Urban fluvial flood modelling using a two‐dimensional diffusion‐wave treatment,part 2: development of a sub‐grid‐scale treatment

This paper develops and tests a sub‐grid‐scale wetting and drying correction for use with two‐dimensional diffusion‐wave models of urban flood inundation. The method recognizes explicitly that representations of sub‐grid‐scale topography using roughness parameters will provide an inadequate representation of the effects of structural elements on the floodplain (e.g. buildings, walls), as such elements not only act as momentum sinks, but also have mass blockage effects. The latter may dominate, especially in structurally complex urban areas. The approach developed uses high‐resolution topographic data to develop explicit parameterization of sub‐grid‐scale topographic variability to represent both the volume of a grid cell that can be occupied by the flow and the effect of that variability upon the timing and direction of the lateral fluxes. This approach is found to give significantly better prediction of fluvial flood inundation in urban areas than traditional calibration of sub‐grid‐scale effects using Manning's n. In particular, it simultaneously reduces the need to use exceptionally high values of n to represent the effects of using a coarser mesh process representation and increases the sensitivity of model predictions to variation in n. Copyright © 2005 John Wiley & Sons, Ltd.     

Coupling the Xinanjiang model to a kinematic flow model based on digital drainage networks for flood forecasting

The Xinanjiang model, which is a conceptual rainfall‐runoff model and has been successfully and widely applied in humid and semi‐humid regions in China, is coupled by the physically based kinematic wave method based on a digital drainage network. The kinematic wave Xinanjiang model (KWXAJ) uses topography and land use data to simulate runoff and overland flow routing. For the modelling, the catchment is subdivided into numerous hillslopes and consists of a raster grid of flow vectors that define the water flow directions. The Xinanjiang model simulates the runoff yield in each grid cell, and the kinematic wave approach is then applied to a ranked raster network. The grid‐based rainfall‐runoff model was applied to simulate basin‐scale water discharge from an 805‐km² catchment of the Huaihe River, China. Rainfall and discharge records were available for the years 1984, 1985, 1987, 1998 and 1999. Eight flood events were used to calibrate the model's parameters and three other flood events were used to validate the grid‐based rainfall‐runoff model. A Manning's roughness via a linear flood depth relationship was suggested in this paper for improving flood forecasting. The calibration and validation results show that this model works well. A sensitivity analysis was further performed to evaluate the variation of topography (hillslopes) and land use parameters on catchment discharge. Copyright © 2009 John Wiley & Sons, Ltd.     

The application of integrated urban inundation model in Republic of Korea

In urban areas with a high building density, features such as roads, buildings and river dykes significantly affect flow dynamics and flood propagation. This should therefore be accounted for in the model set‐up. While 2D hydraulic models of densely urban areas are at the forefront of current research into flood inundation mechanisms, these models are constrained by inadequate parameters of topography and insufficient data. In order to solve these problems, topographic information obtained from digital elevation model (DEM) is directly programmed into the urban inundation model for a densely urban area, without exchanging the input data. In this paper, the extraction of building area is described using a tight coupling approach within a GIS environment, and its influence on the extent of flood inundation with a high building density is estimated. Copyright © 2009 John Wiley & Sons, Ltd.     

Hydraulic model calibration for extreme floods in bedrock‐confined channels: case study from northern Thailand

Palaeoflood reconstructions based on stage evidence are typically conducted in data‐poor field settings. Few opportunities exist to calibrate the hydraulic models used to estimate discharge from this evidence. Consequently, an important hydraulic model parameter, the roughness coefficient (e.g. Manning's n), is typically estimated by a range of approximate techniques, such as ‘visual estimation’ and semi‐empirical equations. These techniques contribute uncertainty to resulting discharge estimates, especially where the study reach exhibits sensitivity in the discharge–Manning's n relation. We study this uncertainty within a hydraulic model for a large flood of known discharge on the Mae Chaem River, northern Thailand. Comparison of the ‘calibrated’ Manning's n with that obtained from semi‐empirical equations indicates that these underestimate roughness. Substantial roughness elements in the extra‐channel zone, inundated during large events, contribute significant additional sources of flow resistance that are captured neither by the semi‐empirical equations, nor by existing models predicting stage–roughness variations. This bedrock channel exhibits a complex discharge–Manning's n relation, and reliable estimates of the former are dependent upon realistic assignment of the latter. Our study demonstrates that a large recent flood can provide a valuable opportunity to constrain this parameter, and this is illustrated when we model a palaeoflood event in the same reach, and subsequently examine the magnitude–return period consequences of discharge uncertainty within a flood frequency analysis, which contributes its own source of uncertainty. Copyright © 2005 John Wiley & Sons, Ltd.     

水文与岸滩变化对滨岸带南荻-芦苇群落适宜生境的影响——以长江武汉河段为例

建立了考虑淹没频率和淹没水深等生境因子的水动力-生境适宜度数学模型,基于三峡水库蓄水前后的长序列水文观测数据和不同时期的河道地形资料,研究了近20年来武汉河段汉口边滩南荻(Miscanthus lutarioriparius)-芦苇(Phragmites australis)群落的适宜生境变化情况,量化了不同因素的影响.结果表明:所建立的生境数值模型能较好地模拟还原南荻-芦苇群落实际空间分布情况.与2001年前的情况相比,若维持地形不变,三峡水库蓄水后的径流过程调平、年内水位变幅减小将导致群落适宜分布带向河道方向转移,且面积减小33.24%;若保持水文条件不变,岸线利用引起的地形坡度坦化将导致群落扩张,其分布面积增加69.11%;由于后者影响占主导地位,在2种因素综合影响下,南荻-芦苇群落向低滩地蔓延的同时呈现了扩张的趋势,面积增加42.53%.进一步发现,若滩地地形变化或人工建筑位于淹没频率在5%~25%区间带内,则水文变化、地形变化2种因素会对南荻-芦苇群落生境产生迭加影响,这种迭加影响甚至会大于单因素影响之和.研究表明岸滩开发等人为干扰导致滨岸滩地改变时,可能会影响滩上植被生长条件,这值得有关部门进行岸线规划、利用和进行生态保护时重点关注.     

Unstructured grid generation using LiDAR data for urban flood inundation modelling

Inundation disasters, caused by sudden water level rise or rapid flow, occur frequently in various parts of the world. Such catastrophes strike not only in thinly populated flood plains or farmland but also in highly populated villages or urban areas. Inundation of the populated areas causes severe damage to the economy, injury, and loss of life; therefore, a proper management scheme for the disaster has to be developed. To predict and manage such adversity, an understanding of the dynamic processes of inundation flow is necessary because risk estimation is performed based on inundation flow information. In this study, we developed a comprehensive method to conduct detailed inundation flow simulations for a populated area with quite complex topographical features using LiDAR (Light Detection and Ranging) data. Detailed geospatial information including the location and shape of each building was extracted from the LiDAR data and used for the grid generation. The developed approach can distinguish buildings from vegetation and treat them differently in the flow model. With this method, a fine unstructured grid can be generated representing the complicated urban land features precisely without exhausting labour for data preparation. The accuracy of the generated grid with different grid spacing and grid type is discussed and the optimal range of grid spacing for direct representation of urban topography is investigated. The developed method is applied to the estimation of inundation flows, which occurred in the basin of the Shin‐minato River. A detailed inundation flow structure is represented by the flow model, and the flow characteristics with respect to topographic features are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Interactions between subgrid‐scale resolution,feature representation and grid‐scale resolution in flood inundation modelling

Numerical modelling of flood inundation over large and complex floodplains often requires mesh resolutions coarser than the structural features (e.g. buildings) that are known to influence the inundation process. Recent research has shown that this mismatch is not well represented by conventional roughness treatments, but that finer‐scale features can be represented through porosity‐based subgrid‐scale treatments. This paper develops this work by testing the interactions between feature representation, subgrid‐scale resolution and mesh resolution. It uses as the basis for this testing a 2D diffusion‐based flood inundation model which is applied to a 2004 flood event in a topologically complex upland floodplain in northern England. This study formulated simulations with different grid mesh resolution and subgrid mesh ratio. The sensitivity of the model to mesh resolution and roughness specification was investigated. Model validation and verification suggest that the subgrid treatment with higher subgrid mesh ratio can give much improved predictions of flood propagation, in particular, in terms of the predicted water depth. This study also highlighted the limitation of using at‐a‐point in time inundation extent for validation of flood models of this type. Copyright © 2010 John Wiley & Sons, Ltd.     

3D float tracking: in situ floodplain roughness estimation

This paper presents a novel technique to quantify in situ hydrodynamic roughness of submerged floodplain vegetation: 3D float tracking. This method uses a custom‐built floating tripod that is released on the inundated floodplain and tracked from shore by a robotic total station. Simultaneously, an acoustic Doppler current profiler (ADCP) collects flow velocity profiles and water depth data. Roughness values are derived from two methods based on (1) run‐averaged values of water depth, slope and flow velocity to compute the roughness based on the Chézy equation, assuming uniform flow, (2) the equation for one‐dimensional free surface flow in a moving window. A sensitivity analysis using synthetic data proved that the median value of the roughness, derived using method 2, is independent of (1) the noise in water levels, up to 9 mm, (2) bottom surface slope, and (3) topographic undulations. The window size should be at least 40 m for a typical lowland river setup. Field measurements were carried out on two floodplain sections with an average vegetation height of 0·030 (Arnhem) and 0·043 m (Dreumel). Method 1 resulted in a Nikuradse roughness length of 0·08 m for both locations. Method 2 gave 0·12 m for Arnhem and 0·19 m for Dreumel. In Arnhem, a spatial pattern of roughness values was present, which might be related to fractional vegetation cover or vegetation density during the flood peak. 3D float tracking proved a flexible and detailed method for roughness determination in the absence of waves, and provided an unrestricted view from shore. Copyright © 2008 John Wiley & Sons, Ltd.     

Unstructured mesh generation and landcover-based resistance for hydrodynamic modeling of urban flooding

Urban flood inundation modeling with a hydrodynamic flow solver is addressed in this paper, focusing on strategies to effectively integrate geospatial data for unstructured mesh generation, building representation and flow resistance parameterization. Data considered include Light Detection and Ranging (LiDAR) terrain height surveys, aerial imagery and vector datasets such as building footprint polygons. First, a unstructured mesh-generation technique we term the building-hole method (BH) is developed whereby building footprint data define interior domain boundaries or mesh holes. A wall boundary condition depicts the impact of buildings on flood hydrodynamics. BH provides an alternative to the more commonly used method of raising terrain heights where buildings coincide with the mesh. We term this the building-block method (BB). Application of BH and BB to a flooding site in Glasgow, Scotland identifies a number of tradeoffs to consider at resolutions ranging from 1 to 5 m. At fine resolution, BH is shown to be similarly accurate but execute faster than BB. And at coarse resolution, BH is shown to preserve the geometry of buildings and maintain better accuracy than BB, but requires a longer run time. Meshes that ignore buildings completely (no-building method or NB) also support surprisingly good flood inundation predictions at coarse resolution compared to BH and BB. NB also supports faster execution times than BH at coarse resolution because the latter uses localized refinements that mandate a greater number of computational cells. However, with mesh refinement, NB converges to a different (and presumably less-accurate) solution compared to BH and BB. Using the same test conditions, Hunter et al. [Hunter NM, Bates PD, Neelz S, Pender G, Villanueva I, Wright NG, Liang D, et al. Benchmarking 2D hydraulic models for urban flood simulations. ICE J Water Manage 2008;161(1):13–30] compared the performance of dynamic-wave and diffusive-wave models and reported that diffusive-wave models under-predicted the longitudinal penetration of the flood zone due to important inertial effects. Here, we find that a relatively coarse-mesh implementation of a dynamic-wave model suffers from the same drawback because of numerical diffusion. This shows that whether diffusion is achieved through the mathematics or numerics, the effect on flood extent is similar. Finally, several methods of distributing resistance parameters (e.g., Manning n) across the Glasgow site were evaluated including methods that utilize aerial imagery-based landcover classification data, MasterMap^® landcover classification data and LiDAR-based feature height data (e.g., height of shrubs or hedges). Results show that landcover data is more important than feature height data in this urban site, that shadows in aerial imagery can cause errors in landcover classification which degrade flood predictions, and that aerial imagery offers a more detailed mapping of trees and bushes than MasterMap^® which can locally impact depth predictions but has little impact on flood extent.     

Flood hydrograph reconstruction from the peak flow value in ephemeral streams using a simplified robust single‐parameter model

Flood hydrographs from ephemeral streams in arid areas provide valuable information for assessing run‐off and groundwater recharge. However, such data are often scarce or incomplete, especially in hyper‐arid regions. The hypothesis of this study was that it is possible to reconstruct a hydrograph of a specific point along an ephemeral stream with the knowledge of only the peak flow rate of a flood event at that point and that this can be done at almost every point along the stream. The feasibility of this approach lies in the shape of the recession stage of the flood hydrograph, which is known to be a repeating phenomenon. The recession stage comes immediately after the peak flow rate, when it begins its decline, and lasts until the flood is extinguished. A general shape of the flood recession stage can be provided. Because the recession stage represents ~80% of the duration of a flood event, it can provide a general idea of the flood hydrograph's shape. A simple model based on geometric progression is suggested to describe the repeating recession stage of a flood. The advantage of the proposed model is that it requires only one parameter: the recession characteristic at a fixed point along the ephemeral stream, termed recession coefficient q. By knowing the recession coefficient of a fixed point and the peak flow rate of a flood event at that point, one can plot the flood hydrograph. A good agreement is shown between the observed and computed values of the recession stage. Copyright © 2016 John Wiley & Sons, Ltd.     

Unstructured grid based 2-D inversion of VLF data for models including topography

We present a 2-D inversion code incorporating a damped least-squares and a minimum-model approach for plane wave electromagnetic (EM) methods using an adaptive unstructured grid finite element forward operator. Unstructured triangular grids permit efficient discretization of arbitrary 2-D model geometries and, hence, allow for modeling arbitrary topography. The inversion model is parameterized on a coarse parameter grid which constitutes a subset of the forward modeling grid. The mapping from parameter to forward modeling grid is obtained by adaptive mesh refinement. Sensitivities are determined by solving a modified sensitivity equation system arising from the derivative of the finite element equations with respect to the model parameters. Firstly, we demonstrate that surface topography may induce significant effects on the EM response and in the inversion result, and that it cannot be ignored when the scale length of topographic variations is in the order of magnitude of the skin depth. Secondly, the dependency of the inversion on the starting model is discussed for VLF and VLF-R data. Thirdly, we demonstrate the inversion of a synthetic data set obtained from a model with topography. Finally, the inversion approach is applied to field data collected in a region with undulating topography.     

Modelling the effect of time‐dependent river dune evolution on bed roughness and stage

This paper presents an approach to incorporate time‐dependent dune evolution in the determination of bed roughness coefficients applied in hydraulic models. Dune roughness is calculated by using the process‐based dune evolution model of Paarlberg et al. ( 2009 ) and the empirical dune roughness predictor of Van Rijn ( 1984 ). The approach is illustrated by applying it to a river of simple geometry in the 1‐D hydraulic model SOBEK for two different flood wave shapes. Calculated dune heights clearly show a dependency on rate of change in discharge with time: dunes grow to larger heights for a flood wave with a smaller rate of change. Bed roughness coefficients computed using the new approach can be up to 10% higher than roughness coefficients based on calibration, with the largest differences at low flows. As a result of this larger bed roughness, computed water depths can be up to 15% larger at low flow. The new approach helps to reduce uncertainties in bed roughness coefficients of flow models, especially for river systems with strong variations in discharge with time. Copyright © 2010 John Wiley & Sons, Ltd.     

Improvement of surface run‐off in the hydrological model ParFlow by a scale‐consistent river parameterization

We propose an improvement of the overland‐flow parameterization in a distributed hydrological model, which uses a constant horizontal grid resolution and employs the kinematic wave approximation for both hillslope and river channel flow. The standard parameterization lacks any channel flow characteristics for rivers, which results in reduced river flow velocities for streams narrower than the horizontal grid resolution. Moreover, the surface areas, through which these wider model rivers may exchange water with the subsurface, are larger than the real river channels potentially leading to unrealistic vertical flows. We propose an approximation of the subscale channel flow by scaling Manning's roughness in the kinematic wave formulation via a relationship between river width and grid cell size, following a simplified version of the Barré de Saint‐Venant equations (Manning–Strickler equations). The too large exchange areas between model rivers and the subsurface are compensated by a grid resolution‐dependent scaling of the infiltration/exfiltration rate across river beds. We test both scaling approaches in the integrated hydrological model ParFlow. An empirical relation is used for estimating the true river width from the mean annual discharge. Our simulations show that the scaling of the roughness coefficient and the hydraulic conductivity effectively corrects overland flow velocities calculated on the coarse grid leading to a better representation of flood waves in the river channels.     

Optimal use of high‐resolution topographic data in flood inundation models

In this paper we explore the optimum assimilation of high‐resolution data into numerical models using the example of topographic data provision for flood inundation simulation. First, we explore problems with current assimilation methods in which numerical grids are generated independent of topography. These include possible loss of significant length scales of topographic information, poor representation of the original surface and data redundancy. These are resolved through the development of a processing chain consisting of: (i) assessment of significant length scales of variation in the input data sets; (ii) determination of significant points within the data set; (iii) translation of these into a conforming model discretization that preserves solution quality for a given numerical solver; and (iv) incorporation of otherwise redundant sub‐grid data into the model in a computationally efficient manner. This processing chain is used to develop an optimal finite element discretization for a 12 km reach of the River Stour in Dorset, UK, for which a high‐resolution topographic data set derived from airborne laser altimetry (LiDAR) was available. For this reach, three simulations of a 1 in 4 year flood event were conducted: a control simulation with a mesh developed independent of topography, a simulation with a topographically optimum mesh, and a further simulation with the topographically optimum mesh incorporating the sub‐grid topographic data within a correction algorithm for dynamic wetting and drying in fixed grid models. The topographically optimum model is shown to represent better the ‘raw’ topographic data set and that differences between this surface and the control are hydraulically significant. Incorporation of sub‐grid topographic data has a less marked impact than getting the explicit hydraulic calculation correct, but still leads to important differences in model behaviour. The paper highlights the need for better validation data capable of discriminating between these competing approaches and begins to indicate what the characteristics of such a data set should be. More generally, the techniques developed here should prove useful for any data set where the resolution exceeds that of the model in which it is to be used. Copyright © 2002 John Wiley & Sons, Ltd.     

Comparing the performance of a 2‐D finite element and a 2‐D finite volume model of floodplain inundation using airborne SAR imagery

The performances of a finite volume model (SFV) and finite element model (TELEMAC‐2D) in reproducing inundation on a 16 km reach of the river Severn, United Kingdom, are compared. Predicted inundation extents are compared with 4 airborne synthetic aperture radar images of a major flood event in November 2000, and these are used to calibrate 2 values of Manning's n for the channel and floodplain. The four images are shown to have different capacities to constrain roughness parameters, with the image acquired at low flow rate doing better in determining these parameters than the image acquired at approximately peak flow. This is assigned to the valley filling nature of the flood and the associated insensitivity of flood extent to changes in water level. The level of skill demonstrated by the models, when compared with inundation derived using a horizontal water free surface, also increases as flow rate drops. The two models show markedly different behaviours to the calibration process, with TELEMAC showing less sensitivity and lower optimum values for Manning's n than SFV. When the models are used in predictive mode, calibrated against one image and predicting another, SFV performs better than TELEMAC. Copyright © 2007 John Wiley & Sons, Ltd.     

Regionalization of floods in New Brunswick (Canada)

This study uses the method of peaks over threshold (P.O.T.) to estimate the flood flow quantiles for a number of hydrometric stations in the province of New Brunswick, Canada. The peak values exceeding the base level (threshold), or `exceedances', are fitted by a generalized Pareto distribution. It is known that under the assumption of Poisson process arrival for flood exceedances, the P.O.T. model leads to a generalized extreme value distribution (GEV) for yearly maximum discharge values. The P.O.T. model can then be applied to calculate the quantiles X <sub>T</sub> corresponding to different return periods T, in years. A regionalization of floods in New Brunswick, which consists of dividing the province into `homogeneous regions', is performed using the method of the `region of influence'. The 100-year flood is subsequently estimated using a regionally estimated value of the shape parameter of the generalized Pareto distribution and a regression of the 100-year flood on the drainage area. The jackknife sampling method is then used to contrast the regional results with the values estimated at site. The variability of these results is presented in box-plot form. Received: June 1, 1997     

Regionalization of floods in New Brunswick (Canada)

This study uses the method of peaks over threshold (P.O.T.) to estimate the flood flow quantiles for a number of hydrometric stations in the province of New Brunswick, Canada. The peak values exceeding the base level (threshold), or `exceedances', are fitted by a generalized Pareto distribution. It is known that under the assumption of Poisson process arrival for flood exceedances, the P.O.T. model leads to a generalized extreme value distribution (GEV) for yearly maximum discharge values. The P.O.T. model can then be applied to calculate the quantiles X <sub>T</sub> corresponding to different return periods T, in years. A regionalization of floods in New Brunswick, which consists of dividing the province into `homogeneous regions', is performed using the method of the `region of influence'. The 100-year flood is subsequently estimated using a regionally estimated value of the shape parameter of the generalized Pareto distribution and a regression of the 100-year flood on the drainage area. The jackknife sampling method is then used to contrast the regional results with the values estimated at site. The variability of these results is presented in box-plot form. Received: June 1, 1997     

Back‐calculation of bedload transport in steep channels with a numerical model

In August 2005 severe flood events occurred in the Alps. A sediment routing model for steep torrent channel networks called SETRAC has been applied to six well‐documented case study streams with substantial sediment transport in Austria and Switzerland. For these streams information on the sediment budget along the main channel is available. Flood hydrographs were reconstructed based on precipitation data and stream gauges in neighbouring catchments. Different scenarios are modelled and discussed regarding sediment availability and the effect of armouring and macro‐roughness on sediment transport calculations. The simulation results show the importance of considering increased flow resistance for small relative flow depth when modelling bedload transport during high‐intensity flood events in torrents and mountain rivers. Without any correction of increased flow resistance using a reduced energy slope, the predicted bedload volumes are about a factor of 10 higher on average than the observed values. Simulation results were also used for a back‐calculation of macro‐roughness effects from bedload transport data, and compared with an independent estimate of flow resistance partitioning based on flow resistance data. Copyright © 2010 John Wiley & Sons, Ltd.     

Progress in simplifying hydrologic model parameterization for broad applications to post-wildfire flooding and debris-flow hazards

Predicting the timing of overland flow in burned watersheds can help to estimate debris-flow timing and the location of debris-flow initiation. Numerical models can produce flow predictions, but they are limited by our knowledge of appropriate model parameters. Moreover, opportunities to test and calibrate model parameters in post-wildfire settings are limited by available data (measurements of debris-flow timing are rare). In this study, we use a unique data set of rainfall and flow-timing data to test the extent to which model parameters can be generalized from an individual watershed to other watersheds (0.01 km ² to >1km ²) within a burned area. Simulations suggest that a single, low, saturated hydraulic conductivity value can be used in post-wildfire landscapes with reasonable results. By contrast, we found that watershed-scale effective Manning roughness parameter values decrease as a power-law function of basin drainage area. Thus a Manning roughness parameter calibrated for a single basin within a burned area may not provide adequate results in a different watershed. However, when flow velocity is modeled independently for hillslopes and channels, and different roughness parameters are used for those morphometric units, there is no drainage-area dependence on the roughness parameters. Moreover, we found that it was possible to use field-measured grain size data to parameterize the roughness for both hillslopes and channels. Thus our results show that, employing this generalizable approach, it is possible to use field measurements to fully parameterize a model that produces peak flow timing to within a few minutes in storms lasting several hours. Further, we demonstrate how model simulations can be leveraged to identify areas within a watershed that are most susceptible to debris flows. This modeling approach could be used for decision making in hazardous burned areas and would be especially useful in ungaged basins. © 2019 John Wiley & Sons, Ltd.     

Grid size effects analysis and hydrological similarity of surface runoff in flatland basins

The effects of grid-size modification on the derived topographic attributes are analysed and a procedure for scaling model parameters and similarity assessment between flow variables is proposed. Hydrological simulations are performed with a physically-based and spatially-distributed quasi-2D mathematical model. The scaled model parameters are the effective roughness coefficient associated with overland flow (n_ov) and the transverse slope in the cell (TSC). To scale the selected parameters, the criterion of equilibrium storage conservation between the different grid sizes is applied. Three basins of the central-east region of Argentina are modelled. The spatial variability of basin geomorphology is quantified using the entropy concept. The simulation results show that when grid size is increased, to obtain similar hydrological responses it is necessary to increase the n_ov or to reduce the TSC. In terms of similarity, the best results are achieved when TSC is scaled, particularly when water depths are considered.