Lidar DEM and Computational Mesh Grid Resolutions Modify Roughness in 2D Hydrodynamic Models
Abstract
Topography and the computational mesh grid are fundamental inputs to all two-dimensional (2D) hydrodynamic models, however their resolutions are often arbitrarily selected based on data availability. With the increasing use of drone technology, the end user can collect topographic data down to centimeter-scale resolution. With this advancement comes the responsibility of choosing a resolution. In this study, we investigated how the choice of mesh grid and digital elevation model (DEM) resolutions affect 2D hydrodynamic modeling results, specifically water depths, velocities, and inundation extent. We made pairwise comparisons between simulations from a 2D HEC-RAS model with varying mesh grid resolutions (1 and 2 m) and drone-based lidar DEM resolutions (0.1, 0.25, 0.5, 1, and 2 m) over a 1.5 km reach of Stroubles Creek in Blacksburg, Virginia. The model was rerun for up to ±4% change in floodplain roughness to determine how the DEM and mesh grid changes relate to an equivalent change in roughness. We found that the modeled differences from resolution change were equivalent to altering floodplain roughness by up to 12% for depths and 44% for velocities. The largest differences in velocity were concentrated at the channel-floodplain interface, whereas differences in depth occurred laterally throughout the floodplain and were not correlated with lidar ground point density. We also found that the inundation boundary is dependent on the DEM resolution. Our results suggest that modelers should carefully consider what resolution best represents the terrain while also resolving important riparian topographic features.
Key Points
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Two-dimensional hydrodynamic model results are affected by digital elevation model and computational mesh grid resolutions
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Resolution changes are equivalent to altering floodplain roughness by up to 12 percent for depths and 44 percent for velocities
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Modeled inundation boundary is dependent on digital elevation model resolution
1 Introduction
Two-dimensional (2D) hydrodynamic models of waterways are important for helping answer a variety of engineering and management questions, related to flooding, flow alterations from structures, restoration, and habitat assessment (Fleischmann et al., 2019; Jafarzadegan et al., 2023; Singh, 2009). These models simulate water depth, water velocity, and inundation extent (Brunner, 2016; Lai, 2020). In pursuit of making an accurate model, the modeler must make various decisions about terrain resolution, computational mesh size, and roughness.
A fundamental input in all 2D hydrodynamic models is a digital representation of topography, which is typically represented by a digital elevation model (DEM) raster. DEMs are created by interpolating elevation data collected using remote sensing, such as light detection and ranging (lidar), interferometric synthetic aperture radar (InSAR), or structure from motion photogrammetry (Bates, 2012; Muhadi et al., 2020). Even though DEM resolution can affect estimated inundation extents (Horritt & Bates, 2002; Yu & Lane, 2006), water depths (Savage, Pianosi, et al., 2016; Xu et al., 2021), and excessive resolution can result in little model improvement (Horritt & Bates, 2001; Savage, Bates et al., 2016), DEM resolution is usually arbitrarily chosen based on data is availability (Adams et al., 2021). Channel bathymetry is typically combined with a DEM (Dey et al., 2022) and has also been found to significantly affect estimated discharge and water level results due to erroneous river cross-sectional area (Bomers et al., 2019; Caviedes-Voullième et al., 2012).
Within 2D hydrodynamic models, the study area must be discretized and represented as computational meshes. Averaging occurs within each mesh cell, thus the model does not fully represent the true hydraulic variability of the river and floodplain (Bradley, 2023). In order to address this, mesh resolution should be selected so that hydraulically important flow features, landcovers, and structures are properly represented (Bilgili et al., 2023; Dottori et al., 2013; Horritt et al., 2006; Mazdeh et al., 2023; Wright et al., 2022). If the mesh is too coarse, erroneous estimates may create a resultant outflow hydrograph that is dampened or smoothed (Bilgili et al., 2023; Yu & Lane, 2006), while too fine a mesh would result in increased model run times and a decreased inundation extent (Hardy et al., 1999; Mandelbrot, 1967). Discretization can be in rectangular grids, triangular meshes, or other unstructured formats, which can be done in many 2D hydrodynamic models, such as Delft3D, SRH-2D, Fast-Mech and HEC-RAS. Mesh shape and size are also important considerations since they can have a stronger effect on modeled results than roughness spatial distribution (Caviedes-Voullième et al., 2012). Additionally, some models, such as HEC-RAS, incorporate sub-mesh grid topography, thus allowing models to include very high-resolution topographic data. This is done by retaining details like hydraulic radius, volume, and cross sectional area to be used for coarser numerical modeling (Brunner, 2016; Casulli, 2009; Casulli & Stelling, 2011). Refinement of the mesh in the main channel and in other hydraulically influential areas has been shown to have an overall effect on modeled results since coarse resolution meshes misrepresent the channel cross-section, thus altering modeled velocities and total inundated area (Bilgili et al., 2023; Bomers et al., 2019; Bradley, 2023; Yu & Lane, 2006). Despite the overall effects that mesh and DEM resolutions have on models, they are usually not altered because calibration is typically done by altering the roughness values (Attari & Hosseini, 2019; Ballesteros et al., 2011; Bilgili et al., 2023; Ferreira et al., 2021).
Previous studies examining the effects of mesh grid and DEM resolutions on hydrodynamic models have been on larger rivers (channel widths greater than 40 m) using meter-scale lidar or InSAR based DEMs (Cobby et al., 2003). To achieve a similar channel width to DEM and mesh resolutions ratio for smaller streams (widths less than 15 m; Czuba & Allen, 2023), DEM resolution must be finer. Proper modeling of smaller streams is important for estimating flows due to their usually underpredicted flood potential while accounting for up to 80% of total channel length of river networks (Cornwall, 2021; Wohl, 2017). Streams are often the focus of projects and modeling efforts that involve stream restoration, mitigation banks, carbon crediting, expanded infrastructure construction, and municipal flood modeling. Historically, topographic data for such projects were collected via surveys or pre-existing DEM rasters were utilized.
The advent of drone technology has given the responsibility of choosing resolution to the end user. Papaioannou et al. (2020) examined the effect of varying drone structure from motion photogrammetry DEM resolution with mesh resolution in the context of fish habitat hydrodynamic modeling (7 m channel width). Median water depth and velocities values stayed approximately constant for resolutions smaller than 1 m, with smaller variations in water depths. While drone photogrammetry is widely used, this remote sensing technique does not penetrate vegetation canopy, thus resulting in a digital surface model and not a DEM (Dandois & Ellis, 2013; Hugenholtz et al., 2013; Prior, Thomas, et al., 2022; Westoby et al., 2012). Alternatively, drone lidar systems can penetrate the canopy and thus accurately represent topography and thus produce a DEM, which then can be used for a wide variety of hydrology applications (Acharya et al., 2021), including hydraulic modeling (Muhadi et al., 2020). They can collect much denser point clouds than what common airplane lidar can offer. Drone lidar systems can produce hundreds of points/m2, whereas traditional systems typically report tens of points/m2. With this increased amount of data, DEM resolution can be as fine as centimeters (Muhadi et al., 2020). It is unknown how the choice of fine-scale DEM resolution may affect hydrodynamic models of smaller streams.
Our study aims to fill this gap by investigating how mesh grid resolution and drone-based lidar DEM resolution affect hydrodynamic modeled results along a 4.5 m wide stream in Virginia. Drone lidar data was collected and five DEMs were created with resolutions of 0.1, 0.25, 0.5, 1, and 2 m. Two computational meshes at 1 and 2 m resolutions, along with the DEMs were used in a 2D Hydrologic Engineering Center-River Analysis System (HEC-RAS) model. For each mesh and DEM combination, modeled depth and velocity rasters were compared for 11 flow scenarios and the inundation extent was analyzed from the maximum flow scenario. This research informs hydrodynamic modelers how differing resolutions of DEM and computational mesh may affect their modeling results, particularly by modifying roughness.
2 Methods
2.1 Study Area
The study area is in southwest Virginia, USA (Figure 1h) along 1.5 km of Stroubles Creek within the Stream Research, Education, and Management (StREAM) Lab at Virginia Tech (37°12’N, 80°26’W). Its watershed (15.3 km2) includes the Virginia Tech campus and the majority of Blacksburg, Virginia. This section of Stroubles Creek was restored in 2010 from 200 years of cattle and agricultural practices which placed this waterway on the U.S. Environmental Protection Agency's 303(d) list of impaired streams since 2003 for sedimentation (Benham et al., 2003; Wynn et al., 2010, 2012). The restoration of the study area, model extent outlined in Figure 1a, included altering vertical stream banks to a 3 to 1 slope to about where the crosshairs are located in Figure 1a. Downstream of the crosshairs, the restoration created inset floodplains along the channel that then transitioned into a 3 to 1 slope (Christensen et al., 2024). The entire study area also had native riparian vegetation planted at the time of the restoration and excluded cattle from the floodplain. The planted native riparian vegetation from the restoration has resulted in tall trees, dense mats of tall grasses, and the floodplain is irregular with pits and troughs from past land use of pastureland, resulting in a very complex floodplain.
Study area map of Stream Research, Education, and Management (StREAM) Lab. (a) Aerial imagery with model extent outlined in red. (b) 0.1 m resolution digital elevation model (DEM) of model extent. (c–g) show the DEM at different resolutions located in the black rectangle in (b). (h) Location of StREAM Lab in southwest Virginia, USA.
For this study, the channel is defined as the area that is filled by base flow with a typical width of approximately 4.5 m for this section of Stroubles Creek. The inset floodplain is defined as the floodplain immediately next to the channel, but below the main floodplain, and includes the inset floodplains created in part of the restoration as well as the naturally formed inset floodplains in the other section of the restoration (upstream of the crosshairs in Figure 1a) (Azinheira et al., 2014; Royall et al., 2010). The inset floodplain has an average approximate width of 13 m and is completely submerged at a water depth of 0.25 m during 5.25 m3/s flow scenarios. The rest of the floodplain is referred to as the main, higher-elevation floodplain. This is the majority of the model extent and has an average width of about 140 m. When referring to the channel-floodplain interface, we are referring to the inset floodplain main floodplain interface because the channel and the inset floodplain will be inundated for all our results.
2.2 Lidar Data
The drone used to collect lidar data was a Vapor35 (AeroVironment) with an attached YellowScan Surveyor Core lidar unit (Monfeerier-sur-Lez). This unit consists of a Velodyne VLP-16 laser scanner (Velodyne) and a GNSS-inertial Trimble APPLANIX APX-15 (Trimble). The lidar system records two returns per pulse and uses a wavelength of 905 nm. We planned and created our flights using the wePilot1000 flight control system and the weGCS ground control system software (weControl SA). All flights were flown at a 30 m altitude, with 20 m flight-line spacing, which was recommended by YellowScan staff for optimum point spacing and density. Flights were conducted on 11 November 2021 (upstream of the crosshairs in Figures 1a) and 13 December 2021 (downstream of the crosshairs in Figure 1a) during leaf-off conditions.
The data were corrected using a local CORS base station and was outputted into a LAS file format in UTM zone 17N. The point clouds were then corrected using stationary objects in the floodplain as described in (Hession et al., 2023; Prior, Czuba, et al., 2022). To do this, the point clouds were aligned to the 2018 Virginia Geographic Information Network (VGIN) lidar point clouds (VGIN, 2018) and surveyed points along the sampling bridges. Surveyed points were collected using a Trimble R12 GNSS System (Trimble). Alignment was done within the CloudCompare software (https://www.danielgm.net/cc/) by first applying a minimum filter to both the VGIN and collected point clouds. Then the iterative closest point (ICP) tool was used to minimize the difference between the VGIN and collected point clouds. The ICP method is a common method used to align point clouds to one another (Choi et al., 2012; He et al., 2017; Zhang et al., 2015). The minimum filter was used as a computationally efficient tool to isolate ground points for alignment. Since ground filters each have their own peculiarities, a minimum point filter provides more robust replicability because there are no parameters to adjust as it is a simple binning operation. The ICP tool produced a matrix that was then used to transform the collected point clouds to better align with the VGIN point cloud. Lastly, manual adjustment was done to better align with the surveyed sampling bridge points. Once each scan was corrected, they were all then merged into one point cloud.
The corrected point clouds resulted in approximately 450 points/m2 with a ground point density of 251 points/m2. The simple morphological filter (Pingel, 2021; Pingel et al., 2013) was then applied to the lidar point cloud to identify ground points. Details of this processing can be found in the following data publication (Hession et al., 2023).
2.3 DEM Creation
All sampling bridges along StREAM Lab were removed from the point cloud. The lidar points classified as ground were then used in the “LAS Data set to Raster” tool in ArcGIS Pro (version 2.9.2, ESRI) to create DEMs at resolutions of 0.1, 0.25, 0.5, 1, and 2 m. In this study, 0.1 and 0.25 m DEM are considered fine resolution, 0.5 m DEM is considered moderate resolution, and 1 and 2 m DEM are considered coarse resolution (Figures 1c–1g). The tool's interpolation type was set to binning, cell assignment was set to nearest, and void fill method was set to natural neighbor.
The “LAS Data set to Raster” was utilized since it is a common tool that is well documented for and generally accessible for replicability purposes. Binning was chosen for interpolation type since it results in smoother rasters and does not include relatively obvious discontinuities that other methods tend to include (Vosselman & Maas, 2010). Nearest neighbor was used for cell assignment since it pulls the nearest value for the cell value. Natural neighbor was used since it is better than all other interpolations methods available in ArcGIS Pro since it does not introduce artificial artifacts that the other methods do (Crema et al., 2020). The other methods are known to produce an overly complex surface if they are not fine tuned to specific terrain features (Hengl & Reuter, 2008). Since near infrared light is absorbed by water, the lidar point cloud could not produce accurate estimations of streambed bathymetry. We surveyed bathymetry as cross-sections at the top and toe of banks, the thalweg, and any other distinct topographic features in the channel during December of 2021. This was done using a Trimble R12 GNSS System (Trimble) with the cross-sections spaced approximately 7 m apart (less than two channel widths). More cross-sections were also collected in areas with distinct bathymetric features. These data were then corrected using the Online Positioning User Service maintained by NOAA (NOAA, 2023). The “Topo to Raster” in ArcGIS Pro was used to make an interpolated elevation model at 0.1 m resolution from the bathymetry cross-sections. The DEMs and the bathymetry raster were then merged using the “Mosaic to New Raster” tool within ArcGIS Pro. This final DEM can be found in the following data publication (Hession et al., 2023).
2.4 Hydrodynamic Model
For our study, we used the 2D hydrodynamic model: 2D HEC-RAS, which incorporates the Saint Venant equations to simulate unsteady flow, developed and maintained by the US Army Corps of Engineers (Brunner, 2016). The calibrated and validated 2D HEC-RAS model created in Prior et al. (2021) was used for this study. Within this model, we imported all DEMs as terrain data and created two computational mesh grids at resolutions of 1 and 2 m. The computational mesh grid outline can be seen in Figure 1a. For the 1 and 2 m computational mesh grids, 98,269 cells and 34,674 cells were in the model domain of 87,346 m2. A refinement region of 0.5 m grid cell size was placed in the channel to refine the computations within the main channel relative to the floodplain areas. The channel was refined to have eight cells for representing the channel width, thus the refinement region had 11,672 cells for a channel area of 2,918 m2. Breaklines were placed along the top of the inset floodplain main floodplain interface so that water did not prematurely flood the floodplain unless the bank elevation was overtopped. This was necessary because of how 2D HEC-RAS uses hydraulic attribute tables for calculating and assigning flood extent within each cell of the mesh grid. The downstream boundary condition was set as normal depth with a friction slope of 0.0025. The upstream boundary condition was a flow hydrograph.
The details of model calibration and validation for the Manning's roughness values are described in Prior et al. (2021) and are briefly summarized here. The model was calibrated using velocities and WSEs from three uplooking velocity sensors as well as surveyed inundation extent during a flood event. The model was validated using 17 wells that laterally span the floodplain for a range of 7 flow scenarios and had an RMSE of 0.15 m. The resulting calibrated Manning's roughness value was 0.5 for the entire floodplain (including the inset floodplain) and 0.04 for the channel (Prior et al., 2021).
Flows were selected starting with flow in the main channel and increasing the flow in increments about every 0.25 m3/s, until the highest realistic flow of 20 m3/s, which resulted in about 0.7 m depth of water in the floodplain. The 20 m3/s flow scenario is the highest flood that has been recorded at this site since the beginning of data collection efforts in 2010. The input flow hydrograph included initial low flows that slowly filled the main channel and the inset floodplain to maintain stability at the beginning of the simulation run. Each flow was held constant for a day of model simulation so that the results represented steady state conditions. We only report results once the inset floodplain first becomes inundated, and therefore simulate 11 flows between 5.25 and 20 m3/s. A simulation for every DEM-mesh grid combination was created, resulting in 10 simulations, each with 11 flows.
2.5 Simulation Output Analysis
The inundation boundary for the maximum flow scenario of 20 m3/s was exported as a shapefile for each simulation. The number of puddles, number of islands, and perimeter were recorded for each inundation boundary shapefile. Islands in the inundation extent occurred when there is incomplete inundation of the terrain, leaving dry patches surrounded by water. Conversely, there can also be disconnected patches of water that are separate from the main continuous inundation extent, which we are calling puddles.
All depth and velocity results were exported from the ten HEC-RAS DEM-mesh grid simulations as rasters for all the 11 flow scenarios, thus resulting in 220 rasters (2 results, 10 simulations, 11 flow scenarios). These rasters were then imported into MATLAB (Version 2018b; MathWorks inc.) for further processing and comparison. We interpolated the depth and velocity outputs into a regularly spaced grid, using the mesh grid function within MATLAB, and then differenced the values between each DEM-mesh grid combination to create 25 pairwise comparisons of depth and velocity for each of the 11 flow scenarios which resulted in 550 rasters (2 results, 25 pairwise comparisons, 11 flow scenarios). We reported the absolute value of differences from these pairwise comparisons to simplify the presentation of results. Additionally, we compared rasters of velocity and depth differences to ground lidar point density via Spearman coefficients. Figure 2 shows an overview of the workflow, along with resulting outputs from the simulations.
Workflow diagram showing inputs and simulation outputs.
Additionally, the model was rerun with only the floodplain roughness modified (channel Manning's roughness was kept constant at 0.04, DEM resolution was kept constant at 0.5 m, and mesh grid resolution was kept constant at 1 m) to assess how changes in depth and velocity correspond to equivalent changes in floodplain roughness. The model was run 14 times for up to ±4% change in floodplain roughness from a base Manning's roughness of 0.5. Depth and velocity rasters were then exported for the maximum flow scenario (20 m3/s) of each of these runs. Following the same methods from above, all the rasters were processed in MATLAB to interpolate depth and velocity outputs into a regularly spaced grid. Each scenario was then subtracted from the reference scenario, where floodplain roughness was 0.5, to examine how floodplain roughness change affected modeled results. The absolute values of these comparisons were reported.
3 Results
3.1 Spatial Variation
Spatial difference maps were created at three flow scenarios and for two pairwise comparisons that represent the small to large differences of DEM resolutions. These pairwise comparisons demonstrated the spatial variation in differences of depth, from the moderate DEM resolution (0.5 m) compared to a similar resolution of 0.25 m (Figures 3a–3c, 3g–3i, 3m–3o) and to the largest resolution of 2 m (Figures 3d–3f, 3j–3l, 3p–3r). For different flows, differences generally increased when moving downstream, from top to bottom. This might be related to the downstream boundary condition. When contrasting these two pairwise comparisons, there are more stark and random differences for the pairwise comparison between the 0.5 and 2 m DEM (Figures 3d–3f, 3j–3l, 3p–3r), which is expected because this comparison has a larger difference in resolution.
Absolute value of differences in depth from two pairwise comparisons between the 0.25 and 0.5 m digital elevation model (DEM) resolution simulations (a–c, g–i, m–o), and between the 0.5 and 2 m DEM resolution simulations (d–f, j–l, p–r). All results shown are at a mesh grid resolution of 1 m. Three flow scenarios for each pairwise comparison are displayed: 5.25 m3/s (a, g, m, d, j, and p), 10 m3/s (b, h, n, e, k, and q), and 20 m3/s (c, i, o, f, l, and r).
In isolated parts of the floodplain (Figures 3a–3c, 3d–3f, 3m–3o, 3p–3r), some spatial variability was evident, but tended to become uniform at the highest simulated flow. This uniformity was more spatially consistent for the pairwise comparison with the smallest difference in DEM resolution (Figures 3a–3c, 3m–3o). Lastly, no correlation was found between differences in depth and lidar ground point density for the entire floodplain with Spearman coefficients ranging from 0.10 to −0.07. The p-values were all zero due to the sheer number of data points (over five to 6 million, depending on the flow scenario) (Gómez-de-Mariscal et al., 2021; Lin et al., 2013). For the overall spatial variability of depth difference, dependency was linked to longitudinal location, rather than lidar ground point density. It is important to note that the lidar ground point density for all of our DEMs was very high (0.1 m pixel: 3 points/m2; 0.25 m pixel: 16 points/m2; 0.5 m pixel: 63 points/m2; 1 m pixel: 251 points/m2; 2 m pixel: 1,004 points/m2). These point densities are incredibly high when compared to airplane lidar, which typically results in 30 points/m2 or less for the point cloud and even less are representing ground topography. Thus, in our case, ground point density was not correlated with differences, but a lower ground point density could have a strong correlation with differences.
For the same two pairwise comparisons, the largest velocity differences (Figure 4) tended to occur in and around the interface between the channel and the inset floodplain, and between the inset floodplain and the main floodplain. There were differences occurring in the main floodplain above the inset floodplain, but these appeared to be random and not dependent on longitudinal location (Figure 3). This was also the case between flow scenarios. There were greater differences for the 0.5 m DEM and the 2 m DEM pairwise comparison (Figures 4d–4f, 4j–4l, 4p–4r), which was expected since this pairwise comparison had the greatest resolution difference. Higher differences in velocity were also present in the main floodplain.
Absolute value of differences in velocity from two pairwise comparisons between the 0.25 and 0.5 m digital elevation model (DEM) resolution simulations (a–c, g–i, m–o), and between 0.5 and 2 m DEM resolution simulations (d–f, j–l, p–r). All results shown are at a mesh grid resolution of 1 m. Three flow scenarios for each pairwise comparison are displayed: 5.25 m3/s (a, g, m, d, j, and p), 10 m3/s (b, h, n, e, k, and q), and 20 m3/s (c, i, o, f, l, and r).
In isolated parts of the entire floodplain (Figures 4a–4c, 4d–4f, 4m–4o, 4p–4r), spatial variability of the velocity differences stayed consistent as flow increases, unlike depth differences in Figure 3. Additionally, for the larger difference in DEM resolution (Figures 4d–4f, 4p–4r) there were high velocity differences in the main floodplain that were comparable to differences in and along the channel floodplain interface. As with the depth differences, there were no correlations between velocity differences and lidar ground point density for the entire floodplain with Spearman coefficients ranging from −0.33 to −0.07. The p-values were all zero due to the sheer number of data points (over five to 6 million, depending on the flow scenario) (Gómez-de-Mariscal et al., 2021; Lin et al., 2013). As previously stated, this may be due to the high ground point density in this study. These spatial patterns shown in Figures 3 and 4 were similar for all other pairwise comparisons.
In addition to the differences in depths and velocities, resolution also affected how the flood extent was represented in the model. This was apparent when examining the flow inundation boundary (here at the maximum flow we simulated; Figure 5). Several aspects of the flow inundation boundary were dependent on DEM resolution: perimeter, number of islands, and number of puddles. All these aspects increased with finer DEM resolution, as shown in the spatial maps (Figures 5a–5d) and summarized in Figure 5e. We also found that mesh grid resolution did not greatly affect the perimeter, number of islands, and number of puddles.
Inundation boundary characteristics for the 20 m3/s flow scenario. (a–c) show a zoomed in section of the inundation boundary resulting from three of the models. (d) shows panels (a) through (c) stacked on top of each other. (e) shows the perimeter, number of islands, and number of puddles for each digital elevation model mesh grid combination.
3.2 Flow-Dependent Variation
In general, each model produced the same trend of average depth and velocity decreasing until the water filled in the inset floodplain and spilled onto the main floodplain for the remaining flow scenarios. This general trend is shown in Figure 6, where 5.25 m3/s is where the inset floodplain was overtopped, and main floodplain was then inundated. The minimum values in Figure 6 occur once the inset floodplain was filled (9.4 m wide; Christensen et al., 2024). The main floodplain (140 m wide) was more than 10 times the width of the inset floodplain, thus the flow after the inset floodplain was filled spreads out widely in the main floodplain.
Average depth and velocity for simulation using 0.5 m digital elevation model (DEM) resolution and 1 m mesh grid resolution. This generally represents the trend for average depth and velocity of all model results for different combinations of DEM and mesh grid resolution in this study. Note that the initial decrease in both parameters represents the water rising in the inset floodplain and eventually spilling onto the main floodplain at flow scenario 5.25 m3/s.
The largest differences in depth, approximately 1.7–2.5 cm (90th percentiles), occurred at the 5.25 m3/s flow scenario for all DEM pairwise comparisons (Figure 7a), which corresponded to the inset floodplain being overtopped as shown in Figure 6. Differences in depth decreased to roughly a constant value (90th percentile ranging from 1 to 0.2 cm) for each pairwise comparison after the overtopping scenario as flows increased. Conversely, differences in velocity (Figure 7c) drastically decreased as flow increased, demonstrating that DEM resolution has greater effects on velocities at low flows. Figure 7b shows that the largest differences in depth, approximately 10 mm for the 90th percentile of the 20 m3/s flow scenario, generally occurred between models that had the largest difference in DEM resolution, and eventually decreased between models that had the least difference in DEM resolution (approximately less than 4 mm, 90th percentile), with some inconsistences between mesh grid resolution. Differences in velocity (Figure 7c) followed this trend more clearly, where large differences occurred with larger differences in DEM resolution. These differences ranged from upwards of 25 mm/s for the lowest flows to less than 7 mm/s for the 90th percentiles of the highest flows. This basic trend held true for all the difference results at each flow scenario (Figures 7a and 7d).
Absolute value of differences in depth (a and b) and velocity (c and d) for 11 flow scenarios, where mesh grid resolution was kept constant. Purple boxplots correspond to the first pairwise comparison in Figures 3 and 4 (a–c, g–i, m–o). Blue boxplots correspond to the second pairwise comparison in Figures 3 and 4 (d–f, j–l, p–r). Each of the other colors represent all of the other pairwise comparisons. The top and bottom ends of each box respectively represent the 75th and 25th percentiles and the middle line represents the median. The top and bottom whiskers respectively represent the 90th and 10th percentiles.
We separated the boxplots that corresponded to Figures 3 and 4 to easily compare across different flows (Figure 8). From this separation, both sets of differences had similar trends, but at different magnitudes. The 90th percentile whiskers highlighted the differences and the trends that are shown in Figures 3 and 4. The pairwise comparison with the largest difference in DEM resolution (blue boxplots in Figure 8a) had larger differences in depth when the inset floodplain was overtopped (90th percentile: 20 mm; 50th percentile: 3 mm) than the other comparison (90th percentile: 10 mm; 50th percentile: 2 mm). Both depth differences eventually decreased to less than 10 mm. The differences in velocity were consistently more dissimilar between these two model comparisons, with the 75th percentile of the smaller difference in DEM resolution (purple boxplots in Figure 8b) being approximately equal to the 50th percentile of the larger difference in DEM resolution (blue boxplots in Figure 8b). Low flows produced higher differences in velocity for both comparisons (large DEM resolution difference: 90th percentile = 25 mm/s, 50th percentile = 6 mm/s; small DEM resolution difference: 90th percentile = 12 mm/s, 50th percentile = 2 mm/s). These differences continually decreased as flow increased, ultimately with all differences converging to less than 10 mm/s.
Absolute value of differences in depth (a) and velocity (b) from two pairwise comparisons that generally represent the overall trends in Figures 3 and 4. The pairwise comparisons include simulations using 0.25 m digital elevation model (DEM) and 0.5 m DEM resolutions both with a 1 m mesh grid resolution (purple) and include simulations using 0.5 m DEM and 2 m DEM resolutions both with a 1 m mesh grid resolution (blue). The top and bottom ends of each box respectively represent the 75th and 25th percentiles and the middle line represents the median. The top and bottom whiskers respectively represent the 90th and 10th percentiles.
For pairwise comparisons that varied mesh grid resolutions while keeping DEM resolution constant, differences in depth also increased when the channel was overtopped at flow scenario 5.25 m3/s (Figure 9a) with 90th percentiles ranging from 7 to 15 mm, similar to Figures 7a and 8a, but smaller in magnitude. This trend was not observed for velocities (Figure 9c), similar to Figures 7b and 8c. Differences in depth did decrease while flow increased until 10 m3/s (90th percentiles ranging from less than 5–7 mm), and then started to increase as flow increased (90th percentiles ranging from 12 to 5 mm for the 20 m3/s flow scenario). Differences in velocity steadily decreased as flow increased, similar to Figures 7b and 8c, with the 90th percentile ranging from 20 mm/s to 16 mm/s for the lowest flow and ranging from 6 mm/s to less than 5 mm/s for the highest flow. When examining each flow scenario individually, the 0.5 m DEM depth difference tended to have the largest differences at low flows (90th percentile: 20 mm, 50th percentile: 2 mm), but as flow increased the 0.25 m DEM depth difference and 2 m DEM depth difference had the larger differences (Figure 9b). Conversely, each flow scenario for velocity differences followed the consistent trend of increased differences with coarser DEM resolution (Figure 9d).
Absolute value of differences in depth (a and b) and velocity (c and d) for 11 flow scenarios, where digital elevation model resolution is kept constant. The top and bottom ends of each box respectively represent the 75th and 25th percentiles and the middle line represents the median. The top and bottom whiskers respectively represent the 90th and 10th percentiles.
To better understand how alterations in DEM resolution might be reflected as roughness, we reran the model 14 times with ±4% floodplain roughness change with the channel roughness kept as constant at 0.04. The depths and velocities from the max flow scenario were exported and compared to the respective results from the model with 0.5 floodplain roughness (Figure 10). This scenario was chosen as the reference model because it represents a medium resolution scenario (0.5 m DEM with a 1 m mesh grid) for our study site by representing the channel width with about eight cells. With an increase in floodplain roughness, as expected, depth in both the floodplain and channel increased (Figures 10a and 10b). This was consistent with a decrease in velocity over the floodplain (Figure 10c). However, velocity in the channel increased with increasing floodplain velocity (Figure 10d). This may seem counter intuitive, but recall that only floodplain roughness was changed and that increased floodplain roughness (without changing channel roughness) means that more water was being conveyed in the channel.
Change in depth and velocity as a result of changing floodplain roughness. Change in depth over the floodplain (a) and channel (b). Change in velocity over the floodplain (c) and in the channel (d). These results are relative to floodplain and channel depths and velocities from a model with floodplain roughness of 0.5 and channel roughness of 0.04. All compared modeled runs are identical except for changing floodplain roughness. A line was fitted to the medians and respective statistics were reported. The top and bottom ends of each box respectively represent the 75th and 25th percentiles and the middle line represents the median. The top and bottom whiskers respectively represent the 90th and 10th percentiles.
These results directly show the effect of DEM resolution on modeled results. For example, from Figure 7, for a mesh grid of 1 m, a change in DEM resolution from 0.1 to 2 m resulted in a 2.4 mm median change spatially across all cells in depth (10th percentile: 0.5 mm, 90th percentile: 10.6 mm) and a 2.3 mm/s median change in velocity (10th percentile: 0.4 mm/s, 90th percentile: 7.3 mm/s). This corresponds to a median roughness increase of 0.006 (10th percentile: 0.001, 90th percentile: 0.026; Figure 10a) for depths and corresponds to a median roughness decrease of 0.02 (10th percentile: −0.003, 90th percentile: −0.063; Figure 10c) for velocities.
For a 0.5 m DEM, a change in mesh grid resolution from 1 to 2 m resulted in a 1.7 mm median change in depth (10th percentile: 0.4 mm, 90th percentile: 6.9 mm) and a 1.4 mm/s change in velocity (10th percentile: 0.2 mm/s, 90th percentile: 5.3 mm/s; Figure 9). This results in a median roughness increase of 0.005 (10th percentile: 0.001, 90th percentile: 0.017; Figure 10a) for depth and results in a median roughness decrease of 0.01 (10th percentile: −0.002, 90th percentile: −0.05; Figure 10c). In general, most of the depth and velocity changes were between 5 and 25 mm and mm/s, respectively. These changes result in a floodplain roughness of 0.5 increasing by up to 0.06 or by 12% for depths and decreasing by 0.22 or by 44% for velocities (Figures 10a and 10c). These floodplain roughness changes were calculated using the equations in Figures 10a and 10c.
4 Discussion
From these results, we conclude that changing DEM resolution has a similar effect to altering the roughness in 2D HEC-RAS, thus DEMs and mesh grids will create some amount of artificial roughness. Unresolved roughness, as described in (Mazdeh et al., 2023), is roughness sourced from real features in the landscape that are not being resolved in either the DEM or the computational mesh. When referring to artificial roughness, we are referring to microtopography that might not represent the actual ground variation and is rather sourced from the imperfect ground algorithms that must be used. Artificial roughness is most prominent in our study, due to the high resolution point cloud, and thus the high resolution DEMs. This can result in centimeters of difference throughout the floodplain for depth estimates (Figure 3), for a fixed roughness value, and tends to be concentrated on the channel-floodplain interface for velocity estimates (Figure 4). We found that these variations are concentrated in complex areas of the model, such as the channel-floodplain interface (Figures 4, 7, 8, and 9a) and during low flows (Figures 7-9), but will eventually decrease to a uniform value across the floodplain as flow increases.
We found that changes in velocities and depths in both the floodplain and channel follow a linear trend (Figure 10). As roughness increases, floodplain and channel depths are also increasing while floodplain velocities are decreasing. Channel velocities are increasing with increased floodplain roughness because as depth is increasing with roughness in the floodplain and channel, more water is being conveyed in the channel instead of the floodplain. This is happening because of continuity and because in-channel roughness is not changing, thus channel velocities are increasing. This finding demonstrates that increasing floodplain roughness, because of DEM and mesh grid resolutions could have unexpected magnitude increases to the channel velocities. The majority of the differences in depth and velocity that we report are between 5 and 25 mm and mm/s, respectively. These differences are equivalent to increasing floodplain roughness (from 0.5) by up to 0.06 or by 12% for depths and decreasing by 0.22 or by 44% for velocities (Figures 10a and 10c).
We found that model differences had no correlation to lidar ground point density, by visual inspection of spatial patterns (Figures 3 and 4), and via Spearman coefficient calculations. We suspect that if this study was repeated using a less dense point cloud, collected from an airplane perhaps, then there may be correlations between model differences and low lidar ground point density because the ground interpolator used to create the DEM would have to do more estimations where low lidar ground point density is present. Our lidar system produced a point cloud density of approximately 450 points/m2 (251 points/m2 ground point density), while lidar collected from airplanes, such as the U.S. Geologic Survey's 3D Elevation Program, typically have point cloud densities of 30 points/m2 or fewer (Heidemann, 2018). This translates to 450 points in a 1 m2 pixel for a drone lidar DEM raster and 30 points in a 1 m2 pixel for an airplane lidar DEM raster. If the pixel was to decrease to 0.1 m2, the drone system would provide about five points/pixel, whereas the airplane system would provide less than one point/pixel.
An analysis of the inundation extent (Figure 5) showed a distinct dependency between DEM resolution and flood boundary characteristics. These results are important to consider because inundated area would thus be affected by these results. Inundated area is an important parameter for understanding and estimating floodplain biogeochemical cycling estimations (Boulton et al., 2010; Goldman et al., 2017; McClain et al., 2003; Mulholland & Webster, 2010; Stegen et al., 2016) and sediment floodplain deposition (Zwoliński, 1992). Additionally, inundation boundaries for high flow scenarios are also important for dam breach analysis (Wahl, 2004), emergency management preparedness (Kundzewicz et al., 2010), and property damage estimations (Thakali et al., 2017; Wing et al., 2017). High resolution DEMs represent topographic variability in greater detail, often having many pits and mounds. These features are the source of topographic roughness that we have examined when comparing model simulations, and thus affect how the inundated extent is defined. These features also affect the ability to generate streamlines from a velocity field (Sumaiya et al., 2024). Depending on the goals of the hydrodynamic model, the final quality of the flood inundation boundary might influence the choice of DEM resolution.
One potential parameter that could be used to guide modelers on selecting a DEM or mesh grid resolution is the ratio of channel width to resolution. It has been shown that accurate representation of the channel is a dominant factor in hydrodynamic modeling, with regard to resolution and roughness (Bilgili et al., 2023; Caviedes-Voullième et al., 2012; Savage, Bates, et al., 2016). Because of this, modelers should consider a range of ratios of channel width to resolution that would work for their study sites. To contextualize our findings with other hydrodynamic modeling studies, we found that channel width to DEM resolution ratio tends to range from 2 to 175 (Abu-Aly et al., 2014; Cobby et al., 2003; Cook & Merwade, 2009; Mason et al., 2003; Modi et al., 2022; Papaioannou et al., 2020). Mesh grid resolution was not clearly reported in the cited literature, thus we cannot comment on that ratio. We also found that while there is more hydrodynamic literature, many of them do not clearly report channel width, DEM resolution, and mesh grid resolution. For our study both ratios ranged from 2 to 45.
An important aspect to understand from our results is that whatever resolution is selected, the exact calibrated roughness value could be different for different resolution choices. Different roughness values could be applied to the same landscape (using different DEM and mesh grid resolutions) and both would be appropriate if calibrated correctly with velocity and depth field data. Our results show that the appropriate roughness values will vary between models of the same location because of the added roughness from DEM and mesh grid resolutions. This complicates using look-up tables for selecting roughness parameters or using the roughness parameters from other models.
There are several modeling aspects that need to be considered when choosing DEM and mesh grid resolutions. Features in the floodplain that could alter or influence flow and wetting, such as negative relief features (Fivash et al., 2023; Lewin & Ashworth, 2014) like floodplain channels (Czuba et al., 2019; Sumaiya et al., 2021), should be spatially represented in the model with sufficient resolution (Adams & Zampiron, 2020; Bilgili et al., 2023; Dottori et al., 2013; Kasprak et al., 2019; Mazdeh et al., 2023; Yu & Lane, 2006). Additionally, increasing roughness in these areas might also be an important consideration (Caviedes-Voullième et al., 2012; Mazdeh et al., 2023). These complex areas could also benefit from a mesh refinement area (Wright et al., 2022). One definite location of a mesh refinement area is the main channel. The channel should be represented by at least several cells of the DEM and mesh grid so that cross section is accurately represented and so that depth and velocity can be resolved by the model in multiple locations across the channel, which subsequently affects the channel floodplain interface (Bilgili et al., 2023; Savage, Bates, et al., 2016). If the model is specifically being used to simulate low to bankfull flow scenarios, channel and near-channel representation seems to be very sensitive because our findings show that DEM and mesh grid resolutions tend to have greater effects in these lower flow scenarios.
Lastly, limitations on computational power should always be considered. High resolution data used as inputs for any model could cause it to become unstable and crash. Even if the model stabilizes by using a small timestep, the high resolution inputs could cause the runtime to be excessive (Bilgili et al., 2023; Dottori et al., 2013; Savage, Bates et al., 2016). This could make model calibration and validation steps extend from days to weeks. Ultimately, the modeler will have to consider where they are willing to compromise, while also considering how to represent reality and at what resolution for the question of interest.
While this study specifically examines the effect of resolution on modeling, future work should include modeling with a DEM generated from a less dense point cloud or other 2D models. Future work could also include representing a distinct floodplain feature at several resolutions and analyzing how the results differed from each other and from field data. This could better inform how important certain floodplain features are to hydrodynamic modeled results. Additionally, future research could include repeating this study with other 2D models that do not have the same unique sub-mesh grid considerations that HEC-RAS uses. Because we found that resolution can add unresolved roughness, it would be expected that a model not using sub-mesh grid topography would result in different calibrated roughness values and unresolved roughness values.
5 Conclusion
We investigated how mesh grid resolution and DEM resolution affected hydrodynamic simulation results of water depths, velocities, and inundation boundary. We did this by comparing results from a 2D HEC-RAS model (mesh grid resolutions of 1 and 2 m) that utilizes drone-based lidar DEMs of several resolutions (0.1, 0.25, 0.5, 1, and 2 m) over the StREAM Lab at Virginia Tech. To further show how resolution can result in a change in roughness, the model was rerun for up to ±4% change in floodplain roughness with 0.5 floodplain roughness being the base comparison.
From the pairwise comparisons of the 11 flow scenarios, we found that the largest differences in depths when comparing DEM resolution occurred when the floodplain was first inundated and decreased as flow increased, which was also true for differences in velocities when mesh grid resolution was varied. The differences in depths when mesh grid resolution was varied were not consistent with this trend. Differences in velocities were concentrated on the channel-floodplain interface while differences in depths occurred throughout the floodplain. Most of the differences in depth and velocity that we reported were between 5 and 25 mm and mm/s, respectively. These differences are equivalent to increasing floodplain Manning's roughness (from 0.5) by up to 0.06 or by 12% for depths and decreasing by 0.22 or by 44% for velocities (Figures 10a and 10c). Additionally, differences in depth and velocity were not correlated with lidar ground point density, though this might be due to the very high ground point density of our data (251 points/m2) which is characteristic of drone lidar systems. Differences and ground point density might be correlated if the latter were much lower than our data. Lastly, the inundation boundary and the number of islands and puddles were dependent on the DEM resolution.
We showed that DEM and mesh grid resolutions of 2D hydrodynamic modeling affect modeled depths, velocities, and inundation boundary. Modelers should consider what resolution best represents the main channel while also resolving important riparian topographic features. Future research should include analysis of how resolving floodplain features via DEM, mesh grid, or refinement areas affect modeled results. Once these limitations are addressed, modelers can confidently select a resolution from drone-based lidar data to best represent their area of interest.
Acknowledgments
This work is supported by the Virginia Agricultural Experiment Station (Blacksburg); the USDA National Institute of Food and Agriculture, U.S. Department of Agriculture (Washington, DC); Virginia Tech Interdisciplinary Graduate Education Program in Remote Sensing; Virginia Space Grant Consortium; and the National Science Foundation Graduate Research Fellowship Program under Grant 1650114. Special thanks to Laura Lehmann (StREAM Lab manager and drone pilot), Nicholas D. Christensen (collected bathymetry data), and Reilly Oare (conducted model simulations).
