Using Block Kriging as a Spatial Smooth Interpolator to Address Missing Values and Reduce Variability in Maize Field Yield Data

Round 1

Reviewer 1 Report

The article is stressing a methodological approach to estimate average production levels based on small plots - the analysis is limited and not adequately presented.

Methodology
- adding formulas to explain the difference between Log10, Point Kriging & Block Kriging could add value and readability
- Border of ONE plant are considered largely insufficient from most authors - please add some reference that allow you to adopt such a method
L119-121 better immediately after sentence '..Gaspardo'.
L147-148 '..whereas .. grids.' - not clear

Results
- Please add Measure Units (kg/m2, t/ha)
L233 - 'demonstrated graphically' is a non scientific statement
Figure 4 - There is no reason to connecting points -please consider to adopt another kind of meaningful graph
Figure 5 - The surface plot are used to interpolate values and increase resolution - in this case they are meaningless as plant data are pointwise - suggest to remove

Table 5 - suggest add semi-variograms

Discussion
The section should be about results (discussing tables and figures etc) - Apart of some contents (L275-281, L288-290) that seem more appropriate in introduction, most of the contents should be placed in conclusion.

The article is written in a comprehensible English
but should be refined, as in e.g.
L29 - '..variance ..' -> '.. variability ..'
L36 -'..extreme values..' -> '..outliers..'

Author Response

We would like to thank the reviewer for his/her valuable comments.

Reviewer comment 1: "The article is stressing a methodological approach to estimate average production levels based on small plots - the analysis is limited and not adequately presented."

Response on comment 1: We added a new section in the text regarding the theoretical background of log-transformation and Kriging. In addition, we modified Figure 4 by including the results of the two interpolation methods vs the original data for the three plots, along with the scatter plots regarding the results of the “measured vs estimated (for both Point and Block Kriging) data”. This was made to facilitate understanding of the outcome resulted from the application of the proposed methodology. A short text was also added to explain the importance of the contour maps as a tool that allows comparison between Point and Block Kriging results, which indicates clearly the smoothing effect provided by Block Kriging.

Reviewer comment 2: “Methodology: - adding formulas to explain the difference between Log10, Point Kriging and Block Kriging could add value and readability”.

Response on comment 2: Done. Instead of just adding formulas for the methods of log10-transformation and Kriging, we added a separate section (as theoretical background) explaining the different approach of each method along with their corresponding equations used for the estimation of the values. We believe that this addition will further enhance the readability and understanding of the proposed methodology.

Reviewer comment 3: “- Border of ONE plant are considered largely insufficient by most authors - please add some reference that allow you to adopt such a method”.

Response on comment 3: Done. Following the instructions of the reviewer, we added references to support the choice of having only one plant as field margin and a short text explaining how we set the ‘crop edge’ in our case study. As mentioned in the text now (line 53), margin plants are not used in some plot experiments, while in other experiments a specific number of plants or a “crop edge” field margin is used to control various factors depending on the experimental design used and the purpose of the study. For example, in a four-treatment plot experiment, Ndakimemi et al. (2022) used an only 0.5 m field margin in their plots with dimensions 15 × 15 m. Additional relative information was added to the text.

Reviewer comment 4: “L119-121 better immediately after sentence '..Gaspardo'.

Response on comment 4: Done. Moved just after “.. Gaspardo”.

Reviewer comment 5: “L147-148 '..whereas .. grids.' - not clear”.

Response on comment 5: Done. Deleted.

Reviewer comment 6: “- Please add Measure Units (kg/m2, t/ha)”

Response on comment 6: Done. Added “(g per plant)”.

Reviewer comment 7: “L233 - 'demonstrated graphically' is a non-scientific statement.”

Response on comment 7: Done. It is now replaced by “revealed”.

Reviewer comment 8: “Figure 4 - There is no reason to connecting points -please consider adopting another kind of meaningful graph”.

Response on comment 8: Done. Following the suggestion of the reviewer we removed the lines connecting the point values. In addition, we have also added three new graphs to display the results in a better way.

Reviewer comment 9: “Figure 5 - The surface plots are used to interpolate values and increase resolution - in this case they are meaningless as plant data are pointwise - suggest to remove”.

Response on comment 9: Contour maps are used to enhance the understanding of the methodology as they allow comparison between the original data and the results of the interpolation methods. The main goal of these maps is not to increase resolution, but rather to estimate missing values (spots with no values in Figures 1 and 2) and provide a visual representation of the 'smoothing' effect produced by Block Kriging compared to Point Kriging. Therefore, we believe that the contour maps should remain in the manuscript as they contribute to better understanding of the existed differences between the Kriging methods used.

Reviewer comment 10: “Table 5 - suggest add semi-variograms”

Response on comment 10: We provide in the text (Table 5) the geostatistical variables of the best-fitted variogram models for both Point and Block Kriging data in the three field plots and the measures for the cross-validation of the results (R², RSS, RMSE). If needed, we can provide the semi-variograms in a supplementary file; we believe that adding more detailed info about variograms is out of scope since the aim of the manuscript is not to choose the best variogram type or interpolation method but rather to compare the results of an interpolation method to the commonly used so far log10-trasformation method.

Reviewer comment 11: “Discussion - The section should be about results (discussing tables and figures etc) - Apart of some contents (L275-281, L288-290) that seem more appropriate in introduction, most of the contents should be placed in conclusion."

Response to comment 11: Done. Following the suggestion of the reviewer we moved the paragraph “Summarizing .. large areas” to the conclusions.

Reviewer comment 12: “The article is written in a comprehensible English but should be refined, as in e.g. L29 - '..variance ..' -> '.. variability ..', L36 -'..extreme values..' -> '..outliers..'"

Response to comment 12: Done. We made modifications throughout the text. We would like to thank the reviewer for his positive feedback and suggestions.

Reviewer 2 Report

Manuscript evaluation

Summary

This research compares the performance of log10-transformation and Block Kriging in reducing the variability and estimating fresh weight (FW) plant maize fresh weight. The main objectives were to verify whether maize plants harvested in the border rows significantly affect the variability and mean values of those grown in the central rows and whether block kriging is preferred over log10-transformation. The authors masterfully argue and justify their study, describing the main limitations of the method most commonly used to reduce the existing data variability between experimental units (which is the log10-transformation of raw data). The state of the art is well outlined and the research objectives are clearly stated. Materials and statistical methods were adequately described and the main questions posed in the research were addressed. In the results, the authors listed their main findings, which are highlighted in their main conclusions. Block kriging, proposed as an alternative to log10-transformation, proved to be more suitable for reducing data variability without changing means, leading to more accurate estimates of crop yield, estimating and filling in missing values, smoothing non-representative values or extremes, adjust the estimated values to take into account the spatial correlation of the experimental units, among others. And that corresponds to a legitimate contribution in the field of knowledge.

 

General concept comments

Overall, the text is well written and organized. However, I believe that some results could be better presented. The discussion could also be expanded with more emphasis on the main findings of the authors. Finally, the conclusion could be improved, to make the main results clearer to the reader. The authors place a summary before presenting the main conclusions. I believe it would be better to withdraw this summary; list the main conclusions and in item 2) put the information that is in this introductory summary.

 

Revision

The subject addressed in the research is very interesting. The importance of the theme is well placed by the authors in the introduction. The limitations of the log10-transformation are well emphasized and the negative implications of its use have been clearly considered. By proposing the comparison of Block Kriging with the log10 transformation, the authors address an important gap, that is, to verify the efficiency of the proposed method in comparison with the one more traditionally used to reduce variability in data, evidencing the use of more efficient tools.

I believe that the material, experimental design and control methods used are appropriate for conducting the study. This was stated in sufficient detail to allow replication of the research by other researchers.

In the results section, the authors focused on the main results found and were faithful to the research objectives. The wording of the text is clear. However, I would like to draw attention to subsection 3.5, in which the description of the results in Table 5 was overly summarized. It is important to make the results and discussion clear to the reader. Tables and graphs, in general, are in sufficient quantity and quality, allowing the interpretation and illustration of the results. I draw attention only to Figure 4, where in the caption it is almost impossible to see the dot in front of “all original”.

In the “conclusions” subsection, the authors were also faithful to the main results, according to the objectives. However, the authors present a short summary of the results before actually presenting the main conclusions. In this sense, the text would be clearer if the authors started with the main conclusions and put the information in the introductory summary, in item 2) which specifically speaks of the advantages of the Block Kriging method.

The references used are relevant, current and appropriate. These references are well mixed, contributing to the contextualization, justification and validation of the research results and conclusions.

Specific Comments

The manuscript is generally well organized and structured. However, I would like to highlight some points that could be improved.

1) In the caption of Figure 4, I almost couldn't see the dot in front of “all original”. Would it be possible to improve this?

2) In item 3.5 of the results, the authors mention that the most appropriate adjusted model for maize data interpolated by points and blocks in the three field plots was the exponential. Based on what do the authors say this? A call to Table 5 is placed, but it only presents the results of the exponential model and does not show why this model would be the most suitable compared to any other. In addition, the authors draw attention to the fact that “the R2 values calculated from the adjusted exponential variogram models in the corn fresh weight data interpolated by block kriging were greater than the respective R2 values of the punctual kriging data in the three plots ”. What does that mean? It needs to be made clear to the reader. Furthermore, in Table 5 more comparison measures are presented, but they were not mentioned in the text. This information needs to be better described and what it means. This has not been discussed comprehensively. I recommend improving the wording, considering the measures highlighted in Table 5, to make this clearer to the reader.

 

3) In the “Conclusions” section, the authors present an introductory summary with the main advantages of the block kriging interpolated method. Then they make a call for the main conclusions. To make the text clearer, I suggest that the authors start by describing the main conclusions and put the information from the introductory summary in item 2) that describes the main ones for block kriging.

 

Comments for author File: Comments.pdf

Author Response

Response to Reviewer 3

We would like to thank the reviewer for the valuable comments and suggestions for our manuscript. We addressed all the issues mentioned and we tried to make improvements throughout the manuscript. Please, find below a point-by-point description of how each comment was addressed.

 Reviewer comment 1: "The subject addressed in the research is very interesting. The importance of the theme is well placed by the authors in the introduction. The limitations of the log10-transformation are well emphasized, and the negative implications of its use have been clearly considered. By proposing the comparison of Block Kriging with the log10 transformation, the authors address an important gap, that is, to verify the efficiency of the proposed method in comparison with the one more traditionally used to reduce variability in data, evidencing the use of more efficient tools."

Response to comment 1: We would like to thank the reviewer for the positive comments on the proposed methodology.

Reviewer comment 2: “I believe that the material, experimental design, and control methods used are appropriate for conducting the study. This was stated in sufficient detail to allow replication of the research by other researchers.”

Response to comment 2: We would like to thank the reviewer for his very positive feedback.

Reviewer comment 3: "In the results section, the authors focused on the main results found and were faithful to the research objectives. The wording of the text is clear. However, I would like to draw attention to subsection 3.5, in which the description of the results in Table 5 was overly summarized. It is important to make the results and discussion clear to the reader. Tables and graphs, in general, are in sufficient quantity and quality, allowing the interpretation and illustration of the results. I draw attention only to Figure 4, where in the caption it is almost impossible to see the dot in front of “all original”.

Response to comment 3: We would like to thank the reviewer for his very positive feedback. Regarding Table 5, we added some text to elaborate on the data presented. Also, we fixed some values in Table 5 that were transferred incorrectly in the text. In Figure 4, we added a plot at the left of the graphs, and we drew cross sections representing locations of data on the right side. By setting cross sections, we believe it improves comprehension and readability regarding the smoothing effect of Block Kriging on data. In addition, we made some visual improvements on the symbols used in the scatter plots (bigger squares for Block Kriging and bigger dots for original data).

We are very thankful for the valuable comments of the reviewer that gave us the opportunity to improve the quality of our manuscript.

Reviewer comment 4: "In item 3.5 of the results, the authors mention that the most appropriate adjusted model for maize data interpolated by points and blocks in the three field plots was the exponential. Based on what do the authors say this? A call to Table 5 is placed, but it only presents the results of the exponential model and does not show why this model would be the most suitable compared to any other. In addition, the authors draw attention to the fact that “the R2 values calculated from the adjusted exponential variogram models in the corn fresh weight data interpolated by block kriging were greater than the respective R2 values of the punctual kriging data in the three plots”. What does that mean? It needs to be made clear to the reader. Furthermore, in Table 5 more comparison measures are presented, but they were not mentioned in the text. This information needs to be better described and what it means. This has not been discussed comprehensively. I recommend improving the wording, considering the measures highlighted in Table 5, to make this clearer to the reader."

Response to comment 4: Thank you for this comment. We added the following text "The most suitable fitted model for both Point and Block Kriging interpolated maize data in the three field plots was the exponential (Table 5) and it was selected after comparing the performance of other models based on their R² values and RMSE (Root Mean Square Error)". We also made some modifications/corrections to the values of Table 5 regarding R² values and RSS/RMSE. The R² values of Point Kriging is very close to 1 as an exact interpolator, and the estimation is very close to the original data. The R² values of Block Kriging is also very high showing a good fit of the model. We also added some text regarding RSS/RMSE.

Reviewer comment 5: In the “Conclusions” section, the authors present an introductory summary with the main advantages of the block kriging interpolated method. Then they make a call for the main conclusions. To make the text clearer, I suggest that the authors start by describing the main conclusions and put the information from the introductory summary in item 2) that describes the main ones for block kriging.

Response to comment 5: Thank you for this comment. We followed your suggestion, and we re-arranged/re-write the text in the conclusions section.

 

 

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Dear authors,

slmost every suggestions have been receipt and adjustements made.

I still disagree on the need of representing spatial data on a time-line like plot (Fig 4), and suggest to remove the 1:1 points in Fig.5. As told previously Fig.6 suggests the possibility to interpret yield as a continuous variable (e.g. soil fertility) which in your discrete approach is not possible.

Author Response

Response to Reviewer 2

We would like to thank the reviewer for the positive feedback and for the valuable comments and suggestions for our manuscript. We addressed all the issues mentioned and we tried to make improvements throughout the manuscript. Please, find below a point-by-point description of how each comment was addressed.

Reviewer comment 1: "Almost every suggestion has been receipt and adjustments made."

Response on comment 1: We would like to thank the reviewer for the valuable comments on the improvement of the quality of the manuscript. So far, we have adopted almost all the suggestions proposed and we made changes throughout the text.

Reviewer comment 2: "I still disagree on the need of representing spatial data on a timeline like plot (Fig 4) and suggest removing the 1:1 points in Fig.5."

Response on comment 2: The graphs presented in Figure 4 play a crucial role by showcasing the individual smoothing effect of Block Kriging on data values at each point/plant location, in comparison to the Point Kriging method and the original data. Hence, we firmly believe that they hold significance and should be retained. To enhance the figure, we introduced a schematic view of an experimental plot to the left of the graphs and included cross-sections, which depict the locations of the data. By representing data in cross-sections, we believe it enhances the understanding and readability regarding the smoothing effect of Block Kriging on the data. We have, nevertheless, made attempts to incorporate 3D views and actual locations of plants in each of the experimental plots, but this was impossible as the data visualization was inadequate and not clear. Therefore, we opted for a 2D view in the form of graphs as a more suitable approach.

We agree with the reviewer that the 1:1 plotting of the original data in Figure 5 can be omitted, therefore we removed them.

Reviewer comment 3: "As told previously Fig.6 suggests the possibility to interpret yield as a continuous variable (e.g. soil fertility) which in your discrete approach is not possible.”

Response to comment 3: Figure 6 presents the output of the two interpolation methods used (Point and Block Kriging) in the three experimental plots that were in the same region. In all experimental plots, the same hybrid was seeded, and same agricultural practices were implemented throughout. Consequently, the observed variability in yield data (fresh weight) is likely attributed to environmental conditions and soil characteristics, rather than the hybrid itself. Hence, it can be inferred that interpolation can be effectively applied to the original point data within each plot, treating yield as a continuous variable. Besides, although interpolation was used to estimate the missing values in specific plant locations, in fact, the estimation/outcome is indeed a surface (grid with values for the whole area of each plot). Therefore, although the case seems to be a discrete sampling approach that refers to specific plant locations with distances between, in fact the maize yield can be considered as a continuous variable. The interpolated data allows the estimation of yield values in all points between the plants in each plot, as if plants were emerged in each point of the area considering the variability due to soil fertility/environmental conditions. In addition, the contour maps for both Point and Block Kriging methods offer a very useful visual way that allows the comparison of their performance and specifically, it points out that Block Kriging can deliver a smoother effect on data.

Therefore, we are thankful for the valuable comment of the reviewer as it gave us the opportunity to add some more text (line 352 – 357) explaining why interpolation can safely be applied in the case of maize yield fresh weight data. 

 

 

 

Author Response File: Author Response.pdf