1. Introduction
Flooding is a major natural hazard. Once floods occur, the casualties and financial losses for highly populated areas are inevitably large (e.g., [
1,
2,
3]). Flooding is generally a function of river overflows, storm surges, and intense rainfall. Thus, strategies to mitigate flooding hazards include structural measures, such as detention basins and levee projects, and non-structural measures, such as floodplain regulations, emergency preparedness, and early warning systems [
4]. A robust and reliable model is necessary to predict the effect of flooding and to implement appropriate strategies [
5].
Several studies have developed simplified flood inundation models [
4,
6,
7,
8,
9,
10,
11,
12] to simulate potential flood areas. These models are based on the digital elevation model (DEM) and use a simple set of rules to simulate the spread of flood water over a given area. As a consequence, the models require less computational resources than complex two-dimensional (2-D) inundation models (e.g., WASH-123D [
13,
14] and FLO-2D [
15]) and may be more practical for real-time warnings. These complex models consider detailed hydraulic processes by solving complicated governing equations (e.g., Saint Venant equations) that are computationally intensive [
16]. Several studies used adaptive grids, parallel computing, or Graphics Processing Units (GPUs) to accelerate computer speed at real-time level (e.g., [
17,
18]). To develop a high-performance real-time forecasting system by using these complex models, however, requires higher hardware resources and technical skill. Therefore, the development of simplified and cost-effective models (e.g., [
6,
8,
10,
11,
12,
19]) is still a topic of interest. Lhomme
et al. [
7] developed a simplified hydraulic model (the rapid flood spreading method, RFSM) to maintain model runtimes at practical levels. The concept behind the RFSM is to spread the total flood volume in floodplain areas over the floodplain by considering the topography. Zerger
et al. [
4] used a flat-water assumption model to simulate coastal storm-surge risk for the coastal community of Cairns, Australia. The flat-water assumption involves distributing water between cells and their neighboring cells until the water levels are equal. Moreover, Chen
et al. [
19] used a flat-water model to simulate non-riverine, urban flooding on the campus of the University of Memphis, Tennessee. The authors noted that a traditional approach to apply a flat-water model is to determine route starting cells, which are a collection of cells from which flooding is assumed to originate, from the lowest elevation. Rather than the traditional approach, they used a collection of route starting cells based on the highest one percent of the flow accumulation values. However, the details regarding the selection process of routing start points were not addressed in the study.
The studies noted above assumed that water spreads from the lowest elevation locations in a given area to determine the route starting cells. However, the assumption that water spreads from the lowest elevation area may oversimplify the effect of topography on flooding. This assumption may only be applicable in flat floodplain areas. In hilly areas, the runoff water is accumulated in a local depression or channel. Soulis [
20] considered the flow direction and accumulation to the DEM-based hydrological models. He concluded that it can be applied in arbitrarily shaped areas and not strictly in the limits of specific watershed. This study thus applies the flow direction and accumulation to identify the route starting cells. These ordered cells can be used to improve the performance of simplified inundation models.
In this study, a simplified inundation model (hereafter called SPM) using the flat-water assumption is proposed. A collection of route starting cells is identified using two different grid cell ordering approaches: (1) A traditional approach using the lowest elevation assumption (hereafter called SPME), which is based on topographic data; and (2) a novel approach using the D-infinity (means an infinite number of possible single flow directions) contributing area assumption, which is based on the amount of flow into a cell (hereafter called SPMD). The highest values of flow accumulation are then selected as the route starting cells. The two approaches were compared. Because the historical data are insufficient for meaningful comparisons, the same simulations performed by WASH123D were used as a benchmark to evaluate the performance of the SPM. Application of the SPM to three towns that are subject to flooding in Pingtung County demonstrates the method’s effectiveness and applicability in flood prone areas.
4. Results and Discussion
Figure 6,
Figure 7,
Figure 8,
Figure 9 and
Figure 10 present the comparisons of the SPM
D (left) and SPM
E (right) for the three towns. In these figures, the flooding areas simulated from the SPM and WASH123D are “light blue” and “green”, respectively. SPM
D and SPM
E represent the SPM with the D-infinity approach and the lowest elevation approach, respectively. The overlapping flood areas and observations are “red” and “light yellow”. The purple dots are route starting cells where floods originate.
Figure 11 presents the comparison of the model performance for various thresholds. For example, the grey line identifies that the performance for a threshold = 0.3 m and the cells with water depth above the threshold were treated as flooded cells. Chen
et al. [
19] described that the thresholds were chosen based on experimental values. Ishigaki
et al. [
28] suggested that inundation depth = 0.3 m is the safety limit for elders to walk through. Hereafter this study evaluates the model performance using a threshold = 0.3 m. When comparing the results in Pingtung (
Figure 6), the SPM
D (0.33) has better fit indicators than the SPM
E (0.16) (
Figure 11). The performance increases by 106%.
Figure 7 shows the comparison with observations. The SPM
D provided a better comparison than SPM
E in the central part of Pingtung. However, both models did not generate floods in northeastern Pingtung. It is explained by the fact that the flood occurred because of a levee failure. None of these models can forecast it at present. The comparisons in Hengchun (
Figure 8 and
Figure 9) also indicate that the SPM
D outperforms the SPM
E. The fit indicators for the SPM
D and SPM
E are 0.23 and 0.12, respectively. A 91 percent increase in the performance is identified. In comparison with the observations, SPM
D was able to forecast floods in the central part of Hengchun, but SPM
E was not.
Figure 6.
Overlapping flood areas at the grid level between WASH123D and SPMD (a) and SPME (b) in Pingtung.
Figure 6.
Overlapping flood areas at the grid level between WASH123D and SPMD (a) and SPME (b) in Pingtung.
Figure 7.
Overlapping flood areas at the grid level between the observed floods and SPMD (a) and SPME (b) in Pingtung.
Figure 7.
Overlapping flood areas at the grid level between the observed floods and SPMD (a) and SPME (b) in Pingtung.
Figure 8.
Overlapping flood areas at the grid level between WASH123D and SPMD (a) and SPME (b) in Hengchun.
Figure 8.
Overlapping flood areas at the grid level between WASH123D and SPMD (a) and SPME (b) in Hengchun.
Figure 9.
Overlapping flood areas at the grid level between the observed floods and SPMD (a) and SPME (b) in Hengchun.
Figure 9.
Overlapping flood areas at the grid level between the observed floods and SPMD (a) and SPME (b) in Hengchun.
Figure 10.
Overlapping flood areas at the grid level between WASH123D and SPMD (a) and SPME (b) in Linbian.
Figure 10.
Overlapping flood areas at the grid level between WASH123D and SPMD (a) and SPME (b) in Linbian.
Figure 11.
Comparison of the model performance between SPMD and SPME using the performance indicator for various threshold values.
Figure 11.
Comparison of the model performance between SPMD and SPME using the performance indicator for various threshold values.
Figure 12 shows the model performance between SPM
D and SPM
E for various DEM resolutions. By using various DEM resolutions in Pingtung and Hengchun, the SPM
D constantly has higher fit indicators than the SPM
E. The result confirmed the above mentioned comparisons that using D-infinity approach has a better performance than using the lowest elevation. Also,
Figure 12 shows that the fit indicators in Pingtung and Linbian decline with increasing DEM resolution, especially for the SPM
D. Since the SPM
D is based on the D-infinity contributing area, the resampled rough DEM loses some detailed topographical information, e.g., artificial drainage channels, which may result in rough or incorrect flow direction and flow accumulation. In contrast, the SPM
E have similar fit indicators at different DEM resolution. This is because the resampled DEM does not change the spatial pattern of lowest elevation distinctly. The results suggest that SPM
D is more sensitive to the accuracy and resolution of a DEM than is SPM
E.
Figure 12.
Comparison of the model performance between SPMD and SPME using the performance indicator for various DEM resolutions.
Figure 12.
Comparison of the model performance between SPMD and SPME using the performance indicator for various DEM resolutions.
The result of the two cases demonstrates that selecting the route starting cells is important for the flat-water model. Using the most commonly applied lowest elevation approach, the SPM
E forecasted the flood areas at relatively lower locations, which were consistent with the topographic depressions in
Figure 5. Logically, the low-lying cells have a high risk of flooding. Elevation alone, however, is not sufficient to explain urban flooding with a relatively gentle slope because the flooding may also originate where high flows from a local sub-watershed occurred, depending on the selection of the route starting cells. Thus, the D-infinity contributing area approach is introduced into the flat-water model. This approach not only considers elevation but also includes accumulated water from the upstream area. The improved performance is confirmed in the above mentioned comparisons
However, the results of the comparison in Linbian are the opposite: the fit number is higher for the SPM
E than for the SPM
D, although the overlapping areas with WASH123D are similar (
Figure 10). The performance of the fit indicators for the SPM
D and SPM
E are 0.20 and 0.24, respectively, decreasing by 16% for a threshold = 0.3 m (
Figure 11). Previous studies (e.g., [
4,
19]) demonstrated that choosing the lowest elevation for the route starting cells in the flat-water assumption is appropriate in flat areas. However, Falter
et al. [
12] found a problem related to simplified flood models: isolated ponds were simulated by the infilling at the lowest point. This problem is likely to be less important in areas with a complex topography. Unfortunately, no studies (e.g., [
4,
12,
19]) have provided the definition of a flat area. An additional problem is apparent. The results of SPM
Es (
Figure 6,
Figure 7,
Figure 8 and
Figure 9) show that the flooded areas are originated from globally low-lying locations (purple points). It does not provide better forecasts in comparison with SPM
D. However, the finding is not applied to the application in the flat area. In Linbian, all of the elevations are below 10 m, and most of them range 0–2 m; thus, the area is topographically flat (
Figure 5). The performances of the SPM
E and SPM
D are highly similar, as shown in
Figure 10 and
Figure 11. SPM
E selects the lowest one percent of all cells to start flooding. For Linbian, the corresponded elevation is 0 m and there are more cells with the same elevation. This study added those extra cells into routing start cells, as shown in
Figure 10. The results showed that the flooded area is identical to the covered area of the routing start cells. SPM
E did not generate the flooded area at the top-right region in comparison with SPM
D. It slightly increased the performance of SPM
E.
In the present study, we were unable to determine with certainty which approach is better for particular topographies. This topic should be addressed in future SPM improvements. For more complex topography, such as that in Pingtung and Hengchun, the changes in elevation are significant, and the SPMD performed relatively well. Despite the slight decrease in the case of Linbian, SPMD is recommended for all topographies. In summary, SPM is currently not acceptable for use by public officials. However, this study proposed a novel idea, i.e., the consideration of elevation and flow accumulation (SPMD) instead of only elevation (SPME) to identify locations where flooding originates, that can be applied in a simplified inundation model.
During an emergency, rescue resources are limited and are usually collected in a central emergency response center in a large administrative area. Then, decision-makers allocate the limited resources to smaller districts according to the flooding risk. Apel
et al. [
29] suggested that simplified models offer the best spatially distributed representation of maximum inundation depths. Combined with flood loss models, simplified models are valuable for rapid flood-loss estimations. Because of the efficiency of SPM, another aspect of the model is described. Decision-makers require fast analyses to evaluate the possible flood threat or to prioritize zones with a high flood risk when multiple zones are present. In this study, a large administrative area is defined as a town, and a zone is defined as a village for which decision-makers allocate rescue resources. Using the same fit indicator in Equation (2),
Table 1 presents the analysis results in terms of the overlapping flood forecasts at the village level. The SPM
D still performed better than the SPM
E. The best fit number occurred in Pingtung at 0.69 with the SPM
D, which is 0.5 higher than the number achieved with the SPM
E. All of the fit numbers of SPM
E are close to 0.7. Thus, approximately 70% of the forecasts are consistent with WASH123D at the village level. The SPM
D can provide timely information with acceptable accuracy at the village level and serve as an easy-to-use tool for decision makers to prioritize villages with a high risk of flooding.
Table 1.
Comparison of overlapping villages between WASH123D, SPMD, and SPME using the performance indicator.
Table 1.
Comparison of overlapping villages between WASH123D, SPMD, and SPME using the performance indicator.
Town | Fit Indicator |
---|
SPMD | SPME |
---|
Pingtung | 0.69 | 0.19 |
Hengchun | 0.71 | 0.65 |
Linbian | 0.75 | 0.75 |
5. Conclusions
The development of simplified inundation models has become popular for providing efficient forecasts. A simplified inundation model was proposed in this study based on the flat-water assumption. Selecting a collection of route starting cells is important for applying this type of simplified model. This study used two approaches to select the collection of cells from which flooding is assumed to originate: First, the lowest elevation approach, which includes elevation as the single criterion; and second, the D-infinity contributing area approach, which is a novel approach that considers elevation, flow direction, and flow accumulation to select route starting cells. The results showed that using the D-infinity contributing-area approach can improve the performance of the simplified model in various topographical conditions. However, the improvement in very flat areas was not significant. Different topographies affect the applications of the different methods when identifying route starting cells. To improve the performance of SPM, various approaches should be used in particular topographical areas; additional details, such as frictional effects and improved hydraulic connections in the flood water spread and the capabilities of steady and unsteady flood simulations, will be of interest in future studies.
A simplified inundation model was developed for its efficiency. Based on the comparison in this study, WASH123D required an average of 10–15 min to simulate flooding based on domain sizes of 9000–85,000 cells, whereas the SPMD required less than 2 min. The calculation time can decrease within 1 min if the flow accumulation is preprocessed. The same inputs (i.e., total rainfall and the DEM) were used for the comparison. The SPMD was approximately 5–10 times more efficient than WASH123D in terms of the calculation time. A total of 33 townships are located in Pingtung County; thus, running the SPM will ultimately save time. The SPM is relatively stable and does not exhibit problems related to numerical dispersion during urgency due to a simplified assumption of water spread and straightforward model input. However, the SPM will not be considered for practical use until its predictions are comparable to those obtained from complex inundation models. The SPMD provides acceptable comparisons at the village level based on the comparison in this study. The model cannot provide detailed flooding information, such as the time of flood occurrence. The model does not include the drainage system just yet and provides overestimated predictions. It needs to add vertical source/sink terms (i.e., drainage systems) and temporal capabilities (i.e., unsteady simulation) to perform better simulation scenarios. The present model is suitable for rapid assessments when there is a lack of information, such as boundary conditions and model parameters, to run a complex inundation model. The modeling results are useful for decision makers to perceive flood risks in the area and allocate rescue resources. If there is a limited response time and a detailed simulation is needed, the model can prioritize the areas of flood risk. The operator can assign preference to high flood risk areas, where a complex inundation model can then be run. A goal for improving the SPM is to provide predictions at the cell level that are comparable to those obtained from complex models.