4.1. Three UK EA Benchmark Test Cases
Within the first study, two scenarios were analyzed. First, the model was set to act as a fully CA-based model, and in the second scenario, the model was set to act as a hybrid model (i.e., a combination of CA-4D and D-Flat). The purpose of these two scenarios was to evaluate the improved performance of the DEM-incorporating model in terms of accuracy and efficiency.
shows the parameters of various simulations used to simulate the EA benchmark test cases. The most important parameter for CA-4D is the parameter α in Equation (4). This value has a significant impact on the actual computation time to finish a run. The parameter α should be low enough to ensure model stability but high enough to ensure computational efficiency. In conclusion, a higher α value returns a coarser precision but with a faster run time. For the hybrid simulation, many parameters must be determined based on professional judgment or trial-and-error rules. An important configuration step is to set the ratio of grid resolution between coarse grid resolution (CA-4D) and fine grid resolution (D-Flat). If the ratio (hereafter referred to as the DEM ratio) is high, the computation time may decrease significantly. The prediction accuracy may decrease for the following reasons. The assumption of flat-water theory in D-Flat is limited to small and flat areas. If the topography of the applied area (i.e., each color block on the right in Figure 3
) changes dramatically or the area is too large, the assumption may not be sustained. A higher DEM ratio makes the IZ larger and may cause the D-Flat assumption to not be sustainable. Second, the results of CA-4D serve as input to the D-Flat model in HIM. The CA results have an impact on the prediction accuracy. It tends to oversimplify the topographic effect and provides fewer details by running CA-4D with a coarser grid. In this work, a 4–5 DEM ratio was used. For example, Table 1
shows that a ratio of 5 was applied in the HIM for the EAT2 scenario. This means that an integration of the CA-4D model with a 100 m × 100 m DEM and the D-Flat model with a 20 m × 20 m DEM was considered. The resolution of the final results was 20 m × 20 m, which is consistent with the results of the CA-4D model only. The second important parameter is the output frequency, which determines when the data are being extracted or saved. In the case of the HIM, it is the time when the data from the coarse CA–4D results are interpolated to a finer resolution using the D-Flat model. If a very small output frequency is used, then the computational time will increase due to excessive D–Flat model activation. In this case, the HIM uses the output frequency that is already set consistent with the benchmark. The last important parameter is the increment constant (inc_const). This constant determines how much water is added to fill the lowest elevation within the IZ during each iteration. Selecting a smaller increment constant leads to better performance. However, it necessitates more simulation time. Ref. [50
] performed a sensitivity analysis regarding the increment constant. The model performance was found to not improve for increment constants smaller than 0.001 m. Hence, the HIM used 0.001 m as a default value for the increment constant. For both models, a finer grid resolution was used as the final result.
The purpose of implementing EAT2 is to evaluate the capability of the model to determine the inundation extent and final flood depth, which involves low-momentum flow over complex topography. The region, as shown in Figure 5
a, has an area of 2000 m × 2000 m and 16 locations with ~0.5 m deep depressions. A uniform Manning coefficient of 0.03 was applied to the whole domain, and a 20 m resolution DEM was expected to be used. The initial condition was a dry bed with a closed boundary area. The inflow boundary was applied along a 100 m line running south from the northwest corner, the value of which is given in Figure 5
b. The original problem specified 16 output points at the center of each depression, where points 1–4 start from the lower left depressions (X, Y = 250 m, 250 m) to the upper left (X, Y = 250 m, 1750 m).
shows a comparison of the water levels at points 1, 2, 3, and 4 for CA-4D, HIM, TUFLOW, and LISFLOOD-FP. The results agree well. However, for the CA-4D result, there is a small discrepancy in water level compared with the TUFLOW and LISFLOOD-FP results, especially at point 1, which is far from the inflow source. The difference in the maximum water levels is 10 cm. At point 1, the CA-4D result slightly lags those of TUFLOW and LISFLOOD-FP in terms of the time when the water begins to fill the depression. This occurs at t = ~3 h in TUFLOW and LISFLOOD-FP and at t = ~6 h in CA-4D. Interestingly, unlike the CA-4D result, the HIM result at point 1 tends to be similar to those of TUFLOW and LISFLOOD-FP.
shows a comparison of the flood extent between CA-4D (a) and the HIM (b) at t = 48 h. The HIM shows significant inundation at point 9, while the CA-4D output is completely dry. The discrepancy occurs due to the different grid resolutions that were used. For the HIM, a 100 m grid resolution was used as an input, while for the full CA-4D scenario, a 20 m grid resolution was used. Since the coarse grid resolution data tend to oversimplify the topographic information, the final results of the flood extent might be different. Since there are no observation data, this paper assumes that the flood map produced by CA-4D represents the true value. In this way, the impact of the DEM model can be identified. Based on the performance indicator TPR, the HIM successfully predicts 85% of the area identified by CA-4D as inundated. The FDR shows the percentage of the overpredicted area by the HIM. Based on the calculation, the FDR is 18.32%. The last performance indicator, RMSE, is 0.047 m. The results show that the DEM model does not strongly negatively impact the results.
The EAT4 test consisted of a 1000 m × 2000 m horizontal floodplain with a ground elevation of 0 m, and a flood wave occurred due to an overtopping embankment defense failure. The flow boundary condition, as shown in Figure 8
b, was applied at the central-west border (x = 0, y = 1000 m). A uniform Manning coefficient of 0.05 m−1/3
s was applied to the whole domain. The scenario was simulated until the time reached 5 h with 6 specified points (see Figure 8
a). Figure 9
shows the water level versus time at points 1, 3, 5, and 6. The results obtained from CA-4D and the HIM are in very good agreement with those from TUFLOW and LISFLOOD-FP, with no significant discrepancy. This means that the CA-4D model and HIM show good performance in modeling wave propagation. The HIM successfully predicted 97.7% of the inundated area predicted by CA-4D, and only 0.39% of the area was overpredicted by the HIM. The RMSE value was only 0.0035 m, which is almost negligible.
Unlike EAT2 and EAT8A, which involve complex topography, EAT4 involves only flat topography with a 0 m ground elevation. Therefore, the HIM results, which are very sensitive to the grid resolution, do not differ from the other model results. The only difference is the flood extent area. Figure 10
shows that the inundation area produced by the HIM is slightly larger than that of the CA-4D results. As shown in Figure 11
, at t = 1 h, the water already propagated at x = 420 m in the HIM and x = 380 m in the CA-4D model. A similar phenomenon was also observed by Hsu et al. [51
], who found that the inundation area may increase with coarser DEMs. This makes sense since the HIM model takes the results from the coarse CA-4D as input. However, the difference may be only minimally detectable in flood extent maps.
The goal of the EAT8A test is to simulate 2D flood routing within an urban area (Glasgow, UK). The boundary conditions involve two inflow sources: uniform rainfall across the area and surcharge flow located at (x, y = 920 m, 61 m), where the values are given in Figure 12
. The study area is approximately 0.4 km2
with an average slope of 4.3%, and the ground elevation ranges from 21 m to 37.6 m. The provided DEM, see Figure 13
, is a 0.5 m resolution DEM (no vegetation or buildings) created from LiDAR data. The model is expected to simulate flood routing using a 2 m resolution DEM. Two Manning values are used: 0.02 for road and pavement and 0.05 elsewhere. All boundaries of the domain are closed, and the initial condition is a dry bed.
shows that the temporal water levels obtained by CA-4D and the HIM are in good agreement with those of TUFLOW and LISFLOOD-FP. All stage hydrographs show two peaks. This phenomenon is caused by the two inflows coming at different times. Although the results are well correlated, some small discrepancies occur in the HIM and CA-4D results. Some small oscillations in the CA-4D and HIM models at point 3 are visible even though they do not greatly disrupt the overall results. Hunter et al. [15
] mentioned that this kind of problem is likely, especially when considering deep water. It could be solved easily by reducing the value of parameter α. However, doing so would dramatically increase the computation time.
Some differences occurred in the predicted maximum water level. At points 1 and 6, the hybrid simulation predicted values 5–10 cm and 2–3 cm, respectively, higher than the other models’ results. Moreover, at point 2, the hybrid simulation gave the lowest maximum water level compared to the others, especially the TUFLOW result. This primarily occurred because, at point 2, the water movement was primarily driven by momentum. LISFLOOD and CA-4D, which neglect the momentum equation, returned similar results. Figure 15
shows the flood extent predicted by CA-4D and the HIM. Visually, the inundation areas predicted by both models exhibit very good agreement. This conclusion is supported by a TPR value equal to 84.5%, an FDR value equal to 15.6%, and an RMSE value equal to 0.08 m. The results are also in good agreement with those of Jamali et al. [49
]. Three models—namely, TUFLOW, HEC-RAS, and CA-ffé—were applied by Jamali et al. [49
], and only a slight difference was found in the maximum inundation depth.
4.2. Coastal Areas of Chiayi County
The Chiayi County area is a low-elevation and relatively flat area located near the coastal region. The total area of the simulated domain is approximately 33 km2
. A rainfall event of 550 mm over 30 h was applied to the whole domain, and the temporal distribution is shown in Figure 16
. The drainage system was not included since this is not yet implemented in the HIM. However, this is reasonable in this case since the drainage system was reported as having failed due to a high tide. The full simulation time was 36 h. To examine the effect of the DEM ratio, two scenarios that used different DEM ratios were simulated. Two coarse DEMs with resolutions of 25 and 40 m, obtained from averaging the 5 m DEM, were used as an input for the CA-4D model, and within this study, these are called the C25 m and C40 m scenarios, respectively. The D-Flat model interpolated the outputs from CA-4D into 5 m resolution results.
shows the DEM of the area with the observation points, indicated by the red dots, and the maximum flood extent predicted by both DEM ratios. The water flows from east to west due to topography. Two detention ponds are located on the left-hand side of the map. The DEM ratio has a significant impact on the model performance. Figure 17
a,c show that the two ratios produce almost identical maximum flood extents. Floodwater accumulates in particular on the left-hand side of the map, and some differences are found in the areas near the boundaries. This study area is similar to the ET4 case, in which the area is topographically flat. The result shows that the impact of the DEM ratio is small when the study area is flat. Hence, this allows for a higher DEM ratio to be used. In this case, the DEM ratio of C25m is 5, while that of C40 m is 8.
The maximum flood depths were collected at three different locations, as shown in Figure 17
a. It is known that the observations are not from gaging stations but local surveys. Table 2
shows the comparisons between the observation data and the simulation results. The observations showed that the locations of points 1 and 2 were inundated, and point 3 was not. The HIM results are consistent with this finding. Overall, there is no significant difference between the C25 m and C40 m results. However, compared to the observation data, there is a 50% difference at point 2. This study used TUFLOW to simulate the study area and used the results to verify the HIM performance. The HIM and TUFLOW results are compared with observations in Table 2
. The difference is less than 10 cm in all observations. The results confirm the flood prediction capability of the HIM.