Manning Friction Coefficients Research Articles

Integration of physically-based numerical tools and socio-hydrological variables in urban flood modeling

Floods are considered the most destructive natural catastrophes on the planet; therefore, studying their dynamics in the context of each region is a fundamental pillar of society. A very popular tool for studying the degree of threat is physics-based modeling using 2D models. It is imperative to include physical, hydrological, and anthropogenic variables in flood modeling approaches. The reviewed literature did not develop a methodology or strategy to facilitate this process. Based on this reason, it was considered for Riohacha, a coastal city in northern Colombia. A survey was conducted to determine social, economic, and flood depth variables during extreme events. Twenty socio-hydrological variables were obtained from the survey analysis using Kruskal–Wallis and multiple correspondence analysis (MCA) tests. Flood depth was the response variable used to select the socio-hydrological variables, among which the following stood out: age of the house, internal slope, toilet overflow, proximity to a wetland, paved road, raft area, and slope of the soil in front of the house. An iterative process supported by a Support Vector Machine (SVM) dummy was used to determine the appropriate combination of parameters and optimize the calibration process of the TELEMAC-2D hydrodynamic model. The curve number (CN) and Manning friction coefficient were used as calibration parameters. The optimization process was performed by entering the dummy SVM into the socio-hydrological variables CN and Manning's n to test up to 20,000 possible combinations of the parameters and evaluate the mean absolute error (MAE), mean error (ME), absolute relative error (RAE), root mean square error (RMSE), and inertia root mean squared error (IRMSE). The best combination of parameters to simulate an extreme flood event and determine the metrics with the observed and simulated flood depths was entered into TELEMAC-2D. This paper presents a methodological proposal for optimizing the calibration process of physics-based flood models (traditional method), considering socio-hydrological variables, to articulate it as a new step in the modeling protocol. In the traditional simulation, an RMSE of 0.48 m, MAE of 0.37 m, and IRMSE of 1.37 m are obtained, which decrease to 0.33 m, 0.27 m, and 0.92 m, respectively, when the socio-hydrological variables are included. Contrary to the previous metrics, the ME improves slightly from 0.15 m with the traditional method to 0.17 m when the socio-hydrological variables are included. These results can be improved using a digital terrain model (DTM) that more realistically represents the complexity of the urban fabric. With only 7 iterative processes, the model calibration was optimized using only seven iterative processes. Therefore, the proposed methodology was established as a tool for optimizing the flood modeling processes.

Bathymetry and friction estimation from transient velocity data for one-dimensional shallow water flows in open channels with varying width

The shallow water equations (SWE) model a variety of geophysical flows. Flows in channels with rectangular cross sections may be modeled with a simplified one-dimensional SWE with varying width. Among other model parameters, information about the bathymetry and friction coefficient is needed for the correct and precise prediction of the flow. Although synthetic values of the model parameters may suffice for testing numerical schemes, approximations of the bathymetry and other parameters may be required for specific applications. Estimations may be obtained by experimental methods, but some of those techniques may be expensive, time consuming, and not always available. In this work, we propose to solve the inverse problem to estimate the bathymetry and the Manning's friction coefficient from transient velocity data. This is done with the aid of a cost functional, which includes the SWE through Lagrange multipliers. We prove that the velocity data determine uniquely the derivative of the bathymetry in a linearized shallow water system. That is, the inverse problem is identifiable. The solution is obtained by solving the constrained optimization problem by a continuous descent method. The direct and the adjoint problems are both solved numerically using a second-order accurate Roe-type upwind scheme. Numerical tests are included to show the merits of the algorithm.

Roles of the stolon and erect grass species in surface–subsurface flow generation and red soil loss

Grass planting is an important and typical measure for soil and water conservation, while the roles of stolon and erect grass species in affecting surface–subsurface flow and soil erosion processes are little understood. Experimental plots (2 m × 0.5 m × 0.5 m) using red soil with two rainfall intensities (60 and 120 mm h−1) and grass coverage (30 % and 70 %) were conducted in laboratory rainfall simulation experiments. Two common and endemic stolon (Eremochloa ophiuroides) and erect (Lolium perenne) grass species were selected due to their fast growth, power adaptability, and wide application in reducing runoff and soil loss; and the bare soil plot was set up as the control. The results showed that bare plot had the highest mean surface flow coefficient (73.5 %), and then were L. perenne (57.1 %) and E. ophiuroides (44.9 %). The mean subsurface flow coefficients were found in order of E. ophiuroides (25.7 %), L. perenne (13.0 %) and bare plot (7.2 %). The role of stolon grass rather than erect grass in reducing surface flow but improving subsurface flow led to lower surface flow hydraulic characteristics such as flow velocity, Reynolds number, Darcy–Weisbach coefficient and Manning friction coefficient, and hydrodynamic characteristics like flow shear stress and stream power. Furthermore, the stolon grass generated the lowest soil loss rate (0.8 g m−2 min−1), while the values on erect grass and bare plot were 2.5 and 10.7 g m−2 min−1, respectively. The indicator of eroded sediment median size also proved the higher efficiency of stolon grass in soil loss control, with values of 31.8, 58.6 and 69.6 μm on stolon grass, erect grass and bare plots, respectively. The lower soil loss on stolon grass cover plot was attributed to the lower surface flow and hydraulic–hydrodynamic characteristics. The stolon grass was more sensitive to the coverage and rainfall intensity, which was explained by the higher flow and sediment trapping capability (2.2 ∼ 4.4 times) under lower coverage and rainfall intensity than erect grass, even under high rainfall intensity (1.1 ∼ 3.2 times). The stolon grass played more beneficial roles in soil and water conservation than erect grass, which was closely related to above-ground and under-ground parts of grass. This study can provide a better understanding of the roles of stolon and erect grass species for soil and water conservation and management practices.

Coastal flooding and mean sea-level rise allowances in atoll island

Atoll islands are among the places most vulnerable to climate change due to their low elevation above mean sea level. Even today, some of these islands suffer from severe flooding generated by wind-waves, that will be exacerbated with mean sea-level rise. Wave-induced flooding is a complex physical process that requires computationally-expensive numerical models to be reliably estimated, thus limiting its application to single island case studies. Here we present a new model-based parameterisation for wave setup and a set of numerical simulations for the wave-induced flooding in coral reef islands as a function of their morphology, the Manning friction coefficient, wave characteristics and projected mean sea level that can be used for rapid, broad scale (e.g. entire atoll island nations) flood risk assessments. We apply this new approach to the Maldives to compute the increase in wave hazard due to mean sea-level rise, as well as the change in island elevation or coastal protection required to keep wave-induced flooding constant. While future flooding in the Maldives is projected to increase drastically due to sea-level rise, we show that similar impacts in nearby islands can occur decades apart depending on the exposure to waves and the topobathymetry of each island. Such assessment can be useful to determine on which islands adaptation is most urgently needed.

Hydraulic Reconstruction of the 1818 Giétro Glacial Lake Outburst Flood

AbstractIn the spring of 1818, ice avalanches from the Giétro Glacier created an ice dam, which in turn formed a glacial lake in the Drance Valley (Canton of Valais, Switzerland). Today, its maximum volume is estimated to have been 25×106 m3. Cantonal authorities commissioned an engineer named Ignaz Venetz to mitigate the risk of the ice dam's failure. He supervised the construction of a tunnel through which a large volume of water was drained as the lake rose (9×106 m3 according to his estimates and 11×106 m3 according to our model). After 2.5 days of slow drainage, the ice dam failed on 16 June 1818 and caused major flooding in the Drance Valley up to 40 km downstream, resulting in about 40 deaths. Venetz's lake monitoring notes, numerous testimonies gathered in the disaster's aftermath, and our field survey have made it possible to collect a wealth of information on this event, which is one of the world's major documented glacial lake outburst floods. Reconstructing major outburst floods remains challenging because not only do they involve enormous volumes of water spreading over long distances but they are also associated with additional physical processes such as massive erosion; intense transport of ice, sediment, and debris; and damage to vegetation and buildings. This paper attempts to reconstruct the 1818 Giétro flood by focusing on its water component. We develop a simple model to estimate the initial hydrograph during the slow drainage and failure phases. The flood's features are deduced by solving the shallow‐water equations numerically. The computational framework involves six free parameters, of which five are constrained by physical considerations. Using iterative manual parameter adjustments, we matched the numerical simulations to the historical data. We found that the peak discharge was close to 14,500 m3/s, the flood's front velocity was about 6 m/s, and flow depth varied considerably along the River Drance's bed (from 30 m just downstream of the ice dam to 2 m on the alluvial fan, 24 km west of the dam). To achieve a good agreement between computations and historical data, we had to select a high value for the Manning friction coefficient n (with n as large as 0.08 s/m1/3). As the Drance Valley is narrow, high flow resistance caused the flood's leading edge to behave like a plug, moving at a fairly constant velocity, with little dependence on what happened behind it. This result may explain why a simple flood routing model is able to reproduce the flood's features, because in an Alpine valley, a lateral spreading of the water volume is limited.

Urban flood modelling combining cellular automata framework with semi-implicit finite difference numerical formulation

Urban flooding is increasingly pervasive, with dreadful impacts on people and development assets. Whilst the frequency of occurrence of this hazard, mainly from pluvial events, is of fundamental importance in climate change and earth sciences research, the severity of its impacts motivates major debates within the context of flood risk management and sustainable urban development. The present study focuses on the development of a novel flood model, as a contribution to meeting the challenges of flood risk assessment within data poor urban areas such as in Nigeria. The new model combines the full functionality of cellular automata (CA) framework with a semi-implicit finite difference numerical scheme (SIFDS), whilst the resulting algorithms were programmed within MATLABTM programming platform. In this study, computation complexity and distributed topographic data requirement, both which are associated with flood modelling, and which tend to present a major limitation to flood modelling in the developing countries (DCs) are being addressed. A highly urbanized area within the Lagos metropolis of Nigeria was chosen as a case study to validate the model and to simulate the July 10th, 2011 flooding event. A 2-m horizontal resolution LiDAR DEM, published Manning's friction coefficients and rainfall intensity, were used as data inputs into the new flood model. Simulated results compared well with actual flooding inundations, reported by urban residents, and detailed in some literature and by the media. The Pearson correlation coefficient (r) between predicted flood depth and estimated values is 0.968. It is expected that the challenges of urban flooding in Lagos particularly and in the DCs generally will be better addressed if robust, but low-cost flood models are developed and utilized in the assessment of flood damage.

Effects of flow hydraulics on total nitrogen loss on steep slopes under simulated rainfall conditions

Abstract Flow hydraulics play important roles in soil erosion and loss of soil nutrients. A better understanding of the relationship between flow hydraulics and nutrient losses will improve chemical transport modeling. The laboratory experiment was conducted to determine flow hydraulics' effects on total nitrogen (TN) loss. The impacts of rainfall intensities (0.6, 1.1, 1.61, 2.12, and 2.54 mm·min−1) and slope gradients (10°, 15°, and 20°) on TN loss were also studied. Selected soils were derived from purple sandy shales, which are the main parent materials in Wangjiaqiao watershed, southern China. Results show that negative linear relationships (R2 = 0.71) were observed between the rate of Manning roughness coefficient to average flow depth and the unit area runoff-associated TN transport rate. There was a good linear relationship between the unit area sediment-associated TN transport rate and Reynolds numbers (R2 = 0.90), flow velocity (R2 = 0.87), and stream power (R2 = 0.73), while Froude numbers, Darcy–Weisbach and Manning friction coefficients were not good hydraulic indicators of the sediment-associated TN loss of purple soil. The equation including stream power and flow velocity may have a better correlation coefficient (R2 = 0.94).

Quantifying the importance of spatial resolution and other factors through global sensitivity analysis of a flood inundation model

AbstractWhere high‐resolution topographic data are available, modelers are faced with the decision of whether it is better to spend computational resource on resolving topography at finer resolutions or on running more simulations to account for various uncertain input factors (e.g., model parameters). In this paper we apply global sensitivity analysis to explore how influential the choice of spatial resolution is when compared to uncertainties in the Manning's friction coefficient parameters, the inflow hydrograph, and those stemming from the coarsening of topographic data used to produce Digital Elevation Models (DEMs). We apply the hydraulic model LISFLOOD‐FP to produce several temporally and spatially variable model outputs that represent different aspects of flood inundation processes, including flood extent, water depth, and time of inundation. We find that the most influential input factor for flood extent predictions changes during the flood event, starting with the inflow hydrograph during the rising limb before switching to the channel friction parameter during peak flood inundation, and finally to the floodplain friction parameter during the drying phase of the flood event. Spatial resolution and uncertainty introduced by resampling topographic data to coarser resolutions are much more important for water depth predictions, which are also sensitive to different input factors spatially and temporally. Our findings indicate that the sensitivity of LISFLOOD‐FP predictions is more complex than previously thought. Consequently, the input factors that modelers should prioritize will differ depending on the model output assessed, and the location and time of when and where this output is most relevant.

Hydraulic characteristics and sediment generation on slope erosion in the Three Gorges Reservoir Area, China

Abstract Hydrological processes play important roles in soil erosion processes of the hillslopes. This study was conducted to investigate the hydrological processes and the associated erosional responses on the purple soil slope. Based on a comprehensive survey of the Wangjiaqiao watershed in the Three Gorges Reservoir, four typical slope gradients (5°, 10°, 15°and 20°) were applied to five rainfall intensities (0.6, 1.1, 1.61, 2.12 and 2.54 mm·min-1). The results showed that both surface and subsurface runoff varied greatly depending on the rainfall intensity and slope gradient. Surface runoff volume was 48.1 to 280.1 times of that for subsurface runoff. The critical slope gradient was about 10°. The sediment yield rate increased with increases in both rainfall intensity and slope gradient, while the effect of rainfall intensity on the sediment yield rate was greater than slope gradient. There was a good linear relationship between sediment yield rate and Reynolds numbers, flow velocity and stream power, while Froude numbers, Darcy-Weisbach and Manning friction coefficients were not good hydraulic indicators of the sediment yield rate of purple soil erosion. Among the three good indicators (Re, v and w), stream power was the best predictor of sediment yield rate (R2 = 0.884). Finally, based on the power regression relationship between sediment yield rate, runoff rate, slope gradient and rainfall intensity, an erosion model was proposed to predict the purple soil erosion (R2 = 0.897). The results can help us to understand the relationship between flow hydraulics and sediment generation of slope erosion and offer useful data for the building of erosion model in purple soil.

Impacts of sediment load on Manning coefficient in supercritical shallow flow on steep slopes

AbstractThe Manning equation is one of the most widely used formulae for calculating the velocity of shallow overland flow in hydrological and erosion models. Precise estimation of the Manning's friction coefficient (n) is critical to determining overland flow and soil erosion processes. Few studies have been conducted to quantify the effects of sediment load on Manning's n on steep slopes. This study was conducted to investigate the potential effects of sediment load on Manning's n in a flume with a fixed bed, under wide ranges of hydraulics and sediment loads. Slope gradient varied from 8·7 to 34·2%, unit flow rate from 0·66 to 5·26 × 10−3 m2 s−1, and sediment load from 0 to 6·95 kg m−1 s−1. The Reynolds number ranged from 350 to 5899. Results showed that Manning's n varied in both sediment‐free and sediment‐laden flows ranging from 0·012 to 0·055. The apparent Manning's coefficients of sediment‐laden flow were much greater than those of sediment‐free flow. The mean Manning coefficient of sediment‐laden flow was 51·27% greater than the mean value of sediment‐free flow. For sediment‐laden flow, Manning's n could be estimated with a power function of unit flow discharge and sediment content. Further studies are needed to quantify the potential effects of sediment load on the Manning's n on erodible beds and in fields. Copyright © 2010 John Wiley & Sons, Ltd.

Assimilation of spatially distributed water levels into a shallow-water flood model. Part II: Use of a remote sensing image of Mosel River

With rapid flood extent mapping capabilities, Synthetic Aperture Radar (SAR) images of river inundation prove to be very relevant to operational flood management. In this context, a recently developed method provides distributed water levels from SAR images. Furthermore, in view of improving numerical flood prediction, a variational data assimilation method (4D-var) using such distributed water level has been developed in Part I of this study. This method combines an optimal sense remote sensing data (distributed water levels extracted from spatial images) and a 2D shallow water model. In the present article (Part II of the study), we also derive water levels with a ±40 cm average vertical uncertainty from a RADARSAT-1 image of a Mosel River flood event (1997, France). Assimilated in a 2D shallow water hydraulic model using the 4D-var developed method, these SAR derived spatially distributed water levels prove to be capable of enhancing model calibration. Indeed, the assimilation process can identify optimal Manning friction coefficients, at least in the river channel. Moreover, used as a guide for sensitivity analysis, remote sensing water levels allow also identifying some areas in the floodplain and the channel where Manning friction coefficients are homogeneous. This allows basing the spatial segmentation of roughness coefficient on floodplain hydraulic functioning.

Runoff hydraulic characteristics and sediment generation in sloped grassplots under simulated rainfall conditions

Evaluation of grass influence on soil erosion process can provide important information in soil and water conservation. The laboratory experiment was conducted to study runoff and sediment producing processes and runoff hydraulics in the grassplots with different covers (35%, 45%, 65% and 90%) and bare soil plot (control) at a slope of 15. The results showed that grass significantly reduced runoff and sediment. Compared with bare soil plot, the grassplots had a 14-25% less runoff and an 81-95% less sediment, and played a more important role in reducing sediment at the final stage of rainfall. There was a significantly negative logarithmic relationship between sediment yield rate (SDR) and cover (C): SDR = 1.077-2.911 ln(C) (R-2 = 0.999'). Sediment yield rate of grassplots decreased with rainfall duration, and decreased linearly as runoff rate increased. Overland flow velocities deceased with increase in grass cover, and the cover had greater effect on lower slope velocity than upper one. Froude numbers decreased with increase in cover, and flow regimes of all treatments were laminar and tranquil. Darcy-Weisbach and Manning friction coefficients of grassplots increased as ground cover increased. Therefore, increase in grass coverage can efficiently reduce soil loss and improve ecological environments. (c) 2006 Elsevier B.V. All rights reserved.

An integrated model for the Orbetello lagoon ecosystem

This paper describes the evolution in time and space of the submersed vegetation in the Orbetello lagoon. This model was developed for the local Lagoon Management Office to predict the development of both macroalgae and macrophytes and test effect of the harvesting decisions. Based on a previous model describing the interactions between nitrogen and the submersed vegetation [Giusti, E., Marsili-Libelli, S., 2005. Modelling the interactions between nutrients and the submersed vegetation in the Orbetello lagoon, Ecol. Model. 184, 141–161], this paper presents several further major improvements introducing the dynamics of phosphorus as a second nutrient, extending the generality of the model to all nutrient conditions and providing a better fit of the observed behaviours, a cellular automaton to describe the dynamics of wigeongrass ( Ruppia maritima) and a hydrodynamic model for the water movements. The three models are now synchronized and run in the same context with the Manning friction coefficients acting as a feedback link from the hydrodynamic model to the vegetation dynamics. Another important feature is the wind module, generating synthetic wind time-series required as an input to the hydrodynamic model to produce long-term simulations. The integrated model has been implemented as a stand-alone executable code which can be used as a decision support system. Three-year simulations show the expansion of the existing Ruppia prairies in accordance with the observations.

Integrated two-dimensional macrophytes-hydrodynamic modeling

Lake Saint-Francois is the first fluvial lake downstream of the Great Lakes. Aquatic macrophytes are abundant because of water level stabilization and increased nutrient loads. The influence of plants on flow modification is very important and must be considered in order to simulate hydrodynamic conditions. The spatial distribution of plant species is linked to their instream flow preferences. Several abiotic variables are of importance: light penetration, wave energy, current velocity, nutrients in substrate and physical characteristics of the substrate are controlling the species and their biomass. Field characterization of macrophytes was performed using echosounder transects in association with a submersible video camera. This technique allowed the calibration of each echofacies for species identification and their relative proportion, height and density. The main eleven assemblages appear to be strongly correlated with abiotic conditions. A basic interpretation key was set up in order to describe plant distribution over the entire lake. Species, relative proportion, density and plant height were interpolated between transects. This information is used to adjust the Manning's friction coefficient for each assemblage. Simulations of the flow fields with plants and in absence of plants show a contrasted pattern. During the summer (with plants), the flow is mainly concentrated in deep channels where velocities are clearly increased by approximately 20% compared to spring-fall simulation (without plants).

Currents and Sediment Transport in Mangrove Forests

A field study of the tidal currents, cohesive sediment dynamics and transport of organic carbon in a highly vegetated mangrove swamp was carried out at Middle Creek, Cairns, Australia. The interaction of tidal currents and the vegetation generated jets, eddies and zones of stagnant waters which were numerically modelled. A high value of the Manning friction coefficient ( n=0·1) was derived by the dense vegetation. About 80% of the suspended sediment brought in from coastal waters at spring flood tide was trapped in the mangroves, corresponding to about 10–12 kg of sediment m −1creek length/spring tide, resulting in a rise of the substrate by about 0·1 cm year −1. The selective trapping of clay was caused by flocculation of the finer particles in the mangroves. There was an indication of a slight inwelling of organic carbon. Creek water was readily differentiated from mangrove water by large differences in the molecular weight distribution of the dissolved organic carbon.

Longshore current on a barred beach: Field measurements and calculation

Measurements of the longshore current on a barred beach made during the 1990 Duck Experiment on Low‐Frequency and Incident‐Band Longshore and Across‐Shore Hydrodynamics (DELILAH) field data collection project conducted at Duck, North Carolina, revealed an unexpected and persistent broad peak in the current velocity in the trough between the nearshore bar and the shore. This paper introduces longshore current and associated wave measurements from DELILAH together with a numerical model capable of describing the field observations. An existing numerical model of the mean current is modified to include a general transport equation for the mean turbulent kinetic energy created by wave breaking, and Reynolds stress components needed to calculate the longshore current and mean water level are reexpressed to include the turbulent momentum transport. In comparison to predictions from the original model, the modified model produces much improved agreement with the measured current velocity on the barred profiles in the field measurements and with the velocity profile and mean water level generated on a uniformly sloping laboratory beach by monochromatic waves. Three forms of a bottom friction coefficient are examined, and the open‐channel‐flow Manning friction coefficient is selected because of best agreement and consistency. Values of the Manning friction coefficient required to calibrate the model agree with values normally assigned to the related bottom roughness in open‐channel flow.

Reliability of flood discharge estimates

The high accuracy of normal river discharge measurements is contrasted with the approximate methods used to estimate large floods. The most commonly used method, the slope–area method, is examined and it is argued that there is likely to be a strong upward bias in these flood estimates. Sources of error are subdivided into four main types: (i) error in the Manning friction coefficient, (ii) error in after-flood measurements of channel cross section, (iii) estimation of surface slope and energy grade line from high-water marks, and (iv) the effects of erosion and sediment transport. These various factors are seen to be influenced by channel curvature and meandering, floodplain flow and interaction with the main channel, and changes to channel geometry during a flood. From theoretical work on high sediment transport, it is argued that up to one third of the channel slope is required for moving the sediment, so that only two thirds of the slope is available for transporting the water. Key words: floods, river flow, channel friction, sediment transport, floodplains, meandering.