Dear Editor, dear authors,

I find the topic of the submitted manuscript very interesting and also within the scope of HESS. Rapid flood prediction mapping in urban areas has a few challenges when compared with flood modelling purposes (e.g., fluvial flood mapping). The authors identify these challenges and propose a data-driven flood model based on LSTM networks and Bayesian optimisation.

The optimisation part is interesting, but the implementation and justification of the LSTM flood model lacks, in my opinion, novelty. One of the arguments of the authors for using LSTM to predict flooding is its suitability to predict time series, i.e. to include the time dimension in the flood prediction mapping. However, they fail to do so as they predict only the maximum water depth maps. This has been presented in previous recent studies (that are correctly acknowledge by the authors); so, what are the novel aspects of this study? simple a different newtok architecture? I believe this is not for a scientific contribution that aims to contribute to the advance of the (applied) science.

One of the main challenges about data-driven models, in general, is the capabilitiy of the models to generalise to different case studies or contexts. This aspect is not investigated nor discussed in the manuscript - it is only briefly mentioned, and for the 1st time, in the conclusions section. Since terrain elevation is not part of the inout data set, it seems that the proposed model is not at all generalisable to other cases.

The limitations of the model and study presented at the end of the Conclusions section are very similar to those of other previous studies. If the authors are aware of these limitations from previous studies, I would expect them to try to address at least some of the previous studies limitations to improve the knowledge.

As mentioned above, I think the part of the optimisation could be better explored in the manuscript. Perhaps this could be the novel contribution of the study?

The  manuscript is, in general, well written, making it easy to read.

Specific comments:

- Line 43: this is valid also for physically-based models. Rephrase?

- Line 113 & 115: why different models Mike Urban & Flood vs Mike 21? please provide justification or mention only the model used.

- Line 145: can "... for the long-term memory of data" be better described?

- Line 149: unclear sentence. It seems that something is missing.

- Lines 279 - 282: this can't be seen in the plots. The colour scale does not have units. How does the colour scale relate to the yy axis?

- Line 306: the worst and best cases are also interesting to be analysed and discussed.

The author used the rainfall as the input to generate simulated flood inundation maps. The paper is well organized, and the LSTM model and Bayesian optimization method appers to be correct and effective. However, there are three major issues. First, the summary of the earlier work needed improvement.There are many related papers using data-driven approach to generate flood maps, however the authors do not include them in the introduction. Second, a research may be regarded as a novel study if it resolves a problem or constraint in earlier studies. However, the LSTM is a new neural network layer that can perform better than ANN or linear regression models, and this manuscript does not appear to have demonstrated its novelty. Lastly, this manuscript lacked baseline models and results, which prevented me from knowing how much better the LSTM model is than a simple average baseline, linear regression model, or an ANN model.

Details:

1. Method section 2.2. If my understand is correct, all the flood maps are simulated by your physically-based model. Thus, your are developing a deep learning model as a surrogate model of your Mike series models. Such studies have been studied in the past several years using Deep Learning models (see the following papers). If the main difference between your study and theirs is the use of LSTM other than a fully connect layer, this is not novel enough.

Berkhahn, S., Fuchs, L., & Neuweiler, I. (2019). An ensemble neural network model for real-time prediction of urban floods. Journal of hydrology, 575, 743-754.

Lin, Q., Leandro, J., Wu, W., Bhola, P., & Disse, M. (2020). Prediction of maximum flood inundation extents with resilient backpropagation neural network: case study of Kulmbach. Frontiers in Earth Science, 8, 332.

2. What is the color in Figure 6a represents? Can you provide more details about this figure? It seems like the inccrease of the number of optimizations does not decrease the error much.

3. Are your figures 9 and 10 captions correct? And, is your legend correct for Figure 10? The base color Cyan should represents0 on your Y-axis, but the legend shows it is 0.5 relative error.

4. Can you provide results from several baseline models to justify your model performance is good? Some sample baselines could be: 1, models such as ANN as Berkhahn, S., Fuchs, L., & Neuweiler, I. (2019) did (deep learning model using only FC layers other than LSTM). 2, a Lasso or Ridge Regression (or machine learning models) for each point with the overall rainfall as input, water depth as output. 3, an average/median flood map of the training dataset (a.k.a. simple average, see the link below). Without these baselines, your results in Figure 8a and 8b cannot prove much -- we know your model is good, but we don't know how good your model comparing to other simple linear models or simple average of training sets.

https://otexts.com/fpp2/simple-methods.html