I enjoyed reading this elaborated work on a sophisticated energy balance land surface model CLM5. It is well written and organized. Evaluating such complex model at hourly time step and at multi objective manner with Tikhonov regularization approach is novel as Tikhonov regularization has been usually applied in groundwater water models.

Specific comments:

Recent literature on spatial calibration of LSM is missing from Introduction section.

Some examples are as follows:

-Page2/41 Line24, doi: 10.5194/hess-21-2053-2017

-P2 Line 25 or 31, a small scale hydrologic study on spatial calibration using RS products can be included (doi:10.5194/hess-22-1299-2018).

-P2 Line 26 FLUXNET, doi: 10.5194/hess-21-5987-2017

-P2 Line 28, doi: 10.1029/2020WR028393

-Page 7 Line 11: “1000 years” please explain how?

-P7L14: “final simulations” why only before final simulations and not during calibration? Please explain more..

-P8L5 to11: this paragraph should be moved to the section 2.3 describing calibration approach to avoid repetition.

-P8L27: “Focus was given to a set of 30 time-invariant model parameters.” Apparently no sensitivity analysis was applied? Why?

-In a calibration framework it is essential to apply SA first to reduce search dimension. May be some of the 30 parameters have zero influence on the objective function? Did you utilize PEST’s local sensitivity analysis option?

-Section 2.3: The reader can be curious about several details of the calibration framework.

1)what was the user defined maximum number of iterations for such a sophisticated mode?

2)computer runtime statistics and cluster properties (logical processors, ram capacity, intel/amd etc)

2)Pest has three search algorithms LM, SCE-UA and CMAES. Can “Tikhonov regularization” be used together with one of these search algorithms?

3)sharing PEST control file “.pst” in appendices (or supplementary) can be good for this open access journal.

-only eq 10 is bias insensitive metric. Why the authors did not choose a spatial metric focusing on patterns of fluxes in growing season? Evaluating hourly (unstable) fluxes can be misleading. Instead evaluating monthly patterns of SWC, AET, SM can be a robust guide for the model. Fig 2-3-4 are showing only temporal aspects of the fluxes/states but this kind of finite element based LSMs can provide maps outputs. The authors should show also some map results. Looking at only time series can be boring.

-why Pareto approach was not used for multi-objective calibration to avoid dominating solutions. Pareto DDS algorithm (available in Ostrich) could offer multiple non dominating solutions. PEST doesn’t include this algorithm yet.

Denager et al. implemented multi-objective calibration of point-scale CLM5 using several types of flux/states observations of LE, H, recharge (q) and SWC from the Danish hydrological observatory HOBE. This topic of constraining model parameters against multi-source observations is quite relevant to the HESS journal, and it can be a valuable contribution to the community after addressing my following comments listed below. Additionally, the paper is clearly written and well-referenced; some parts require revisions, as follows. English typos should be double-checked, and some textual suggestions are further provided at the end. In the figures, I often can’t distinguish individual scenarios. Differences between individual calibration scenarios are not clearly depicted. Please, improve the readability of the figures.

1) Title requires modification. It needs to be clear from the title. that the calibration is for one point-scale site.

2) The abstract should be more concise and to the point, highlighting concrete results of the present study, and quantifying the results. So, please remove/rewrite too general statements, which are probably better suited for discussion of the results or conclusions. E.g. I suggest removing “Furthermore, reliability of the optimized model parameters can be estimated by statistical measures such as identifiability and relative error variance reduction. As in most other eddy covariance studies, closure of the land surface energy balance is not achieved on observation data.” The following statement, “The fact that CLM5 is not capable of matching sensible heat, not even with advanced parameter optimization of model parameter values, suggests that the lack of energy closure is due to biases in the sensible heat flux” is probably also not the most suitable one for the abstract. Instead, I would like to know from the abstract, which of the considered variable was most useful in improving the process representation. Did calibration of one variable improve the model’s predictive skill of another (uncalibrated) variable? Which one? Also, an abstract should mention at which site (i.e., agricultural field observatory in Denmark) the CLM5 is established.

3) Second half of the Introduction should clearly point out the research gap and your contribution to filling it in. Clearly stating the novelty of your manuscript somewhere in the last two paragraphs of the Intro.

4) Regarding the experimental design (Page 8, Line 8), please be consistent; earlier, you mention four variables (LE, H, recharge (q) and SWC); here, you mention six different observation data sources. Which one is correct, then? Please, synchronise, otherwise it is confusing. Table 1 already includes the calibrated parameter values, It is not clear how these parameters were identified when Table 1 was first introduced. From Table 1, it looks like you calibrated sand and clay contents directly. Was Clapp-Hornberger exponent B also part of the calibration process? As it is not part of Table 1. Please, clarify.  

5) Figure 1 is a rather set of tables than a figure. Increase the font and readability of the Table.

6) Why the calibration of LE (scenario A), does not improve the climatology of LE during March at all? (see Figure 4, please clarify)

7) How is it possible that the calibrated sand and clay values have such a large spread among scenarios? Sand[%] and Clay[%] could probably be well estimated by field measurements which you have available.  I would instead calibrate some parameters which can not be measured in the field.

8) It might also be interesting to see the scenarios aggregated into monthly seasonal values in addition to the diurnal climatology.

Data availability: under the provided link, data can not be easily found. Also, the processing codes are not available.

Textual suggestion:

Page 2, Line 13: practice is to use => practice to use

Page 3, Line 13: list of LSM is too short, why not be more extensive here, include some more operationally used LSMs.

Page 3, Line 25: correct parenthesis around the reference.

Page 4 Line 6: few => a few

Page 4 Line 13: observations are available => observations available

Page 4 Line 16: combine => combines

Page 5 Line 16: were => was

Page 5 Line 23: of => between

Page 6 Line 11: reach => reaches

Page 6 Line 24: leaf => leaves

Other textual English improvements should be double checked as well.

Overall, Denager et al presents an interesting and impressive study, involving a complex model (CLM), top-level observations (especially regarding the water balance) and an advanced calibration scheme for optimizing the model parameters. Yet, the results are somewhat contradictory, and the manuscript should be improved before acceptance.

I also find it a somewhat remarkable result, that such elaborate setups and multitude of observations are needed to improve the model performance. To me, it pointsrather to issues in the model (unless all issues can be blamed on the lack of energy balance closure). Given the text in the introduction, and especially the highly relevant quote by Clark et al., I question whether the approach of keeping the highly complicated LSMs and needing to perform elaborate model calibrations (involving a large number of observations really) really is a good way forward for the community. It would be interesting if the authors could comment on this aspect in the study.

Results and main conclusion: The many small tables of Figure 1 are hard to read and also hard to interpret. I assume that it is the results in these summary tables that lead the authors to their main conclusion “that mathematical regularization is a compelling method to improve current practice of using look up tables to define parameter values in LSMs” (a similar claim is made in the first paragraph of the Discussion, page 19).

The authors should explain clearly how they reach this conclusion, since their approach also shows obvious weaknesses. Compared to the control, several error metrices increase when applying the optimization. A further example is that they can only demonstrate improvement by letting observed soil content properties drift away from their observations values (page 17, lines 9-23). Doesn’t this rather point to a need for improving the model physics?

Another conclusion (lines 13-14, page24) is that use of soil moisture data in the optimization improved soil water storage modeling. Isn’t this a rather expected result? Maybe a quantification of this improvement would be vmore relevant, or a comment on how the model physics could potentially be improved for sites as well as a comment on what to do for the vast majority of sites where such elaborate measurements are not present.

The authors considerable emphasis on the question whether LE or H is the main culprit when it comes to the lack of energy balance closure (Conclusions, lines 18-20). They highlight that their results point to H, but their site appears to have many more observations related to the water budget than for the heat balance. Neither air nor soil temperature is used in any of the calibration scenarios. Could this result not have been the complete opposite, if they had instead focused on the heat budget and neglected to include all the soil water and moisture parameters? My recommendation is to treat this result with more caution, and at least remove it from the abstract. Rather, the authors should highlight other advantages of their results, for example the relevant conclusion stated on lines 21-25 of the Conclusion.

In agreement with another reviewer, I think that the manuscript would gain in value if the authors focused more on how to choose target calibration variables, and what the presented results tell could us in terms of method applicability and generality.

MINOR

Regarding conservation of energy (Eq 1). The equation should at least include the heating of the surface, the top soil and the air, which must be included in any land surface model.

Numerous places in the paper the term “physical laws” are mentioned and these should be replaced with the precise terms. Which physical laws are, for example, used to simulate H and LE (page 7, row 3)? LSMs typically apply parameterizations including many parameters.

Table 1: In two places, the percentage value of sand content exceeds 100% indicating that the parameter values have not been properly bounded.

Appendix A: The columns for X and Z appear to be swapped.

Appendix A: The authors claim that the site is homogeneous, which means that the measured LAI on the site is valid for the whole footprint of the EC flux observations. The scenarios based including LE tends to yield larger values for LAI compared to the observed values, which could indicate the presence of photosynthesizing plants in the footprint of the EC observations. There are very few sites that can be characterized as being completely homogeneous, and all inhomogeneities add to the mismatch between the model world and the real-world situation.