An Empirical Seasonal Rainfall Forecasting Model for the Northeast Region of Brazil

Round 1

Reviewer 1 Report

The authors sufficiently implemented my comments to the manuscript-version submitted last autumn. I don't have any further comments.

Author Response

Dear Reviewer,

Thanks for the previous suggestions, they were fundamental for us to present a revised version much better than the previous one.

Sincerely,
The authors

Reviewer 2 Report

The paper presents the implementation and performance assessment of an empirical seasonal rainfall forecasting model applied to the Northeast region of Brazil. It is a suitable topic for Water MDPI journal. The manuscript is professionally written, clear, and easy to read. The results are relevant, well presented and discussed.

I recommend a revision of the manuscript following my comments below.

• Section 2.5: The coefficients should be more detailed/explained, and the authors should certify that all the variables have been defined (e.g., N, BSref).
• Figure 4: The colorbar should be named/defined, and the longitude and latitude axes should be labelled.
• The results could be more quantitatively (in the present version, they are mostly qualitatively) presented and discussed.

Author Response

Dear Reviewer,

First of all, we would like to thank you very much for your kind words towards our work, and naturally, for the minor revisions that you requested, which were points that did demand corrections and/or improvements.

As you can see from this final version, we did our best to meet your recommendations, and we proceeded very carefully.

We used the “track changes” function, so that you can visualize the modifications. Section 2.5 was rewritten. Figure 4 was corrected. And the Results section underwent several additions in order to improve the quantitative analysis, which was indeed incomplete.

Sincerely,

The authors

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

This paper assess the predictability of interannual rainfall variability in Feb-Mar-Apr over Notheast region of Brazil (NEB) using statistical model based on the lag-relationship between the predictand which is decomposed into a few modes by EOF and corresponding observed SST modes (predictor). The authors comfirmed the effectiveness of their statistical method by comparing it with the multi-model seasonal prediction conducted by AOGCMs (NMME). The approach seems to be reasonable and based on the physical teleconnection mechanisms, although there are some authors' subjective judgements and explanation are sometimes inadequate. I recommend major revision.   Major points   1. Figure 2 is inadequate to describe the statistical model.    In phase 1,  - Lead-lag relationship is unclear. I guess that SST fields lead CPn (rainfall?) time series. (Please describe CPn.) - The equation at the bottom of the Phase 1 panel (Index n = SST....) means projection. Please use the mathematical terminology. - In the statistical model, generally, the target month for the prediction is excluded from the training period of the statistical analysis of EOF to prevent the signals of forecast months from being included in the statistical function. This procedure should be repeated every hindcast year.    In phase 2, the variable "A" and "B" is different from the A and B appeared in the phase 1 panel. I guess A is climatology and B is regression coefficient of rainfall onto principal components of EOF. Please describe it.   In phase 3, I guess "EOF pattern" means an eigen vector, and you intend to explain the reconstruction process. Please use the mathematical terminology. From phase 1 to 3, some detailed equations are needed to make it easier to understand.   2. In Fig. 3, the predictor domain of X (precipitation by hindcasts) was designed to be larger than NEB. Because GCM prediction is not good at simulating regional scale precipitation over land surface, large-scale precipitation anomalies over ocean would be main contributor as the predictor. This viewpoint should be added in the text. In addition, in the pre-orthogonalization process of CCA for NMME, there is no guarantee that each mode has a one-to-one correspondence between X-eof1 and Y-eof1, X-eof2 and Y-eof2, ... X-eof5 and Y-eof5. To keep consistnecy between X and Y, the singular value decomposition (SVD) analysis would be more adequate than two independent EOF analyses. By the way, how did you decide the number of mode (top five modes?) to use for CCA? Did you conduct CCA after reconstructing the variable from the 5 modes or did you conduct CCA for each EOF mode?   3. L190-195: Why can you consider that 70% (the first 3 modes) are reasonable and the other modes mean noise? The consideration is too subjective. Please show the other modes and what feature can be regarded as noise. And also, please check the results when you use the other choice of modes (the first 4 modes, 5 modes, 6modes, etc.) .   4. L249: The reason why you chose the "two-month" lagged SST is unclear. Is it because the skill score was the highest (depend on the result?) or because there is social demand?   Minor issues   5. L21: asses -> assess   6. L57-L77: Please add following citations: - Imada, Y., S. Kanae, M. Kimoto, M. Watanabe, and M. Ishii, 2015: Predictability of persistent Thailand rainfall during the mature monsoon season in 2011 using statistical downscaling of CGCM seasonal prediction. Monthly Weather Review, 143, 1166-1178. - Chu, J.-L., H. Kang, C.-Y. Tam, C.-K. Park, and C.-T. Chen, 2008: Seasonal forecast for local precipitation over northern Taiwan using statistical downscaling. J. Geophys. Res., 113, D12118. - Kang,H., K.-H.An, C.-K. Park, A. L. S. Solis, andK. Stitthichivapak, 2007: Multimodel output statistical downscaling prediction of precipitation in the Philippines and Thailand. Geophys. Res. Lett., 34, L15710. - Kang, I.-S., J.-Y. Lee, and C.-K. Park, 2004: Potential predictability of summer mean precipitation in a dynamical seasonal prediction system with systematic error correction. J. Climate, 17, 834–844.   7. L109: "model" -> "statistical model"   8. L127: Please start this paragraph with the word "Phase 3 consists in ...".   9. Fig. 2, Phase 1: serie -> series   10. L161: "predictive" -> "predictor"   11. L165: "predicting" -> "predictand"   12. Equation (1)-(4): Descriptions of the variables (r_forecast, r_reference, BS_ref) are inadequate. In Equation (3) and (4), please insert "x 100" if you want to show them using the unit % as shown in Fig. 8(c) and Fig. 10.   13. L180:  "EmpM's performance" -> "EmpM's relative performance" Please add explanation of the abbreviation "EmpM".   14. Explanation from L181 to L186 should appear just after the f_t and O_t definition.   15. L223: "meridional" -> "zonal"(?)   16. L233-235: Fig. 5(f) and Fig. Fig. 7(c) show typical features of interdecadal Pacific oscillation (IPO). It is known that IPO was positive in 1980s and 1990s, and negative in 2000s.   17. L266: Many readers are not familiar with the name of these states. Please show these states on the map of Figure 8.   18. Fig. 5 and Fig. 6: Please describe that "mode 1 (a and b), mode 2 (c and d), mode 3 (e and f) in the figure caption.   19. L288: Figure 7c -> Figure 8c

Author Response

Dear referee, we send you in the attached file, point-to-point answers regarding everything that was asked/suggested. The answers are in blue.

Appreciatively,

The authors

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions:

 

1. Line 117: SST teleconnection patterns (December) lead NEB precipitation (FMA), not time-lagged. Also check this in other places, such as in the caption of Fig. 6.

 

2. CCA has corrected NMME in pattern, so the comparison with NMME is not objective.

 

3. For the interpretation of teleconnection patterns, the best variable to be used for depicting Rossby wave path, particularly in the lower latitudes, is the stream function at higher troposphere (e.g., 200hPa) and with the anomalous stationary wave activity fluxes (Takaya, K. and H. Nakamura, 2001: A Formulation of a Phase-Independent Wave-Activity Flux for Stationary and Migratory Quasigeostrophic Eddies on a Zonally Varying Basic Flow. J. Atmos. Sci., 58, 608–627.)

 

4. Line 275: “spatial correlation” usually refers to as pattern correlation, while here it looks the spatial pattern of temporal correlation.

 

5. The EmpM just gives deterministic forecasts, how is the BS skill calculated? Is it calculated temporally? If yes, how is the probabilistic quantity is defined? It is not quite clearly described.

Author Response

Dear referee, we send you in the attached file, point-to-point answers regarding everything that was asked/suggested. The answers are in blue.

Appreciatively,

The authors

Author Response File: Author Response.docx

Reviewer 3 Report

The manuscript presents the methodology and results of an empirical model that is applied to forecast seasonal rainfall in North-Eastern Brazil (NEB). The performance of the empirical model is assessed against the forecast made by the North American Multimodel Ensemble (NMME). It is shown that forecasts for the February-March-April (FMA) season made via the empirical approach are superior to those by NMME over most of the study area. The empirical model includes the first three modes (EOFs) of NEBs precipitation for the studied season FMA, which explain about 70% of the rainfall variability, and sea surface temperatures (SST) during December. Teleconnections between the SST and rainfall pattern over NEB within the three modes are presented. They build the basis for skillful forecast of seasonal precipitation in the study area.

 

The manuscript is written well and needs only minor revisions. For the revision, please refer to the comments I made in the manuscript pdf-file. Most important is the enhancement of the figure captions in order to allow for an understanding of the figures without reading the main text.

Comments for author File: Comments.pdf

Author Response

Dear referee, we send you in the attached file, point-to-point answers regarding everything that was asked/suggested. The answers are in blue.

Appreciatively,

The authors

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Unfortunately, the authors' responses are only partial answers to my comments and are inadequate. 

In my previous review, I commented that "in the pre-orthogonalization process of CCA for NMME, there is no guarantee that each mode has a one-to-one correspondence between X-eof1 and Y-eof1, X-eof2 and Y-eof2, ... X-eof5 and Y-eof5. To keep consistnecy between X and Y, the singular value decomposition (SVD) analysis would be more adequate than two independent EOF analyses. By the way, how did you decide the number of mode (top five modes?) to use for CCA? Did you conduct CCA after reconstructing the variable from the 5 modes or did you conduct CCA for each EOF mode? "

Those my comments raised questions about the unclear background mechanism behind this prediction method. 

However, the authors' reply is only that;

"The canonical-correlation analysis (CCA) was applied by resorting to the "Climate Prediction Tool (CPT)", an application available for Windows and Linux that automates post-processing and downscaling of NMME predictions (or any other climate model, for that matter). It is the application that automatically decides how many modes will be used for each variable. The reconstructions were made using the modes that were selected by the application."

In the next question from me in the previous peer review, the authors repeated a similar answer. It seems that they do not understand the content because they rely on an existing application. 

As it is, the content is insufficient for both science and engineering papers, and I recommend major revisions.

The other comments are as follows, partly a repeat of the previous one:

• Please modify Figure 2 as it is misleading due to lack of explanation of terms and symbols: "A" and "B" in phase 1, 2, and 3 is misleading; Does EOF(x) indicate an eigen vector?; Does P(xx) indicate a predictand?; Subscripts are not readable.

 

• At L112, please correct "the main components (PCs)" to "the principle components (PCs, denoted CPn in the figure)". Please omit "(denoted CPn in the figure)" at L116.

 

• In the statistical model, generally, the target month for the prediction is excluded from the training period of the statistical analysis of EOF to prevent the signals of forecast months from being included in the statistical function. This procedure should be repeated every hindcast year. The procedure in this paper does not seem to employ this method. Please modify the procedure appropriately. That change will reduce your predictive skills, but that's the right thing to do. 

 

• L231-246 and Fig. 5f: Again, the third mode shows a typical feature of interdecadal Pacific oscillation (IPO). Yous should not comment on ENSO in this paragraph because a typical ENSO pattern appears in the first mode. EOF3 should be independent from EOF1.

Author Response

Reply to the Referee

CPT is a widely used tool aimed to generate operational forecasts, having been previously used in several other studies (references properly identified in the manuscript). We used it with grounds on those precedents. However, unfortunately, there is no detailed documentation on what exactly the software does in the background, i.e., step-by-step. We know that the series are pre-processed through EOF, as it would be impossible (due to computational limitations) to apply all the series directly to the CCA, and that assumption was confirmed by an email communication with the developer. However, concerning the choice made by the software on how many modes and principal components, it remains unknown to us.

When running the software, we are given the option of choosing a maximum and minimum number of principal components to be used, to which we normally enter 1 for the lowest number and 10 for the highest. Then it is up to the software to determine an optimal number of modes to be used within that interval.

At the current step of the peer-review procedures, we estimate that it would not be reasonable to await a new reply from the CPT developer on that matter, as we cannot anticipate the time it would take to obtain the answer. Moreover, an email would not be considered as a valid reference. We reiterate that other works have used that model with no problems whatsoever.

Therefore, we decided to reorganize the pertinent section. We simplified that part of the manuscript based on other (cited) studies. We emphasized the fact that CPT is a known, established method in the literature. We made all the necessary mentions to the software. We also changed Figure 3 with simplification in mind, in order to provide the reader with a better understanding, as the Figure now shows only Domains X and Y.

As for the cross-validation, we think that the reader of this esteemed journal is of a technical nature and, therefore, familiarized with such terminologies, rendering unnecessary to explain the expression itself. Furthermore, we recognize that the expression was not used for mentioning the NMME downscaling, and that is why, on the present revision, we mentioned it for the CCA, adding the explanation that the technique is automatically applied by CPT.

Regarding the hypothesis of an influence from the PDO, we analysed the signal and decided to accept the excellent suggestion of the referee. The signal does point to the PDO and could not be related to ENSO, given that the first signal already showed that relation and the two modes are orthogonal to each other, i.e., with no correlation. We thereby made the necessary changes concerning the phenomenon that is responsible for mode 3.

We also take this opportunity to let you know that the manuscript has undergone a comprehensive grammar and writing revisions. The modifications made on those regards are highlighted in golden/yellow.

Finally, we would like to express our gratitude for all of your remarks. We did our best to meet your recommendations, and our work is now definitely better than before because of that. We now look forward to your approval of the present revision, so that the work will be able to go on with the following procedures towards publication, given that acceptance recommendations have already been made by the other referees.

Thank you once again.

Sincerely,

The authors.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

I entrusted the decision to the editor.