Having carried out hydrological modelling for the past 30 years it is interesting to see how the use of different performance criteria has developed. The Nash-Sutcliffe Efficiency (NSE) criteria has been the main criteria for flooding issues (and very often a general criteria on the overall performance of a model) for a long time. It has a number of well documented drawbacks but has the advantage of the values being widely understood. Kling-Gupta Efficiency (KGE) and its variants have become more popular recently but my feeling is that it is less well understood and some of the issues associated with its use have not been fully explored.

This paper is a useful addition to the subject of different performance criteria as it clearly shows that in the KGE there can be counterbalancing errors (i.e sometimes an over estimation and sometimes an under estimation of discharge) which produce a higher value without there being an improvement in the model. Whereas these counterbalancing error do not occur for the NSE. The authors summarize the issue and their contribution very well when they say “The aim of this paper is primarily to raise awareness among modellers. Performance criteria generally comprise several aspects of the characteristics of a model into a single value, which can lead to an inaccurate assessment of said aspects. Ultimately, all criteria have their flaws and should be carefully selected with regards to the aim of the model”

The paper is well written and presented. There is a good summary of the current state in the use of different performance criteria in hydrological models. The use of both a sythentic time series and a real case study gives more confidence in the issue of these counterbalancing errors.  Overall, it is a good bit of work with a clear conclusion reached. I am happy to accept the paper with minor revisions

Specific comments:

• I wonder if it would be useful to mention some of the benchmarking studies in hydrological modelling (e.g. Seibert et al. 2018) which I feel are a useful addition with regards to the performance criteria of the models.
• L98 (Equation 11). This is the Gupta(2009) equation. This is surely wrong as the last term should be minus not plus.
• L133-135. I do not understand this bit. I can see there are 361 transformation between -0.36 and 0.36 but I need not understand where the logarithmic scale comes in and how you get from here to the w values
• L195 (Figure 4). Would it be useful to also show the “Bad-Bad” model on this figure?
• Change “consisting in” to “consisting of”
• Maybe change “both ways” to “both sides” or “both directions”
• Change “succeed to reproduce” to “succeed in reproducing” or “successfully reproduce”
• L273-L274. “In general, the ANN model can be described as better because it is closer to the observed values in the high and low flow periods”. As a hydrological modeller I agree the ANN model is better. But surely the whole point of performance criteria is to objectively decide which model is better. So how do you decide it is better when the performance criteria do not agree? There is no easy answer but I feel it is an important question that should be considered in more detail.
• There is no reference to Figure 7, should it be here.
• L300-L303. I do not think this bit adds anything. I would remove these lines.
• In Equation 22 the order of the parameters is alpha, beta, r. On Line 344 and subsequent lines it is r, alpha, beta. This is confusing. So when you look at (1-2-2) and you look at equation 22 everything needs to be swapped around as the 1 corresponds to r which is the last term in the equation
• Change “associated to” to “associated with”
• Change “include to” “include the”

Seibert, J., Vis, M. J., Lewis, E., & Meerveld, H. V. (2018). Upper and lower benchmarks in hydrological modelling. Hydrological processes.

Gupta, H. V., Kling, H., Yilmaz, K. K., & Martinez, G. F. (2009). Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. Journal of hydrology, 377(1-2), 80-91.

Paper summary and overall evaluations

The paper examines several goodness-of-fit, skill scores used for hydrologic model evaluations based on the synthetic flow data and real simulation data. In the paper, the types of the skill scores are classified into two—1) multi-variant-based skill scores such as KGE (the skill score computed based on multiple metrics like bias, variability error, correlation etc. using distance measures) and its variants and 2) NSE. The paper focused on the impacts on the skill scores (also its components - bias and variability error if applicable), originating from the situation where under- and over-estimation on the peak flow can exist in one hydrograph. Also, the paper discusses compensation between the components of the skill scores, namely bias and variability. The paper concludes KGE type scores can be inflated for the hydrograph include both under- and over-estimation of the event (because of lower bias and variability error over the time series), which does not necessarily represent “accurate” simulations. The paper suggests that weighting KGE components mitigates this misleading score values. 

I think the hydrologic modeling community intuitively realizes this counter-balancing issue in the KGE type scores. The paper explicitly illustrated the issues clearly and would be nice reference for the hydrologic modelers. I think the paper is also in fairly good in shape in terms of the presentations and writing, and I don’t find any major comments, and only several minor comments.

Another thought: the overall results are mostly due to the fact that the skill scores use bias, instead of the error in the magnitude (e.g., root-mean square of error, absolute error). I wonder if it is worth trying modifying KGE components into two components - absolute error and correlation. I am not requesting the authors do (I don’t even know this is a good idea), but reading the paper makes me think about it. 

Minor comments

I do understand why NSE is included as “recommended skill scores” given the context of this paper, but still not sure if it is good idea to state so because NSE has one separate issue (underestimating variability so, peak-flow is underestimated and low flow is overestimated). I would suggest stating NSE is less impacted by counter-balance error in the hydrograph, but has its own issue for the practical applications.

Section 4.  In real case study, the paper use “reservoir model” for actually some bucket type, conceptual hydrologic model. I suggest avoiding using “reservoir model” because some readers (including me) are confused with reservoir “operation” model (i.e., lake model).

L264. The paper said “third flood event (May 2017) is better simulated by the ANN”. I don’t see this. Both ANN and reservoir models similarly underestimate the flows.  Also, the statements after because are unclear to me.

L269-273. I suggest using the dates to point which events are referred to.