Optimal Estimate of Global Biome—Specific Parameter Settings to Reconstruct NDVI Time Series with the Harmonic ANalysis of Time Series (HANTS) Method
Round 1
Reviewer 1 Report
This paper presented a study on the optimisation of user-defined parameter values of HANTS for reconstructing NDVI time series at the global scale. It determined the optimal values for the number of frequencies, fitting error tolerance, degree of over-determinedness, and regularisation factor by assessing the performance of the HANTS model for the reconstruction of NDVI time series over 20 years. The methodology is sound and the results are correct and were well discussed. There are some very minor English grammar errors. I suggest the authors carefully proofread the paper again and do some minor text editing.
Author Response
We appretiate the suggestions from the reviewer. And we checked the whole manuscript again for grammer errors and revised accordingly.
Reviewer 2 Report
Hi Authors
Can you please attend to the comments on the attached PDF.
Regards
Comments for author File: 
Comments.pdf
Author Response
We had responsed each comments in the PDF. Please see the attachment.
Author Response File: Author Response.pdf
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
Comments as below:
- Zhu et al. (2015) suggested a method to predict Landsat surface reflectance at any given time. Can you compare your method with this one from the principle and results?
- How will the algorithm perform on the cropland especially double cropping?
- Page 5, Line 168, can you introduce more about the BELMANIP2 sites from the perspectives of land cover types or vegetation type of these sites and the clear data frequency of these sites?
- For the result session, I suggest using ecoregion (or other zonal analysis) to summarize the optimal parameter configuration. The descriptions are too subjective. For example, “such as tropical rainforest regions, since the small seasonality of NDVI can aggravate 426 collinearity of the observations and the solutions of the system of equations. For high latitudes, a Delta <0.5 is preferred”, what regions are humid area and high altitude? Otherwise, the analysis is meaningless, readers hardly get useful advises in their future researches.
- The limitations of the method are not fully addressed.
Reviewer 2 Report
The basic idea of harmonic regression has been applied to a range of problems in remote sensing for quite a long time, but there are still open questions and the basic motivation of the paper is valid. However, I have major concerns about the presented research that will be discussed below.
Issue 1: Reference data
From line 50 to line 86, the authors correctly outline the problem of artifacts (i.e. invalid observations due to clouds and other atmospheric conditions) in time series data and why techniques like the presented iHANTS are necessary to reduce their effect. The logical consequence is that any QC information like the one supplied with the used MOD09GA product must be flawed – otherwise there would be no need for further noise reduction or outlier elimination with algorithms like HANTS. However, the authors claim that a „time series generator“ described in Section 2.2.2. somehow uses this flawed QC information to create reference, artifact-free time series. In my opinion, the QC information, which is itself unverified, cannot be used to generate a valid reference. I understand that acquiring good reference data is often a problem in remote sensing, but the described workaround it is not scientifically sound.
Issue 2: Methodologically questionable properties of the HANTS method
The design of the Fitting Error Tolerance (FET) parameter, which also acts as outlier threshold at the same time, is hardly an optimal solution. The fact that it needs to be given as an absolute value in data units makes it very hard to tune and generalize for different situations. Since the authors apply an iteratively reweighted least squares approach, they might be familiar with the work of Huber (1964) and later approaches to robust regression which use thresholds based on probabilities and data-driven weighting. Standard implementations of these approaches have no restriction regarding the direction of outliers, but they could be easily adaptable to problems (like NDVI fitting) where this is appropriate.
The authors should also rethink the Degree of over-Determination (DoD) parameter, as the present definition as an absolute number of observations in the range 0 – 12 can lead to strange situations. An example: Lets assume a model with 3 frequencies (NF=3) should be fitted using N0=23 observations (compare line 265). At least 7 valid observations are required for a solution, however, we also set DoD to a value of 3 to ensure some overdetermination. With this setting, the algorithm may in theory discard as many as 13 observations (=56% of the total) as outliers (7+3+13=23). To my knowledge, statistical literature agrees that no robust method can identify more than 50% of the data as outliers, because “if more than half of the observations are contaminated, it is not possible to distinguish between the underlying distribution and the contaminating distribution Rousseeuw & Leroy (1986).“ (cited from Wikipedia accessed on 2021-04-25, https://en.wikipedia.org/wiki/Robust_statistics#Breakdown_point).
Allowing a very low DoD (or even none) makes no sense for a robust regression method, since the power to correctly identify outliers comes from overdetermination. Very low DoD values also explain the problems described in line 268 to 270. With almost no overdetermination, numerical instabilities occur. With enough overdetermination, e.g. using at least as many observations as two times the number of parameters to estimate, I know harmonic regression to be very stable.
As a last remark, to me the conducted research seems a little out-dated. More sophisticated implementations of harmonic regression based on data-driven parametrization are in use for change detection and classification applications for several years now, but they can also be applied for gap-filling (Zhu et al., 2015).
References
Huber, P. J. (1964). Robust Estimation of a Location Parameter. The Annals of Mathematical Statistics, 73-101.
Zhu, Z., Woodcock, C. E., Holden, C., & Yang, Z. (2015). Generating synthetic Landsat images based on all available Landsat data: Predicting Landsat surface reflectance at any given time. Remote Sensing of Environment, 162, 67-83.
