Enhanced Prediction of Solar Radiation Using NARX Models with Corrected Input Vectors

Round 1

Reviewer 1 Report

This manuscript is about Solar radiation prediction using NARX models with enhanced input vectors. The main object is to analyze and set up the input vectors of the NARX models to enhance the solar radiation forecasting. I have some detailed comments listed below to help improving this article.

1, The title is ‘enhanced input vectors’, the final goal is to enhance the solar radiation forecasting. Could the authors think about a way to make the title more impressive?

2, It is not quite convincing that the conclusion is ‘using input vectors formed only with the solar radiation and the temperature’. Relative humidity should play important roles scientifically speaking. On the other side, suppose you only use solar radiation to do the solar radiation forecasting, the results might be also reasonable during most days. While it would be hard to forecast during sometimes period with abrupt condition changes. It’s true that more variables input without proper mechanisms would bring spurious results. While a forecast system should have the ability to develop to fit more cases.

3, Please elaborate the caveat and limitation of this study. What’s the next step for this study to improve?

Author Response

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Reviewer 2 Report

This manuscript presents a methodology based on NARX to forecast solar radiation. The topic of the paper is adequate for the journal. To my knowledge, using this particular methodology is relatively new matter within the solar radiation field. The application of the method to three different locations across Mexico, and the comparison with a standard method (persistence) gives additional value to this research.

However, a relatively important amount of work must be dedicated to the manuscript before being suitable for publication. I would like to rise two important points: 1) the structure of the paper; 2) the (lack of) rigor as far as the physics of solar radiation is concerned.  

Structure of the paper:

Initially, sections 1 and 2 are correct. Then section 3 has some deficiencies, such as using third level sections (3.2.1) as the only subsection of the second level sections. More importantly, section 3 brings “methods” in the title, and section 4 contains “methodology” which results in some confusion to me. Moreover, at least first part of section 4 (that is including 4.1 and at least part of 4.1.1) should come with last part of section 3, as it corresponds to computations related to the Smart Persistence method. Section 5.3 should also go much earlier in the manuscript, as this section is the explanation of the NARX methodology. Of course some details cannot be explained so early (for example, the exact composition of input vectors) but all actually, such detail is unnecessary. Figures 8-9-10 can be synthetized in one single figure, with one single panel. This figure would be more general, but this is what the reader needs to understand the method. Right now, in these three figures there are a total of 13 panels that basically explain the same thing. Fig. 5 and 6 could probably go earlier too.

Physics of radiation:

There are several matters to improve in this aspect. First, it must be said that radiation is a phenomenon, while irradiance and irradiation are different ways to measure it. Irradiance is power per unit surface (W m-2) so it may correspond to an instantaneous value or to an average. Then there is irradiation, which is energy, for a given period of time, per unit surface (J m-2). This seems to be the variable that is meant in this study, but it should be made clear to which time period corresponds (hourly, I think). Then, there are different symbols for the same variable (SR, I, I_clr, I_csk,…). What does it mean “maximum value of solar radiation”? (irradiance?, hourly irradiation?) I don’t understand the time (hours) variation shown in Fig. 3. Eq. 14-16-17 are empirical (or semi-empirical) expressions, this should be clarified and an adequate referencing is needed. It is mentioned that solar radiation presents seasonality and “seasonality every 24 hours”. The second cycle is not called seasonality, but daily cycle or daily evolution. Units are lacking is some tables (9-10-11) and figures (13). Other units have no sense (W/m2*h).

In addition to these two general and major comments, which need a bit of rewriting and restructuring of the paper, there are several other minor comments and technical aspects to be solved. I’m not going to give here an exhaustive list, as I leave it for a second round of review if the editor allows this second round. Nevertheless, I will mention some of these matters:

• From the very beginning (end of introduction) it should be made clear which variable are you going to forecast (hourly irradiation, if I understood) and in which time frame (so, ho long in advance: 1 day?)
• MSE and RMSE are obviously related indices; only one is enough to assess the performance (I would suggest RMSE).
• Figure 12 is unnecessary; you could show the increase of skill in an additional column in Tables 9-10-11.
• Figure 13. Instead of showing one week of data for each site, you could show, with more detail (more visibility), 1-2 days that allow to comment situations when Smart Persistence is better, and situations when NARX is better. This would also imply a little more interpretation and discussion of results; in the present manuscript, results are described but hardly ever they are discussed.

Author Response

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Round 2

Reviewer 1 Report

This version is fine. 

Author Response

Thank you very much!

Reviewer 2 Report

Authors have adequately addressed most of my previous comments. The paper may be accepted, provided that some minor changes are applied to further improve it.

Minor comments and suggested changes:

Abstract. It should be established from the very beginning that this are 1-hour in advance forecasts. This must be included in the abstract.

Line 23. Define SR here (it’s been done in the abstract, but it must be defined again in the main text)

Line 24. I would say that forecasting 1-h in advance is more relevant in “operation” than in “design”

Lines 65-66. The sentence “the above implies that for the model can rebuild a time series, it always needs a previous real data of the input variables” is unclear to me and should be rewritten

Table 2, Pyranometer range. The values given are not a range of possible measurements (as it is for other probes), but a range of the wavelength to which the instrument is sensitivity. I mean that these values doesn’t have the same meaning as for the other instruments.

Line 179. Sentence “when it passes from the extraterrestrial region to the terrestrial region through the atmosphere” can be simply (and more correct) written as “when it passes through the atmosphere”.

Line 186. You mean the “extraterrestrial hourly MEAN IRRADIANCE” (as I mentioned in my previous report, you should be careful in misuse of terms radiation, irradiance, irradiation).

Lines 192. “…solar IRRADIANCE…”

Line 226 states that “This section explains how the solar irradiation under clear sky conditions was calculated.” But this is not explained in this section (it has been done in previous sections). And, recall, you are working with irradiances, not irradiations.

Section 4.1. This should be explained better. How does fig 4 show which variables have collinearity? I’m not used to this kind of representation, so I can’t see what you mean. Moreover, to my understanding, collinearity is a property between two variables, so how come "only the temperature showed collinearity"? I would expect that a couple of variables show collinearity, but not a single variable.

Lines 298-299. What are FAC and FACP?

Lines 344-359. Most of this new text is unnecessary, as it is a summary of previous sections.

Line 361. And eq. (20) too.

Author Response

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Author Response File: Author Response.pdf