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# Summary

Palerme and Müller use random forest regression to predict Arctic sea-ice drift speed and direction from a set of predictors that contains besides dynamical sea-ice drift forecasts (TOPAZ4) also wind forecasts, geographical coordinates, sea-ice concentration and thickness, and distance from land. Using both buoy and satellite-derived drift for training and evaluation, the authors find that the predicted drift slightly outperforms the original TOPAZ4 drift forecasts at all lead times considered (1-10 days); mean absolute errors are reduced by roughly 5-10%. In my view the study is very relevant and innovative, scientifically sound, and well presented. What I think deserves additional effort is to illuminate more clearly what happens within the "black box" of the random forecast algorithm, for example, which of the predictands are picked how often to split nodes, what the output resolution of the individual trees is, how the predictands "modify" the TOPAZ4 drift forecasts, how that compares to simpler bias corrections, and how such characteristics change with lead time. With more explanations along these lines, the article could help readers (including myself) to better understand how the approach really functions, thereby providing an educational example how ML methods can help us to enhance predictions beyond the direct outputs of numerical models. In summary, I recommend publication of this work in The Cryosphere subject to minor(-to-major) revisions as detailed in the following.

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# Specific comments

Regarding the term "calibration": In my view it would be helpful to clarify in how far the presented approach is a "calibration" of dynamical model-based drift forecasts. Typically, calibration in this context means to use raw dynamical model forecasts and to modify them in some systematic way, e.g., to remove model biases. However, here the TOPAZ4 drift forecasts are used qualitatively in the same way as the other predictands, which appears to be a conceptual deviation from the standard calibration approach and leads to interesting questions. For example, would there be ways to formulate the random forecast algorithms such that they are explicitly used to modify the raw TOPAZ4 drift forecasts rather than predicting the drift "from scratch"? Or is that basically equivalent to the way it's currently being done, treating the TOPAZ4 drift just like any other predictand? I would be good to provide some clarification and/or discussion in this regard.

P2L47+56: "... have been used for training some random forest algorithms ...": First, from these sentences it is at first not clear that you are not talking about previous work, but that this is what has been done in the present study. Second, the "some" sounds very vague, maybe you can refer here to Sect. 3.2.

Sect. 2.2.: I think it would help to make very clear here that the TOPAZ4 drift forecasts are the basic ingredient here, but that other predictands are added and actually treated in the same way as the TOPAZ4 drift forecasts within the random forest algorithms, see my previous remarks.

P3L79-80: "while TOPAZ4 forecasts are produced daily, only the forecasts starting on Thursdays are initialized using data assimilation": This sounds as if the forecasts starting on other days than Thursdays would not at all be affected by data assimilation, but I assume that they are affected by previous data assimilation, that is, from the last Thursday (and earlier), right? So I would say they are still "initialized", just not with particularly timely observations.

P4L91: "The initial bearing on the great-circle path": From the context one can guess what is meant by "bearing" here, but is this word really correct?

P5L120: "as independent data sets": Please clarify what you mean here exactly by "independent".

P5L121-133: Given that, if I understand correctly, the main motivation for subsetting the SAR data is to avoid the use of highly-correlated neighbouring data points and thus overfitting, wouldn't it be more effective to do the thinning in a more systematic way by omitting more points in data-rich regions rather than subselecting completely randomly without taking data density into account?

P5L130: By evaluating only over the period June-November 2020, doesn't this potentially introduce a seasonal bias for the evaluation? (This also raises the question whether it would be worthwile considering to add the time of the year as an additional predictand?)

P5L133: "10^4 training data sets": Should this be "data points"?

P5L143: Here again, the TOPAZ4 drift forecasts are mentioned just alongside all other predictands - shouldn't they he highlighted much more upfront as the "main predictors" (which are to be "calibrated")?

P5L143: Also, I think it would be good to state clearly that for a specific lead time only the forecasts (TOPAZ4 & IFS) for that specific lead time are used as predictands - or is that not the case?

P6L153-155: "maximizing the depth of the decision trees" - First, given that the decision trees are based on quasi continuous predictor variables as well as continuous target variables, there does not appear to be an absolute "maximum" depth. Can you please specify what depth is actually used? Second, related to this, how meany leaves do the individual decision trees have, and how are the associated predicted values distributed? Do the resulting distribution densities approximately match the distributions of the target variables (or does the "resolution" vary in a specific way)?

P6L153-155: "setting the number of predictor variables considered for splitting the nodes at three": First, I speculate this small number of random predictands per split "forces" the algorithms to use the less-informative predictands (other than TOPAZ4 drift and IFS winds) more often than a decision tree would do that can always choose from all predictands. Can you provide some more insight into this? Second, related, which predictands are chosen how often to split nodes? I imagine over a large number of layers, TOPAZ4 drift (or IFS winds) would always be preferred over other predictands as long as those main predictands are not yet used so often that the resulting resolution of the target variable is approximately as high as the effective accuracy of those forecasts in the first place. Do you find such a systematic behaviour, that the "main" predictands dominate the upper layers and "other" predictands gain importance in lower layers? Moreover, does the relative "use frequency" of different predictands change for the different lead times? For example, I could imagine that the relative importance of TOPAZ4 drift versus winds might change with lead time, which might in turn be related to the way IFS forcing and perturbations are used to drive the ice and ocean in TOPAZ4?

Sect. 4.3: First of all, I really like these sensitivity experiments to quantify the impacts of individual predictors. As mentioned above, I think it would be really helpful to add more information about how often the predictands are actually used in the regression trees, which I suppose would provide similar information about relative importance from a very different angle - in fact without the need to run additional algorithms. Furthermore, it is not surprising that the TOPAZ4 dirft forecasts (speed for speed, direction for direction) are the most important predictands, right? Again, this makes me wonder how the approach followed here relates to classical "calibration", that is, to use a raw forecast and "modify" it based on some additional information, and how the final forecasts derived here deviate from the raw forecasts. E.g., are the raw drift speeds and directions systematically corrected (on average) in one or the other way - and maybe this depends on the region (e.g., CAA vs. open ocean), the lead time, and the sea-ice thickness or concentration? Some more information and discussion regarding these aspects would in my view be very helpful.

Following up on the previous point(s), I am wondering in how far similar improvements (over raw TOPAZ4 drift) might have been achieved with a simpler ("classical") calibration approach, e.g., by correcting the drift speeds and directions with some constant factors and/or offsets? In this regard, it would also he helpful to see if mean biases for speed and direction exist that could be corrected for by such a trivial calibration approach. On the other hand, if such simple biases are absent, that might be a strong argument against such simplistic calibration, right?

Review of Calibration of sea ice drift forecasts using random forest algorithms.

The manuscript describes a new method that post-processes numerical forecasts of sea ice drift using either in situ drifting buoys or satellite images for the training of a random forest algorithm. The results are evaluated against ice drift observations but in a different period, posterior to the training data. The results reveal that there is a systematic component of the ice drift forecast error that can be corrected by machine learning, although the reduction of error remains often less than 10%. The ML algorithms learns more efficiently from the buoys data than from the satellite images, highlighting the problem of temporal averaging. 

The drift direction can mostly be improved in the short forecast range, likely because of the unpredictability of wind directions, but interestingly the algorithm is more often able to correct drift speed at longer forecast horizons, which I did not expect. The authors could spice up their article by analysing what their algorithm does to the sea ice drift speed that improves the skills at a 10 days range: are the drifts made systematically faster or slower? This kind of analysis can - if understood - lead to improvements of the forecast systems. More generally, not seeing what the algorithm does to the forecast is a little frustrating. An example of comparison of original to postprocessed and to observed sea ice drifts could be more convincing than cold-blooded skills scores. 

One general remark pertains to the Lagrangian nature of sea ice drift. The variable influencing the drift at a lead time of several days may not be at the same location as the sea ice drift value. This issue is not addressed in the paper, what do the authors expect to be the effect of considering both the predictor and the target at the same location?

The authors have also neglected the seasonal changes of the forecast model performance, as well as the long-term model drift (or rather the absence of sea ice acceleration) as pointed out originally by Rampal et al. (2011) and then Xie et al. (2017) using an almost identical model. Can the algorithm learn the seasonality of the errors or could it be improved if trained separately on summer and winter data? 

The manuscript cites the relevant literature and is original in its goals. I am not aware of any similar study carried out elsewhere. The article is logically structured and reads quite well. The figures are generally nice and clear. Exceptions are noted in detailed comments below. 

Based on the above, I recommend the manuscript is published with minor corrections. 

Detailed comments:

• P1, l21: The relationship is complex and nonlinear in the ice pack where the rheology is active, but for low ice concentrations, the ice is in free drift and should be a linear function of the winds (the Nansen relationship). 
• P2, l29: “but they obtained”: false opposition. Is there any reason why RF or CNNs would have an advantage for sea ice concentrations? 
• P3, l78: The overestimation of sea ice drift was reported in reanalysis, but since the decadal acceleration of sea ice drift is not reproduced by the model, the bias should be smaller in recent times, as can be seen in the TOPAZ4 validation pages: https://cmems.met.no/ARC-MFC/V2Validation/timeSeriesResults/year-day-01/SItimeSeries_year-day-01.html#drift (accessed 2nd March 2021) 
• l108: "different algorithms were used": “models” should not be synonymous with “algorithm” (the Random Forest is one algorithm, from which you can build several models). Maybe use "distincts models were developed to..."?
• L148: At which point is the averaging used? Is it related to the averaging of each prediction tree? 
• L148 If the predictive variable is a complex number, isn't it similar to predict normalised u and v components (with a norm of 1)? In that case, this choice is apparently contradictory with the assertion line 90: "In order to predict independent variables, it has been chosen to forecast the direction and speed of sea-ice drift rather than the eastward and northward components"
• Section 3.2: It is very positive that sensitivity studies are detailed. The algorithms were tuned against the size of the training set (period for buoys, subsampling rate for SAR), size of the forest (number of trees), other parameters of the RF. It is not clear to me which criteria were used for this tuning. On which dataset the error has been computed to evaluate the tuning? Is it the one used to evaluate the results (buoys in June-November 2020) or the one used to evaluate the importance of predictor variables (section 4.3)? 
• L183: The period chosen for evaluating the model is mostly in the summer season (June-November)? Do you expect it to be representative of the winter? The link above shows a seasonal signal in the drift bias, though not a large one. 
• L206-2018. It is fair to note the absence of data where the performance deteriorates. This however deserves an explanation as to how the random forest algorithm extrapolates the training data spatially. Does it find the most analogous situations where and when training observations are available? The authors explain that the random forest does provide the average of an ensemble but it would be good to have insights about the values returned, for example, in places of intermittent landfast ice. 
• L224-226 "The selection of the data sets used for training and evaluating the random forest models is a random process according to the forecast start date to avoid the influence of neighboring grid points with very similar conditions," this point of correlations between training and validation data (leading to data leakage) is essential to avoid correlation between training/validation data that could lead to data leakage and overfitting. It would be beneficial for the community to give more details (even if it is given in appendix) about your selection procedure.
• l 236: Intuitively one may expect that the areas of thicker ice drift slower than thin ice due to the increased resistance to stress. 
• Section 4.3. This sensitivity study is important. But I am surprised not to see the standard "Importance variable" diagnostic available in any random Forest algorithm? Even if the results are redundant with your study, it would have offered another point of view of variable importance.
• L258: It is correct to mention the changes in operational systems but the authors should note that even with unchanged reanalysis systems, the gradual acceleration of ice drift is not reproduced by the models and may also affect the training over long periods. 
• L261: I may have misunderstood this point. I do not expect any 7-days frequency signal in sea ice drift so Thursdays are representative of the rest of the week. 
• Code availability: I would like to point out that there is not enough details given on the results so it can be reproduced. It is said that "the codes used for this analysis can be made available upon request." but without the code, it is not possible to reproduce the results as the RF models are not detailed.
• Figures 2 and 10: the crosses colours are not colourblind-friendly. Try a simpler scale - a gradient - that can easily distinguish the high from the low percentages. The general tendency is more interesting to me than the exact values. 
• Figures 4 and 5: do we need to see both the MAE and the RMSE? 

References: 

Rampal, P., Weiss, J., Dubois, C. and Campin, J.-M.: IPCC climate models do not capture Arctic sea ice drift acceleration: Consequences in terms of projected sea ice thinning and decline, J. Geophys. Res., 116, C00D07, doi:10.1029/2011JC007110, 2011.

Xie, J., Bertino, L., Counillon, F., Lisæter, K. A. and Sakov, P.: Quality assessment of the TOPAZ4 reanalysis in the Arctic over the period 1991–2013, Ocean Sci., 13(1), 123–144, doi:10.5194/os-13-123-2017, 2017.

See attached