This paper presents a new objective function for automatic calibration of 3D hydrodynamic models based on water temperature and velocity data. The case study is a tropical lake, where the authors tested their DYNO+PODS for calibrating a Delft3D model against a subset of previously simulated 3D flow and temperature fields from a run assumed to be the "truth". I strongly appreciate this approach as it provides the full control of the optimization. Moreover, as the authors stressed many times (maybe too many, a lot of repetitions could be avoided), the use of velocity data together with water temperature is not so diffused yet in the field of lakes hydrodynamic modeling but it is crucial to have consistent results and realistic flow fields. Hence I welcomed the authors effort in quantifying how important it is.

Optimization algorithms as well as suitable objective functions for calibrating complex models are needed in the wide environment of hydrological numerical applications. I enjoyed the reading of the manuscript, which is well written and clearly structured. I appreciated how the authors describe their DYNO and tested its performances. Some clarifications are required, in my opinion, to make the optimization part (which is not the focus of the manuscript but still a key part of it) more accessible to the wide public of HESS, but in general I believe this work is worthy for publication on HESS after some minor revisions.

I’d like the authors to consider deepening the analysis on two more aspects which I believe worth a little discussion:

• Computational costs: Addressing this aspect is mandatory in a paper on optimization algorithms. The authors make some general considerations here and there, but maybe a dedicated paragraph would be more appropriate. My questions: 
  1. How many (real) runs of the hydrodynamic model were necessary to get the final solution for e.g. each trial/each configuration of Dyno (temp, vel, both)?
  2. What is the computational cost (wall clock time) of these tests? e.g. how much time compared to the error?
• Application to real data from observations: The authors auspicate that future users will test the DYNO against observations and so do I. So my questions are:
  1. Are there any constraints in the time/space frequency of the observations? In order to calibrate e.g. their Delft3D lake model to some temperature profiles and some current measurements, how should this data be? E.g. should temp and vel be simultaneous/in the same locations/same depths? As far as I understood, this is indeed the case of the data used in the authors' application, but this is not that common in standard monitoring schemes, where data are sparse and often not simultaneous. So basically, does this optimization (I guess this applies to PODS rather than DYNO) handle sparse observation? 
  2. Did the authors test their DYNO+PODS by changing e.g. the sampling time or the number of locations of their "truth"? I guess the more data the better, but I'd greatly appreciate some discussion on this. Is there an optimal number of locations/time frequency which gives a satisfactory calibration?

Attached are few minor comments/suggestions to improve the paper. 

Overview:

The manuscript is well-written and clear in its intent and results. It is close to publishable if the authors place their approach to calibration in the appropriate context. I am classifying this as "major revisions" because I think the issues are important, but they should not necessarily take a lot of work to implement.

Specific Comments

1.  I would have liked to see the introduction have a little that explains the context for the authors choice to test their calibration against a calibrated model rather than against observations. This choice gives them more data to compare against, but with the drawback that the "true" data are biased in exactly the same way as their calibrated results. This is an acceptable, but limited approach -- acceptable because it is useful in understanding and illustrating the new calibration method -- but limited in that it cannot be used to say anything about what might occur when compared to real world data.  This idea is emphasized in comment 2 below.

2.  I strongly disagree with the penultimate sentence of the abstract, that the study "suggests that both temperature and velocity measures should be used for hydrodynamic model calibration in real practice."  Similar language is found elsewhere in the paper. The model "suggests" nothing and we must remain skeptical about the value of calibration in a real world context without direct illustration of its importance. Unfortunately, the authors' methodology does not support this suggestion or any suggestion about real-world practice. The authors are testing their calibration against results of a calibrated model -- not the real world. The ability to more precisely capture the calibrated model (by a variant of the same model) cannot be used to imply that real world will be also represented more accurately.  This is a fundamental confusion of "precision" -- how close are my answers to grouped together, with "accuracy" -- how close do my answers reflect the real world. The authors have not included any comparisons of their model to real-world data hence they cannot make any statements or suggestions about likely accuracy in representing real-world phenomena.  

2.  If the authors want a stronger paper, they can either compare to real-world observations in a different time period as a classic validation test, or they can examine some important phenomena that are not directly included in the observational data set. For example, the timing  of global overturns of the lake are arguably an important phenomena that can be computed from real-world observed data -- the model results for the different calibrations in predicting timing of overturns could be analyzed. I may be wrong, but I suspect that the differences between the various models may not be as significant when compared in their prediction of a large-scale phenomena. The paper would still be publishable, but future researchers would be able to see that control of model biases are likely more important than calibration in capturing real world behaviors.

3.  The authors should include a comparison to an uncalibrated run (using conventional default values).

4.  The authors should discuss the choice of calibration parameters -- how were they chosen, why were they chosen, and what does it mean to hold these as constant parameters.  Arguably, a sensitivity study should have been done prior to choosing the calibration parameters. I am somewhat concerned about whether it is physically meaningful to calibrate as fixed parameters values that arguably depend on time-varying physics (e.g., Secchi depth, Ozmidov length scale, Dalton number, Stanton number).

5.  The authors should provide some discussion about the physical meaning of the errors in the results. For example, the Ozmidov length scale in the "true solution" is 0.015, but the "best" calibration has more than double this value; at the same time, the background vertical diffusivity in the calibration is about 3/5 of the true value and the Secchi depth is overestimated by 13%. These all exert controls on vertical mixing, and the wide disparities for different calibration methods makes me question as to whether calibration can really be effective to capture the complex, time-varying behaviors of vertical mixing in a stratified system with the given turbulence model. I do not expect the authors to solve such a problem, but I think they should discuss the implications. Replacing Table 5 with a well-constructed bar graph (with appropriate normalization) would help the readers see which parameters are doing all the work.

Path to acceptance:

The authors need to carefully limit their language so that the manuscript reflects what can truly be understood from the model and refrain from speculation about real-world behaviors unless they specifically bring new real-world comparisons into the manuscript.

Short summary of the manuscript

The authors present a new metric, the Dynamically Normalized Objective function (DYNO), the can be implemented in multi-variable calibration problems. Target variables in model calibration usually differ in their value ranges and error structures which can impede a balanced calibration for all variables. In an optimization procedure DYNO dynamically normalizes the error metric of each calibrated variable by the range its error metric that was identified until the respective iteration step. This range is dynamically updated in each iteration step. The normalized values are summed into a single metric that can be used in an optimisation search routine. 

The proposed metric is tested in a synthetic hydrodynamic lake model study, where 9 model parameters were optimized by minimizing the the errors between synthetic observation velocity and temperature data and the simulated values at different locations and depths.

General evaluation and major comments

Overall, I think the manuscript is well structured and the methodology is well prepared. The presented tables and figures support the findings that were presented in the text and provide good insights in the functionality of the presented algorithm. While I think the overall quality of the manuscript in its present form is already good, I see some crucial points that require clarification. Other less significant points should also be improved to improve the quality and readability of the manuscript. I will outline my major concerns in the following and will address smaller issues in a line-by-line notation in the following section. 

1. Synthetic study design:
   
   The observation data were generated with the same model structure that was later on investigated in the case study. Which means that "observed" variables (in this case velocity and temperature) were calculated with the exact same set of equations that in the following calculated the simulated variables. I think this property of the observation data could potentially impair the entire analysis and favour the simultaneous calibration of velocity and temperature.
   
   As the authors outline in section 3.5 of the manuscript, multi-variable calibration problems are often affected by trade-offs between the variables for which performance metrics should be optimized (minimized). One reason for that is that models are simplification of the represented reality and parameters can affect multiple processes, sometimes in the opposite directions. Thus a change of a parameter value into one direction could improve the performance of one metric, while deteriorating the performance of another metric at the same time. This is different in the synthetic example where in fact the reality and the model are the same thing. Thus the "observed" time series of velocity and temperature perfectly agree with the model simplifications and assumptions.
   
   Thus, in such a case providing both, temperature and velocity, to the search algorithm should better constrain the parameter response surface than only providing one of the two variables. If this hypothesis is sound, then the presented results would by affected by this effect. In this case only a real case scenario could provide an honest comparison of the three cases.
2. Number of iterations of the search algorithm
   
   This comment is somehow related to the previous one. In theory it should be possible for the search algorithm to identify the "true" parameter set that was used to generate the synthetic observation data. This global minimum is present on the parameter response surfaces of all three calibration scenarios and has a value of 0 independent of the used metric (DYNO or the single performance metrics). Thus, when not ending up in a local minimum all three cases should converge towards this global minimum. As outlined above, I simply think that the Cal-Both scenario does this quicker due to the given reasons. 
   
   In the presented results all "best" solutions did not find the global minimum. As far as I got it right from the text, each experiment involved 8 iterations with 24 parallel evaluations in each iteration step. Given a computation time of 5 hours per simulation run (according to the text and thus 5 hours per parallel iteration) one experiment takes 1.6 days. I am wondering if experiments with larger numbers of iterations were performed (that are maybe just not shown). I would be interested how the convergence of the three calibration experiments develops with larger number of iterations.
3. Consistency in the nomenclature
   
   Overall I think the outline of DYNO and the explanation of variables is well done. Yet, I found some inconsistencies in the nomenclature and some mathematical definitions that must be improved. I will address these (at least the ones that I found) in the line-by-line comments.
4. English language
   
   Overall I think the manuscript is well written. In some sections of the manuscript I found that the same errors repeat in every second line (e.g. singular/plural, missing articles). Although I am not a native speaker myself I had the impression that the manuscript could require some proof reading. Some sentences I had to read over and over again, but they still do not make sense to me. I addressed them as well in the line-by-line comments.
5. Non-color blind color theme in figures
   
   Although this does not affect me, I would advise to change the color theme in the figures and refrain to use red and green at the same time (8% of males are affected by red-green color blindness). 

Line-by-line comments

    

p.1 L13, p.4 L123 and further: Please use a consistent naming for Dynamically Normalized Objective function. Either all first letters caps or none. It differs throughout the text. Also only use the acronym after it was first introduced in the text.

p.1 L21 - 22: Please rephrase this sentence. Further, I think the statement is not universally true how it is formulated, that calibrating only one variable does not improve the calibration of another variable.

Eq. 2, Table 1: Consistent notation of Sim and Obs necessary. Either capital first letter or lower case. 

Table 1: Please rephrase the sentence: "The set of variables the observation data of which is used in calibration"

Table 1: I would suggest to add the vector {x₁, ..., x_d} to the definition of X as e.g. Table 2 refers to them.

Table1 and throughout the text: I would suggest to use the nomenclature Sim^k_j,t (same for Obs) in the definition and throughout the text to indicate the time dependency. This nomenclature is in fact introduced later in the manuscript. Also the definition refers to the time t which is not indicated in the variable.

p.5 L153: ...multiple variables with a single objective function.

p.5 L159: Please remove \textit{value} as the distribution of NRMSE is not a single value.

p.5 L160: Same as above.

p.5 L160: Hence , ...

p.5 L163: Again consistent naming of DYNO or removing the full name as the acronym was already introduced.

p.5 L166: ...all evaluations in ψ found so far?

p.5 L166: The variable ψ was not introduced at this point and is I think not defined in the manuscript.

p.5 L167: The mathematical formulation...

p.6 L172: ...all evaluations ...

p.6 L172 - 174: Please rephrase this sentence. It is in my opinion not clear what is meant.

p.6 L180 - 185: The procedure as described is confusing and does not really make sense to me. A calibrated model exists from a previous study. This calibrated model was taken, but different parameters based on "expert guessing" were then used to run the model. So it is not the calibrated model anymore?

p.6 L186: Replace a by the as you did not use a parameter set but the parameter set X^R.

p.6 L193: ...the true values of the parameter vector X^R are...

p.6 L194: I would replace value with set.

p.6 L202 - 203: This sentence is not clear to me.

p.7 L226: coefficients

p.8 L229: the Manning formulation

p.8 L229: ...which is a parameter tha should also be calibrated.

p.8 L232: ...are parameterized...

p.8 L237: Manning coefficient

Section 2.5: This section is actually a repetition of L146 - 150

p.9 L280: Remove them

p.9 L287: I would suggest to replace a roughly by an approximately

Caption Table 3: formulations

p.10 L309: Use the acronym DYNO instead

p.10 L317: Replace is with are

Figure 2: The positions of the labels Yes and No in the stopping criteria are not clear to me.

p.12 L359 - 366: The argumentation in this paragraph could be affected by the affect of synthetic observation data as outlined in the first major remark.

p.13 L395: Missing end '.' of sentence?

p.13 L395 - 399: This sentence is confusing and might require rephrasing.

p.14 L406 - 416: I had the impression that many articles were missing here. This paragraph is hard to read in general and could potentially be revised.

p.15 L431: the calibration...

Figure caption Fig. 5 L451: in terms of...

Figure 6: Values in the darkest hex tiles are almost not readable.

p.19 L536 - 539: This sentence was not clear to me and might require revision.

p.20 L553 - 566: Again, the argumentation in this paragraph could be affected by the affect of synthetic observation data as outlined in the first major remark.

p.20 L573: Remove these

p.20 L574: suggest to have

p.21 L613: We conclude that the Dynamically Normalized Objective Function that we propose