Flood Discharge Prediction using Two-Dimensional Inverse Modeling

A new approach to estimate flood discharges in complex river geometries is presented. Discharges are determined through the combination of nonintrusive measurements of surface velocities and water levels with a Navier–Stokes solver and an inverse optimization algorithm. The numerical model is based on a finite-element solution of the two-dimensional Reynolds-averaged Navier–Stokes equations with a k–ε turbulence model, allowing for computation of the free water surface on adaptive, unstructured grids. The inverse modeling technique uses the Levenberg–Marquardt minimizing algorithm. In order to rule out uncertainties from the numerical model and to strictly quantify the effect of measuring errors, measurements are generated synthetically through forward computations. The methodology is illustrated for the gaging station of the Saltina River at Brig, Switzerland, which involves a complex bed geometry and where laboratory measurements for transcritical flows were available. For perfect measurements the discharge can in principle be estimated to an accuracy of ≈2%, independently of the number of measurements. Measurement errors in the water level have a small influence on the estimated discharge, whereas errors in velocity lead to a major discharge error. This error can be minimized by increasing the number of measurement points and choosing appropriate measurement positions.     

Simulating Bed-Load Transport in a Complex Gravel-Bed River

An existing two-dimensional mobile-bed hydrodynamic model has been modified to simulate bed-load transport in a complex gravel-bed river. We investigated the sensitivity of predicted bed load to control parameters, and compared model predictions of flow depth, shear stress, and gravel transport with field measurements made from the river. The predictions are based on concurrent field data of flow discharge, water level, and sediment for model input. The model takes into account multiple-fraction transport rates, and continuously updates the river bed and surface grain-size distribution. The model predictions are in reasonable agreement with field measurements.     

Quenching Differential Thermal Analysis and Thermodynamic Calculation to Determine Partition Coefficients of Solute Elements in Simplified Ni-Base Superalloys

In this article, a profile-fitting methodology was developed to measure the partition coefficients of solute elements during the solidification of Ni-base alloys. Better agreement with the theoretically calculated values is expected if the accuracy of the composition and the homogeneity of the model alloys are enhanced. Regular differential thermal analysis (DTA) measurements were consistently higher than the theoretical transition temperatures, and the differences were smaller when compared to the predictions performed with the thermodynamical database developed by Du et al. The better agreement between the experimental results and the theoretical predictions made with the newly developed database suggests that improvements in the accuracy of the theoretical predictions can still be obtained and are necessary for accurate freckling prediction. Quenching modified DTA (MDTA) experiments were proven to be appropriate for directly measuring the average partition coefficients of the solute elements. Regarding the cooling rate of the first stage of the quenching experiments, it was assumed successfully that the cooling rate prior to the quenching step of 0.083 Ks⁻¹ was sufficiently slow to permit easy quenching, while being fast enough for the primary solidification reaction to depart from the equilibrium model and being closer to the Scheil model of segregation. The minimization of the error function defined from the Scheil equation was found to be an appropriate method for describing the segregation profiles of the quenched samples and permitted good estimations of the partition coefficients of the solute elements. The reliability of the methodology was found to be satisfactory given that the magnitudes calculated for the partition coefficients of the solutes in the multicomponent alloy 718 were found to be very close to the values reported in the literature.     

Total Load Transport Formula for Flow in Alluvial Channels

A user-friendly total bed-material load transport formula for flow in alluvial channels under equilibrium transport conditions has been developed based on dimensional analysis. The main advantages of this formula are its ease of computation, accuracy in prediction, and the wide range of application. The total sediment discharge gt is computed directly and is linearly related to the new total load transport parameter, TT. The latter involves variables that can be easily measured in field conditions, i.e., flow depth, mean flow velocity, energy slope, median sediment size and density, and water temperature. The factor of proportionality k in the formula has been checked for a wide range of hydraulic conditions and it remains a constant equal to 12.5. Comparisons between the computed and measured total sediment discharge indicate that the predictions are good.     

Sediment Diversion through Irrigation Outlets

To avoid sediment deposits in the downstream portion of irrigation channels, the outlets must extract a concentration equal to or higher than the one in the channel. In Pakistan, although channels have been designed in that way, the present management leads to a general deposition of sediments. A few concentration measurements and the use of a 3D model of one outlet suggest that the sediment discharge in the outlet is close to the one contained in the current tube entering the outlet. Finally, a simple model with one parameter is proposed to compute the sediment concentration in the outlet.     

Prediction of Sediment Load Concentration in Rivers using Artificial Neural Network Model

An artificial neural model is used to estimate the natural sediment discharge in rivers in terms of sediment concentration. This is achieved by training the network to extrapolate several natural streams data collected from reliable sources. The selection of water and sediment variables used in the model is based on the prior knowledge of the conventional analyses, based on the dynamic laws of flow and sediment. Choosing an appropriate neural network structure and providing field data to that network for training purpose are addressed by using a constructive back-propagation algorithm. The model parameters, as well as fluvial variables, are extensively investigated in order to get the most accurate results. In verification, the estimated sediment concentration values agree well with the measured ones. The model is evaluated by applying it to other groups of data from different rivers. In general, the new approach gives better results compared to several commonly used formulas of sediment discharge.     

Parameter Estimation for Muskingum Models

A methodology for parameter estimation for the Muskingum model of streamflow routing is developed. The methodology minimizes the outflow prediction errors subject to the satisfaction of the streamflow-routing equations for all time stages in the routing process. The routing equations incorporate the Muskingum channel storage models. An algorithm is developed for parameter estimation that iteratively solves the governing equations to identify the Muskingum model parameters.     

Estimation of Uncertainty in Long-Term Sewer Sediment Predictions Using a Response Database

Regulations require U.K. water companies to reduce the number of properties at risk of sewer flooding. One of the potential causes of sewer flooding is the presence of persistent sediment deposits in sewers, such deposits are a common problem in many combined sewers. Although the regulations are risk based, there is a gap in the current knowledge on how the risk assessment is affected by the uncertainty in sewer sediment transport prediction. This paper describes the development of a methodology for estimating uncertainty in sewer sediment deposit depth predictions using existing empirically calibrated sediment load equations and Monte Carlo simulations combined with a response database. This methodology has been used to estimate the range of uncertainty of in-pipe deposit build-up predictions for a U.K. combined sewer system that suffered persistent deposition problems.     

Probabilistic Failure Prediction for Deteriorating Pipelines: Nonparametric Approach

Component failures in water distribution systems are usually predicted by parametric models where the model parameters are determined by projecting the past failure rates of the component to the future. This paper shows that in such techniques, failures are implicitly assumed to be stationary random processes. However, due to the nonstationary nature of some influencing factors, this assumption may lead to inaccurate predictions. A new nonparametric technique is developed for failure prediction of classes of pipes considering this nonstationary process. The presented technique uses limited data that are typical to the databases of water distribution systems. In this method, maximum likelihood estimates of the probability of future failures are calculated and used, both to predict the number of failures occurring within a specified period of time in future, and to provide some lower and upper bounds (confidence intervals) for the estimations. This technique is applied to predict the failures of water pipes in western suburbs of Melbourne. Results of the predictions are compared with the empirical results from a failure record. Deviation of these predictions from empirical measures in terms of both rejection rates and mean-square errors of predictions are acceptable.     

Integrated Approach to Determining Postreclamation Coastlines

An integrated approach is presented for determining the harmonized optimal coastline from given options for large-scale coastal reclamation. The approach incorporates results from hydrodynamic, sediment transport, and water quality models and ecological impact considerations. These models predict reclamation impact on tidal flow, sediment deposition and erosion, and water quality under different scenarios. The impact on sensitive coastal ecosystems is considered indirectly in terms of the qualitative relationship to results from the sediment transport model. The analytical hierarchy process method is applied to determine the weights of various control factors and to integrate the model predictions. A sensitivity analysis is made to assess the effect on the final results of modeling errors and uncertainty in the weights assigned, and thus to enhance the reliability of decision making. Although the methodology given herein emphasizes reclamation in a bay with multifold functions, the procedure is potentially applicable to most coastal reclamation projects, except single-option schemes. An application to Deep Bay coastline is described in the companion paper.     

Fluid Mechanics of Triangular Sediment Oxygen Demand Chamber

Benthal respiration rates are often measured in situ by a sediment oxygen demand (SOD) chamber in which a continuous flow is generated above the sediment. The steady three-dimensional turbulent flow field inside a triangular SOD chamber (previously used in field investigations) is computed using the renormalization group (RNG) k–ε model on an unstructured tetrahedral mesh. The numerical predictions reveal a highly complicated flow characterized by (1) a jet flow near the level of the inlet, with strong downflow near the outlet end; (2) significant reverse bottom currents; and (3) strong secondary circulations in the triangular cross section. Good mixing is achieved, with mean near-bottom velocities about 10 times greater than that determined from the inflow discharge and cross-sectional area. The computed velocity field is well supported by laboratory velocity measurements using laser-Doppler anemometry (LDA). The implications on SOD chamber design are also discussed with reference to computed flow fields in representative dome-shaped and rectangular chambers used in field application. The present study explains the previous large discrepancies in SOD field measurement using chambers of different designs, and points to the importance of hydrodynamics of SOD chambers.     

Simulation of the St. Francis Dam-Break Flood

A two-dimensional (2D) simulation of flooding from the 1928 failure of St. Francis Dam in southern California is presented. The simulation algorithm solves shallow-water equations using a robust unstructured grid Godunov-type scheme designed for wetting and drying and achieves good results. Flood extent and flood travel time are predicted within 4 and 10% of observations, respectively. Representation of terrain by the mesh is identified as the dominant factor affecting accuracy, and an iterative process of mesh refinement and convergence checks is implemented to minimize errors. The most accurate predictions are achieved with a uniformly distributed Manning n = 0.02. A 50% increase in n increases travel time errors to 25% but has little effect on flood extent predictions. This highlights the challenge of a priori travel time prediction but robustness in flood extent prediction when topography is well resolved. Predictions show a combination of subcritical and supercritical flow regimes. The leading edge of the flood was supercritical in San Francisquito Canyon, but due to channel tortuosity, the wetting front reflected off canyon walls causing a transition to subcritical flow, considerably larger depths, and a standing wave in one particular reach that accounts for a 30% fluctuation in discharge. Elsewhere, oblique shocks locally increased flood depths. The 2D dam-break model is validated by its stability and accuracy, conservation properties, ability to calibrate with a physically realistic and simple resistance parametrization, and modest computational cost. Further, this study highlights the importance of a dynamic momentum balance for dam-break flood simulation.     

Sediment Concentration Distribution of Debris Flow

A theoretical model to simulate the sediment concentration distribution for debris flow with a high concentration is presented by means of the maximum entropy principle, which is a new approach. The result shows that a theoretical relationship is developed to simulate the sediment concentration distribution as a function of the entropy parameter, which can be determined from the equilibrium sediment concentration of debris flow. By comparison with two existing relations, the proposed equation is found to give significantly better agreement with experimental data obtained by Tsubaki et al. than others. To determine the entropy parameter, a semiempirical analysis on the equilibrium sediment concentration of debris flow is also developed. The analysis is achieved by modifying the equilibrium sediment concentration equation proposed earlier by the writers. The modified equation proposed in this study can be applicable to both the forefront concentration and the average global concentration of debris flow. Compared with other researchers’ studies, the modified equilibrium sediment concentration equation is found to be in excellent conformity with theirs when taking 0.04 as the empirical coefficient.     

Parameter Identifiability for Three Sediment Entrainment Equations

A process-based erosion model is used to study parameterization problems of sediment entrainment equations in overland flow areas. One of the equations for entrainment by flow is developed based on a theory of excess stream power, while the other two relate to excess hydraulic shear. The investigation is conducted in two steps. The first step examines parameter optimization for simulated data sets where the parameter values are known. In the second step, parameter optimization for the most robust equation is examined using experimental data from rainfall simulator plots. Results demonstrate that although the model is capable of estimating total sediment yields with relatively small errors in parameter estimates, the converse is true when the optimization is performed for sediment concentrations. Although sediment yields calculated from simulated sediment concentrations match well with observed data, the parameter estimates generally underestimate sediment concentrations on the rising limb of the sediment graphs, and they overestimate them on the falling limb. This difficulty might be related to structural problems in the model, and unique solutions for parameter estimates cannot be obtained.     

Probabilistic Model for the Assessment of Cyclically Induced Reconsolidation (Volumetric) Settlements

A maximum likelihood framework for the probabilistic assessment of cyclically induced reconsolidation settlements of saturated cohesionless soil sites is described. For this purpose, over 200 case history sites were carefully studied. After screening for data quality and completeness, the resulting database is composed of 49 high-quality, cyclically induced ground settlement case histories from seven different earthquakes. For these case history sites, settlement predictions by currently available methods of Tokimatsu and Seed (1984), Ishihara and Yoshimine (1992), Shamoto et al. (1998), and Wu and Seed (2004) are presented comparatively, along with the predictions of the proposed probabilistic model. As an integral part of the proposed model, the volumetric strain correlation presented in the companion paper is used. The accuracy of the mean predictions as well as their uncertainty is assessed by both linear regression and maximum likelihood methodologies. The analyses results revealed that (1) the predictions of Shamoto et al. and Tokimatsu and Seed are smaller than the actual settlements and need to be calibrated by a factor of 1.93 and 1.45, respectively; and (2) Ishihara and Yoshimine, and Wu and Seed predictions are higher than the actual settlements and need to be calibrated by a factor of 0.90 and 0.98, respectively. The Wu and Seed procedure produced the most unbiased estimates of mean settlements [i.e., their calibration coefficient (0.98) is the closest to unity], but the uncertainty (scatter) of their predictions remains high as revealed by the second to last smaller R2 value, or relatively higher standard deviation (σε) of the model error. In addition to superior model predictions, the main advantage of the proposed methodology is the probabilistic nature of the calibration scheme, which enables incorporation of the model uncertainty into mean settlement predictions. To illustrate the potential use of the proposed model, the probability of cyclically induced reconsolidation settlement of a site after a scenario earthquake to be less than a threshold settlement level is assessed.     

Performance of Bed-Load Transport Equations Relative to Geomorphic Significance: Predicting Effective Discharge and Its Transport Rate

Previous studies assessing the accuracy of bed-load transport equations have considered equation performance statistically based on paired observations of measured and predicted bed-load transport rates. However, transport measurements were typically taken during low flows, biasing the assessment of equation performance toward low discharges, and because equation performance can vary with discharge, it is unclear whether previous assessments of performance apply to higher, geomorphically significant flows (e.g., the bankfull or effective discharges). Nor is it clear whether these equations can predict the effective discharge, which depends on the accuracy of the bed-load transport equation across a range of flows. Prediction of the effective discharge is particularly important in stream restoration projects, as it is frequently used as an index value for scaling channel dimensions and for designing dynamically stable channels. In this study, we consider the geomorphic performance of five bed-load transport equations at 22 gravel-bed rivers in mountain basins of the western United States. Performance is assessed in terms of the accuracy with which the equations are able to predict the effective discharge and its bed-load transport rate. We find that the median error in predicting effective discharge is near zero for all equations, indicating that effective discharge predictions may not be particularly sensitive to one’s choice of bed-load transport equation. However, the standard deviation of the prediction error differs between equations (ranging from 10% to 60%), as does their ability to predict the transport rate at the effective discharge (median errors of less than 1 to almost 2.5 orders of magnitude). A framework is presented for standardizing the transport equations to explain observed differences in performance and to explore sensitivity of effective discharge predictions.     

System Identification through Model Composition and Stochastic Search

System identification methodologies are useful for identifying characteristics of structural systems using measurement data. However, incorrect systems might be identified when many combinations of system characteristics result in the same predicted responses at measured locations. The reliability of identification is affected by a number of factors that most previous work has overlooked. This paper presents a system identification methodology that explicitly treats factors that affect the success of identification. Rather than simply determining parametric values, this methodology also involves identification of model characteristics including boundary conditions. Due to inevitable modeling errors, models that provide absolute minimum differences between predictions and measurements are rarely correct models. In such situations, the challenge is to define a population of candidate models that result in such differences being below threshold values that are determined by the magnitude of modeling errors. The methodology is illustrated using a case study in civil engineering. This work contributes to providing engineers with general strategies to meet interpretation challenges associated with sensor data.     

A method to correct for scatter, spillover, and partial volume effects in region of interest analysis in PET

Scatter and spatial resolution effects degrade the accuracy of radioactivity concentration estimates obtained from positron emission tomography (PET) data. We present and evaluate a methodology for region quantification which accounts for these degradations. The method is based on analysis of sinogram data and does not require dynamic data sequences to be reconstructed. Moreover, estimates of region variance are also produced which may be used to define weights for model analyses that use weighted least squares minimization in order to obtain unbiased parameter estimates. We evaluate the method using both simulation and measured data and find that, with an appropriate model of scatter and spatial resolution effects, it is unbiased and capable of quantifying myocardial concentration with no more than a 5% error in accuracy for myocardium as thin as 10 mm.     

Bootstrapping for pharmacokinetic models: visualization of predictive and parameter uncertainty

PURPOSE: We explore use of "bootstrapping" methods to obtain a measure of reliability of predictions made in part from fits of individual drug level data with a pharmacokinetic (PK) model, and to help clarify parameter identifiability for such models. METHODS: Simulation studies use four sets (A-D) of drug concentration data obtained following a single oral dose. Each set is fit with a two compartment PK model, and the "bootstrap" is employed to examine the potential predictive variation in estimates of parameter sets. This yields an empirical distribution of plausible steady state (SS) drug concentration predictions that can be used to form a confidence interval for a prediction. RESULTS: A distinct, narrow confidence region in parameter space is identified for subjects A and B. The bootstrapped sets have a relatively large coefficient of variation (CV) (35-90% for A), yet the corresponding SS drug levels are tightly clustered (CVs only 2-9%). The results for C and D are dramatically different. The CVs for both the parameters and predicted drug levels are larger by a factor of 5 and more. The results reveal that the original data for C and D, but not A and B, can be represented by at least two different PK model manifestations, yet only one provides reliable predictions. CONCLUSIONS: The insights gained can facilitate making decisions about parameter identifiability. In particular, the results for C and D have important implications for the degree of implicit overparameterization that may exist in the PK model. In cases where the data support only a single model manifestation, the "bootstrap" method provides information needed to form a confidence interval for a prediction.     

The influence of temperature gradient zone melting on microsegregation

Adding an algorithm for considering temperature gradient zone melting (TGZM) to an existing numerical model for predicting microstructure and microsegregation allows the prediction of migration distances of dendrite arms and asymmetric concentration distributions in the arms. Provided that detailed information on the time dependence of the temperature gradient as well as the cooling rate is available from heat flow calculations, accurate predictions of the type and amount of secondary phases or dendrite arm spacings are possible for cooling conditions at which TGZM is active. Parameter studies are performed to investigate the influence of TGZM for typical temperature gradients (0.01 to 10 K/mm). Sawtoothlike concentration distributions are predicted for high-temperature gradients. A binary Al-6.8 wt pct Cu alloy is solidified unidirectionally and asymmetrical concentration profiles are measured. Considering TGZM in the simulation results in good agreement of model predictions with experimental measurements in the position of the minimum concentration and the asymmetric shape of the concentration profile as well as dendrite arm spacings and amount of second phase.