Stochastic modelling of a diffusive wave for flood propagation using the random walk particle tracking method in a hypothetical city

Deterministic numerical schemes have been widely used for the solution of the diffusive wave (DW) equation, however, these schemes are computationally costly and suffer instability issues. This paper presents a stochastic random walk particle tracking (RWPT) method to solve such an equation for a dam‐break flow problem. Three different wave duration scenarios are presented for simulations of the DW for flood flows in a hypothetical city. The hypothetical city is represented by a domain of size 2,000 m by 500 m in x and y directions, respectively. The domain is divided into 25 m by 25 m cells. A dam is located at the upstream of the hypothetical city. Each scenario has a distinct propagation pattern after the dam is breached. Analysed and presented are 18 different simulations, which are composed of three different building configurations, two different bed slopes, and three different shapes of hydrographs. In this method, the flood volume is divided into a large number of particles where each particle carries a fixed amount of the flood volume. These particles undergo convective and diffusive movements, and their superposition represents propagation of the DW in the flow domain. The solution algorithm of the RWPT‐based equations is used to compute flood inundation depths in the hypothetical city. Comparison is drawn among the simulated results from three different shapes of the inflow hydrographs. The proposed stochastic method has two major advantages over traditional deterministic schemes: (a) greater efficiency, thus lesser computational costs, and (b) no instability issues.     

Development of a modelling methodology for the investigation of riparian hydrological processes

The riparian zone is in intimate contact with the river and, as such, is a critical zone for understanding hydrological problems. This paper presents a general modelling methodology for the assessment of riparian hydrological processes. It is applicable to a wide range of riparian spaces and incorporates current expertise in numerical methods. A core part of the modelling methodology is the random walk particle method (RWPM). We develop an RWPM as part of the ESTEL2D subsurface flow model, test it against analytical solutions and apply it to the simulation of parcels of water as they move through the riparian zone. The modelling methodology provides a new opportunity to assess fundamental hydrological process issues such as the proportioning of pre‐event and event water storm runoff, and reversals of flow in floodplains. Copyright © 2005 John Wiley & Sons, Ltd.     

Stochastic analysis of estuarine hydraulics

A new methodology is presented for the solution of the stochastic hydraulic equations characterizing steady, one-dimensional estuarine flow. The methodology is predicated on quasi-linearization, perturbation methods, and the finite difference approximation of the stochastic differential operators. Assuming Manning's roughness coefficient is the principal source of uncertainty in the model, stochastic equations are presented for the water depths and flow rates in the estuarine system. Moment equations are developed for the mean and variance of the water depths. The moment equations are compared with the results of Monte Carlo simulation experiments. The results confirm that for any spatial location in the estuary that (1) as the uncertainty in the channel roughness increases, the uncertainty in mean depth increases, and (2) the predicted mean depth will decrease with increasing uncertainty in Manning'sn. The quasi-analytical approach requires significantly less computer time than Monte Carlo simulations and provides explicit     

Stochastic modelling of erosion and deposition in cohesive soils

A new stochastic method of detachment rate estimation was used in erosion modelling. This method was based on calculating the probability of driving forces exceeding resistance forces in the interaction of oscillating flow and structured soil. Knowledge of the probability density functions for flow velocity, soil cohesion, aggregate size and soil integrity makes it possible to calculate theoretically the erosion rate of cohesive soil for any combination of these stochastic variables. The proposed theory explains the variability in relationships between rate of detachment and flow velocity. With flow velocity, detachment rate increases more rapidly for more integrated soil with higher cohesion and larger aggregates. This theory also shows the great difference between soil erosion type for relatively high and relatively low flow velocities, and explains rather high errors, even with detailed models, in the calculation of low soil erosion rate. Copyright © 2004 John Wiley & Sons, Ltd.     

Improving rainfall–runoff modelling through the control of uncertainties under increasing climate variability in the Ouémé River basin (Benin,West Africa)

ABSTRACT

The objective of this paper is to understand how the natural dynamics of a time-varying catchment, i.e. the rainfall pattern, transforms the random component of rainfall and how this transformation influences the river discharge. To this end, this paper develops a rainfall–runoff modelling approach that aims to capture the multiple sources and types of uncertainty in a single framework. The main assumption is that hydrological systems are nonlinear dynamical systems which can be described by stochastic differential equations (SDE). The dynamics of the system is based on the least action principle (LAP) as derived from Noether’s theorem. The inflow process is considered as a sum of deterministic and random components. Using data from the Ouémé River basin (Benin, West Africa), the basic properties for the random component are considered and the triple relationship between the structure of the inflowing rainfall, the corresponding SDE that describes the river basin and the associated Fokker-Planck equations (FPE) is analysed.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR D. Gerten     

Stochastic modelling of soil moisture dynamics in a grassland of Qilian Mountain at point scale

Stochastic modeling of soil moisture dynamics is crucial to the quantitative understanding of plant responses to water stresses,hydrological control of nutrient cycling processes,water competition among plants,and some other ecological dynamics,and thus has become a hotspot in ecohydrology at present.In this paper,we based on the continuously monitored data of soil moisture during 2002―2005 and daily precipitation date of 1992―2006,and tried to make a probabilistic analysis of soil moisture dynamics at point scale in a grassland of Qilian Mountain by integrating the stochastic model improved by Laio and the Monte Carlo method.The results show that the inter-annual variations for the soil moisture patterns at different depths are very significant,and that the coefficient of variance(CV) of surface soil moisture(20 cm) is almost continually kept at about 0.23 whether in the rich or poor rainy years.Interestingly,it has been found that the maximal CV of soil moisture has not always appeared at the surface layer.Comparison of the analytically derived soil moisture probability density function(PDF) with the statistical distribution of the observed soil moisture data suggests that the stochastic model can reasonably describe and predict the soil moisture dynamics of the grassland in Qilian Mountain at point scale.By extracting the statistical information of the historical precipitation data in 1994―2006,and inputting them into the stochastic model,we analytically derived the long-term soil moisture PDF without considering the inter-annual climate fluctuations,and then numerically derived the one when considering the inter-annual fluctuation effects in combination with a Monte-Carlo procedure.It was found that,though the peak position of the probability density distribution significantly moved towards drought when considering the disturbance forces,and its width was narrowed,accordingly its peak value was increased,no significant bimodality was observed in the soil moisture dynamics under the given intensity of random fluctuation disturbance.     

Stochastic sketching of infiltration-advance isochrones

A technique has been developed for predicting the irregular advance pattern often observed as water spreads on the surface of the ground. The technique is a combination of stochastic sketching, potential theory, probability theory, and a mass balance equation in the form of an advance equation. The technique can be used on flat as well as sloping terrain and addresses any form of obstructions or constraints to the flow of the water. The stochastic sketching portion of the technique uses cellular automata with transition probability movement rules to sketch the dynamics of small volume water elements in the defined environment. Randomly selected small volume flow path segments are computed and plotted. The envelope of these segments defines the wetted area and the advance front. Several examples are presented showing the patterns produced for various situations.     

Stochastic and statistical methods in hydrology and environmental engineering

Recent developments in stochastic and statistical methods in hydrology and environmental engineering presented in the upcoming sequence of research papers are evaluated, compared and put into proper perspective. These papers are being published as a memorial to Professor T. E. Unny who was a founding Editor of the journalStochastic Hydrology and Hydraulics. As explained in this introductory paper, other activities that took place to celebrate Professor Unny's lifetime academic accomplishments include an international conference held in his honor at the University of Waterloo in June, 1993 and the publication of a four-volume conference proceedings in 1994.     

Analysis and modelling of rainfall fields at different resolutions in southern Italy

Abstract

The spatial and temporal variability of the scaling properties and correlation structure of a data set of rainfall time series, aggregated over different temporal resolutions, and observed in 70 raingauges across the Basilicata and Calabria regions of southern Italy, is investigated. Two types of random cascade model, namely canonical and microcanonical models, were used for each raingauge and selected season. For both models, different hypotheses concerning dependency of parameters on time scale and rainfall height can be adopted. In particular, a new approach is proposed which consists of several combinations of models with a different scale dependence of parameters for different temporal resolutions. The goal is to improve the modelling of the main features of rainfall time series, especially for cases where the variability of rainfall changes irregularly with temporal aggregation. The results obtained with the new methodology showed good agreement with the observed data, in particular, for the summer months. In fact, during this season, rainfall heights aggregated at fine temporal resolutions (from 5 to 20 min) are more similar (relative to the winter season) to the values cumulated on 1 or 3 h (due to convective phenomena) and, consequently, the process of rainfall breakdown is nearly stationary for a range of finer temporal resolutions.

Editor D. Koutsoyiannis; Associate editor A. Montanari     

结构地震反应性态的物理随机最优控制

本研究发展了结构地震反应性态的随机最优控制理论和方法。这一研究建立在物理随机系统思想的新理论框架下,突破了以I^to随机微分方程描述动力系统的经典随机最优控制的藩篱。提出了基于系统二阶统计量评价、单目标超越概率和多目标能量均衡的控制器参数设计准则,以及基于概率可控指标的控制器位置设计准则,并将它们统一为物理随机最优控制的广义最优控制律。数值算例分析表明,本文发展的物理随机最优控制方法能够实现结构地震反应性态的精细化控制。     

Limits on the validity of infinite length assumptions for modelling shallow landslides

The infinite slope method is widely used as the geotechnical component of geomorphic and landscape evolution models. Its assumption that shallow landslides are infinitely long (in a downslope direction) is usually considered valid for natural landslides on the basis that they are generally long relative to their depth. However, this is rarely justified, because the critical length/depth (L/H) ratio below which edge effects become important is unknown. We establish this critical L/H ratio by benchmarking infinite slope stability predictions against finite element predictions for a set of synthetic two‐dimensional slopes, assuming that the difference between the predictions is due to error in the infinite slope method. We test the infinite slope method for six different L/H ratios to find the critical ratio at which its predictions fall within 5% of those from the finite element method. We repeat these tests for 5000 synthetic slopes with a range of failure plane depths, pore water pressures, friction angles, soil cohesions, soil unit weights and slope angles characteristic of natural slopes. We find that: (1) infinite slope stability predictions are consistently too conservative for small L/H ratios; (2) the predictions always converge to within 5% of the finite element benchmarks by a L/H ratio of 25 (i.e. the infinite slope assumption is reasonable for landslides 25 times longer than they are deep); but (3) they can converge at much lower ratios depending on slope properties, particularly for low cohesion soils. The implication for catchment scale stability models is that the infinite length assumption is reasonable if their grid resolution is coarse (e.g. >25 m). However, it may also be valid even at much finer grid resolutions (e.g. 1 m), because spatial organization in the predicted pore water pressure field reduces the probability of short landslides and minimizes the risk that predicted landslides will have L/H ratios less than 25. Copyright © 2012 John Wiley & Sons, Ltd.     

Estimation of water saturation dependence of dispersion in unsaturated porous media: experiments and modelling analysis

In the dispersion theory, a linear relationship has been verified between the coefficient of hydrodynamic dispersion and water velocity, both in saturated and in unsaturated porous media. But for unsaturated soils the variability of flow directions and microscopic velocities can be larger than in saturated soils because of the lower degree of water saturation. This leads to an increased dispersion. Therefore, relationships between water content and relative water velocity fluctuations and water content together with the coefficient of dispersivity in unsaturated porous media respectively have been investigated systematically by displacement experiments in glass beads and coarse-textured sandy soil columns. The breakthrough curves (BTCs) of chloride showed that an increase of solute mixing with a decrease of water content was caused by an increase of flow velocity fluctuations for different pathways. In order to explain the observed tailing effect in unsaturated flow, two mathematical models were used to fit theoretically derived nonlinear functions of water content dependent dispersivities for both porous media. The close agreement between the observed and computed results suggests that the theoretical model of hydrodynamic dispersion can be extended to transport in unsaturated porous media, providing that BTCs of the effluent water are used to estimate representative dispersivity parameters of soils.     

Stochastic modelling of relative water permeability in vegetative soils with implications on stability of bioengineered slope

Vegetation is known to influence the hydrological state variables, suction \( \left( \psi \right) \) and volumetric water content (\( \theta_{w} \)) of soil. In addition, vegetation induces heterogeneity in the soil porous structure and consequently the relative permeability (\( k_{r} \)) of water under unsaturated conditions. The indirect method of utilising the soil water characteristic curve (SWCC) is commonly adopted for the determination of \( k_{r} \). In such cases, it is essential to address the stochastic behaviour of SWCC, in order to conduct a robust analysis on the \( k_{r} \) of vegetative cover. The main aim of this study is to address the uncertainties associated with \( k_{r} \), using probabilistic analysis, for vegetative covers (i.e., grass and tree species) with bare cover as control treatment. We propose two approaches to accomplish the aforesaid objective. The univariate suction approach predicts the probability distribution functions of \( {\text{k}}_{\text{r}} \), on the basis of identified best probability distribution of suction. The bivariate suction and water content approach deals with the bivariate modelling of the water content and suction (SWCC), in order to capture the randomness in the permeability curves, due to presence of vegetation. For this purpose, the dependence structure of \( \psi \) and \( \theta_{w} \) is established via copula theory, and the \( k_{r} \) curves are predicted with respect to varying levels of \( \psi - \theta_{w} \) correlation. The results showed that the \( k_{r} \) of vegetative covers is substantially lower than that in bare covers. The reduction in \( k_{r} \) with drying is more in tree cover than grassed cover, since tree roots induce higher levels of suction. Moreover, the air entry value of the soil depends on the magnitude of \( \psi - \theta_{w} \) correlation, which in turn, is influenced by the type of vegetation in the soil. \( k_{r} \) is found to be highly uncertain in the desaturation zone of the relative permeability curve. The stochastic behaviour of \( k_{r} \) is found to be most significant in tree covers. Finally, a simplified case study is also presented in order to demonstrate the impact of the uncertainty in \( k_{r} \), on the stability of vegetates slopes. With an increment in the parameter \( \alpha \), factor of safety (FS) is found to decrease. The trend of FS is reverse of this with parameter \( n \). Overall FS is found to vary around 4–5%, for both bare and vegetative slopes.     

基于物理的随机地震动模型研究

基于物理联系研究地震动随机性,建立了随机地震动与基底输入傅氏谱、场地固有圆频率和场地等价阻尼比之间的物理关系,从随机傅氏谱函数角度描述了地震动随机过程的随机性本质。结合Ⅳ类工程场地的实测地震动记录资料,由数值方法识别了给出基本随机变量的概率分布参数。与实测记录对比表明,本文建立的随机地震动模型具有明确的物理概念,可充分反映地震动的变异性特征。     

Historical overview of 2D and 3D hydrodynamic modelling of shallow water flows in the Netherlands

Ocean Dynamics - This paper contains a historical overview of 2D and 3D hydrodynamic modelling in the Netherlands from the 1960s till now. It started in the 1960s with two-dimensional...     

Stochastic analysis of spatiotemporal solute content measurements using a regression model

A regression model is used to study spatiotemporal distributions of solute content ion concentration data (calcium, chloride and nitrate), which provide important water contamination indicators. The model consists of three random and one deterministic components. The random space/time component is assumed to be homogeneous/stationary and to have a separable covariance. The purely spatial and the purely temporal random components are assumed to have homogenous and stationary increments, respectively. The deterministic component represents the space/time mean function. Inferences of the random components involve maximum likelihood and semi-parametric methods under some restrictions on the data configuration. Computational advantages and modelling limitations of the assumptions underlying the regression model are discussed. The regression model leads to simplifications in the space/time kriging and cokriging systems used to obtain space/time estimates at unobservable locations/instants. The application of the regression model in the study of the solute content ions was done at a global scale that covers the entire region of interest. The variability analysis focuses on the calculation of the spatial direct and cross-variograms and the evaluation of correlations between the three solute content ions. The space/time kriging system is developed in terms of the space direct and cross-variograms, and allows the separate estimation of the regression model components. Maps of these components are then obtained for each one of the three ions. Using the estimates of the purely spatial component, spatial dependencies between the ions are studied. Physical causes and consequences of the space/time variability are discussed, and comparisons are made with previous analyses of the solute content dataset.     

浅水湖泊水质系统滤波模型研究

本文建立了浅水湖泊水质系统滤波模型和相应算法,根据滇池流场比较稳定等特点,对湖泊进行单元分区,考虑模型误差扰动和观测误差扰动的存在,建立系统的状态方程和观测方程,然后采用吉尔（Gill)算法求解微分方程,进行系统多点连续模拟和实时预报,用此法对1988年滇池BOD,COD时空变化进行连续预报,取得满意结果。