Dear authors,

You paper received very critical reviews that asked for substantial revisions. Note that the criticism does not only address the presentation of your study but also the contribution of your work to the field.

In particular the following key criticism needs to be addressed in your revised manuscript which will be send for further review:

1) you need to go belong the linear regression analysis of the basic parameters; if a large spatio-temporal dataset is used please consider clustering analysis and/or principal component analysis and/or Bayesian statistics

2) you need to include a literature review describing what is the current state of knowledge in the field and how your study (or objective of your study) advances the current state of knowledge in the field

3) you need to provide a detailed description of the methods used (e.g. data pre and post processing, uncertainty analysis)

4) you need to expand the discussion and conclusions sections so that they reflect/include all the key results from your analysis

5) you need to pay particular attention to the language and structure of the paper: use clear sentences and logical flow, avoid grammatical and spelling errors, avoid repetitions and redundancy, and definitely proof-read the manuscript before re-submission (I would also recommend giving your manuscript to a native English speaker for proof-reading if this is possible for you)

Best regards,
Valentina

Dear authors,

I received the comments from referees on your revised draft. Despite your extensive revisions, one of the referees is still not convinced by the contributions of your study to the field. Please try to be clear in your discussion and conclusion how your study advances the current knowledge in the field.

Furthermore, as indicated by the referee, there is an ambiguity between between lake and river ice throughout the manuscript to the point that it is not clear which one you are reporting on (is it river ice characteristics or lake ice?) These are fundamentally two different processes of ice formation and decay. Please try to address these issues carefully.

The objectives of each data processing step are not clearly outlined. Some parameters seem to have unusual naming (such as Negative Cumulative Air Temperature which is referred to as cumulative degree day of freezing in the literature). Please chose a correct (commonly used) terminology and stick with it throughout the text.

Furthermore, there are still typos and redundancy in the writing (see my specific comments).

In the light of this criticism I have reviewed the revised version myself. Please find below my specific comments. I am asking you to address the comments (more general comments above and all of my specific comment below) and submit the revised manuscript with line-by-line responses to the comments.

Best regards,
Valentina

Specific comments:

Abstract: 'Five typical geographic zones were identified applying a rotated empirical orthogonal function.' -> It's not clear what is meant by five typical geographical zones. Typical of what? Also to what data is the EOF applied?

Page 2: 'The earliest ice record in the literature dates back to 150 years ago (Magnuson et al., 2000)' -> is this referring to the earliest ice record in the world or in China? Please clarify this in the sentence.

Page 2, ln 49: 'At medium and large scales, ' -> provide example in km for what is considered mediium and large scales here.

Page 2, ln 54: 'but their spatial resolutions are too large' -> do you mean too coarse? 'at small scales' -> better say at local scales (or define what is meant by small scales).

Page 2, ln 60: 'include regular observations' -> not clear what is meant by regular? Do you mean continuous monitoring by automated stations?

Page 2, ln 62: 'Ice parameters differ greatly' -> provide some examples for ice parameters here: Ice parameters, such as xxx, differ greatly

Page 2, ln 67: 'These models consider the energy exchange and physical changes ...' -> not all of the models you listed will consider these processes but probably only 'physics-based' model. The empirical models will be focused solely on data. Please revise.

Page 2, ln 72: 'to validate and improve accuracy and reliability. '-> to validate and improve accuracy and reliability of what?

Page 3, ln 77: 'the effect of snow cover can’t be ignored.' Change 'can't ' to 'cannot'. Also provide a reference(s) for this statement.

Page 3, ln 78: 'snow depth outweighs air temperature during the ice forming process' -> better say 'the effect of snow depth on the ice forming process is larger than the effect of air temperature.

Page 3: ln 79: Compared to other studies, air temperature had a greater effect on ice thickness than snow depth and were attributed this to the high snowfall in the study area (Gao and Stefan, 2004).' Better say: 'In contrast to these studies, Gao and Stefan (2004) found that air temperature had a greater effect on ice thickness formation than the snow depth.

Page 3, ln 80: 'Besides' -> change to 'Furthermore'

Page 3, ln 83: 'ignored the changing status of ice formation processes' -> not clear what is meant by the 'changing status'. Would it be better to say 'ignored the different stages of ice formation'?

Page 3, ln 84: 'The relative influence of snow depth and air temperature on the ice regime deserves further exploration in Northeast China.' Change to: The relative influence of snow depth and air temperature on the river/lake ice regimes in Northeast China deserves more exploration.

Page 3, ln 84-94: This paragraph repeats what has already been stated in the introduction. Please revise the whole paragraph to avoid any repetition and redundancy. Indicate the research questions and also briefly mention in very general terms (2-3 sentences) how the key questions will be answered in this study (what methods and observations you'll be using).

Section 2.2.1: Makes sure to indicate how many measurement site are on river ice and home many on lake ice. One of the reviewers pointed out that this has not been clearly stated.

I would suggest removing the abbreviations here (FUS, FUE, BUS, BUE, CFD, IT, MIT, ASD) as there are too many abbreviations in the study and it is hard to keep track. Too many abbreviations can disrupt the narrative. If you are using these abbreviations in the figures, then introduce them in the figure captions.

Page 4, Line 133: 'establish the regression model' -> it is not clear what regression model you will be establishing. Will this regression model be described later? If yes, then say 'establish a regression model, which we describe below.'

Section 2.3 I suggest to provide here a short summary of overall methodology, so the readers can get a general idea of what is to follow and how it fits together. So here you would mention the key steps you will use (krigging, EOF and regression) outlining the main objective of each step. Then in each section that follows you provide more details on each step (as you have already done). Without this summary, it is very hard to comprehend why you chose to use each of this methods.

Section 2.3.1: Please include more details on what data is used here, i.e. to which data is krigging applied to and what is the specific goal (in your study) that you try to achieve with the krigging. As it currently ready, the section generally describes krigging, but necessary specifics for your study/data are not given.
'The average values of five ice phenology indicators' -> please specify the indicators and specify how the averaging is performed (in time or space or both?)

Section 2.3.1: Same comment as above. Please explain why EOF is used here (what are you trying to achieve in your study) and to what data EOF method is applied.

'The major advantages of the EOF method is to separate the uncorrelated components that confuse the spatial information and make it hard to interpret a physical phenomenon.' -> you speak about the advantages of EOF which you then immediately present as problematic and therefore use the rotated EOF to solve those problems. So the section here is somewhat confusing. Please revise so that it is clear: what the advantages of rotated EOF are, and why for your specific case you chose to use rotated EOF rather than EOF.

Page 5: Please reduce the use of abbreviations. For example, remove BLR and ATC.

Page 5, ln 180: 'the Y data were the five day ice thickness values, and the X data included snow depth over ice and air temperature on the river bank. -> is the Y data the ice thickness values on rivers or lakes? Please clarify. Also, is Y-data presented as five day moving average throughout the whole observational period? Please clarify. For many observations (points) do you have in the regression model? Do you apply any cross-validation, i.e. using section of the data for the model calibration and then another section (independent of calibration data) for validation? If you don't use any cross-validation, how do you prevent over-fitting to noise?

Results and Discussion: due to too many abbreviations it is hard to follow the narrative. I hope this will improve with the removal of abbreviations and using the full words.

Page 6, line 210: 'The general spatial trend was a tendency to advance as the latitude increased for the FUS and FUE...' Not clear what is meant by 'a tendency to advance', advance in what? Please revise.

Page 6: Results from EOS -> it seems that you are visually clustering the PC results (on the map). Is that correct? If yes, please state so. Currently it reads as if you are visually identifying the modes of PC, while these are actually derived from the EOF method itself.

Page 8, ln 259: 'an analysis of the annual changes was not conducted because the time series were not long enough' -> what is considered long enough here?

Page 8, ln 263: 'matrix between lake ice phenology' -> what variables are use for the ice phenology? Please clarify this already in the methods section.

Page 8, ln 281: 'Although a uniform observation protocol was required, the repaid transition between frozen river and open water for two or three days with floating ice and the inhomogeneities among different stations could not be ignored.' The use of terminology here, such as 'protocol' and 'repaid', does not seem right. Please revise with wording that is appropriate for physical processes. Start by simplifying the sentence. What do you actually try to say here?

Page 9, ln 290: 'Moreover, whether the status of river ice was steady or not also could not be neglected when studying the role of snow cover. ' Not clear what you mean by 'steady' river ice. Please clarify. Also, it is not clear how the role of snow cover is influenced by the steadiness (?) of river ice.

Page 9, ln 295: 'and the snow mixes with surface ice into slush and promotes melting.' Please elaborate this a bit more as snow can turn into slush regardless of the presence of ice. Also, please briefly elaborate (add a sentence) on why would the slush promote melting.

Section 3.3.2. In this section it would be interesting to relate you finding from the regression modelling and the zones you identifies from EOF analysis. Is the model performing better or worse for different zones.

Page 9; Ln 302: 'which is consistent with previous studies. ' Provide some references here for the studies.

Page 9, ln 305: 'was not as significant as in previous studies'. Again, provide some references here for the studies.

Page 9, line 306: 'Average air temperatures were most commonly calculated over fixed time periods at regional scales, for example as moving averages for certain time periods. ..' Are you referring to previous studies or to your study in this paragraph? It is not clear from the text.

Page 9, ln 310: 'Heat loss is mainly made up of sensible and latent heat exchange,' -> do you have evidence for this from your results or are you referring to previous work. If latter, please provide reference.

Page 9, line 315: 'dominated during the transition process.' -> the transition process of what?

Conclusions: Please do not use any abbreviation in the conclusions are it disrupts the narrative (especially for the reader who will just read the conclusions of your study). To reiterate: use the abbreviations only in the figures if necessary.

Page 10, line 330: 'The peaks of snow depth and ice thickness fell behind air temperature for almost one month' -> do you mean the peaks are lagging behind the peaks in air temperature by one month? Please revise as the current sentence is somewhat ambiguous.
Page 10, line 332: 'The yearly analysis failed to explain the relationship between ice regime and snow depth and air temperature' -> the 'yearly analysis' does not sound right. Do you want to say the you found no relationship between annual time-series of ice thickness and snow depth or air temperature?

Page 10, line 333: 'Based on monthly correlation analysis' -> Change to: Based on the analysis of monthly timeseries

Page 10, line 334: 'as the ice cover become steady' -> again, it is not clear what you mean by steady. Do you mean 'as the ice cover reached its maximum value for the season'?

Page 10, ln 335: 'Additionally, air temperature associated with ice phenology more closely than ice thickness.' Better say; the temporal variability in air temperature was more correlated with the variability in ice phenology than in ice thickness.

Page 10, line 339: 'air temperature on bank and negative cumulative air temperature.' Isn't the temperature always measured on the river bank? Please try to be consistent throughout the whole manuscript.

Page 10, line 341: remove: 'rather than air temperature through the heat loss of ice formation and decay.' You are dealing with the results of an empirical model (not physics-based) so threat the results as such. You can state that the negative cumulative air temperature is acting like a proxy for the heat loss during the ice formation and decay.

Page 10, line 348: 'The work herein will provide a valuable reference for the retrieval of ice development by remote sensing.' Better say: Data analyzed in this study present a valuable reference for the remote sensing observations of river/lake ice thickness in this area.

Page 10, line 349: 'Knowing the long-term change of river ice and the future projection could provide information for evaluating the influence of climate on social-economics, ecological environment and human activists across the riparian zones.' The sentence is too generic. Please remove.

Dear authors,

I've reviewed your re-revised manuscript. Please incorporate the following minor revisions (mainly editorial) before I can proceed with the acceptance of your manuscript for the publication. I'll emphasise again to please correct any typos and grammar inconsistencies throughout the text (especially in the revised text that has been added recently).

Thank you,
Valentina

Title: I think the title is somewhat narrowly defined as you analyse more than snow cover as predictor of ice thickness evolution. I suggest an alternative title: 'Investigation of spatial and temporal variability of river-ice phenology and thickness across Songhua River Basin, Northeast China'

Abstract:

'ice phenology and ice thickness...' change to river-ice phenology and river-ice thickness'

'Using ice records of local hydrological stations...' Change to -> Using daily ice records of XX hydrological stations across the region, we examined the spatial variability in the ice phenology and ice thickness from 2010 to 2015.'

'The cluster pattern of yearly maximum ice thickness has been measured by Global and local Moran's I.' Change to: 'We identified four spatial clusters based on Moran's I spatial autocorrelation applied to yearly maximum ice thickness.'

The high values clustered in the Xiao Higgan Mountains...' change to 'High values of ice thickness clustered in the ...

'Six Bayesian regression models were built between ice thickness, air temperature, and snow depth in three sub-basins of the Songhua River Basin.' Change to: 'In three sub-basins of the Songhua River Basin, we developed six Bayesian regression model to predict ice thickness from air temperature and snow depth.

'The determine R2 of Bayesian linear 25 regression ranged from 0.80 to 0.95, and root mean square errors ranged from 0.08 to 0.18.' Change to: 'The goodness of the fit (R^2) for these regression models ranged from 0.80 to 0.95, and the root mean square errors ranged from 0.08 to 0.18' -> shouldn't there be a unit for the root mean square error? Is it meters?

Line 81: 'The reliance on information makes the physically-based model more suitable for small watershed applications within 100 km2 . The empirical model enables it possible to predict the changes in ice regime from limited climate data for larger basin applications (Yang et al., 2020). 'Change to: 'As this information is more readily available on local scales, the physically-based models are more suitable for small watershed applications (e.g. within 100 km^2). On the other hand, empirical models are more commonly used to predict changes in ice regime from relatively limited climate data available over larger basins (Yang et al, 2020).'

Line 108: 'and compared' -> 'and compare'

Line 110: 'was quantitatively explored' -> 'is quantitatively explored'

Line 160-165: Change to paragraph to the following (please correct/edit if necessary):
'Our overall method can be summarized in the following steps: First, we use Kriging to spatially interpolate in situ measurements of ice phenology. Second, we use Morai's I spatial autocorrelation to identify spatial clusters based on the interpolated ice phenology data. Finally, for each cluster, we analyze the drivers of spatial and temporal variability of the river ice thickness. To do so, we use the Bayesian linear regression to quantify the links between the river ice thickness and snow depth and air temperature.'

Line 370-373: Change this section to:
'For the Bayesian linear regressions, we used the field measurements that span from November to March, thus focusing only on the cold part of the year. During this period, the river surface is completely frozen, and the air temperature that falls below 0℃ promotes the ice growth. April is the month when the rise of air temperatures above 0℃ enables the river ice to melt.'

Line 375-380: Change this section to:
'The correlation in Figure 7 between air temperature and ice regime was not as significant as found in some previous studies (e.g. Gao and Stefan, 2004). One of the reasons is that previous studies often averaged the air temperatures over a longer period and at a regional scale, therefore loosing the signal on seasonality at a local scale (e.g. Pavelsky and Smith, 2004; Yang et al., 2020). To circumvent this shortcoming, we applied the regression analysis on seasonal time series of ice thickness and air temperature.'

Line 410: 'important role as the ice cover becomes completely frozen' -> shouldn't it be 'as the river becomes completely frozen'?

Line 414: ' considering two types of air temperature' -> 'considering air temperature, as well as cumulative air temperature.'

Line 416-417: Change to: 'According to the performance metrics (R^2, root mean square error), the cumulative air temperature of freezing is shown to be a better predictor than the air temperature in simulating the ice thickness changes.

Line 418: 'ice process' -> 'ice thickness evolution'

Line 420: Remove this sentence since it is a repetition: 'The results suggested that heat exchanges between the river surface and the atmosphere dominated the ice process, and cumulative air temperature of freezing influenced the thickness is more sensitive indicators of heat loss of ice growth and decay than the air temperature.'

Line 425: 'The work herein will provide a valuable reference for the retrieval of ice development by remote sensing. Therefore, we plan to use satellite data to enlarge our study scope in our future work.' Change to: 'Data analysed in this study present a valuable reference for future studies that rely on remote sensing observations of river ice thickness in this area.