Enhancing tidal prediction accuracy in a deterministic model using chaos theory

The classical deterministic approach to tidal prediction is based on barotropic or baroclinic models with prescribed boundary conditions from a global model or measurements. The prediction by the deterministic model is limited by the precision of the prescribed initial and boundary conditions. Improvement to the knowledge of model formulation would only marginally increase the prediction accuracy without the correct driving forces. This study describes an improvement in the forecasting capability of the tidal model by combining the best of a deterministic model and a stochastic model. The latter is overlaid on the numerical model predictions to improve the forecast accuracy. The tidal prediction is carried out using a three-dimensional baroclinic model and, error correction is instigated using a stochastic model based on a local linear approximation. Embedding theorem based on the time lagged embedded vectors is the basis for the stochastic model. The combined model could achieve an efficiency of 80% for 1 day tidal forecast and 73% for a 7 day tidal forecast as compared to the deterministic model estimation.     

Three-dimensional semi-idealized model for tidal motion in tidal estuaries

In this paper, a three-dimensional semi-idealized model for tidal motion in a tidal estuary of arbitrary shape and bathymetry is presented. This model aims at bridging the gap between idealized and complex models. The vertical profiles of the velocities are obtained analytically in terms of the first-order and the second-order partial derivatives of surface elevation, which itself follows from an elliptic partial differential equation. The surface elevation is computed numerically using the finite element method and its partial derivatives are obtained using various methods. The newly developed semi-idealized model allows for a systematic investigation of the influence of geometry and bathymetry on the tidal motion which was not possible in previously developed idealized models. The new model also retains the flexibility and computational efficiency of previous idealized models, essential for sensitivity analysis. As a first step, the accuracy of the semi-idealized model is investigated. To this end, an extensive comparison is made between the model results of the semi-idealized model and two other idealized models: a width-averaged model and a three-dimensional idealized model. Finally, the semi-idealized model is used to understand the influence of local geometrical effects on the tidal motion in the Ems estuary. The model shows that local convergence and meandering effects can have a significant influence on the tidal motion. Finally, the model is applied to the Ems estuary. The model results agree well with observations and results from a complex numerical model.     

A stochastic optimization model based on adaptive feedback correction process and surrogate model uncertainty for DNAPL-contaminated groundwater remediation design

A stochastic optimization model based on an adaptive feedback correction process and surrogate model uncertainty was proposed and applied for remediation strategy design at a dense non-aqueous phase liquids (DNAPL)-contaminated groundwater site. One hundred initial training samples were obtained using the Latin hypercube sampling method. A surrogate model of a multiphase flow simulation model was constructed based on these samples employing the self-adaptive particle swarm optimization kriging (SAPSOKRG) method. An optimization model was built, using the SAPSOKRG surrogate model as a constraint. Then, an adaptive feedback correction process was designed and applied to iteratively update the training samples, surrogate model, and optimization model. Results showed that the training samples, the surrogate model, and the optimization model were effectively ameliorated. However, the surrogate model is an approximation of the simulation model, and some degree of uncertainty exists even though the surrogate model was ameliorated. Therefore, residuals between the surrogate model and the simulation model were calculated, and an uncertainty analysis was conducted. Based on the uncertainty analysis results, a stochastic optimization model was constructed and solved to obtain optimal remediation strategies at different confidence levels (60, 70, 80, 90, 95%) and under different remediation objectives (average DNAPL removal rate ≥?70,?≥?75,?≥?80,?≥?85,?≥?90%). The optimization results demonstrated that the higher the confidence level and remediation objective, the more expensive was remediation. Therefore, decision makers can weigh remediation costs, confidence levels, and remediation objectives to make an informed choice. This also allows decision makers to determine the reliability of a selected strategy and provides a new tool for DNAPL-contaminated groundwater remediation design.     

Investigation of the model complexity required in runoff simulation at different time scales / Etude de la complexité de modélisation requise pour la simulation d'écoulement à différentes échelles temporelles

Abstract

The “optimal” model complexity is defined as the minimum watershed model structure required for realistic representation of runoff processes. This paper examines the effects of model complexity at different time scales, daily and hourly. Two watershed models with different levels of complexity were constructed and their capability to simulate runoff from a watershed was evaluated. Both models were tested on the same watershed using identical meteorological input, thereby assuring that any difference between model outputs is due only to their model structure. It is demonstrated that, at a daily time scale, a simple model gives good results. For the mountain situation, in which snowmelt is a dominant influence, the nonlinearity of the runoff processes is moderate, and therefore a simple model works well. The model produced good results over a period of 28 years of continuous simulation. However, this simpler model was inadequate when tested on an hourly time scale due to greater nonlinear effects, especially when modelling high-intensity rainfall events. Therefore, the hourly simulation benefited from the more complex model structure. These model results show that optimal watershed model complexity depends on temporal resolution, namely the simulation period and the computational time step. It was shown that certain process representations and model parameters that appeared unimportant during the long-term simulation had significant effects on the short-term extreme event model simulation.     

On the Integrability of Limited-Area Numerical Weather Prediction Model ALADIN over Extended Time Periods

This note summarizes results of the first integration of regional numerical weather prediction model ALADIN in a climate mode. The ALADIN model, developed in an international cooperation led by Météo France, is operationally used for weather prediction. The grid step of the model is 12 km; the integration domain covers a major part of Europe. A one-month-long run has been performed with this model on observed boundary conditions (represented by assimilations by the global model ARPEGE). It is demonstrated that no excessive error is generated and accumulated in the model during the integration; hence the model is integrable for extended time periods and may serve a basis for a development towards a regional climate model.     

计算岩石波速空间平均的极限近似模型

本文在传统的岩石波速空间平均模型（Voight模型,Ruess模型,Hill模型和几何平均模型）的基础上,提出了一种极限近似模型.在这种模型中,它是利用作者提出的一个基于Hill模型（即代数平均模型）和几何平均模型的递推关系式,并利用这个关系式计算求出模型的极限近似值,该值介于Hill模型和几何平均模型之间,是具有典型代表意义的一个值.     

Transport in chemically and mechanically heterogeneous porous media: V. Two-equation model for solute transport with adsorption

In this paper we develop the two-equation model for solute transport and adsorption in a two-region model of a mechanically and chemically heterogeneous porous medium. The closure problem is derived and the coefficients in both the one- and two-equation models are determined on the basis of the Darcy-scale parameters. Numerical experiments are carried out for a stratified system at the aquifer scale, and the results are compared with the one-equation model presented in Part IV and the two-equation model developed in this paper. Good agreement between the two-equation model and the numerical experiments is obtained. In addition, the two-equation model is used, in conjunction with a moment analysis, to derive a one-equation, non-equilibrium model that is valid in the asymptotic regime. Numerical results are used to identify the asymptotic regime for the one-equation, non-equilibrium model.     

Integrated numerical modeling for basin-wide water management: The case of the Rattlesnake Creek basin in south-central Kansas

The objective of this article is to develop and implement a comprehensive computer model that is capable of simulating the surface-water, ground-water, and stream-aquifer interactions on a continuous basis for the Rattlesnake Creek basin in south-central Kansas. The model is to be used as a tool for evaluating long-term water-management strategies. The agriculturally-based watershed model SWAT and the ground-water model MODFLOW with stream-aquifer interaction routines, suitably modified, were linked into a comprehensive basin model known as SWATMOD. The hydrologic response unit concept was implemented to overcome the quasi-lumped nature of SWAT and represent the heterogeneity within each subbasin of the basin model. A graphical user-interface and a decision support system were also developed to evaluate scenarios involving manipulation of water rights and agricultural land uses on stream-aquifer system response. An extensive sensitivity analysis on model parameters was conducted, and model limitations and parameter uncertainties were emphasized. A combination of trial-and-error and inverse modeling techniques were employed to calibrate the model against multiple calibration targets of measured ground-water levels, streamflows, and reported irrigation amounts. The split-sample technique was employed for corroborating the calibrated model. The model was run for a 40 y historical simulation period, and a 40 y prediction period. A number of hypothetical management scenarios involving reductions and variations in withdrawal rates and patterns were simulated. The SWATMOD model was developed as a hydrologically rational low-flow model for analyzing, in a user-friendly manner, the conditions in the basin when there is a shortage of water.     

Modeling undertow due to random waves

A numerical model of undertow due to random waves is developed. The model includes three sub-models: (i) a model for multi-directional and multi-frequency random wave transformation, (ii) a surface roller evolution model, and (iii) a model for calculating the vertical distribution and the mean value of the undertow velocity. The calculation of wave trough level is performed based on a theory for the wave asymmetry. The model was successfully validated against small- and large-scale laboratory experiments. Thus, the model is expected to provide reliable input for the modeling of sediment transport and morphological change due to waves and currents.     

Error analysis for the evaluation of model performance: rainfall–runoff event summary variables

This paper provides a procedure for the evaluation of model performance for rainfall–runoff event summary variables, such as total discharge or peak runoff. The procedure is based on the analysis of model errors, defined as the differences between observed values and values predicted by a simulation model. Model errors can (i) indicate whether and where the model can be improved, (ii) be used to measure the performance of a model, and (iii) be used to compare model simulations. In this paper, both statistical and graphical methods are used to characterize model errors. We explore model recalibration by relating model errors to the model predictions, and to external, independent variables. The R‐5 catchment data sets that we used in this study include summary variables for 72 rainfall–runoff events. The simulations used in this study were previously conducted with the quasi‐physically based rainfall–runoff model QPBRRM for 11 different characterizations of the R‐5 catchment, each with increasing information or a refined spatial discretization of the overland flow planes. This paper is about proposing model diagnostics and not about procedures for using diagnostics for model modification. Copyright © 2007 John Wiley & Sons, Ltd.     

A review of analogue model studies of the coast effect

This work reviews electromagnetic analogue model studies of the coast effect, dealing particularly with a vertical interface model, a thin conducting sheet model, a wedge model, and a wedge underlain by a conducting block simulating an upwelling in a conducting zone beneath the coast. The vertical interface model results and the infinitely conducting thin sheet model results show good agreement with calculated values. It is concluded that a sloping sea-land interface alone cannot account for the experimentally observed coast effect, but that a sloping sea-land interface underlain by a conducting step could produce the observed coast effect.     

Model structure exploration for index flood regionalization

Although the nonlinear power form model structure is widely accepted by practitioners in the flood regionalization modelling, there is a lack of studies on whether there is a room for further improvement, and if the answer is yes, what should be done to explore alternative model structures. A framework is proposed in this study towards investigating this issue by the following steps: (i) a universal data‐driven model is utilized to see if there is a room for improvement compared with the conventional model, and (ii) if improvement is achieved, this means that there should exist more effective model structures than the current form. However, because the universal data‐driven models are usually opaque, more explicit model structures should be explored, which are convenient for practical usage. In this study, the proposed framework is applied in a case study using the catchment characteristics from the Flood Estimation Handbook in conjunction with the gamma test, support vector machine (SVM) and genetic programming (GP). First, the gamma test is used for the purpose of input variables selection where no model structure needs to be defined as a priori, and therefore, the result can be applied to any model structures for model building. Second, an SVM, which is a powerful data‐driven nonlinear model capable of modelling a variety of nonlinear systems, is applied to the index flood model for the first time. Once the best model is determined using those two data‐driven tools, GP is employed to find an alternative model structure. As the SVM is not formulated for producing explicit model functional form, the GP offers an advantage at this point where it can infer an explicit mathematical model functional form. Copyright © 2012 John Wiley & Sons, Ltd.     

Coupled Stress Release Model for Time-dependent Seismicity

—Based on the original stress release model of seismicity proposed by Vere-Jones (1978), this paper has developed a stochastic coupled stress release model of time-dependent seismicity, which considers the earthquake interaction and stress transfer between different seismic subregions. As an example, the model is applied to a statistical analysis of the historical earthquake catalog with magnitude M ≥ 6.0 during the period from 1480 to 1996 in North China. According to the Akaike information criterion (AIC), the results show that the coupled stress release model is better than the original model, which demonstrates the existence of long-range correlations between different seismic subregions. We also apply both the stochastic (original and developed coupled) models to analyze the synthetic catalog produced by a cellular automata model, which is based on mechanics of a slide-spring-damper system to model the fault network. The stress release model provides a good fit to the synthetic regional stress, and the coupled stress release model provides an improvement in fit to the synthetic catalog over the original model.     

The effect of forcing and landscape distribution on performance and consistency of model structures

It is often challenging to determine the appropriate level of spatial model forcing and model distribution in conceptual rainfall‐runoff modelling. This paper compares the value of incorporating both spatially distributed forcing data and spatially distributed model conceptualisations based on landscape heterogeneity, applied to the Ourthe catchment in Belgium. Distributed forcing data were used to create a spatial distribution of model states. Eight different configurations were tested: a lumped and distributed model structure, each with four levels of model state distribution. The results show that in the study catchment the distributed model structure can in general better reproduce the dynamics of the hydrograph, and furthermore, that the differences in performance and consistency between calibration and validation are smallest for the distributed model structure with distributed model states. For the Ourthe catchment, it can be concluded that the positive effect of incorporating a distributed model structure is larger than that of incorporating distributed model states. Distribution of model structure increases both model performance and consistency. Copyright © 2015 John Wiley & Sons, Ltd.     

Field Test of a Hybrid Finite‐Difference and Analytic Element Regional Model

Regional finite‐difference models often have cell sizes that are too large to sufficiently model well‐stream interactions. Here, a steady‐state hybrid model is applied whereby the upper layer or layers of a coarse MODFLOW model are replaced by the analytic element model GFLOW, which represents surface waters and wells as line and point sinks. The two models are coupled by transferring cell‐by‐cell leakage obtained from the original MODFLOW model to the bottom of the GFLOW model. A real‐world test of the hybrid model approach is applied on a subdomain of an existing model of the Lake Michigan Basin. The original (coarse) MODFLOW model consists of six layers, the top four of which are aggregated into GFLOW as a single layer, while the bottom two layers remain part of MODFLOW in the hybrid model. The hybrid model and a refined “benchmark” MODFLOW model simulate similar baseflows. The hybrid and benchmark models also simulate similar baseflow reductions due to nearby pumping when the well is located within the layers represented by GFLOW. However, the benchmark model requires refinement of the model grid in the local area of interest, while the hybrid approach uses a gridless top layer and is thus unaffected by grid discretization errors. The hybrid approach is well suited to facilitate cost‐effective retrofitting of existing coarse grid MODFLOW models commonly used for regional studies because it leverages the strengths of both finite‐difference and analytic element methods for predictions in mildly heterogeneous systems that can be simulated with steady‐state conditions.     

地球外部扰动重力严密改化模型及分析检验

直接积分模型是计算地球外部扰动重力的主要数学工具,将全球积分模型改化为局域积分模型是实现地球外部重力场赋值的前提条件.相比表层积分模型和向上延拓积分模型,Stokes积分模型要求的输入信息种类最少,故在减轻数据保障压力方面具有比较明显的优势.在实施Stokes积分模型工程化应用过程中,我们发现扰动重力径向分量积分模型从...     

Moving window kriging with geographically weighted variograms

This study adds to our ability to predict the unknown by empirically assessing the performance of a novel geostatistical-nonparametric hybrid technique to provide accurate predictions of the value of an attribute together with locally-relevant measures of prediction confidence, at point locations for a single realisation spatial process. The nonstationary variogram technique employed generalises a moving window kriging (MWK) model where classic variogram (CV) estimators are replaced with information-rich, geographically weighted variogram (GWV) estimators. The GWVs are constructed using kernel smoothing. The resultant and novel MWK–GWV model is compared with a standard MWK model (MWK–CV), a standard nonlinear model (Box–Cox kriging, BCK) and a standard linear model (simple kriging, SK), using four example datasets. Exploratory local analyses suggest that each dataset may benefit from a MWK application. This expectation was broadly confirmed once the models were applied. Model performance results indicate much promise in the MWK–GWV model. Situations where a MWK model is preferred to a BCK model and where a MWK–GWV model is preferred to a MWK–CV model are discussed with respect to model performance, parameterisation and complexity; and with respect to sample scale, information and heterogeneity.     

Fully fluid-solid coupling dynamic model for seismic response of underground structures in saturated soils

The seismic response characteristics of underground structures in saturated soils are investigated. A fully fluid-solid coupling dynamic model is developed and implemented into ABAQUS with a user-defined element to simulate the dynamic behavior of saturated soils. The accuracy of the model is validated using a classic example in literature. The performance of the model is verified by its application on simulating the seismic response characteristics of a subway station built in saturated soils. The merits of the model are demonstrated by comparing the difference of the seismic response of an underground structure in saturated soils between using the fully coupling model and a single-phase medium model. The study finds that the fully coupling model developed herein can simulate the dynamic response characteristics of the underground structures in saturated soils with high accuracy. The seismic response of the underground structure tends to be underestimated by using the single-phase medium model compared with using the fully coupling model, which provides a weaker confining action to the underground structure.     

NUMERICAL SIMULATION OF SEDIMENT RELEASE FROM RESERVOIRS

1 INTRODUCTION Reservoirs sedimentation is a serious problem in many countries, including the I. R. of Iran. Accumulation of sediment deposits decreases worldwide reservoir storage capacity by one percent per year (Mahmood, 1987). The loss of reservoir st…