the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 28 Jun 2023
Quantify and reduce flood forecast uncertainty by the CHUP-BMA method
Abstract. The Bayesian model averaging (BMA), hydrological uncertainty processor (HUP), and HUP-BMA methods have been widely used to quantify flood forecast uncertainty. This study, for the first time, introduced a copula-based HUP in the framework of BMA and proposed the CHUP-BMA method to bypass the need for normal quantile transformation of the HUP-BMA method. The proposed ensemble forecast scheme consists of 8 members (two forecast precipitation inputs, two advanced long short-term memory (LSTM) models, and two objective functions used to calibrate parameters) and is applied to the interval basin between Xiangjiaba and Three Gorges Reservoir (TGR) dam-site. The ensemble forecast performance of the HUP-BMA and CHUP-BMA methods is explored in the 6–168h forecast horizons. The TGR inflow forecasting results show that the two methods can improve the forecast accuracy over the selected member with the best forecast accuracy, and the CHUP-BMA performs much better than the HUP-BMA. Compared with the HUP-BMA method, the forecast interval width with the 90 % confidence level and continuous ranked probability score metrics of the CHUP-BMA method are highest reduced by 28.42 % and 17.86 %, respectively. The probability forecast of the CHUP-BMA method has better reliability and sharpness and is more suitable for flood ensemble forecasts, providing reliable risk information for flood control decision-making.
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Status: final response (author comments only)
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RC1: 'Comment on hess-2023-106', Anonymous Referee #1, 21 Jul 2023
The paper proposes a new CHUP-BMA ensemble forecasting method by incorporating the CHUP-derived posterior distribution of the observed flow into the BMA framework. It has the advantage that the initial state constraints can be considered in the BMA while avoiding the normal quantile transformation of the HUP-BMA method. Based on deep learning, an ensemble forecasting scheme considering input, model structure, and parameter uncertainty is constructed in Three Gorges Reservoir, China, and the effectiveness of the CHUP-BMA method in reducing forecast uncertainty is verified. The study is innovative and theoretically rigorous and has promising results with solid application potential. Some questions need further discussion.
1. The sources of Figure 3 and Table 2 need to be explained to improve the reasonableness of the paper.
2. Various model inputs (e.g., rainfall, tributary flows, etc.) exist in the interval basins. The article only considers the input uncertainty of rainfall, and it is suggested to add a reason for this in subsection 3.2.1.
3. Line 255. You should briefly introduce the LSTM in subsection 3.2.2 to improve the paper's readability. In addition, it is recommended to cite references more relevant to the LSTM.
4. Deep learning parameters significantly impact forecast accuracy, so it is recommended to show the values of deep learning parameters. The study should concentrate on ensemble forecasting methods rather than deep learning models. Therefore, the model parameter values can be shown in the appendix.
5. Line 369, add a description of the member type with better forecast accuracy, i.e., the input composition, the model structure, and the objective function of the selected parameters.
6. There are numerous evaluation metrics in deterministic and probabilistic forecasting. Briefly explain the reasons for the metrics chosen in the paper.
7. Line 465, replacing 'concentration' with 'sharpness' as 'reliability (α_index), concentration (IGS),' should correspond to the name of Figure 13.
8. To improve modeling rationality, explain why observations are used as model tributary inputs in training and validation periods.
9. In the outlook, adding the construction of the CHUP-BMA method using a more flexible vine copula will make the CHUP-BMA method more competitive.Citation: https://doi.org/10.5194/hess-2023-106-RC1 -
AC1: 'Reply on RC1', Shenglian Guo, 26 Jul 2023
Dear reviewer #1,
We are grateful to reviewer #1 for taking the time to read our manuscript and for their detailed and professional comments. We have provided point-by-point responses to all comments. Please refer to the supplementary document (Reply on RC1.pdf).
Sincerely yours,
July 26, 2023
Prof. Shenglian Guo
State Key Laboratory of Water R & H Engineering Science
Wuhan University, Wuhan, Hubei Province, 430072, P. R. China
E-mail: slguo@whu.edu.cn
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AC1: 'Reply on RC1', Shenglian Guo, 26 Jul 2023
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CC1: 'Comment on hess-2023-106', Shaokun He, 21 Oct 2023
Cui et al. (2023) mainly proposed a CHUP-BMA method to solve the unreasonable assumption of normal distribution of the BMA framework in hydrological forecast field. This specialized theory has been applied to the Three Gorges region of China to demonstrate its feasibility. The study is interesting and meaningful to the hydrological forecast community. However, it needs some revision before it is up to the publication standard of HESS.
- Lines 8-10, the statement is not accurate. As I know, few existing literature (with Copula tool or without it) has been devoted to avoiding the normal transformation in the HUP-BMA method.
- Lines 68-70 are not clear. It is ambiguous that " When the member forecasts are the same, the ensemble forecasts produce the same conditional probability distribution and lack rationality". The parameters of the BMA method include membership weights and variances, and the posterior distribution of the ensemble forecast is not necessarily the same even if the forecast members have the same results. In order to reflect the necessity of the initial state, the article should be changed to " When the forecast results of a member are the same at different moments, the same forecast conditional probability distribution will be generated, which is not reasonable." It is important to highlight that the distribution is the same at different moments.
- Line 79, missing punctuation.
- Line 120, unit superscript error.
- Line 186, the symbol cm() does not appear in Eq. (12).
- Line 279is not clear. To improve the readability and logic of the paper, it is suggested to revise as “the forecasted flow of the upstream mainstream station”.
- Line 339, whether these distributions and Copula functions passed the K-S test or other assumption tests?
- Line 498, although the authors do not mention it, it is necessary to mention the improvement room of the inherent mechanism of the CHUP-BMA method.
Citation: https://doi.org/10.5194/hess-2023-106-CC1 -
AC2: 'Reply on CC1', Shenglian Guo, 01 Nov 2023
Dear CC #1,
We are grateful to CC #1 for taking the time to read our manuscript and for the detailed and professional comments. We have provided point-by-point responses to all comments. Please refer to the supplementary document (Reply to CC1’ comments.pdf).
Sincerely yours,
November 1, 2023
Prof. Shenglian Guo
State Key Laboratory of Water R & H Engineering Science
Wuhan University, Wuhan, Hubei Province, 430072, P. R. China
E-mail: slguo@whu.edu.cn
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CC2: 'Comment on hess-2023-106', Guang Yang, 23 Oct 2023
The paper couples the Copula-based hydrological uncertainty processor with the Bayesian model averaging method to quantify and reduce uncertainty in flood forecasting upstream of the Three Gorges Reservoir in the Yangtze River basin, China. The topic is timely and the paper is technically sound. The paper could benefit from additional clarification in some sections.
Line 9: The full name of "CHUP-BMA" needs to be given the first time it is mentioned.Lines 68-70: The description here is not clear to me, e.g. why the BMA ignores the constraint of initial conditions. Further explanation of the reason and how the HUP-BMA mentioned later can obtain the posterior distribution function of the observed flow is suggested in the Introduction section.
Lines 85-86: It seems that this work is motivated by the copula-based HUP method in Liu et al. I suggest giving a brief description of this method and how it is used to improve forecast accuracy here.
Line 87: I suggest presenting the objectives and research steps one by one. For example, the novelty of this work can be introduced in the previous paragraph, along with the shortcomings of current methods, and then the implementation of the proposed method in streamflow forecasting can be briefly introduced.
Section 3.2: It seems that the model structure uncertainty in this study is considered by using two forecast models with LSTM-RED structure. why not using two different types of models (e.g., ANN-based vs. tree-based or physical-based vs. data-driven models)?
Also, what is the purpose of using MAE and MSE as prediction evaluation metrics in this work? These two metrics are similar to each other. In order to account for model parameter uncertainty, it seems more appropriate to use three apparently different evaluation metrics, such as Nash-Sutcliffe efficiency, mean absolute error (MAE), and relative error of total discharge (RE).
Some reference to the first mentioned methods is suggested, e.g. the reference to the "Adam method" is suggested in line 283.
Citation: https://doi.org/10.5194/hess-2023-106-CC2 -
AC3: 'Reply on CC2', Shenglian Guo, 01 Nov 2023
Dear CC #2,
We are grateful to CC #2 for taking the time to read our manuscript and for the detailed and professional comments. We have provided point-by-point responses to all comments. Please refer to the supplementary document (Reply to CC2’ comments.pdf).
Sincerely yours,
November 1, 2023
Prof. Shenglian Guo
State Key Laboratory of Water R & H Engineering Science
Wuhan University, Wuhan, Hubei Province, 430072, P. R. China
E-mail: slguo@whu.edu.cn
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AC3: 'Reply on CC2', Shenglian Guo, 01 Nov 2023
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RC2: 'Comment on hess-2023-106', Anonymous Referee #2, 15 Feb 2024
The authors combine the copula-based hydrological uncertainty processor (CHUP) and Bayesian model averaging (BMA) to obtain a novel approach to statistical post-processing of hydrological ensemble forecasts. The proposed approach is promising and the presented results are fair, but the paper needs some improvement and it also raises some questions.
Major comments:
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L28: The cited paper Sloughter et al. (2010) deals with post-processing wind speed forecasts. The BMA model for precipitation is introduced in Sloughter et al. (2007).
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I am also missing references to BMA models for hydrological forecasts, e.g. Hemri et al. (2013) or Baran et al. (2019).
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Eq.4: In the original description of the HUP, different CDFs are considered for the forecasts and the observations, moreover, in the former case it is considered as an initial estimate. Does such a relaxation make sense here as well?
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Section 3.1.2. introducing the HUP follows the structure of Sections 2.1.2 – 2.1.4 of Darbandsari and Coulibaly (2021); however, one should mention that the Markov process of Eq.5 is stationary and define exactly how θt in L169 is related to Eq.7 (see Darbandsari and Coulibaly, 2021, Eq.10).
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L310: “The IGS metric indicates the sharpness of the probabilistic forecast”. The IGS, similar to the CRPS addresses simultaneously both calibration and sharpness, as indicated in the cited work of Gneiting et al. (2005). Hence, I think referring to IGS as a measure of concentration is slightly misleading.
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In Section 4, I would definitely consider the corresponding scores (or at least some of them) for the ensemble forecasts as well.
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What can be said about the statistical significance of the score differences between HUP-BMA and CHUP-BMA?
Minor remarks, typos:
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L205-206: “It has been studied that the BMA method with sliding windows can obtain better probabilistic forecast performance”. Better compared to what?
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L307: “indicative function” → “indicator function”
References
- Baran, S., Hemri, S. and El Ayari, M. (2019) Statistical post-processing of water level forecasts using Bayesian model averaging with doubly-truncated normal components. Water Resour. Res. 55, 3997–4013.
- Hemri, S., Fundel, M. and Zappa, M. (2013) Simultaneous calibration of ensemble river flow predictions over an entire range of lead times. Water Resour. Res. 49, 6744–6755.
- Sloughter, J. M., Raftery, A. E., Gneiting, T. and Fraley, C. (2007) Probabilistic quantitative precipitation forecasting using Bayesian model averaging. Mon. Weather Rev. 135, 3209–3220.
Citation: https://doi.org/10.5194/hess-2023-106-RC2 -
AC4: 'Reply on RC2', Shenglian Guo, 26 Feb 2024
Dear reviewer #2,
We are grateful to reviewer #2 for taking the time to read our manuscript and for their detailed and professional comments. We have provided point-by-point responses to all comments. Please refer to the supplementary document (Reply on RC2.pdf).
Sincerely yours,
February 26, 2024
Prof. Shenglian Guo
State Key Laboratory of Water R & H Engineering Science
Wuhan University, Wuhan, Hubei Province, 430072, P. R. China
E-mail: slguo@whu.edu.cn
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RC3: 'Comment on hess-2023-106', Anonymous Referee #1, 28 Feb 2024
In this round of revision, the authors have satisfactorily addressed all my concerns and significantly improved the manuscript and the language. The authors have proposed a novel approach, combining the copula-based hydrological uncertainty processor and Bayesian model averaging, to obtain statistical post-processing of hydrological ensemble forecasts, significantly reducing flood forecasts. I recommend accepting the revised manuscript.
Citation: https://doi.org/10.5194/hess-2023-106-RC3 -
AC5: 'Reply on RC3', Shenglian Guo, 08 Mar 2024
We are glad to know that we have addressed your comments and concerns. Thanks again!
Citation: https://doi.org/10.5194/hess-2023-106-AC5
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AC5: 'Reply on RC3', Shenglian Guo, 08 Mar 2024
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