Downstream Boundary Conditions Research Articles

Flood Hazard Analysis of Proposed Regulator on Shatt Al-Arab River

Recently, the Shatt Al-Arab River has suffered from increased salinization of its water due to the reduction of freshwater from its tributaries, mainly from the Tigris River, which has resulted in long-distance salinity intrusion. Therefore, there is a need to establish a regulator in the Abu-Flus district to prevent salt intrusion. The aim of the study is to investigate the effect of a proposed regulator on the Shatt Al-Arab River with simulations using the Hydrologic Engineering Center’s River Analysis System (HEC-RAS) model. The upstream boundary conditions were the daily discharges of Tigris River and the downstream boundary conditions were the hourly water stages of the Shatt Al-Arab River. The river model was operated by using the daily discharges recorded in 2014 for calibration and verification of the model. Then, a program operated with a suggested regulator and a flood wave assumed a 200 m3/s peak flow for a duration of 27 days. The flooding occurrence period of the flood wave was investigated under the effect of three study cases of regulator gates, which were fully open (case B1), tide gate (case B2), and fully closed (case B3). The results showed that flooding inundation occurred only in two cases (B2 and B3). These results will encourage the construction of the regulator considering certain precautions.

Study on Mathematical Model of Water and Sediment in front of the Dam under Multi-control Boundary Conditions

Aiming at mathematical model of flow and sediment under multi-control boundary conditions in front of dams of hydropower station, a step-by-step solution method is proposed in this paper. In the first step, the influence of constraints such as the water intake of the power station is not considered. The water level control condition of the exit section is given according to the scheduling mode of the hydropower station, and the discharge is given by the inlet boundary. In the second step, the water level as the upstream boundary condition of the model according to the condition of the first step is obtained, and the discharge of the water intake of the hydropower station is defined as the downstream boundary condition. The mathematical model is used to perform simulation analysis on the Dashixia Reservoir. The analysis results show that the generator set, the middle desilting hole and the front area of emptying tunnel platform form scouring funnels after 50 years of operation, the sediments in front of the reservoir spillway are mainly flat silting and do not form flushing funnels. This method can reflect the influence of multiple constraint boundaries in front of the dam.

Identification of Scouring Zones in Ungauged River by Simulation: The Case of Galal Badrah River, Iraq

Galal Badrah River is one of Iraqi-Iranian border crossing rivers. This river is usually seasonally flooded during any time started from January to May. Its maximum discharge is 2200 m3/s which was recorded during 1985. During floods, banks of this river at many locations need protection against scour problem during floods. A small dam was constructed on this river in 2010 for the purposes of flood control and storage of water. The weir of the dam has a design discharge of 1250 m3/s. Sediments started to accumulate in the reservoir of the dam that reduce its design capacity to 10% during 2017. The flow of Galal Badrah River was simulated by using HEC-RAS 5.0.3 models. were used to simulate by using. Two hydrographs were used at upstream side of the river, one with a maximum discharge of 1250 m3/s and the other is of 2200 m3/s. A normal flow depth is used as a downstream boundary condition. Results of the simulation showed that the velocities to be higher than allowable velocity of scouring. The protection of Galal Badrah river by stack boulders is suggested to be used to avoid the scour at the river bank. The protection will increase Manning’s roughness coefficient from 0.028 to 0.10. The percentage of reduction in velocities after the river protection for the discharges of 1250 and 2200 m3/s were found to be 65.23% and 60.55%, respectively. The reduction in velocity caused increase in the river water levels. As a result, a flood embankment is required to be constructed on the right bank of the river with a height ranges from 2.5 to 5.6 m depending on the water depth at river cross section.

Improving the Accuracy of Hydrodynamic Simulations in Data Scarce Environments Using Bayesian Model Averaging: A Case Study of the Inner Niger Delta, Mali, West Africa

In this paper, the study area was the Inner Niger Delta (IND) in Mali, West Africa. The IND is threatened by climate change, increasing irrigation, and dam operations. 2D hydrodynamic modelling was used to simulate water levels, discharge, and inundation extent in the IND. Three different digital elevation models (DEM) (SRTM, MERIT, and a DEM derived from satellite images were used as a source of elevation data. Six different models were created, with different sources of elevation data and different downstream boundary conditions. Given that the performance of the models varies according to the location in the IND, the variable under consideration and the performance criteria, Bayesian Model Averaging (BMA) was used to assess the relative performance of each of the six models. The BMA weights, along with deterministic performance measures, such as the Nash Sutcliffe coefficient (NS) and the Pearson’s correlation coefficient (r), provide quantitative evidence as to which model is the best when simulating a particular hydraulic variable at a particular location. After the models were combined with BMA, both discharge and water levels could be simulated with reasonable precision (NS > 0.8). The results of this work can contribute to the more efficient management of water resources in the IND.

On the origin and structure of a stationary circular hydraulic jump

To elucidate the role played by surface tension on the formation and on the structure of a circular hydraulic jump, the results from three different approaches are compared: the shallow-water (SW) equations without considering surface tension effects, the depth-averaged model (DAM) of the SW equations for a flow with a parabolic velocity profile, and the numerical solutions of the full Navier-Stokes (NS) equations, both considering the effect of surface tension and neglecting it. From the SW equations, the jump can be interpreted as a transition region between two solutions of the DAM, with the jump’s location virtually coinciding with a singularity of the DAM’s solution, associated with the inner edge of a recirculation region near the bottom. The jump’s radius and the flow structure upstream of the jump obtained from the NS simulations practically coincide with the results from the SW equations for any flow rate, liquid properties, and downstream boundary conditions, being practically independent of surface tension. However, the structure of the flow downstream of the jump predicted by the SW equations is quite different from the stationary flow resulting from the NS simulations, which strongly depends on surface tension and on the downstream boundary conditions (radius of the disk). One of the main findings of the present work is that no stationary and axisymmetric circular hydraulic jump is found from the NS simulations above a critical value of the surface tension, which depends on the flow conditions, fluid properties, and downstream conditions.

Flow and detailed 3D morphodynamic data from laboratory experiments of fluvial dike breaching

This paper presents a dataset obtained from fifty four laboratory experiments of the breaching of fluvial dikes due to flow overtopping. Data were collected on two complementary experimental setups, each consisting of a main channel representing the river, an erodible lateral dike and a floodplain. The dataset covers seven test series, involving varying hydraulic boundary conditions (e.g. inflow discharge, downstream boundary conditions), main channel dimensions, as well as bottom and dike material. The following experimental data were produced: time series of water levels in the main channel, time series of flow discharges in the main channel and through the breach, as well as high resolution 3D reconstructions of the breach geometry during its expansion. The latter measurements were performed using a novel non-intrusive laser profilometry technique developed for this research. Reuse of the collected data will support efforts to improve our understanding of the physical processes underpinning fluvial dike breaching. It will also enable benchmarking the accuracy of conceptual or detailed numerical models for the prediction of dike breaching, which is central to flood risk management.

Morphodynamic evolution in a meandering reach of the Middle Yangtze River under upstream and downstream controls

Morphodynamic evolution in an alluvial river is usually controlled by various boundary conditions. During the past nearly 50 years, remarkable morphodynamic evolution occurred in the Jianli reach of the Middle Yangtze River owing to the combined effects of an artificial cutoff, the upstream operation of the Three Gorges Project (TGP), and the downstream confluence of the Dongting Lake. To better understand the characteristics of morphodynamic changes in the whole study reach, variations in thalweg shifting and bankfull channel geometry were quantified using a reach-averaged approach, and the effects of upstream and downstream controls were investigated on channel geometry adjustments. Calculated results indicate that: (i) events of an artificial cutoff and high flows caused the average rate of reach-scale thalweg migration to be greater than 35 m/yr, but there was a 22% reduction in the mean migration rate after the TGP operation; (ii) channel geometry adjusted mostly in the aspect of bankfull depth under various river regulation engineering, with the reach-scale bankfull depth increasing by 0.95 m from 2002 to 2016; (iii) the reach-scale bankfull dimensions are closely associated with these accumulated effects of both the altered flow-sediment regime because of upstream dam construction, and the local base-level variation owing to the downstream confluence of the Dongting Lake. Furthermore, these bankfull variables were expressed by power functions of two key parameters, covering the previous five-year average fluvial erosion intensity during flood seasons at Jianli (upstream control), and the corresponding water level difference between Jianli and Lianhuatang (downstream control). The proposed relations were calibrated by the observed data in 2002–2014, and were further verified by measurements in 2015–2016. The proposed methodology can also be applicable to estimate channel geometry adjustments of other similar alluvial rivers controlled by both upstream and downstream boundary conditions.

Kink solutions of the generalized, super-diffusive Burgers equation with memory

Analytical and numerical solutions of the shockwave type to a one–dimensional, generalized Burgers equation with a nonlinear constitutive law that accounts for stress relaxation via a material derivative are reported as functions of the parameters that appear in the equation and the boundary conditions. It is shown that the existence of kink solutions depends on the nonlinear convection and diffusion terms, the viscosity, the relaxation time, and the upstream and downstream boundary conditions. It is also shown that the slope of the kink’s profile decreases as the viscosity coefficient, the upstream–to–downstream velocity ratio and the relaxation time are increased, and the coefficient of the nonlinear convection term is decreased. The slope of the kink’s profile is not an odd function of the coordinate in a reference system moving at the kink’s speed, but it is nearly independent of the relaxation times for small values of this parameter. The kink’s width is found to decrease and increase as the exponent of the nonlinear convection term is decreased and increased from unity, respectively. The kink’s downstream and upstream widths increase and decrease, respectively, as the exponent of the diffusion term is increased, for exponents of the nonlinear convection term greater than unity. It is also shown that the differences between the shock wave profiles corresponding to a material frame–indifferent constitutive equation and those corresponding to Maxwell’s stress relaxation model are at most six percent, but depend strongly on the relaxation time and the exponents of the nonlinear convection and diffusion terms. The local dissipation rate is also determined as a function of the coefficients and powers of the nonlinearities and the relaxation time.

Population dynamics in river networks: analysis of steady states

We study the population dynamics of an aquatic species in a river network. The habitat is viewed as a binary tree-like metric graph with the population density satisfying a reaction-diffusion-advection equation on each edge, along with the appropriate junction and boundary conditions. In the case of a linear reaction term and hostile downstream boundary condition, the question of persistence in such models was studied by Sarhad, Carlson and Anderson. We focus on the case of a nonlinear (logistic) reaction term and use an outflow downstream boundary condition. We obtain necessary and sufficient conditions for the existence and uniqueness of a positive steady state solution for a simple Y-shaped river network (with a single junction). We show that the existence of a positive steady state is equivalent to the persistence condition for the linearized model. The method can be generalized to a binary tree-like river network with an arbitrary number of segments.

Flood routing methods

The hierarchy of one-dimensional equations and numerical methods describing the motion of floods and disturbances in streams is studied, critically reviewed, and a number of results obtained. Initially the long wave equations are considered. When presented in terms of discharge and cross-sectional area they enable the development of simple fully-nonlinear advection-diffusion models whose only approximation is that disturbances be very long, easily satisfied in most flood routing problems. Then, making the approximation that changes in surface slope are relatively small such that diffusion terms in the equations are small, various advection-diffusion and Muskingum models are derived. Several well-known Muskingum formulations are tested; one is found to be in error. The three families of governing equations, the long wave equations, and the advection-diffusion and the Muskingum approximations, are linearised and analytical solutions obtained. A dimensionless diffusion-frequency number measures the accuracies of the approximate methods. Criteria for practical use are given, which reveal when they have difficulties, for streams of small slope, for fast-rising floods, and/or when shorter period waves are present in an inflow hydrograph. They can probably be used in most flood routing problems with an idealised smooth inflow. However the fact that they cannot be used for all problems requires a general alternative flood routing method, for which it is recommended to use the long wave equations themselves written in terms of discharge and cross-sectional area, when a surprisingly simple physical stream model can be used. An explicit finite difference numerical method is presented that can be used with different inflow specifications and downstream boundary conditions, and is recommended for general use.

Formulation of Flood Inundation Map in Jamalpur District by Mathematical Modeling using HEC Packages

Bangladesh lies in the convergence zone of three large rivers of the world-Ganges, Brahmaputra, Meghna, which is called the GBM basin. The Ganges, Brahmaputra and Meghna (GBM) river basins occupy about 1.75 x 106 km2 of the Himalayan region. More than half a billion people in Nepal, India, Bhutan and Bangladesh are directly or indirectly dependent on the water resources of the GBM rivers. Being in this zone, Bangladesh faces heavy rainfall in the monsoon season of June to October, thus a huge amount of water drains out each year through the country. This drain out, along with various other reasons, causes frequent flooding all over Bangladesh. Thus, it is necessary to develop tools for the hydrological study of these three river basins or prediction tools to understand the consequence of different rainfall patterns. The reason of flood in the northern and mid-northern part of Bangladesh is overflowing of Brahmaputra (Jamuna) river. In this thesis work, different hydrologic and hydrodynamic models have been used to go through a number of steps and ultimately, a flood inundation map of Jamalpur district, which lies in the bank of Jamuna river, has been generated. The hydrologic model, HEC-HMS (Hydrologic Engineering Center-Hydrologic Modeling System) has been used to delineate the whole Brahmaputra watershed which lies mostly in the Indian north-eastern region, on the foothills of the Himalayas. Gridded rainfall gages from NASA (National Aeronautics and Space Administration) were used for precipitation input. The model was calibrated and validated for 2 different years at Bahadurabad point at Jamalpur. The purpose of calibration and validation was to set up a certain set of model parameters for different rainfall patterns. HECRAS (Hydrologic Engineering Center-River Analysis System) mathematical model was used to point out the water level for the resultant discharge. With the help of Arc-GIS (Geographical Information System) and HEC-GeoRAS (Hydrologic Engineering Center-Geographic River Analysis System), the flood inundation map of Jamalpur was generated for some of the highest water levels. Expectedly, the highest amount of inundation was observed in the months of July, August and September, the months of high monsoon rainfall. Some of the shortcomings of the thesis work were not counting on the land use pattern of the Brahmaputra basin for discharge, using arithmetic mean for sub basin rainfall gage weights, using observed water level in the downstream boundary condition for HEC-RAS etc. The flood inundation mapping can be used for future flood hazard management for predicted rainfall and help mitigate the damage and further losses. The hydrologic modeling can be used for further calibration for future precipitation prediction, also can be used for categorizing hydrologic characteristics for Brahmaputra basin.

Appropriate unit limits for integrated coastal and river basin management: An application to the Itajaí River basin, SC, Brazil

The Brazilian coastal zone is defined regarding administrative units – the municipalities – without regard to the dynamics of physical systems. This paper uses the definition of an estuary given by Fairbridge (1980) to include a physical criterion in the integrated coastal and water resources management – the tidal influence. The case study was the Itajaí river estuary were the HEC-RAS model was used to solve the Saint-Venant equations and define the tidal river zone. The downstream boundary condition was the astronomical tidal oscillation calculated by the Brazilian Navy. In the upstream boundary the two scenarios of river inflow were modeled: the low, the mean monthly low and mean flow for two branches of Itajaí river. Each scenario estimates the extent of tidal influence (or the length of the estuary). A zone of integrated coastal and water resources management was defined based on the result of the minimum flow scenario. A new territorial boundary structure for the Brazilian integrated management was proposed comparing the result of minimum flow scenario with the municipalities’ areas within the estuarine region: the Coastal Zone (CZ) and the Zone of Coastal Influence (ZCI). The CZ continues to be formally the Brazilian Coastal Zone. However, the ZCI is a new proposal to be the basis for integrated management, consisting of municipalities included within the estuarine limits defined by modeling minus the coastal municipalities. The ZCI should be a buffer zone where the policies of water resources and coastal zone interact jointly. The modeling obtains the estuary limit up to 56.92 km upstream in the Itajaí-Açu branch and 31.84 km in the Itajaí-Mirim branch. The modeling shows to be partially useful for defining a zone of coastal influence, especially in a low tide area. An arbitrary criterion, such as a 50 km line from the coast, could be joined to the estuary definition to better define a zone of coastal influence in areas of extremely high or low tide.

Studying Inertia Effects in Open Channel Flow Using Saint-Venant Equations

One-dimensional (1D) Saint-Venant equations, which originated from the Navier–Stokes equations, are usually applied to express the transient stream flow. The governing equation is based on the mass continuity and momentum equivalence. Its momentum equation, partially comprising the inertia, pressure, gravity, and friction-induced momentum loss terms, can be expressed as kinematic wave (KIW), diffusion wave (DIW), and fully dynamic wave (DYW) flow. In this study, the method of characteristics (MOCs) is used for solving the diagonalized Saint-Venant equations. A computer model, CAMP1DF, including KIW, DIW, and DYW approximations, is developed. Benchmark problems from MacDonald et al. (1997) are examined to study the accuracy of the CAMP1DF model. The simulations revealed that CAMP1DF can simulate almost identical results that are valid for various fluvial conditions. The proposed scheme that not only allows a large time step size but also solves half of the simultaneous algebraic equations. Simulations of accuracy and efficiency are both improved. Based on the physical relevance, the simulations clearly showed that the DYW approximation has the best performance, whereas the KIW approximation results in the largest errors. Moreover, the field non-prismatic case of the Zhuoshui River in central Taiwan is studied. The simulations indicate that the DYW approach does not ensure achievement of a better simulation result than the other two approximations. The investigated cross-sectional geometries play an important role in stream routing. Because of the consideration of the acceleration terms, the simulated hydrograph of a DYW reveals more physical characteristics, particularly regarding the raising and recession of limbs. Note that the KIW does not require assignment of a downstream boundary condition, making it more convenient for field application.

Appropriate Boundary Condition for Dupuit‐Boussinesq Theory on the Steady Groundwater Flow in an Unconfined Sloping Aquifer With Uniform Recharge

AbstractThe application of Dupuit‐Boussinesq theory on the two‐dimensional steady groundwater flow in an unconfined sloping aquifer with uniform recharge is theoretically investigated. The examination of conditions at the downstream and upstream is performed. The method of phase plane is used to geometrically interpret the characteristics of the nonlinear theory by various initial conditions. For phase portrait analysis, three configurations for aquifers are considered. In each type of aquifer three conditions of recharges as well as downstream groundwater tables are also considered for comprehensive analysis. Based on the phase portrait analysis, one explicit formula in terms of known parameters and downstream boundary condition is derived to easily and straightforwardly determine an appropriate upstream boundary condition. The derived explicit formula can facilitate correct modeling using Boussinesq theory.

Overflow Discharges and Flooding Areas from Flood Hydrographs Routing in Arda River, Greece

Flooding is a natural disaster that damages infrastructure, properties, and may even cause loss of life. Major floods occur in the Arda river basin, which is shared between Greece and Bulgaria in Southeastern Europe. A flood warning system can sufficiently minimize adverse effects by helping to create a more successful and well-organized response plan. This paper presents an extensive numerical simulation of flood hydrograph routing between levees of the downstream section of the Arda river for floods with return periods from 2 to 10,000 years, using the one-dimensional software HEC-RAS. The main objective is to calculate the inundation areas, travel times of flood waves, water depths, water levels, flow velocities, and overflow volumes by simulating the hydraulic behavior of the Arda river outside its mountain watershed, where it flows through agricultural plane land with very mild slope. The great importance of the water level at the confluence of the Arda and Evros rivers (downstream boundary condition) has been pointed out for the regions near the confluence because the flow is the subcritical type. A significant finding of this work is the determination of the upper limit of the peak discharge hydrograph entering from the Arda to the Evros river to prevent the flooding of the Evros river. This finding is very important for the management of the flood flows of the Evros river, which is a major river with a complicated river system.

Exact solution of the Linear Parabolic Approximation for flow-depth based diffusive flow routing

The Linearized Parabolic Approximation of the Saint Venant Equations is often used for flood routing, but the corresponding analytic solutions usually neglect the downstream boundary conditions. This is an issue because the presence of hydraulic structures at the end of a river reach, or natural morphologic conditions, may influence the wave propagation. In order to take into account realistic boundary conditions, namely a stage-hydrograph upstream and a stage-discharge relationship downstream, a new set of exact solutions of the Linearized Parabolic Approximation of the Saint Venant Equations with uniformly distributed lateral inflows is presented. This exact solution is demonstrated by using it as a building block in a simplified flood routing model, whose numerical results are compared with those supplied by laboratory experiments from literature. Finally, the new solutions are used to analyze the range of validity of semi-infinite channel models. The comparison shows that semi-infinite channel models are accurate when convective effects are prevailing on diffusive effects, and the downstream boundary condition corresponds to uniform flow conditions. In addition, the results show that semi-infinite channel models based on the knowledge of the upstream stage-hydrograph can predict flow depths better than those making use of a flow hydrograph, while being practically equivalent in predicting flow rates.

Numerical and Experimental Studies in Prediction of Bed Levels of Aggrading Channels

A semi-coupled 1D numerical model is presented to compute transient bed and water levels of aggrading channels due to the overloading of sediments. The numerical model solves mass and momentum equations (i.e. de Saint–Venant equations) for water and continuity equations for sediments simultaneously, using explicit finite difference scheme while considering upstream and downstream boundary conditions in the channel. Series of experimental studies are reported for measurements of bed and water levels in an aggrading channel due to the overloading of uniform sediments, in a flume installed at the Advanced Hydraulics Laboratory of SVNIT. The performance of bed level variation models, with different sediment transport functions, has been validated using the laboratory measurements. The performance of the numerical model is dependent on sediment transport functions. In addition, the performance of the proposed numerical model has been verified with existing numerical models on prediction of bed level variations. The proposed numerical model with recommended sediment transport function has been found to perform better than the existing numerical models on bed level variations of uniform sediment beds.

Prediction of bed level variations in nonuniform sediment bed channel

In the present study, a numerical model, based on one-dimensional de Saint-Venant equations along with sediment continuity equation, is developed for prediction of bed levels in non-cohesive sediments in aggrading alluvial channels. One-dimensional, unsteady flow equations and sediment continuity equations are solved using ‘shock-capturing’, second order accurate, explicit MacCormack finite difference scheme while considering upstream and downstream boundary conditions in the channel. Series of experimental investigations have been undertaken for measurements of bed and water levels in an aggrading channel due to overloading of nonuniform sediments, extracted from the bed of Tapi River at Surat City, in a flume installed in Advanced Hydraulics Laboratory of SVNIT, Surat, India. A satisfactory coupling between the water flow and sediment flow has been achieved. The sediment continuity equation is used for the each size class to compute the volume of each size class after each time step at any computational node in the computational grid. The fractional bed and suspended load transport capacities for different size fractions have been computed using fractional transport laws for nonuniform sediments. The active bed layer concept has been implemented in finite difference scheme to consider the interaction and exchange of sediment and water flow near the mixing layer. The performance of developed numerical model has been satisfactorily verified with independent experimental data of nonuniform sediment bed. Also, consideration of sediment nonuniformity in computation of bed level variation has been demonstrated by comparing the results based on sediment transport functions of uniform and nonuniform sediments.

Lagrangian generic second order traffic flow models for node

Abstract This study sheds light on higher order macroscopic traffic flow modeling on road networks, thanks to the generic second order models (GSOM family) which embeds a myriad of traffic models. It has been demonstrated that such higher order models are easily solved in Lagrangian coordinates which are compatible with both microscopic and macroscopic descriptions. The generalized GSOM model is reformulated in the Lagrangian coordinate system to develop a more efficient numerical method. The difficulty in applying this approach on networks basically resides in dealing with node dynamics. Traffic flow characteristics at node are different from that on homogeneous links. Different geometry features can lead to different critical research issues. For instance, discontinuity in traffic stream can be an important issue for traffic signal operations, while capacity drop may be crucial for lane-merges. The current paper aims to establish and analyze a new adapted node model for macroscopic traffic flow models by applying upstream and downstream boundary conditions on the Lagrangian coordinates in order to perform simulations on networks of roads, and accompanying numerical method. The internal node dynamics between upstream and downstream links are taken into account of the node model. Therefore, a numerical example is provided to underscore the efficiency of this approach. Simulations show that the discretized node model yields accurate results. Additional kinematic waves and contact discontinuities are induced by the variation of the driver attribute.

Discharge and location dependency of calibrated main channel roughness: Case study on the River Waal

To accurately predict water levels, river models require an appropriate description of the hydraulic roughness. The bed roughness increases as river dunes grow with increasing discharge and the roughness depends on differences in channel width, bed level and bed sediment. Therefore, we hypothesize that the calibrated main channel roughness coefficient is most sensitive to the discharge and location in longitudinal direction of the river. The roughness is determined by calibrating the Manning coefficient of the main channel in a 1D hydrodynamic model. The River Waal in the Netherlands is used as a case study. Results show that the calibrated roughness is mainly sensitive to discharge. Especially the transition from bankfull to flood stage and effects of floodplain compartmentation are important features to consider in the calibration as these produce more accurate water level predictions. Moreover, the downstream boundary condition also has a large effect on the calibrated roughness values near the boundary.