The Floodwater Depth Estimation Tool (FwDET v2.0) for improved remote sensing analysis of coastal flooding

Remote sensing analysis is routinely used to map flooding extent either retrospectively or in near-real time. For flood emergency response, remote-sensing-based flood mapping is highly valuable as it can offer continued observational information about the flood extent over large geographical domains. Information about the floodwater depth across the inundated domain is important for damage assessment, rescue, and prioritizing of relief resource allocation, but cannot be readily estimated from remote sensing analysis. The Floodwater Depth Estimation Tool (FwDET) was developed to augment remote sensing analysis by calculating water depth based solely on an inundation map with an associated digital elevation model (DEM). The tool was shown to be accurate and was used in flood response activations by the Global Flood Partnership. Here we present a new version of the tool, FwDET v2.0, which enables water depth estimation for coastal flooding. FwDET v2.0 features a new flood boundary identification scheme which accounts for the lack of confinement of coastal flood domains at the shoreline. A new algorithm is used to calculate the local floodwater elevation for each cell, which improves the tool’s runtime by a factor of 15 and alleviates inaccurate local boundary assignment across permanent water bodies. FwDET v2.0 is evaluated against physically based hydrodynamic simulations in both riverine and coastal case studies. The results show good correspondence, with an average difference of 0.18 and 0.31 m for the coastal (using a 1 m DEM) and riverine (using a 10 m DEM) case studies, respectively. A FwDET v2.0 application of using remote-sensing-derived flood maps is presented for three case studies. These case studies showcase FwDET v2.0 ability to efficiently provide a synoptic assessment of floodwater. Limitations include challenges in obtaining high-resolution DEMs and increases in uncertainty when applied for highly fragmented flood inundation domains.

the requirements of high-resolution elevation data (e.g. LiDAR DEM), which, if available, can increase runtime and introduce numerical instabilities. Unlike confined floodplains, in situ gaging (e.g. tide gaging) cannot be easily translated into flood extent and severity estimates. This challenge is a product of coastal terrain and floodwater origin complexity (i.e. coastal, river and pluvial water accumulation).
Remote sensing-based analysis of flooding, which is largely agnostic with respect to flooding mechanisms and sources, 5 can be used to rapidly generate flood extent maps in near-real-time. These analyses often apply standard algorithms and tools, and for most first-order remote sensing approaches there is no need for supplementary data. Remote sensing has substantial advantages over modeling approaches, especially for emergency response and large-scale analyses, and particularly in coastal regions where accurate flood extent simulations can be challenging (Gallien, 2016). However, the disadvantages of remote sensing approaches include limitations in imagery availability and acquisition time, coarseness of resolution, cloud cover (for optical sensors), 10 nonlinearities in signal reflectance (particularly for radar sensors), and view obstruction by vegetation, topography, buildings, and their shadows. Remote sensing also cannot be readily used to map water depths.
Timely information about floodwater depth is important for directing rescue and relief resources and determining road closures and accessibility. Once available, flood depth information can also be used for post-event analysis of property damage and flood-risk assessment (Islam and Sadu, 2001;Nadal et al., 2009;Nguyen et al., 2016). Several approaches for quantifying 15 floodwater depth using remote sensing-based flood maps have been proposed. Nguyen et al. (2016) combine a flood extent map with hydrodynamic simulations. While accurate, this approach is both data-and computation-expensive, thus hindering its usability for data-scarce, near-real-time, and large-scale applications. Schumann et al. (2007)  As a result, FwDET removes the need for specific data while retaining its usability with complex and fragmented flood extent maps from any source and resolution (i.e., sensor and platform independent).
Since its development in 2017, FwDET has been used in support of emergency response as part of activations of the 25 Global Flood Partnership (GFP; https://gfp.jrc.ec.europa.eu; Alfieri et al., 2018), including the 2017 and 2018 U.S. Hurricane Seasons (Cohen et al., 2018b) and 2018 Philippine and Nigeria flooding. It was also been recently used for disaster resilience research , NASA CAIR, 2018. Findings from these activities are described in Cohen et al., 2018b, including the previously described challenges in coastal flood analysis. The need for fine resolution terrain data (to account for low gradients) mandate considerable improvements in FwDET computational efficiency to reduce run-time. Flood inundation 30 polygons, used in FwDET to identify flooded domain boundary locations (grid-cells), inevitably include those on the shoreline or ocean water (where elevation is equal or below mean sea level), and both introduce erroneous water depth calculations in nearby grid-cells. Furthermore, complex shorelines (e.g., small bays, inlets, barrier islands) can result in nearest flood-boundary cells erroneously located across a waterbody. In this paper, we describe and evaluate version 2.0 of FwDET, which was developed to alleviate these issues. FwDET v2.0 was developed as part of the NASA Applied Sciences Mid-Atlantic Communities and Areas 35 at Intensive Risk (CAIR) demonstration project  and its application within the project is described here. While developed primarily to address coastal issues, FwDET v2.0 retains its applicability to estimating riverine floodwater depth. The use of FwDET v2.0 for riverine flooding is also analyzed herein. FwDET calculates water depth by deducting local floodwater elevation (above mean sea level (amsl)) from the topographic elevation at each grid-cell within the flooded domain. The flooded domain is provided as a GIS polygon layer to FwDET, making the tool agnostic to the source and method used to derive the inundation extent. Elevation of each grid-cell and the floodwater is 5 derived from a Digital Elevation Model (DEM). While any DEM can be used, its horizontal and vertical resolutions can have a major impact on the tool's accuracy. This is discussed in more detail below as well as in Cohen et al. (2018a and2018b). The core of the FwDET algorithm is the identification of local floodwater elevation. FwDET water depth calculation follows this following procedure (described and illustrated in detail in Cohen et al., 2018a): (1) conversion of the inundation polygon to a line layer, (2) creation of a raster layer from the line layer that has the same grid-cell size and alignment as the DEM, (3) extraction of the DEM 10 value (elevation) for these grid-cells (referred to as boundary grid-cells), (4) allocation of the local floodwater elevation for each grid-cell within the flooded domain from its nearest boundary grid-cell, and (5)  For flooding within a river floodplain, associating the appropriate boundary grid-cell is relatively straightforward as illustrated in Figure 1 (top) with a cross-section. In non-continuous flood domains (e.g. in floodplains of braided rivers), isolated 15 areas of non-flooded land can, and quite often, exist. Non-flooded isolated areas can be real or represent an error in the remote sensing analysis due to, for example, undetected flooding under dense vegetation. FwDET identifies the cells around these areas as boundary grid-cells, which, if these are real non-flooded (elevated) areas, is expected to improve the water depth calculations as it provides more localized floodwater elevation data. In coastal floods, the inundation polygon boundary at the coastline or ocean waters cannot be used as boundary grid-cells as the DEM-extracted elevation will not represent the floodwater depth as 20 illustrated in Figure 1 (bottom). These boundary grid-cells should, therefore, be excluded from the analysis. In FwDET v2.0 this is done by removing all boundary grid-cells that have or are immediately adjacent to grid-cells that have an elevation equal to or less than zero. The inclusion of adjacent cells in this conditioning is done as coastal inundation polygons will often end at the coastline and the conversion to a raster will often result in boundary grid-cell immediately inland of the coastline, resulting in elevation (depending on the DEM resolution) that can be slightly greater than zero. 25 The first version of FwDET (v1.0) was implemented using a Python script which utilizes ArcGIS tools (ArcPy library) for its core data analysis (available at https://sdml.ua.edu/models/ and https://csdms.colorado.edu/wiki/Model:FwDET).
Floodwater elevation of the nearest boundary grid-cell is allocated in FwDET v1.0 by iterating over increasing neighborhood sizes of the ArcGIS 'Focal Statistics' tool (ESRI, 2019a). The iteration includes a condition to ensure newly allocated flooded grid-cells receive elevation values from their closest computed neighbor (i.e. nearest boundary grid-cell). This approach has three 30 disadvantages: (1) it requires running the 'Focal Statistics' tool multiple times, reducing FwDET computational efficiency; (2) the size of the largest neighborhood needed to cover the entire flooded domain varies depending on the domain size and the DEM resolution, requiring an a priori estimation of the number of iterations, often resulting in the need to re-run the tool; and (3) it ignores permanent water features (rivers, inlets), and thus can erroneously assigns boundary grid-cell elevations to flooded gridcells on the opposite bank because their Euclidian distance is shorter than to the boundary grid-cells on their side of the waterbody. 35 In FwDET v2.0, allocation of the nearest boundary grid-cell elevation is done with the ArcGIS 'Cost Allocation' tool (ESRI, 2019b). 'Cost Allocation' changes the way in which nearest boundary grid-cells are allocated to a non-iterative approach.
This drastically reduces the run time, as the tool uses one linear process to allocate the value of the input raster's (boundary elevation raster) nearest grid-cell for all cells within the output domain. The tool's 'cost' input raster is used in FwDET v2.0 to prevent boundary grid-cell elevation allocation over permanent water by assigning such grid-cells with high-cost value. The cost 40 raster is calculated by assigning all grid-cells with elevation equal to or less than zero a value of 1000 and all other grid-cells a value of 1. For inland water bodies (e.g., rivers; where permanent water bodies have greater than zero elevation), a cost raster can be calculated from a land-cover map and used as input to FwDET v2.0. The 'Cost Allocation' tool only accepts integers, consequently creating a vertical elevation data resolution of 1 elevation unit (e.g. meter), which was the main reason this tool was not used in previous versions of FwDET. In FwDET v2.0, a float-integer-float conversion is employed to maintain the DEM 5 vertical resolution.
FwDET v2.0 is also available as a Python script and as an ArcGIS Script Tool (see Conclusions section). A QGIS Python script and tool was developed to eliminate dependency on ArcGIS licensing. The QGIS script runtime is shorter than the ArcPy-dependent script but does not yet include a cost raster input and therefore does not solve the above-indicated issue of allocation across permanent water. 10 as Dirichlet open boundary inputs for the street-level model to drive inundation into urban environments and highlight vulnerable infrastructure impacted during the storm. These urban structures were extracted from LiDAR as in Loftis and Taylor (2018) and directly embedded in the model to account for volume displacement within the structure's surface area and form drag as the storm surge flows around each building within the urban environment (Loftis et al., , 2016. The streetlevel model subsequently generated hourly inundation outputs for floodwater depths in meters, which compared favorably 35 with water level sensors and high water marks as noted in . A more complete description of this case study is available in , and Rogers et al., (2018). In this paper, the maximum water depth output was used along with the 1m DEM for the FwDET v2.0 calculation. hydrodynamics model (Nelson et al., 2016; https://www.i-ric.org) was used to simulate the flood. The iRIC-FaSTMECH simulates water velocity and water surface elevation using gaged discharge input at the reach's upstream location and stage at its downstream outlet. Manning's roughness parameter was calibrated, the pressure distribution was assumed hydrostatic and the flow was considered quasi-steady in the model. A more detailed description of this case study is provided by Zhang et al.

Evaluation
(2018) and Cohen et al. (2018a). In this paper, the maximum water depth model output along with the 10-m DEM (NED) were 5 used for the FwDET v1.0 and v2.0 calculations.

Applications
Evaluation of FwDET v2.0 operational applications for three case studies is provided: 1. Hurricane Irene -made landfall along the Mid-Atlantic Coast in late August 2011. To assess flooding from Irene, as part of 10 the CAIR demonstration project, optical remote sensing approaches were used to map water extent, limited to views unobstructed by cloud, high objects like buildings and vegetation. In this study, the highest quality satellite overpass from Landsat was determined to be a Landsat-5 scene obtained on 31 August 2011, five days after the storm made landfall. To identify surface water areas, Landsat-5 surface reflectance was used to compute the modified Normalized Difference Water Index (mNDWI, Xu 2006). Water detections from the Landsat-5 mNDWI product were then combined with the 2011 National 15 Land Cover Dataset (NLCD) to separate flood areas from known permanent water locations. Areas that were identified as water in the mNDWI product and overlapped with identified water pixels in the NLCD were classified as persistent water.
Pixels that were identified as water in mNDWI but not classified as water in the NLCD were determined to be flooded. Due . Several DEM products were tested here as input for the FwDET v2.0 (described later).   Cohen et al., 2018a). FwDET v2.0 ArcGIS script tool allows users to provide a pre-clipped DEM to reduce runtime. This is mostly useful when repeated runs for the same inundation extent are conducted. 10

FwDET v2.0 Application Results
Large-scale coastal flooding, typically associated with tropical cyclones, is challenging to analyze from both an observational (remote sensing, point data) and modeling perspectives. This is because of the diversity in land cover and flooding sources. Storm surge, for example, can be highly energetic but short in duration relative to riverine flooding. That could create observational 15 challenges for remote sensing applications. The NASA CAIR project , NASA CAIR, 2018 utilized FwDET v2.0 to demonstrate the ability to integrate satellite-derived earth observations and physical models into actionable knowledge.
The integration of observations and models allow for a more comprehensive understanding of the compounding risk experienced in coastal regions. The demonstration produced flood inundation maps to predict building-level impacts of a representative storm in the mid-Atlantic region for Hurricane Irene. FwDET v2.0 used best-available remotely sensed imagery to determine inundation 20 depth immediately following the storm.
To estimate floodwater depth following Irene, the Landsat 5 floodwater classification was converted to a polygon layer ( Figure 4) to be used as input for FwDET v2.0. A DEM for the region was compiled by mosaicking the corresponding 30 m spatial resolution NED tiles. While 10 m NED products are available for this region, the 30 m product was used given the resolution of the flood inundation source (30 m Landsat 5 images) and the size of the domain (Figure 4). Although there are insufficient ground-25 based observations to make a quantitative accuracy determination, overall the spatial trends in water depth estimation seem reasonable. The average floodwater depth for the entire domain was 0.64 m with a maximum of 41.7 m. The latter is obviously an over-prediction resulting from the misclassification of floodwater from the satellite imagery or spatial mismatch between the inundation map and the DEM. Zooming in on the Norfolk-Portsmouth area reveals a much smaller flooding extent compared to the model simulation results (Figure 2). This is reasonable given that the model simulated the maximum flooding conditions during 30 the event while the flood inundation layer used here is based on a Landsat 5 image captured 5 days past the Hurricane's landfall.
Under-prediction of flood extent may also be due to challenges in floodwater classification in urban environments at this resolution. depth is 0.92 m with a standard deviation of 1.7m. This is a reasonable result given the other case studies (we do not have comprehensive observed or simulated water depth data for a quantitative assessment). Maximum estimated water depth is 39.6 m which is clearly an overestimation, even though calculations include permanent water features. That is because DEMs typically capture the water surface elevation of permanent water features (see Figure 1).
For the Sri Lanka application case study, the flood inundation map produced by DFO was highly fragmented in most parts 5 of the country leading to many small inundation polygons ( Figure 6). As described earlier, fragments in the inundation extent, assuming it represents reality, can be advantageous as it can shorten the distance to the nearest boundary grid-cells which may yield more accurate (localized) water elevation estimation by FwDET v2.0. However, a highly fragmented inundation extent can be problematic if the flooded sections are small relative to the input DEM resolution and the local terrain gradient. For example, a flooded area with an extent of only a few DEM grid-cells in a flat area may result in a negligible water depth because the elevation 10 of the boundary and inundated grid-cells are similar. High-resolution DEMs outside the U.S. are often difficult to obtain as most countries do not openly share national DEMs, or they do not exist. As a result, in emergency response situations, we often can only use global DEMs as input to FwDET (see Cohen et al., 2018aCohen et al., , 2018b. For this event three DEM products were tested: 1. HydroSHEDS (based on the Shuttle Radar Topography Mission (SRTM) DEM); 3 arc-sec (~90m) resolution.
2. Multi-Error Improved-Terrain (MERIT; Yamazaki et al., 2017); 3 arc-sec (~90m) resolution; http://hydro.iis.u-15 tokyo.ac.jp/~yamadai/MERIT_DEM/index.html 3. ALOS; 30m resolution; http://www.eorc.jaxa.jp/ALOS/en/aw3d30/index.htm While ALOS offers the highest spatial resolution, it is distributed as an integer raster which means that its vertical resolution is effectively 1 m. This is a considerable disadvantage, especially in low slope terrains. MERIT resulted in improved depth estimations over using HydroSHEDS (not shown here) but its horizontal resolution is inadequate considering the resolution 20 of the remote sensing inundation map (10 m) and the high degree of fragmentation in the inundation extent input. Use of the ALOS DEM yielded the most appropriate floodwater depth map ( Figure 6) for the Sri Lanka flood, but with a relatively high degree of uncertainty due to its limited vertical resolution, a high degree of fragmentation relative to the DEM vertical resolution, and mismatch in horizontal resolution between the inundation map and DEM. This event demonstrated challenges associated with high-resolution DEM availability. This case study highlights the need to carefully consider the appropriateness of DEM choice in 25 the context of the resolution and nature of the inundation extent map.

Conclusions
The Floodwater Depth Estimation Tool (FwDET) calculates water depth based solely on an inundation polygon and a DEM. This enables rapid application over large domains and globally, which is highly advantageous for disaster response and large scale or products (FwDET and model-simulated) were also similar. FwDET v2.0 considerably over-predicted maximum flood depth (a grid-cell with the highest value). This can be due to mismatches between the flood boundary and the DEM or inaccurate identification of the appropriate flood boundary grid-cell. In FwDET the nearest boundary grid-cell for each grid-cell within the flooded domain is identified based on Euclidian distance. However complex fluid dynamics and flow paths can result in local floodwater elevation which differs from the nearest boundary grid-cell. These errors are due to the simplicity of FwDET and can 5 lead to unrealistic water depth patters in some locations. The results from this and past papers demonstrate that FwDET can be considered a first-order tool for providing a synoptic overview of floodwater depth distribution. Its ability to provide estimates at finer scales depends on the spatial complexity of the flooded domain and the resolution of the flood extent map and DEM.
Generally, simple flood extents and good correspondence between the inundation map and DEM will yield more accurate depth estimations. 10 FwDET v2.0 was compared to v1.0 using the Brazos case study. Results show that, as expected, the two versions yielded very similar water depth maps for this riverine case study. FwDET 2.0 was able to achieve a considerable improvement in runtime