The Second Derivative of the NDVI Time Series as an Estimator of Fresh Biomass: A Case Study of Eight Forage Associations Monitored via UAS

Round 1

Reviewer 1 Report

The goal of the paper is to show that the second derivative of an NDVI time series can highlight the key points of the growing cycle, and to pinpoint the best period to estimate fresh biomass in fields across eight intercropping forage mixtures. 

The core of the work is to estimate biomass directly from the time series of NDVI instead of ? (crop transpiration coefficient) and on the estimation of the ?0 and ? limits of the summation based on the NDVI curve derived from UAV imagery. They find the time (t) limits by finding the 2nd derivative of a spline smoothed NDVI curve and multiply NDVI by an expansion factor and sum to get biomass. 

The experiment is performed in an ideal setting, with 8 fields of varying crops. 

They validate the model using field-measured biomass from the same time as UAV flights. 

I think it works, based on the validation, but I am not sure about the use of the correlation coefficient of Pearson R instead of R2? Is it because R will be higher than R2?  I think you are trying to predict biomass with NDVI, so you should use R2. An R value of 0.8 would be an R2 of 0.6, which is still strong in environmental work. Also, R2 is used in Figure 4, to measure the relationship between NDVI and biomass, so I do not know why it isn't used elsewhere. 

Aspects to address: 

- How many UAV flights is enough to capture the seasonal time series? 

- When to start and when to stop flying? How do you chose? 

- Is there any sensitivity to the interpolation/smoothing algorithm you chose for the NDVI curve? Or is spline the only way to go? 

- Would NDRE provide any additional information if you had a Red-Edge camera? 

Minor comments: 

Line 192: Plaza et al. (2021) should have a formatted reference. 

Author Response

The goal of the paper is to show that the second derivative of an NDVI time series can highlight the key points of the growing cycle, and to pinpoint the best period to estimate fresh biomass in fields across eight intercropping forage mixtures. 

The core of the work is to estimate biomass directly from the time series of NDVI instead of ? (crop transpiration coefficient) and on the estimation of the ?0 and ? limits of the summation based on the NDVI curve derived from UAV imagery. They find the time (t) limits by finding the 2nd derivative of a spline smoothed NDVI curve and multiply NDVI by an expansion factor and sum to get biomass. 

The experiment is performed in an ideal setting, with 8 fields of varying crops. 

They validate the model using field-measured biomass from the same time as UAV flights. 

I think it works, based on the validation, but I am not sure about the use of the correlation coefficient of Pearson R instead of R2? Is it because R will be higher than R2?  I think you are trying to predict biomass with NDVI, so you should use R2. An R value of 0.8 would be an R2 of 0.6, which is still strong in environmental work. Also, R2 is used in Figure 4, to measure the relationship between NDVI and biomass, so I do not know why it isn't used elsewhere. 

Thank you for this remark. Following this suggestion, we kept R for the exploratory analysis, i.e., the comparison between NDVI observations and the biomass measured at each date (Section 3.1) and we use R² instead for the validation, i.e., to assess the accuracy of the prediction. See changes in lines 24-25 (abstract), 318-319 (2.6, Methods), 424-428 (3.3., Results) and 584 (Conclusions).

Accordingly, the R² in figure 4 has been removed and Tables 6 and 7 have been modified.

Aspects to address: 

- How many UAV flights is enough to capture the seasonal time series? 

Here to performed height flights to characterize the phenologic cycle in its main stages, i.e., leaf development, tillering, booting, heading, flowering, fruiting and ripening, until the senescence. Strictly, only four to six points would have been required for the calculation, corresponding with the main changes in the curve, as seen in figure 3. See new lines 183-184 in the 2.2 Section addressing this explanation.

- When to start and when to stop flying? How do you chose? 

All the flights took place at midday to avoid shadows. Their duration (always the same) was 12 minutes. Please, see lines 179 to 181 in Section 2.2. explaining the mission planning.

- Is there any sensitivity to the interpolation/smoothing algorithm you chose for the NDVI curve? Or is spline the only way to go? 

This interpolation aimed to retrieve a continuous second derivative, as spline does as well as many other polynomial approaches. We chose spline interpolation because it balances smoothness and simplicity. In fact, the software we used (Origin Lab) did not offer any other algorithm excepting for linear interpolation (which was obviously discarded) and beta-spline, which smoothed the curve too much. Frankly, I am not an expert in this matter as to discuss in deep the consequences of other interpolations. We are working in a second test of our WP*NDVI approach with Sentinel 2 and Landsat 8-9 and I think it would be a good opportunity to evaluate other interpolation alternatives. We really appreciate this comment.

- Would NDRE provide any additional information if you had a Red-Edge camera? 

We tried different vegetation indices based in the red-edge band in a previous publication with the same dataset (Plaza et al., 2021). In that work, we correlate a set of indices with different crop parameters (biomass, among others) and we did not find any advantage in using NDRedEdge. On the contrary, the indices based in the red-edge band did not perform well to depict structural parameters such as LAI and biomass. The NDVI was the best positioned to estimate biomass. This is the reason we chose it.

We added lines 540 to 545 in the discussion section to include this idea, and again, we thank the reviewer for this remark.

Minor comments: 

Line 192: Plaza et al. (2021) should have a formatted reference. 

The reviewer is right, thank you. Done

Author Response File: Author Response.docx

Reviewer 2 Report

The results investigated by them are unique well presented as mathematical way. Finally authors presented second derivative and discussed the NDVI time series results. The results of this study seem interesting and can be implemented by other researchers to use the current approaches. The whole manuscript seems good, however, there are some points needed to be considered before the manuscript is accepted:

1.) The abstract section needs to elaborate more on the results. More information needs to be added in the abstract section.

2.) Overall, in the introduction section, you need to explain more about the current issue and problems, then provide a perspective on how to refine the problems.

3.) I suggest the authors to explain more about the image pre-processing. Did you apply atmospheric correction? What are the pre-processing that you have applied to the images?

4.) The discussion part needs to be improved. You need to explain more about your research and compare the results with previous studies. Also, bring the strengths and the limitations of this research into the discussion and discuss them.

5.) On what basis you minimized the mean absolute percentage error of prediction for biomass estimation accuracy?

6.) What threshold values of overall accuracy you considered in RMSE statistic (eqn. 4^th)?

7.) Present an explicit and clear algorithmic steps used in this study data simulation. Please share the codes so that everyone can repeat the experiment.

8.) Use the high resolution image for Figure-3 and Figure-4.

9.) Please check the paper for some grammatical and punctuational errors.

10.) There is a need of couple of more proper reference to support this study.

The paper should be proofread for sentences flow, English grammar correction, and spelling mistakes. 

Author Response

The results investigated by them are unique well presented as mathematical way. Finally authors presented second derivative and discussed the NDVI time series results. The results of this study seem interesting and can be implemented by other researchers to use the current approaches. The whole manuscript seems good, however, there are some points needed to be considered before the manuscript is accepted:

1.) The abstract section needs to elaborate more on the results. More information needs to be added in the abstract section.

We agree with this comment. However, the Journal instructions stated that “the abstract should be a total of about 200 words maximum”. Actually, we have 249, so it seems difficult to add more information. However, and owing another comment of the first reviewer, we added a sentence about the determination coefficient results in lines 24-25.

2.) Overall, in the introduction section, you need to explain more about the current issue and problems, then provide a perspective on how to refine the problems.

The reviewer is right, some focus on the problem about yield estimation should be included. Following this comment, we added a new paragraph in lines 49 to 58 and a new reference.

3.) I suggest the authors to explain more about the image pre-processing. Did you apply atmospheric correction? What are the pre-processing that you have applied to the images?

The radiometric calibration, together with the light condition’s correction, guaranteed the stability of the images regardless of the illumination conditions and the sensor characteristics. In addition, owing the low drone missions height (43 m), the atmospheric interactions were considered negligible, so no correction was done. In this case, the typical processing chain for airborne o satellite optical instruments, which is often based on the ATCOR method or similar approaches, is not adequate. Please, see lines 186 to 207 in Section 2.2.1 and lines 535 to 540 in the Discussion section. The mission planning has also been added in lines 179-184, Section 2.2. We hope all the pre-processing is described in detail.

4.) The discussion part needs to be improved. You need to explain more about your research and compare the results with previous studies. Also, bring the strengths and the limitations of this research into the discussion and discuss them.

Thank you very much for this comment, which contributes to a deeper insight about our approach. We have enlarged the Discussion section regarding: a) the advantage of an early-season estimation (lines 472 to 475), b) other approaches similar to ours (lines 504 to 505), c) the need of robust calibration and correction of the sensor images and the use of other bands instead of red/NIR (lines 535 to 540), and finally d) the potential use of remote sensing sensors instead of costly drone campaigns (lines 563 to 567).

5.) On what basis you minimized the mean absolute percentage error of prediction for biomass estimation accuracy?

I am afraid I could not find an accurate response to this comment. We did not perform any post-treatment to the errors. If the reviewer asks for a way to refine the procedure, I can refer to lines 482-484, in which a potential way to sharpen the calculation and reduce the errors is described by means of adjusting the WP* coefficient.

6.) What threshold values of overall accuracy you considered in RMSE statistic (eqn. 4^th)?

Thank you for the comment, but it is difficult, owing the different values of yield weight, to stablish absolute thresholds of RMSD. Instead, we preferred MAE in percentage as a way to depict the accuracy assessment, as in many other literature (please, see the Discussion section lines 491 to 509.

7.) Present an explicit and clear algorithmic steps used in this study data simulation. Please share the codes so that everyone can repeat the experiment.

The idea you suggest is interesting and therefore we are willing to upload, if possible, all the dataset to the Drones journal and to share it with the scientific community. Regarding the computing codes, actually did not use any particular algorithm, code nor script, since the calculation is very simple and may be performed in any statistic package or conventional spreadsheet. Only a time-series interpolation and a multiplication are needed.

8.) Use the high resolution image for Figure-3 and Figure-4.

I am sorry for this issue. All figures have been created at 300 ppd, but the resolution of the resulting file when uploading the material might have distorted the original quality.

9.) Please check the paper for some grammatical and punctuational errors.

We are sorry for the errors. English proofreading has been performed using the MDPI editing service.

10.) There is a need of couple of more proper reference to support this study.

We added the following new references:

- [6] FAO Handbook on Crop Statistics: Improving Methods for Measuring Crop Area, Production and Yield; Pasetto, L., Ed.; FAO Statistics Division (ESS), 2018

- [61] McBratney, A.; Whelan, B.; Ancev, T.; Bouma, J. Future Directions of Precision Agriculture. Precis. Agric. 2005, 6, 7–23, doi:10.1007/S11119-005-0681-8/METRICS.

- [62] Sekhar Panda, S.; Ames, D.P.; Panigrahi, S. Application of Vegetation Indices for Agricultural Crop Yield Prediction Using Neural Network Techniques. Remote Sens. 2010, 2, 673–696, doi:10.3390/rs2030673.

- [69] Ji, Y.; Chen, Z.; Cheng, Q.; Liu, R.; Li, M.; Yan, X.; Li, G.; Wang, D.; Fu, L.; Ma, Y.; et al. Estimation of Plant Height and Yield Based on UAV Imagery in Faba Bean (Vicia Faba L.). Plant Methods 2022, 18, 1–13, doi:10.1186/S13007-022-00861-7/TABLES/4

- [72] Janoušek, J.; Jambor, V.; Marcoň, P.; Dohnal, P.; Synková, H.; Fiala, P. Using UAV-Based Photogrammetry to Obtain Correlation between the Vegetation Indices and Chemical Analysis of Agricultural Crops. Remote Sens. 2021, 13, 1878, doi:10.3390/rs13101878

Author Response File: Author Response.docx