Residual-Oriented Optimization of Antecedent Precipitation Index and Its Impact on Flood Prediction Uncertainty
, Zichen Hu 2, Shuguang Liu 1,3,*, Guihui Zhong 1, Yiwei Zhen 1, Aleksei Nikolavich Makhinov 4 and José Tavares Araruna 5
Round 1
Reviewer 1 Report
Although the manuscript has the potential to advance our understanding on the precipitation index and its impact on flood prediction uncertainty, the explanation and figure require extensive revision. Please address the comments to improve the quality of your article.
1. In section 2.1, line number 93-94, authors mention "... The uneven temporal distribution of the precipitation causes frequent flood disasters along the river network during rainy periods....". I suggest the authors add a statement similar to "The River networks of a basin depend on external stimuli such as precipitation and serve as the principal channels for transporting water fluxes" with the following citations:
(a) Sarker et al. (2019), Critical Nodes in River Networks, Scientific Reports. https://www.nature.com/articles/s41598-019-47292-4;
(b) Gao et al. (2022), Analyzing the critical locations in response of constructed and planned dams on the Mekong River Basin for environmental integrity, Environmental Research Communications, https://iopscience.iop.org/article/10.1088/2515-7620/ac9459.
2. Please modify figure 1, may be include 1st order, 2nd order etc. steams on your River network. See the aforementioned manuscripts.
3. There is a typo in figure 9! It should be figure 9 not figure 10. Figure 3, 4, 5, 6, 7 and 8 is awful! I would use Python, MATLAB, or some other professional software to generate quality figures.
4. Again figures 11 and 12 are horrible! I would make quality figures using Python, MATLAB, or whatever other professional software.
Author Response
Point 1: In section 2.1, line number 93-94, authors mention "... The uneven temporal distribution of the precipitation causes frequent flood disasters along the river network during rainy periods....". I suggest the authors add a statement similar to "The River networks of a basin depend on external stimuli such as precipitation and serve as the principal channels for transporting water fluxes" with the following citations:
(a) Sarker et al. (2019), Critical Nodes in River Networks, Scientific Reports. https://www.nature.com/articles/s41598-019-47292-4;
(b) Gao et al. (2022), Analyzing the critical locations in response of constructed and planned dams on the Mekong River Basin for environmental integrity, Environmental Research Communications, https://iopscience.iop.org/article/10.1088/2515-7620/ac9459.
Response 1: We agree with the referee and the above literature that river networks critically influence the formation of flood events. Therefore, it is promising to consider the changes in river networks when dealing with flood uncertainty in future work. Supplementary statements and citations are added in Section 3.6 (line 508).
Point 2: Please modify figure 1, may be include 1st order, 2nd order etc. steams on your River network. See the aforementioned manuscripts.
Response 2: We have modified Figure 1 according to the referee’s suggestion.
Point 3: There is a typo in figure 9! It should be figure 9 not figure 10. Figure 3, 4, 5, 6, 7 and 8 is awful! I would use Python, MATLAB, or some other professional software to generate quality figures.
Response 3: We are sorry for wrongly marking Figure 9 as Figure 10. We have corrected it in the manuscript. Other figures are replotted with Origin.
Point 4: Again figures 11 and 12 are horrible! I would make quality figures using Python, MATLAB, or whatever other professional software.
Response 4: We have adjusted Figure 11 and 12 with Origin according to the referee’s suggestion.
Author Response File: 
Author Response.docx
Reviewer 2 Report
This study proposed RAPI to estimate and further link antecedent moisture conditions with flood predictive uncertainty, and it was examined in the Changsha River basin. There was no doubt about the research methodology and the results obtained will contribute to probabilistic flood forecasting using hydrological models.
The following are comments;
1) Please specify the temporal resolution and sub-area (spatial resolution) of the model used.
2) Please check Figure 9 as it was missing. Also, as Figure 9 was missing, I couldn’t understand the contents of Figure 9 in the text.
3) In Figure 10, the observed streamflow on 6/25/2017 was above 95% PUB. Is this mean the underestimation of the forecast in larger streamflows? If so, it is considered problematic in terms of flood forecasting. It is considered essential to add a further discussion regarding this.
4) In terms of uncertainty in flood forecasting, the influence of uncertainty in precipitation observation can be inferred (ex. Shimizu et al, 2020; https://doi.org/10.3390/w12092554). Therefore, it would be desirable to describe how the influence of uncertainty in precipitation observation was taken into account in the RAPI and probabilistic flood forecasting proposed in this study.
Author Response
Response to Reviewer 2 Comments
Point 1: Please specify the temporal resolution and sub-area (spatial resolution) of the model used.
Response 1: Based on the geo-morphological lumping nature of the XAJ model, the rainfall-runoff process of the Changshangang Basin is aggregated into one single cell with equivalent hydrological properties. On the other hand, consistent with the hydrometeorological observations, the time step of the flood simulation is one hour. We added a supplementary description in Section 3 (lines 282-286 ). Also, Figure 6 is replotted to avoid confusion in the modeling time scale.
Point 2: Please check Figure 9 as it was missing. Also, as Figure 9 was missing, I couldn’t understand the contents of Figure 9 in the text.
Response 2: We are sorry for wrongly marking Figure 9 as Figure 10. We have corrected it in the manuscript.
Point 3: In Figure 10, the observed streamflow on 6/25/2017 was above 95% PUB. Is this mean the underestimation of the forecast in larger streamflows? If so, it is considered problematic in terms of flood forecasting. It is considered essential to add a further discussion regarding this.
Response 3: We agree with the referee that the XAJ model underestimates flood peaks. As presented in Figure 3, the pattern of the scatter plot implies that the XAJ model underestimates high flow observations while overestimates low flow observations. The deficit of the XAJ may come from the lumping of the hydrological process. However, the discussion of hydrological model deficits is beyond the scope of this paper. Alternatively, we pay direct attention to the model residual and the resulting predictive uncertainty. The flood event from 6/17/2017 to 7/1/2017 contains the largest flood peak volume (4870 m3/s at 23:00 6/24/2017) and absolute residual value (1746 m3/s at 2:00 6/25/2017). Hence, we choose this flood event as the representative example to show the integral performance of flood prediction performance (see Figures 6,9(a) and 10(a)). It is noteworthy that all flow peak observations in the other 21 flood events are within the range of 95% PUB. The PQQ plots can verify this result in Figures 9(b) and 10(b). Also, Figures 9(a) and 10(a) suggest a better predictive ability of the ‘KF’ scenario than the ‘KA’ scenario during high flow periods, as stated in Section 3.3 and Section 3.5. We add remarks in Section 3.1 (lines 337-340) and Section 3.2 (lines 356-357).
Point 4: In terms of uncertainty in flood forecasting, the influence of uncertainty in precipitation observation can be inferred (ex. Shimizu et al, 2020; https://doi.org/10.3390/w12092554). Therefore, it would be desirable to describe how the influence of uncertainty in precipitation observation was taken into account in the RAPI and probabilistic flood forecasting proposed in this study.
Response 4: We agree with the referee that involving precipitation uncertainty can further improve the estimation of RAPI and its contribution to flood prediction uncertainty. Indeed, the major limitation of this study is the neglect of rainfall uncertainty. The hourly mean areal precipitation calculated from rain gages is assumed to be the ‘true input’ of the XAJ, RAPI, and KRE models. In this way, the computational complexity of the likelihood function (Equation 11) is significantly reduced. However, as the referee suggests, the rainfall estimates are inherently uncertain due to inadequate areal coverage of gaging sites, inaccurate spatial-temporal interpolation, mechanical limitations of pluviometers, etc. Since the hydrological systems are heavily input-driven, inaccurate rainfall characterization can impair the quality of calibration and prediction results. We will further investigate the influence of precipitation uncertainty in further work. Both limitations and recommendations for future work are added in Section 3.6.
Author Response File: Author Response.docx
Reviewer 3 Report
I thank the authors and moving to the paper itself. As far as authors are presenting:
a. flood predictive uncertainty by empirical RAPI
b. MI-LXPM algorithm is applied to search for optimal parameters of constraints.
I am sorry but I have a number of problems with this paper, broadly:
1. What is the nobility of this present study except introducing new technique or any other aspect?
2. What is the limitation of your study?
3. Future scope in terms of scientific must be added at last portion of conclusion section.
4. In Fig 1; please add country then state then your river map.
5. Please add full abbreviation when it appears first in the manuscript. (Ex: Um, Lm, Dm, Im, Sm, K, B, C; Fr)
6. Fig 3, Fig 10; Please add R2 value.
7. Author used only NSE; I suggest please add other evaluating constraints (WI, PBIAS).
8. As it is predictive model; author must add uncertainty analysis.
9. Which software have you used to get figure 8 and what conditions you have applied for that
10. Detail description must be provided for figure 5 and 6
11. You have mentioned data of 2010 to 2018 are considered for research, why not upto 2021
12. Histogram/box plot must be added for better accuracy of model
13. All citation must added in the reference section and vice versa
14. Check the format of reference as per journal guideline
15. Pl. read the paper carefully as some sentences are incomplete and there are some missing article and verbs in the sentences.
16. Add more recent references in context to this research (Preferably 2022)
17. In some part the English is so bad, that it is very difficult to understand while going through the text. The authors may be asked to rectify the mistakes by take up the help of a person who had English as first language.
Author Response
Response to Reviewer 3 Comments
Point 1: What is the nobility of this present study except introducing new technique or any other aspect?
Response 1: Except for the KRE model and its calibration method, the principal nobility of this study is quantitively exploring the influence of antecedent soil moisture on flood prediction uncertainty. The case study shows that the predictive uncertainty magnifies almost 20 times between the minimal and maximum optimal RAPI value. Also, we provide recommendations for regressor choices for probabilistic flood prediction with different magnitudes.
Point 2: What is the limitation of your study?
Response 2: The major limitation of this study is the neglect of rainfall uncertainty. The hourly mean areal precipitation calculated from rain gages is assumed to be the ‘true input’ of the XAJ, RAPI, and KRE models. In this way, the computational complexity of the like-lihood function (Equation 11) is significantly reduced. However, the rainfall estimates are inherently uncertain due to inadequate areal coverage of gaging sites, inaccurate spatial-temporal interpolation, mechanical limitations of pluviometers, etc. Since the hydrological systems are heavily input-driven, inaccurate rainfall characteri-zation can impair the quality of calibration and prediction results. We have added Section 3.6 to introduce the limitation of our study.
Point 3: Future scope in terms of scientific must be added at last portion of conclusion section.
Response 3: According to the limitation of this study, future works are recommended to investigate the influence of rainfall uncertainty on both the estimation of RAPI and flood predictive uncertainty. We have added relevant statements in Section 3.6 (lines 510-517) and the last paragraph of the conclusion section.
Point 4: In Fig 1; please add country then state then your river map.
Response 4: We have added country and province of the study basin in Figure 1.
Point 5: Please add full abbreviation when it appears first in the manuscript. (Ex: Um, Lm, Dm, Im, Sm, K, B, C; Fr).
Response 5: Full abbreviations of the parameters are added in Section 2.2 (lines 123-130).
Point 6: Fig 3, Fig 10; Please add R2 value.
Response6: Following the referee’s suggestion, we added R2 values in both Figure 3 and Figure 7 to better represent fitting performances. Supplementary explanations are also added in Section 3.1 (line 305) and Section 3.2 (lines 356 & 363). As for Figure 10, readers can refer to the and NSE values in the text and Table 3 since they are mathematically identical to the R2 values of the prediction mean and deterministic model output.
Point 7: Author used only NSE; I suggest please add other evaluating constraints (WI, PBIAS).
Response 7: We only present the NSE value to evaluate unbiasedness for two reasons: 1) to keep consistent with the objective function in the first-stage calibration (Equation (10)), and 2) the resulting value of WI and PBIAS reveal the same conclusion as the NSE when comparing the two modeling scenarios.
Point 8: As it is predictive model; author must add uncertainty analysis.
Response 8: This study evaluates the predictive uncertainty quantitatively using the reliability and precision metrics (Section 2.7). The reliability metric quantifies the statistical consistency of a predictive distribution and the observation. Lower reliability metric values indicate that the observations are more likely drawn from the assumed predictive distribution. However, inaccurate predictive distribution with a large standard deviation can also get a low reliability metric value. Hence, we add the precision metric to measure the ‘average’ standard deviation across all evaluated periods. Combining these two indicators, we can reasonably evaluate the performance of the prediction distribution and its corresponding uncertainty. Except for the quantitative metrics, the predictive PQQ plots (Figures 9(b) and 10(b)) are also applied to evaluate the predictive uncertainty visually. A predictive PQQ plot close to the 1:1 line indicates a perfect representation of uncertainty.
Point 9: Which software have you used to get figure 8 and what conditions you have applied for that
Response 9: Statistics of the innovation in Figure 8 are calculated with self-written codes, and the figure is plotted with Origin. The kernel density in Figure 8(b) is estimated using Equation (8) with an optimal bandwidth b=0.04. An additional explanation is added in the caption of Figure 8 to avoid confusion.
Point 10: Detail description must be provided for figure 5 and 6
Response 10: We have added detailed descriptions in the caption of both Figure 5 and Figure 6.
Point 11: You have mentioned data of 2010 to 2018 are considered for research, why not upto 2021.
Response 11: The flow gauging station of the Changshangang River Basin (the Changshangang station in Figure 1) was built in 2010 and relocated downstream in 2018. Hence, we only selected the data from 2010 to 2018 to ensure consistency. The explanation is added in Section 2.1 (lines 102-104).
Point 12: Histogram/box plot must be added for better accuracy of model.
Response 12: The histogram is added in Figure 8(b) to compare the observed innovation distribution and kernel estimates derived from Equation (8).
Point 13: All citation must added in the reference section and vice versa.
Response 13: All citations are double-checked, and the mistakes are revised.
Point 14: Check the format of reference as per journal guideline
Response 14: All citations are double-checked, and the mistakes are revised.
Point 15: Pl. read the paper carefully as some sentences are incomplete and there are some missing article and verbs in the sentences.
Response 15: We have carefully checked and revised the vocabulary and grammar of the whole article. The modified places have been marked using the “Track Changes” function.
Point 16: Add more recent references in context to this research (Preferably 2022).
Response 16: References are updated to the latest research (2022) where possible.
Point 17: In some part the English is so bad, that it is very difficult to understand while going through the text. The authors may be asked to rectify the mistakes by take up the help of a person who had English as first language.
Response 17: Along with point 15, language mistakes have been rectified after consulting native English speakers. The modified places have been marked using the “Track Changes” function.
Reviewer 4 Report
Dear authors,
congratulations for your interesting paper. Some details have arisen and should be corrected before granting its publication so I kindly ask an aswer to the following questions:
Please check carefully your English, some phrases and paragraphs need to be rewritten to make them clearer for the readers.
Regarding the figures, please explain what does mean Obs in Figure 1. Moreover, the quality of your paper will improve if you use colour on Figures 3, 5, 6, 8 and 12, making them more clear and understandable.
Section 3, line 263. You wrote, “while others are pre-determined empirically.” Could you explain why and how you did that?
Section 4. When you closed the introduction, you stated that, in section 4, you would provide some recommendations for practical applications of your method. I could not find such recommendations on section 4 so please add them or remove the previous text.
Best regards,
Author Response
Response to Reviewer 4 Comments
Point 1: Please check carefully your English, some phrases and paragraphs need to be rewritten to make them clearer for the readers.
Response 1: Language mistakes have been rectified after consulting native English speakers. The modified places have been marked using the “Track Changes” function.
Point 2: Regarding the figures, please explain what does mean Obs in Figure 1. Moreover, the quality of your paper will improve if you use colour on Figures 3, 5, 6, 8 and 12, making them more clear and understandable.
Response 2: A detailed description is added in the caption of Figure 1. Following the referee’s suggestion, we have added color to Figures 3, 6, 8, and 12. Supplementary descriptions are added in the caption of changed figures. Figure 5 stays the same because colored outlier markers make the figure unreadable.
Point 3: Section 3, line 263. You wrote, “while others are pre-determined empirically.” Could you explain why and how you did that?
Response 3: The XAJ model is designed to simulate the rainfall-runoff process in humid and semi-humid basins in China by Zhao et al (Ren-Jun, Z. The Xinanjiang model applied in China. J Hydrol 1992, 135, 371-381, doi:https://doi.org/10.1016/0022-1694(92)90096-E.). According to their original paper, some parameters can be pre-determined empirically to reduce the computational difficulty and make the XAJ model more robust. Since our study area is a typical humid basin in China, the pre-determined parameters and their values are chosen following Zhao’s suggestion. Supplementary statement is added in Seciton 3 (line 282)
Point 4: Section 4. When you closed the introduction, you stated that, in section 4, you would provide some recommendations for practical applications of your method. I could not find such recommendations on section 4 so please add them or remove the previous text.
Response 4: We agree with the referee that we did not provide epecific recommendations for practical application. We have deleted corresponding text in the introduction.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
This manuscript can be accepted.
Reviewer 3 Report
Thank you all for revising the manuscript.
