Modeling Spatiotemporal Rainfall Variability in Paraíba, Brazil

Round 1

Reviewer 1 Report

Review of manuscript: Analysis of the spatiotemporal rainfall variability over recent decades in Paraíba, Brazil

Authors: Elias Silva de Medeiros, Renato Ribeiro de Lima, Ricardo Alves de Olinda and Carlo Antonio Costa dos Santos

Analysis of the spatiotemporal rainfall variability is of considerable interest and importance, especially for data scarcity. This paper refers to the methods and in my opinion can be considered for publication, but it requires some revision.

Comments    

The paper analyses the spatiotemporal distribution of rainfall in the north-eastern region of Brazil. The most important problem of this paper is that the title has not much in common to the contents: analysis of the spatiotemporal rainfall variability is lacking. The paper presents mainly methodology, so I recommend to change the title or to add some results. Authors in the abstract inform about “the rainfall estimates from Paraíba [..], that directly affect the water resources of the entire region, providing a detailed spatial analysis of sectors experiencing precipitation conditions ranging from a scarcity to an excess of rainfall”, but results of the study are only shown for January 2015-2018. Among the keywords ”droughts” are mentioned, but in the text the issue is not presented.

If the authors will not change the title, they should add some results (for example for the rest of months) or indicate the years/months with droughts or with excess of water. The paper is quite similar to the paper Raja et al. (Space-time kriging of precipitation variability in Turkey for 453 the period 1976–2010. Theor. Appl. Climatol. 2017), but there authors elaborate more on the results.

Title: does not much fit to the contents

Keywords: droughts – lack in the paper

Comments for author File: Comments.docx

Author Response

Review of manuscript: Analysis of the spatiotemporal rainfall variability over recent decades in Paraíba, Brazil

Authors: Elias Silva de Medeiros, Renato Ribeiro de Lima, Ricardo Alves de Olinda and Carlo Antonio Costa dos Santos

Analysis of the spatiotemporal rainfall variability is of considerable interest and importance, especially for data scarcity. This paper refers to the methods and in my opinion can be considered for publication, but it requires some revision.

Comments     

Reviewer: The paper analyses the spatiotemporal distribution of rainfall in the north-eastern region of Brazil. The most important problem of this paper is that the title has not much in common to the contents: analysis of the spatiotemporal rainfall variability is lacking. The paper presents mainly methodology, so I recommend to change the title or to add some results.

Answer: In fact, the manuscript consists in doing a spatiotemporal kriging and not specifically studying the spatiotemporal variability. When the authors put "analyze the spatiotemporal variability", it was consented to present the spatiotemporal variogram, since it is constituted based on covariance functions.

However, the authors agree with the reviewer's comment and it was proposed to change the title of the paper as well as the objectives.

New Title: "Spatiotemporal Kriging to Interpolate the Precipitation Values in Paraíba, Brazil"

Reviewer: Authors in the abstract inform about “the rainfall estimates from Paraíba [..], that directly affect the water resources of the entire region, providing a detailed spatial analysis of sectors experiencing precipitation conditions ranging from a scarcity to an excess of rainfall”, but results of the study are only shown for January 2015-2018.

Answer: The spatiotemporal interpolation of precipitation was presented only for this period as an example of the results that this technique can provide. However, the authors added in the supplementary material a figure with interpolated values from 2015 to 2020.

Reviewer: Among the keywords ”droughts” are mentioned, but in the text the issue is not presented.

If the authors will not change the title, they should add some results (for example for the rest of months) or indicate the years/months with droughts or with excess of water.

Answer: The keyword "droughts" has been deleted.

Reviewer: The paper is quite similar to the paper Raja et al. (Space-time kriging of precipitation variability in Turkey for 453 the period 1976–2010. Theor. Appl. Climatol. 2017), but there authors elaborate more on the results.

Reviewer: Title: does not much fit to the contents

Answer: The title has been changed.

Reviewer: Keywords: droughts – lack in the paper

Answer: The keyword "droughts" has been deleted.

Reviewer 2 Report

The paper deals with the method of the interpolation of precipitation data based on the kriging technique. The main aim of the paper is to show that the use of spatiotemporal information apparently improves the accuracy of interpolation in comparison to using only spatial information. The technique in general is not new but the results are useful for people dealing with precipitation estimates.

General comments:

In my opinion the English language should be improved.

You use quite formal mathematical description of the problem, e.g. 137-139. However, majority of potential readers is not used to it. I recommend using less formal and more detail description of kriging and terms like sill.

Authors use several times word prediction. In my opinion it is confusing because in fact the paper deals with interpolation. Or am I wrong? This should be clarified. For example, authors use the best linear non-biased predictor but this I know as the best linear non-biased estimate; another example: line 303 predicted values.  

It would be a great benefit of the paper if authors could mention relationship of the applied method and “optimum interpolation” frequently used in meteorological applications.

Specific comments:

Line 104: It should be mentioned that OLS is described later.

Line 105-107: Is it possible to discuss the applied assumptions?

Line 119-119: Could you explain why do you use „quadratic effect“ ?

Eq. 3 – I am confused by used notation. Could you explain relationships among eq. 1, 2 and 3. What is the difference between beta in eq. 2 and 3?

Line 185: RMSE and NSE should be explicitly defined.

Line 197: What do you mean that „allows missing data to be entered”?

Line 215: I do not understand what the sentence starting „Based” says.

Line 213: What data were used? Whole data or data „excluding one station“?

Line 308: I do not understand „while considering“.

Line 341: What do you mean by the standard error? What do you mean by the prediction?  

Author Response

Review of manuscript: Analysis of the spatiotemporal rainfall variability over recent decades in Paraíba, Brazil

Authors: Elias Silva de Medeiros, Renato Ribeiro de Lima, Ricardo Alves de Olinda and Carlo Antonio Costa dos Santos

The paper deals with the method of the interpolation of precipitation data based on the kriging technique. The main aim of the paper is to show that the use of spatiotemporal information apparently improves the accuracy of interpolation in comparison to using only spatial information. The technique in general is not new but the results are useful for people dealing with precipitation estimates.

General comments:

Reviewer: In my opinion the English language should be improved.

Answer: The English language has been revised by a native English.

Reviewer: You use quite formal mathematical description of the problem, e.g. 137-139. However, majority of potential readers is not used to it. I recommend using less formal and more detail description of kriging and terms like sill.

Answer: Formal presentation is necessary, since few works present the mathematical details involving spatiotemporal kriging. The sill in the product-sum covariance model was detailed in the equations (7, 8 and 9).

Reviewer: Authors use several times word prediction. In my opinion it is confusing because in fact the paper deals with interpolation. Or am I wrong? This should be clarified. For example, authors use the best linear non-biased predictor but this I know as the best linear non-biased estimate; another example: line 303 predicted values. 

Answer: The authors used the word prediction to estimate precipitation over time. The word interpolation was used for space precipitation estimates. The model presented in the manuscript is suitable only for interpolation or prediction and not to forecast.

Reviewer: It would be a great benefit of the paper if authors could mention relationship of the applied method and “optimum interpolation” frequently used in meteorological applications.

Answer: Sorry, we can't answer this question. The authors do not master the "optimal interpolation" (OI) technique and we could not compare the methods. In summary, OI is a commonly used technique for sensing remote or re-analyzing data. An interesting article about Kriging and OI was published in Water: Rainfall Spatial Estimations: A Review from Spatial Interpolation to Multi-Source Data Merging.

Specific comments:

Reviewer. Line 104: It should be mentioned that OLS is described later.

Answer: In this manuscript, to adjust a regression model for the trend, the "OLS" method was used. However, the focus of this paper will be on modeling a spatiotemporal covariance function. For this reason, the authors presented the estimation details (weighted least squares) for the adjustment of this function (see line 153-159).

Reviewer. Line 105-107: Is it possible to discuss the applied assumptions?

Answer: Not as simple to discuss, as with any regression model, these assumptions are assumed to facilitate model fit. When we speak of second order stationarity, we are assuming that the expectation of the spatiotemporal residue is constant and equal to zero and that the covariance function of this component depends only on distances (spatial and temporal).

Reviewer. Line 119-119: Could you explain why do you use “quadratic effect” ?

Answer: Before fitting a regression model for the trend, we plotted the longitude x precipitation. Through this graph, we realized that precipitation in the area under study had a quadratic effect in relation to longitude.

Reviewer. Eq. 3 – I am confused by used notation. Could you explain relationships among eq. 1, 2 and 3. What is the difference between beta in eq. 2 and 3?

Answer: We adopt the following model.

Equation 1: Precipitation ~ Trend + Residue.

In equation 2 we are presenting how we get the estimates for the trend component.

Equation 3 is the same as equation 1, and we specify which parameters we would be using to adjust the trend.

Reviewer. Line 185: RMSE and NSE should be explicitly defined.

Answer: In the manuscript, two equations were for for RMSE and NSE.

Reviewer. Line 197: What do you mean that „allows missing data to be entered”?

Answer: As the technique (kriging) allows to make interpolations in any position within the area under study. Therefore, this method can be used to interpolate missing data in locations that have rainfall stations.

Reviewer. Line 215: I do not understand what the sentence starting „Based” says.

Answer: The sentence: “Based on this finding, the substantial spatial and temporal variabilities in the rainfall throughout the state are well known.”

Has been changed to: “Through these results, the spatial and temporal variability in the rainfall throughout the state are well known.”

Reviewer. Line 213: What data were used? Whole data or data „excluding one station“?

Answer: Are you talking about figure 6? If so, excluding one station: Cross-validation was performed, one station was left out (leave-one-out) and interpolation for this station.

Reviewer. Line 308: I do not understand „while considering“.

Answer. The sentence: “…while considering all 269…”. Has been changed to: “…considering all 269…”

Reviewer. Reviewer. Line 341: What do you mean by the standard error? What do you mean by the prediction? 

Answer. Standard error: measures uncertainty about the values estimated by the model. Preciction: corresponding to the values predicted (and not forecast) precipitation.

Round 2

Reviewer 1 Report

In my my opinion this paper could be published in present form.

Author Response

Guest Editor's Comments to Authors:

Editor: The revised title should be further improved. A more suitable title describing better the manuscript and reflect the objectives might be: “Modelling spatio-temporal rainfall variability in Paraíba, Brazil”

Answer: Changes were made to the manuscript as suggested.

Editor: The objectives stated in the Abstract should be made conform to the ones of manuscript.

Answer: Changes were made to the manuscript as suggested.

Editor: Lines 33-35. The first two sentences should be a very general rational which introduces readers to the topic being studied. They should help you to pose the problem.

Answer: The first paragraph of the introduction has changed.

Editor: Lines 35-41. You cannot introduce directly the study case: you can just mention it at the end of the Introduction after the objectives

Answer: The first paragraph of the introduction has changed.

Editor: Lines 69-72. Using a methodology is not a novelty in itself but can be describing a new or an improved approach to ..... A novelty is not even applying a methodology.

Answer: The novelty of the paper It has been modified to: "The novelty of this study was to presenting  in detail a tool for spatial-temporal interpolation of precipitation in the region under study.”

Editor: Lines 72-75. The objectives should be further improved and made clearer. I believe needless to state the two research questions.

Answer: The objective of the research became: "The  purpose of this study was to provide a detailed framework to use the spatio-temporal kriging to model the space-time variability of precipitation data in Paraíba, Brazil." The two research questions was excluded.

Editor: Table 1. Once again, reporting CV does not provide further information. You should provide more statistical information or using boxplots.

Answer: In the manuscript BoxPlots was inserted for each mesoregion in the different months.

Editor: Table 3. In the table caption the meaning of k, RMSE, and NSE have to be explained. Error metrics is needless.

Answer: The table caption became: “Estimations of parameters (Sill, Range and Nugget) of the generalized product-sum variogram model fitted for the residuals, root mean square error (RMSE) and Nash-Sutcliffe efficiency (NSE). The parameter k involves the global sill.”

Author Response File: Author Response.docx