Total Variation-Based Metrics for Assessing Complementarity in Energy Resources Time Series

Round 1

Reviewer 1 Report

The proposal to improve the assessment of complementarity of sources is very well founded. Although the text is didactically very well written, there are few improvements to be made.

1) Line 73: substitute [3738] by [37,38].
2) Standardize symbol of total variation, in equations and in the text.
3) The graphs in figure 3 should be enlarged. It is difficult to read the subtitles.

Author Response

Dear Reviewer, thank you very much for your comments. Here we present you the improvements to our article, according to your recommendations:

1) Line 73: substitute [3738] by [37,38]. Answer: Corrected, thanks.

2) Standardize symbol of total variation, in equations and in the text. Answer: For total variation, we used a standardized symbol called "bigvee". Note that "Var" means variance, not total variation.

3) The graphs in figure 3 should be enlarged. It is difficult to read the subtitles. Answer: Corrected, thanks.

Reviewer 2 Report

In this paper are presented three novel indices based on total variation so that the complementarity in energy resources time series is assured.
These indices are the total variation complementarity index, the variance complementarity index and the standard deviation complementarity index.
Four interesting case studies are presented, of which three for real systems in Colombia.
My comments regarding the paper are:
- present with more details the work of other researchers in different countries;
- the title of the subsection should be "Case study 1", not "Case of study";
- add a Conclusions section.

Author Response

Dear Reviewer, thank you very much for your comments. Here we present you the improvements to our article, according to your recommendations:

1) Present with more details the work of other researchers in different countries; Answer: Included. Thanks.

2) The title of the subsection should be "Case study 1", not "Case of study" Answer: Corrected. Thanks.

3) Add a Conclusions section. Answer: Included. Thanks.

Reviewer 3 Report

This paper introduced three new metrics for assessing complementarity in energy resources time series. In general, it is good and clear. My comments are listed as follows:

1. In Lines 29 to 30, I suggest that this paper's work should be only mentioned at the end of introduction. This paragraph should only introduce the background.

2. “Anti-correlation” seems to have the same meaning as “negative correlation”. Please use either of them instead of using both in Lines 43 to 44.

3. When mentioning the drawbacks of existing metrics (especially from Line 43 to Line 57), is there any reference to support the outcomes? If yes, please add the reference.

4. In Equation 4, I feel that “n-2” should be changed into “n-1”.

5. Figure 3 is a little bit difficult to read. Please use a larger font for the words.

6. In Line 290, there is a typo: “dome” should be modified into “done”.

7. It is better to compare the assessment result between existing metrics (e.g., Pearson’s correlation coefficient) and the three new metrics in the case studies.

8. A conclusion section needs to be added.

Author Response

Dear Reviewer, thank you very much for your comments. Here we present you the improvements to our article, according to your recommendations:

1. In Lines 29 to 30, I suggest that this paper's work should be only mentioned at the end of introduction. This paragraph should only introduce the background. Answer: Corrected. Thanks.
2. “Anti-correlation” seems to have the same meaning as “negative correlation”. Please use either of them instead of using both in Lines 43 to 44. Answer: Corrected. Thanks.
3. When mentioning the drawbacks of existing metrics (especially from Line 43 to Line 57), is there any reference to support the outcomes? If yes, please add the reference. Answer: Almost all the papers related with complementarity quantify it with correlation coefficients, so it is not common to find paper which list the disadvantages of that type of metric. Our proposal is a new approach.  One reference of our previous work is this: D. Cantor, O. Mesa, and A. Ochoa. Complementarity beyond correlation. In J. JURASZ and A. BELUCO, editors, COMPLEMENTARITY OF VARIABLE RENEWABLE ENERGY SOURCES, pages 121–140. Academic Press, Elsevier, London, 2022.
4. In Equation 4, I feel that “n-2” should be changed into “n-1”. Answer: Corrected. Thanks.
5. Figure 3 is a little bit difficult to read. Please use a larger font for the words.  Answer: Improved. Thanks.
6. In Line 290, there is a typo: “dome” should be modified into “done”. Answer: Corrected. Thanks.
7. It is better to compare the assessment result between existing metrics (e.g., Pearson’s correlation coefficient) and the three new metrics in the case studies. Answer: The Pearson correlation coefficient varies between -1 and 1. For complementarity purposes, -1 indicates total complementarity, while 1 indicates zero complementarity. Now, the three new metrics in our paper vary between 0 and 1. A proper way of rescaling the Pearson correlation coefficient to vary between 0 and 1 to make it comparable with our proposal requires a better study. In the paper, one can see that rescaling Φv to Φ′ produces overestimations of complementarity. Perhaps future work may consider other more appropriate ways to rescale the indices. We will take into account your recommendation for future work. Thanks.
8. A conclusion section needs to be added. Answer: Included. Thanks.

Round 2

Reviewer 3 Report

The authors have addressed all my comments. I do not have any further question.