1. This manuscript addresses the lack of a cold hardiness component in equations designed to assess water flow and fitness in landscape-level vegetation models, which don’t work for low temperature climates, particularly with trees that potentially continue photosynthesis/ transpiration during winter.
2. The paper advances a logical addition of a cold hardiness component and includes novel data generated from simulations.
3. The logical addition of a cold hardiness component may not be considered a substantial advance by some readers.
4. The methods and assumptions are valid and clearly outlined. See also comments to the authors.
5. The results are sufficient the interpretations and conclusions. See also comments to the authors.
6. The model appears replicable by others in the field. See also comments to the authors.
7. The authors clearly state which contributions to the model are prior work by other authors and what their contributions are.
8. The title clearly indicates the contents of the manuscript including model name and number.
9. The abstract is clear and concise.
10. The presentation is well structed and clear.
11. The language is fluent and precise.
12. Mathematical formulae, symbols, abbreviations, and units are defined and precise.
13. The manuscript cannot be reduced.
14. The references are appropriate. See also comments to the authors.
15. The supplementary materials are sufficient and appropriate.

Comments to authors: 

Line 175: I suggest the authors consider providing a supplementary file with these data (if possible). 

A crucial point is whether the authors will verify the model, particularly the hardiness estimations, with real experimental (biological) data as opposed to data from the literature.  While the simulations and conclusions look appropriate, I think confidence in the conclusions would be strengthened with a subsequent publication that tests the algorithms with actual biological data.  

Line 175: The authors should consider the findings of Kuprian et al. (Tree Physiology 38, 591–601

doi:10.1093/treephys/tpx142) who examined the relationship between winter desiccation and bud primordia supercooling (hardiness) in Picea abies.  Their results "suggest that there is no causal relationship between desiccation and the supercooling capacity of bud primordia in P. abies, but rather it involves other compounds within the cells of the bud primordium that reduce the water potential".  This may be an important consideration in terms of biomass production as new needles arise from bud primordia.

Figures: Many of the figures are difficult to make out as is the lettering within the figures. I suggest making the line/ symbols heavier and the colors bolder.  

In this manuscript, the authors attempted to incorporate the effect of cold hardening on the hydrological and physiological processes of trees into the CLM5.0-FATES-Hydro. The scheme of cold hardening consists of the hardening scheme (Rammig et al., 2010; some modifications) and the physiological scheme (maximum conductance, parameters for stomatal conductance, hydraulic failure mortality, pressure-volume curve, and carbon starvation mortality). They showed that the inclusions of cold hardening schemes are vital for reproducing the biomass of two boreal forests in Farstanas and Spasskaya Pad. Otherwise, the trees die due to hydraulic failure during the winter, caused by the low water potential of frozen soil and the resulting dehydration of the trees. Therefore, I think their schemes are successfully developed and valuable for many readers who want to model the processes in boreal forests.

I recommend this article be accepted after the revisions listed below.

On the modifications to the scheme by Rammig et al. (2010)

For example, the authors modified the maximum hardiness level (H_MAX) from a constant (i.e., -30 deg C) by Rammig et al.(2010) to the variable changing with the running mean of the annual minimum air temperature of the past 5 years. This may result in a big difference in the simulations, particularly in Spasskaya Pad, but such a result is not shown in the present manuscript. I'd suggest showing the results when the original schemes by Rammig et al.(2010) are adopted so that the importance of the modifications in this study will be emphasized.

Citations of equations

Throughout the manuscript, the citations of equations look strange and probably do not fit the style of GMD. In the case of this manuscript, all the "Eq. XX" should be put in parentheses. For example, in L182, "TH Eq. (1), HR Eq. (2) and DR Eq.(3)" should be "TH (Eq. (1)), HR (Eq. (2)), and DR (Eq.(3))". Please revise all of them.

Symbols in equations

Throughout the manuscript, the symbols differ between the text and the equations. For example, H_MIN and H_MAX in the text are presented as M_min and H_max, respectively, in equations (1), (2), and (3). Please maintain the integrity of symbols.

Section 2.2

I strongly suggest the authors provide the model description of HD (i.e., L191-202) in advance of those of TH, HR, and DR for better readability. 

Besides, the description L191-202 seems not sufficient. For example, HD takes the maximum value H_MIN in summer, but it is not explained. This corresponds to equations (1) and (3) of Rammig et al (2010). Here, Rammig et al. (2010) adopted aggd5 (the accumulated growing degree days), but the authors did not mention it in the manuscript. Is that OK?

Since this hardening scheme is the core of this study, the authors should describe it entirely, even if it is nearly the same as Rammig et al. (2010).

Otherwise, the reader would have to refer to Rammig et al. (2010) when reading this paper.

In addition, according to equations (4) to (6), HD is determined depending on the interrelations between HDP and TH. I'd suggest showing the example of the temporal variation of HD and TH to show how these variables are interrelated.

Figures

As reviewer 1 pointed out, most of the figures are difficult to distinguish between lines, and the legend obstructed the figure. Please try to make it easy to see, and put the legend outside the plot.

L61: It is unclear what "it" stands for here. Is it "plant hydraulics"? If so, I suggest rewriting this sentence as follows.

"Plant hydraulics, apart from its critical role in the survival of plants during droughts, is also a major driver of species distribution."

L110-111: Lawrence et al. (2019) --> (Lawrence et al., 2019)

L178 and the caption of Table 1: Does "the minimum 2m daily temperature" mean the "annual minimum of daily mean air temperature at 2m height"? Describe it clearly.

L192: "the hardiness of the previous day (HDP)" --> "the hardiness level of the previous day (HDP)" or "the HD of the previous day (HDP)"

L245 (Eq. 12): The variables "HFMortScalar" and "percentage" appear here for the first time without any explanation. What are these?

L262: Hd --> HD (italic)

L342: 0.55% --> 55%

L342: (Fig. 8b and c) --> (Fig. 8a and b) Note that Fig. 8c shows the CSM, not HFM.

L356: Insert "(Eq. (10))" to read "since HFM is a function of flc (Eq. (10))".

L359-360: I could not get the meaning of this sentence. Does it mean "The contribution of the changes in K_MAX, g0, and g1 to the reduction of HFM can be seen by comparing Fig. 8b and Fig. S12."?

L439: green --> red

L439: brown --> green

L440: dark green --> (light) blue

Figures 8a and b, S5a and b, S12a and b, S13a and b:  "Hydraulic mortality" in the vertical axis should be "Hydraulic failure mortality" to maintain the integrity of the terms.