DEM Uncertainty Based Coastal Flood Inundation Modeling Considering Water Quality Impacts

Abstract

Wastewater Treatment plants (WWTPs) are among the most critical infrastructures in coastal cities and are subject to failure due to extreme flooding events. Failure of these systems could result in combined sewer overflow (CSO), where the stormwater inundation is getting mixed with wastewater. Digital Elevation Model (DEM) as an essential input for quantifying flooding inundation is subject to uncertainties. In this study, the coastal modeling is performed to estimate flood water level, including wave setup, in an ungauged location, by Delft-3D model. Gridded surface subsurface hydrologic analysis (GSSHA) is used to model and map the extent of inundation and stormwater accumulation. Bivariate analysis of annual/extreme water levels in an ungauged location and the rainfall time series at a nearby station is used to find the 100-year joint design values. Selected major historical storms/hurricanes in the last 50 years are used for this assessment. Furthermore, the impacts of flooding on the state of WWTP functionality are analyzed considering three failure scenarios and the resulting quantity and quality of CSOs. For uncertainty analysis, another 2D hydrodynamic model called LISFLOOD-FP is used, which is less computationally intensive than GSSHA. It is used along with a sequential Gaussian simulation (SGS) algorithm to quantify the effect of DEM error uncertainties on the assessment of flood inundation. A probability map is prepared that shows the full extent of flooding, including the less probable area to be flooded. The proposed algorithm is applied to the southern coast of Brooklyn and the Coney Island WWTP in that area. The results show that how the simulation of ungauged water level data as well as the development of an uncertainty-based flood inundation modeling as well as consideration for water quality impacts could significantly improve our ability for better flood preparedness planning in the coastal cities.

Appendices

Appendix A

Appendix A contains four additional details of the methodology. The first and second parts are the Data Preparation of GSSHA and LISFLOOD models. The third part includes additional explanations of the modelling in the R language environment used in the uncertainty analysis. The last part shows Matren semi variogram used is this study.

1.1 GSSHA Data Preparation

Information and characteristics of the area, including DEM (digital elevation model) and soil cover, and land use, are required to run the GSSHA model. DEM layers are used for the estimation of topographic information of the area as well as for finding the flow directions. The DEM resolution of the study region is 10 meters.

Land use/land cover GIS layers from the USGS site are used to determine aerial weight imperviousness for estimating the volume of water accumulation. The raster file contains different land use in the region with the corresponding manning coefficients ranging from 0.011 for residential/urban areas to 0.035 for agricultural/landscape lands. Soil map of the region is used to estimate parameters such as hydraulic conductivity, porosity, and capillary head used for estimating infiltration rate based on the Green Amp method in the rainfall-runoff model.

1.2 LISFLOOD Data Preparation

Floodplain topography and flow boundary conditions require two types of datasets to run LISFLOOD-FP (Karamouz & Fereshtehpoor, 2019). High-resolution topographic data are increasingly available but still is an important shortage for many urban areas throughout the world. The availability of high-resolution data facilitates developing more accurate tools/models based on resampled low-resolution data. The alternative is to incorporate the error associated with lower resolution NED DEMs compared to 1-m DEM constructed from LiDAR point cloud and generate multiple realizations of the elevation's real state. 1m LiDAR DEMs are available for the study area.

In terms of flow boundary conditions, different types of boundary conditions such as zero flux, uniform flow, fixed and time-varying free surface elevation, fixed and time-varying flow into the domain can be applied on the edge of the simulation domain. For coastal flood modeling, both fixed and time-varying free surface elevations are suitable, but the latter is more precise. As for the focus of this paper, the fixed free surface elevation equal to a given Stillwater elevation is adapted for the edges of the modeling domain.

1.3 DEM error analysis supplement

The packages for analyzing the DEM error in the R language environment are: rgdal (v 1.5-18; Bivand 2020) package for input/DEM data integration and control point structures; gstat (v 2.0-6; Pebesma 2020) package for variogram fitting and kriging interpolation for DEM error analysis and the discretion of SGS method. See Figure 6 part (a) for more details. Figure 6 part (b) shows different steps in preparing the probability map.

1.4 Matern Variogram

In this paper, Matern theoretical variogram has been used as follows.

$$ \gamma (h)={c}_0+c\left[1-\frac{1}{2^{\left(\nu -1\right)}\Gamma \left(\nu \right)}{\left(\frac{h}{a}\right)}^a{K}_{\nu}\left(\frac{h}{a}\right)\right]\kern0.5em $$

where h > 0 is the separation distance between two points, Γ is the gamma function, K_ν is the modified Bessel function of the second kind of order ν, ν > 0 is the smoothness parameter, a > 0 is range, c is the partial sill and c₀ is the nugget.

Appendix B

Appendix B contains more details of the results obtained in the paper, which consists of three sections. In the first section, more details of the ten major hurricanes simulation by the Delft-3D model are presented. According to these results, a correction factor has been obtained to adjust the data for southern Brooklyn coastal area. The second part includes the results of the Mann-Kendall applied method in detecting trends in rainfall and water level data, and the third part includes the 100-year water level hydrograph.

Table 5 shows the characteristics of selected major hurricanes. The correction factor for each hurricane is calculated by dividing the maximum water levels from the ungagged location to the Battery Park station data. The average value of these correction factors is 1.06 and is used to adjust the Battery Park station's time series for Brooklyn. This data is incorporated in the frequency analysis of joint storm and rainfall data for finding the 100-year design values.

Fig. 6

(a) Modelling components used in the R language environment for to asses flooding accumulation considering DEM error and (b) Flood probability map

Table 5 Characteristics of selected major hurricanes experienced in New York City, and a correction factor relating the peak values in Brooklyn and in the Battery Park station

In this paper, the water level and rainfall time series trade-off are assessed by the Mann-Kendall test with the null hypothesis that the trend is not significant. Considering the 95% confidence interval (5% significant level), the value of Z_α/2 is equal to 1.96 which is less than the Z statistic. If the P-value becomes less than 0.05, then the null hypothesis data stationarity is rejected. Table 6 shows a significant trend in the water level data and no apparent trend in rainfall time series. Hence, the non-stationary analysis is only performed on water level time series.

Table 6 The Mann-Kendall test results for rainfall and storm surge time series.

*Z is the test statistics for the Mann-Kendall test.

The water level hydrograph is obtained by rescaling the Hurricane Irene storm hydrograph by the ratio of the 100-year design value to the peak of that hydrograph as illustrated in Figure 7.

Fig. 7

Hydrograph of 100-year water level synthesized using Hurricane Irene as reference hydrograph.