the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Feb 2024
Probabilistic Flood Inundation Mapping through Copula Bayesian Multi-Modelling of Precipitation Products
Abstract. Accurate prediction and assessment of extreme flood events are crucial for effective disaster preparedness, response, and mitigation strategies. One crucial factor influencing the intensity and magnitude of extreme flood events is precipitation. Precipitation patterns, particularly during intense weather phenomena such as hurricanes, can play a significant role in triggering widespread flooding over densely populated areas. Traditional flood prediction models typically rely on single source precipitation data, which may not adequately capture the inherent variability and uncertainty associated with extreme events due to certain limitations in precipitation generation framework, availability or both spatial and temporal resolutions. Moreover, in coastal regions, the complex interaction between local precipitation, river flows and coastal processes (i.e., storm tide) can result in compound flooding and amplify the overall impact and complexity of flooding pattern. This study presents an implementation of Global Copula-embedded Bayesian Model Averaging (BMA) (Global Cop-BMA) framework for improving the accuracy and reliability of extreme flood modelling. The proposed framework integrates a collection of precipitation products with different spatiotemporal resolutions to account for uncertainty in forcing data for hydrodynamic modelling and generating probabilistic flood inundation maps. The methodology is evaluated over Hurricane Harvey, a catastrophic weather event characterized by intense precipitation and compound flooding processes over the city of Houston in the state of Texas in 2017. The results show a significant improvement in predictive accuracy compared to those based on a single precipitation product, demonstrating the merits of the Global Cop-BMA approach. Furthermore, the research extends its impact by generating probabilistic flood extension maps that account not only for the primary influence of precipitation as a flood driver but also for the intricate nature of compound flooding processes in coastal environments.
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RC1: 'Comment on nhess-2024-26', Dino Collalti, 06 Mar 2024
The study explores the potential of incorporating several precipitation products via a copula Bayesian multi-modeling approach to create probabilistic inundation maps. The authors illustrate their technique in the example of Houston during Hurricane Harvey 2017. The manuscript is well-written and relates the various concepts in a resourceful manner. There are three main areas for improvement:
- The role of copula function and the choice for a specific function remains somewhat elusive. For one, Section 2.2 could benefit from being more specific in the role of copula function in replacing the posterior distribution. How does the copula function relate to the prior distribution? In addition, the section would benefit from an introduction of the concept of a copula function in statistical terms so as to convince the reader that the separation of functional dependence and modeling of marginal distributions is appropriate. Besides Section 2.2, the choice of copula in Section 4.1, line 329, is not convincing. It should be argued why only three distinct copula functions are evaluated and how that decision to restrict it to these three took place (one could imagine extreme value copulas or the Normal copula to be a candidate as well). For instance, whether there are certain characteristics that are sought in terms of attainable dependence, dimensionality, etc. Also, please detail the fitting process for evaluation on line 330 - it is unclear. The authors could use a copula cross-validation criterion, for instance, to make their choice tractable and not dependent on the rest of the model.
- Validation: A substantial part of the manuscript aims to validate the approach by comparing the model prediction with the inundation level at certain stations and comparing these against single data-source predictions. As the COP-BMA nests all other single models, it is no surprise that it outperforms the others by design. A better comparison might be not against the other models but against a non-copula BMA. An alternative would be to omit one data source (likely the best performing rain gauge data) and to make the horserace of the COP-BMA against that single model. This comparison has additional implication as it would be a remote sensing data vs. rain gauge data comparison.
- Implication: As already indicated in the previous point raised, the manuscript lacks the precise quantification or discussion of the proposed methodology's advantages and applications. For instance, staying with the case of Hurricane Harvey: what are the computational costs and runtime of the model? Could it be employed in risk assessment with rain-on-grid data forecasts? How much better is it compared to a non-COP BMA? While these questions are for illustration only, the discussion in the manuscript could aim to assess the methodology's benefit in a broader context.
In addition, there are a couple of minor remarks:
- Line 52: please introduce the e HEC-RAS 2D when first mentioning it, briefly.
- Line 83: please discuss the advantages and disadvantages of deterministic vs. probabilistic approach in this setting.
- Line 123: please precisely state which variables are all subject of BMA.
- Line 133: "In other worlds..."
- Line 148: Is the copula function bivariate? Please introduce the concept of a copula function here.
Citation: https://doi.org/10.5194/nhess-2024-26-RC1 -
RC2: 'Comment on nhess-2024-26', Anonymous Referee #2, 29 Mar 2024
The authors have conducted an interesting and complete study on generating probabilistic flood inundation maps by considering the uncertainty associated with the precipitation input for the hydrologic and hydraulic models. The core of the proposed framework for flood inundation mapping is the Copula-embedded Bayesian Model Averaging (Cop-BMA) proposed by the authors in their earlier work. After integrating eight precipitation products, the performance of the Global Cop-BMA was tested based on an extreme flood event, Hurricane Harvey. The authors did a good job of putting everything together in an organized way. However, I still have several questions and suggestions for improving the current work.
- Although the technical details of the copula functions have been presented in the literature, it will be helpful for readers to catch the meanings of new variables presented in this article if these variables are illustrated clearly. For example, what are the terms in the copula function on the right-hand side of Equation (3)?
- As shown in Equation (4), the form of the likelihood function (a product of the probability density at different time steps) is valid when the temporal predictions are independent. But in this study, we may not assume the “hourly” output to be independent of each other. So what are the potential impacts of autocorrelation of the target variables, y, on the Cop-BMA results?
- It is not clear how to transform the rainfall into runoff in the HEC-RAS 2D model. Also, it seems to be unfair to compare the performance of different precipitation products since the infiltration process was not considered in the hydrodynamic modeling process. In addition, in Line 453, why do the infiltration processes mainly impact the “initial” water surface elevation results? How about the “continuous” loss during the flood event?
- Manning values are important parameters in flood modeling and the values will change with the water depth. As presented in Line 192, the Manning values “are further adjusted during the calibration period, 7 days before the occurrence of Hurricane Harvey”, would it be better or necessary to calibrate the roughness parameters based on a similar flood event?
- For the application of Cop-BMA, it is like a trial-and-error procedure to select an appropriate marginal distribution and a copula function for the target variable. Is there any general guidance or suggestion for interested readers if they want to apply the framework to the other areas or variables?
- Some cases in Figures 4 and 6 show that if all the members in the precipitation ensembles consistently overestimated (e.g., NOAA 8770613 and USGS 08074710) or underestimated (e.g., USGS 08072050) the peak WSE, Global Cop-BMA did not help at all. Any comments on that?
- Line 20 and Line 382, could you provide quantitative results to measure the degree of improvement due to the application of the Cop-BMA approach?
- As discussed by the authors, the final flood inundation maps could not be validated effectively because of the scarcity of spatial observed data. Is it possible that the performance of a model member in the ensemble would be better than that of Cop-BMA in terms of the inundation extents, even though its performance in the WSE comparison at one gauge location is not the best?
Minor Issues
- Line 42-43, in BMA applications, I think it is the conditional PDF (the second term on the right-hand side of Equation (1)) rather than the “data” that is assumed to follow a Gaussian distribution. In other words, the pattern of model residuals follows a Gaussian distribution in BMA.
- It would be better if more information can be added to Table 1 or Figure 2. For example, the temporal resolution of discharge and WSE data, the start and end date of the simulation period, indicating which stations are used as boundary conditions and validation, etc. Also, the information of USGS 08074710 was not included in Table 1.
- Line 73: two brackets were used for the reference.
- Please add the units of SSE in Table 3.
Citation: https://doi.org/10.5194/nhess-2024-26-RC2
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