on the floes?
• There isn’t any coupling between atmosphere and ocean and the coupling between ice floes and ocean is only one-way. Can you justify this choice? This may have a significant impact on the accuracy of ocean state estimation, which is shown to perform relatively poorly in the data assimilation experiments.
• Line 229: it is assumed that precipitation causes an increase in ice floe thickness. This may be a reasonable assumption if precipitation is snow, but this is not guaranteed especially during summer and fall and in the MIZ [Boisvert et al. 2023]. Furthermore, solar insolation is set to 1361 W/m² (Table 4), which is very unrealistic for polar winters.
• Line 464: Clearly state that the “truth” is obtained from the full coupled model and describe the numerical scheme used to solve it.
• Line 470: The definition of plentiful and sparse observations is not clear. Have you applied Equation (54) with different values of the threshold?
• Figure 6-7-8: It would be helpful to include the background mean for visual comparison with the analysis.
• Line 485: The manuscript states that the ocean field has limited observability. Could you elaborate on this and possibly provide a more quantitative analysis?
• Figure 8 shows how DA helps to recover the trajectory of a specific floe under sparse observational conditions. However, it seems that the floe under scrutiny is observed at every assimilation cycle within the period analyzed. If this is not the case, please indicate how many times the floe is observed and show this visually.
• Please add Normalized RMSE values for the prior, in addition to the posterior values, to better assess assimilation effectiveness.

Minor comments

• Line 181: there is a reference to the background vertical gradients of total water mixing ratio, but Table 4 reports a value for the background vertical gradients of total water. Is there a difference between total water and total water mixing ratio?
• Is the replacement of contact forces with white noise intended to increase ensemble spread in DA? Please clarify.
• Line 309: what does 𝜓̃_bt,k refer to?
• Line 367: Equation (50) suggests larger floes have higher uncertainty, which contradicts earlier claims. Please clarify or correct the formula.
• Line 385: There is again confusion between total water content and total water mixing ratio.
• Line 447: What is the difference between Equations (49) and (55)? They appear to be similar—clarification would help.
• Line 462: In Equation (50) the uncertainty below the threshold was set at 0.5 km.
• Line 493: in Equation (50) is the threshold.
• Add a list of symbols with definitions and units of measurements.

References

Boisvert, L. N., Webster, M. A., Parker, C. L., & Forbes, R. M. (2023). Rainy Days in the Arctic. Journal of Climate, 36(19), 6855-6878. https://doi.org/10.1175/JCLI-D-22-0428.1

This paper introduces a coupled model of atmosphere, ocean, and sea ice to study the impact of clouds and precipitation on the Marginal Ice Zone (MIZ). The proposed model uses the discrete element method for sea ice dynamics, a two-layer quasi-geostrophic model for the ocean, and a two-layer saturated precipitating quasi-geostrophic system for the atmosphere. The framework examines how cloud cover influences energy balance and ice melt/freeze processes. The paper also  introduced an associated reduced-order model and illustrated its utility in reducing computational cost of data assimilation techniques to infer missing floe trajectories and unobserved wind patterns in presence of cloud-induced uncertainties.

The scientific contents are novel and the paper is well written. The rationale behind the proposed model is well explained with relevant literature thoroughly reviewed. The numerical experiments are also carefully documented, accompanied with several tables listing the involved parameters. 

The following are some minor comments to be taken care of during the revision.

- The subsections 2.2.2--2.2.4 should be one subsection, same for subsections 2.2.5--2.2.7. This would also match the authors intent reflected in Figure 1b about the two drag forces.

- In Section 2, the draft does not seem to mention what happens when the sea ice floes hit the boundary of the spatial domain. Boundary conditions for the atmosphere dynamics seem to be missing as well. 

- Both Brownian motions and Wiener process are used. Maybe stick to one of them? 

- Both "the l-th floe" and "the lth floe" are used in the manuscript. 

- Page 10, Line 194, use $\Phi_1^a$ and $\Phi_2^a$ instead of $\Phi_1$ and $\Phi_2$? 

- There is a discrepancy between the \Delta t value reported in lines 399, 459 and in Table 2.

- Please check the physical units for E_i and E_o in Table 2. 

- Please check the physical units for the background vertical gradient of total water in Table 4.