Dear reviewer:

Thank you for your concerns and comments on our manuscript. Reply to comments, point-to-point, are given as follows:

1.  Can authors explain the limitations of traditional storm surge hydrodynamic models that prompted the development of the Hydrodynamical Cellular Automata Flood Model (HCA-FM), particularly regarding computational efficiency and stability?

Traditional storm surge hydrodynamic models, such as the ADCIRC model, simulate the storm surge inundation by numerically solving full shallow water equations. However, it is hard to balance scientific accuracy, numerical stability, and computational efficiency in computer modeling. The reasons are detailed as follows:

High Computational Cost: The time step of the hydrodynamic model is restricted by the grid resolution to ensure stability, because the stability of the solution is limited by the CFL restriction on the gravity wave speed (√gH ∆t/∆x<C_r, in which a practical C_r upper bound of is 0.5 or smaller). To guarantee the spatial accuracy and computational stability of the storm surge inundation simulation, the grid resolution must be increased, and the time step must be reduced to ensure model stability, which significantly increases the computational cost.

As a result, most hydrodynamic modeling applications require significant computational resources. In addition, many complicated preparations must be done before using a hydrodynamic model, particular for a unstructured mesh, including mesh generation, mesh quality adjustment, and input file generation. It is not convenient for practical use. These limitations have prompted the development of the Hydrodynamical Cellular Automata Flood Model (HCA-FM) to provide a computationally efficient and easy-to-use storm surge flood model.

2.  How does the wetting and drying algorithm derived from simplified shallow water momentum equations contribute to the computational efficiency and stability of the HCA-FM model?

The traditional numerical models require a significant amount of time to solve hydrodynamic equations using discretization methods. However, in HCA-FM, we transform the shallow water equation into a straightforward wetting and drying algorithm and dynamic calculation formula. Based on this, we have developed the efficient grid iteration algorithm of HCA-FM using cellular automata. Therefore, on the premise of ensuring the accuracy of the calculation results, this approach improves computational efficiency and avoids instability that may arise when solving complex equations using discretization methods.

3.  Could authors elaborate on how the rectangle grid and cellular automata algorithm are utilized within the HCA-FM model to improve computational efficiency, and what advantages does this approach offer over traditional methods?

A cellular automata (CA) is typically composed of a group of cells that represent a discretized space, each of which has a state, a distribution of neighboring cells, a discrete time step, and a set of transition rules. The transition rules dominate the update process of CA by determining the new state of each cell in terms of its current state and the states of the cells in its neighborhood. The computational efficiency of the CA algorithm depends on the complexity of the transition rules. The wetting and drying algorithm (transition rules) of HCA-FM, which is derived from the simplified shallow water equations, is very simple and therefore computationally efficient. In comparison, traditional methods like numerical model solve hydrodynamic equations using discretization methods and thus require a significant amount of time. Therefore, HCA-FM has an advantage in terms of computational efficiency.

4.  In evaluating the HCA-FM model, what were the critical criteria used to assess its performance, and how did the model compare to regional field observations and simulations from a widely used hydrodynamic numerical model?

In the comparison of HCA-FM simulations with field observations (Section 3.2), the visual image comparisons were made for the line or polygon features of inundation extent. The experiment contains two typhoon storm surge processes, and the study areas are Cangzhou, Hebei and Shenzhen, Guangdong. The model performance is tested by the fitness of line or polygon features of inundation extent by visual comparison.

In the experiment of comparing simulations between HCA-FM and numerical simulations from ADCIRC+SWAN model (Section 3.3), comparisons were made for inundation extent and depth in Laizhou Bay for two typhoon storm surge processes (Lekima and Polly). The two models are using the same topo data. The index of agreement in the comparison includes the fit ratio δ of inundation extent, squared correlation coefficient R² and root mean squared error RMSE for water depth (page 12, line 255-265). The fit ratio δ ranges from 0 for no overlap to 1 for perfect fit. R² varies between 0 and 1 which a computed value of 1 indicates perfect agreement. A smaller RMSE indicates better agreement.

5.  Can authors provide insights into validating the HCA-FM model against regional field observations, including the specific data sources and methodologies used for comparison?

In the experiments of comparing HCA-FM simulations with field observations, visual image comparisons were made for the line or polygon features of inundation extent. It is important to note that due to the limitations of rough survey data, validation was based solely on inundation extent. Detailed comparisons for water depth had been made between HCA-FM and ADCIRC+SWAN coupled model.

The first experiment compared the inundation extent caused by Typhoon Lekima in Cangzhou, Hebei. Investigation team from the National Marine Environmental Forecasting Center investigated disasters around the south coast of the Bohai Bay. The second experiment compared the inundation extent caused by Typhoon Hato in Shenzhen, Guangdong. The Marine Monitoring and Forecasting Center of Shenzhen organized teams to investigate disasters in key regions. The field survey data in Shenzhen after Typhoon Hato included several locations that were severely affected, which indirectly reflected the inundation extent. Relevant complement will be made in revised manuscript.

6.  What were the main findings regarding the ability of the HCA-FM model to reproduce observed inundation distributions, and how did its predictions compare to those of the hydrodynamic numerical model regarding inundation extent and submerged depth?

In Section 3.2, the simulated ability of HCA-FM is validated comparing its simulation with the observed inundation distribution, as given in Fig. 4 & 5, it is able to reproduce the actual inundation area for both two TC events.

In Section 3.3, as a result in the comparisons between HCA-FM and ADCIRC+SWAN (Fig. 6), the fit ratio δ of inundation extent was 0.92 for TC Lekima and 0.95 for TC Polly. For the submerged depth, the R² were 0.96 for both Lekima and Polly, the RMSE were 0.13 m for Lekima and 0.12 m for Polly. The results indicates a good consistency between the two models. In addition, sensitivity experiments associated with wind force and bottom friction were designed (Table 2), and the results shows that consideration of external forces ensures model’s accuracy towards the storm surge inundation simulation.

7.  The study mentions significantly improved computational efficiency with the HCA-FM model, allowing for inundation predictions within a few minutes. Can authors discuss the implications of this improved efficiency for real-time storm surge forecasting and disaster management?

Hydrodynamic models are generally considered as unviable for areas larger than 1000 km² when the resolution required is less than 10 m. Forecast timeliness is often not met for larger scale forecasts. But the HCA-FM model requires significantly less computer effort than hydrodynamic models. Runtime savings portend that the model is suitable for large floodplains larger than 2000 km². In real-time storm surge forecasting and disaster management, the HCA-FM model can be used in conjunction with the hydrodynamic models. The HCA-FM can quickly forecast the potential regions and hazard level affected by the storm surge to identify the most serious regions, which leaves more and sufficient time for the government to make decisions.

8.  How does the high stability of the HCA-FM model contribute to its reliability in predicting storm surge inundation, particularly under varying environmental conditions and input parameters?

Since the iterative solving process of the HCA-FM is concise, there do not exist many constraints on the stability as those of the numerical model, which depends on factors such as the environment, mesh, and model parameters when solving complex differential equations. Therefore, different environmental conditions, grids and parameters do not affect the stability of the model, thus ensuring the reliability of the model in predicting storm surge inundation. As seen, we perform experiments conducted in different region, and the HCA-FM model performed well in all regions, including Laizhou Bay where it was tested against two typhoons with different tracks. These results suggest that the model is accurate and stable across different study areas and typhoon processes.

9.  Considering the significant advancements demonstrated by the HCA-FM model, what are the potential applications at large space scales, and how might they contribute to more effective disaster prevention and mitigation strategies in coastal regions?

HCA-FM can be used not only for real-time disaster prevention and mitigation by rapidly identifying key affected areas on a large scale, but also for regional storm surge hazard and risk assessment. To conduct a probabilistic risk assessment, it is necessary to analyze the probability statistical characteristics of storm surge disaster-causing factors from their long-term time series. As long-term storm surge flood observations are sparse, a large number of simulations are required. Additionally, risk assessments often cover larger study areas, which can make running simulations using hydrodynamic models prohibitively time-consuming. Therefore, HCA-FM can leverage its computational efficiency to significantly reduce the time spent on probabilistic risk assessment and contribute to more effective disaster prevention and mitigation strategies in coastal regions.

10.  Lastly, based on the findings of this study, what are the critical areas for future research or refinement of the HCA-FM model, and how might it be further optimized for broader practical use in storm surge prediction and coastal zone management?

Since computing the new state of a cell in CA depends only on the state of the neighboring cells at the previous time step, CA algorithms are well suited to parallel computation. It will be considered to apply parallel computation for HCA-FM model for further enhancement of computational efficiency in the future. Additional, consideration will also be given to designing an interactive operating system for the model to cater for more intuitive and easy use. In addition to improvement of efficiency, the principles of the model will also be improved in the future to take into account more comprehensive hydrodynamic mechanisms to improve the simulation accuracy. Relevant complement will be made in revised manuscript.

We have also revised the manuscript to more clearly address the above issues.

Thank you very much for your attention and time.

Yours sincerely,

Xuanxuan Gao

Dear reviewer:

Thank you for your concerns and comments on our manuscript. Reply to comments, are given as follows:

First of all, after introducing the principles of the HCA-FM model, we directly applied the model to real storm surge events in order to compare it with observational inundation data and a widely used numerical model to verify model's accuracy in simulating storm surge induced inundation. We consider that the main purpose of the manuscript is to introduce the construction of the model and to confirm its reliability in practical applications which had been indeed confirmed in the validation experiments.

In addition, we also analyzed the advantages of the HCA-FM model in identifying the storm surge induced inundation over traditional CA models for urban flooding and in computational efficiency over numerical model, which is reflected in the discussions of the manuscript and consists of the following two main aspects:

(1)  Since we have verified the accuracy of HCA-FM model in simulating storm surge inundation through validation experiments, we believe that sensitivity experiments focus on the wind stress and bottom friction terms can be used to analyze the effect of external force terms on the storm surge inundation. In the discussions of the manuscript, we set up experiments by turning off the wind stress or bottom friction terms in HCA-FM. The results show that without considering the forcing of seawater diffusion by external forces such as wind stress or bottom friction, the consistency of the simulated inundation extent and inundation depth with the results of the numerical model are significantly reduced. The effects of these external forces are more prominent for storm surge induced inundation which is usually accompanied by intense weather processes, and thus traditional CA models for urban flooding that do not account for these influences will perform worse in the simulation of storm surge induced inundation.

(2)  In the discussions, we also compare the CPU time spent for inundation simulation by HCA-FM model and ADCIRC+SWAN model, and the results show that the computational efficiency of HCA-FM is improved by about four orders of magnitude compared to the numerical model.

We believe that these work go some way to illustrating the strengths of HCA-FM in these two aspects. We have also envisaged comparing the model with some traditional CA models for urban flooding, but the work has not been carried out at last for the following reasons: urban flooding and storm surge induced inundation are distinctly different in various aspects. There is a difference in the geographic environments in which urban flooding and storm surge occur, as urban flooding CA models mainly simulate the spreading of fluids to areas with lower elevation under gravity, while storm surge inundation usually occurs in coastal areas, where seawater, apart from spreading to areas with lower elevation under gravity, also spreads to areas with higher elevation under dynamic forcing. Therefore, the common CA models in the existing literature triggered by water volume cannot be directly applied to storm surge inundation simulation. Whereas, when storm surge inundation simulation is performed using common CA models triggered by water depth, the water surface will eventually remains flat as an equilibrium. So it is not necessary to apply this type of CA model to storm surge inundation simulation and make comparison with HCA-FM.

We appreciate your suggestions to provide other ideas for related analyses. Currently, we have attempted the following work based on your suggestions (figure in supplement):

Experimental setup: as shown in the figure, a simplified typical terrain for storm surge inundation is designed with a constant slope (1:500), with the left side on the shore side and the right side on the sea side. The inundation source is located at the position where the ground elevation is 0, and the water level is set to be 2.5 m, with a constant flow velocity of 1 m/s. For the onshore winds and bottom friction coefficient, we set up three sets of constant wind speeds of 0, 20, and 40 m/s, and three sets of Manning's coefficient of 0.04, 0.06, and 0.08. According to the combination of the three sets of wind speeds and Manning's coefficient, the inundation simulation is carried out using the HCA-FM model.

The preliminary experimental results are as follows: the figure shows the maximum water level distribution under different wind speed and Manning's coefficient conditions. Bottom friction will hinder the seawater from propagating to the shore, and under the same wind speed condition, the larger the Manning's coefficient (the larger the bottom friction coefficient), the smaller the inundation range and the smaller the inundation depth; the onshore wind will force the seawater to propagate to the shore, and under the same bottom friction condition, the larger the wind speed, the larger the inundation range and the larger the inundation depth. It can be seen that the wind plays an important role in the storm surge inundation process, and if the effect of onshore wind is not considered in the inundation simulation, the potential inundation range and water depth will be underestimated. Thus, it demonstrates that it is necessary to consider wind stress and bottom friction in storm surge inundation modelling, which is the advantage of the HCA-FM model over the traditional urban flooding CA models.

If necessary, we will make additions in subsequent revisions of the manuscript to increase the depth of the discussion.

Thank you very much for your attention and time.

Yours sincerely,

Xuanxuan Gao