Spatial rainfall model using a pattern classifier for estimating missing daily rainfall data

Missing data in daily rainfall records are very common in water engineering practice. However, they must be replaced by proper estimates to be reliably used in hydrologic models. Presented herein is an effort to develop a new spatial daily rainfall model that is specifically intended to fill in gaps in a daily rainfall dataset. The proposed model is different from a convectional daily rainfall generation scheme in that it takes advantage of concurrent measurements at the nearby sites to increase the accuracy of estimation. The model is based on a two-step approach to handle the occurrence and the amount of daily rainfalls separately. This study tested four neural network classifiers for a rainfall occurrence processor, and two regression techniques for a rainfall amount processor. The test results revealed that a probabilistic neural network approach is preferred for determining the occurrence of daily rainfalls, and a stepwise regression with a log-transformation is recommended for estimating daily rainfall amounts.     

Analytical investigation of the exact groundwater divide between rivers beyond the Dupuit–Forchheimer approximation

The groundwater divide is a key feature of river basins and significantly influenced by subsurface hydrological processes. For an unconfined aquifer between two parallel rivers or ditches, it has long been defined as the top of the water table based on the Dupuit–Forchheimer approximation. However, the exact groundwater divide is subject to the interface between two local flow systems transporting groundwater to rivers from the infiltration recharge. This study contributes a new analytical model for two-dimensional groundwater flow between rivers of different water levels. The flownet is delineated in the model to identify groundwater flow systems and the exact groundwater divide. Formulas with two dimensionless parameters are derived to determine the distributed hydraulic head, the top of the water table and the groundwater divide. The locations of the groundwater divide and the top of the water table are not the same. The distance between them in horizontal can reach up to 8.9% of the distance between rivers. Numerical verifications indicate that simplifications in the analytical model do not significantly cause misestimates in the location of the groundwater divide. In contrast, the Dupuit–Forchheimer approximation yields an incorrect water table shape. The new analytical model is applied to investigate groundwater divides in the Loess Plateau, China, with a Monte Carlo simulation process taking into account the uncertainties in the parameters.     

Stochastic dynamic stiffness of a surface footing for offshore wind turbines: Implementing a subset simulation method to estimate rare events

The purpose of this study, which concerns the stochastic dynamic stiffness of foundations for large offshore wind turbines, is to quantify uncertainties related to the first natural frequency of a turbine supported by a surface footing and to estimate the low event probabilities. Herein, a simple model of a wind turbine structure with equivalent coupled springs at the base is calibrated with the mean soil property values. A semianalytical solution, based on the Green׳s function for a layered half-space is utilized for estimation of foundation responses. Soil elastic modulus and layer depth are considered as random variables with lognormal distributions. The uncertainties are quantified, and the estimation of rare events of the first natural frequency is discussed through an advanced reliability approach based on subset simulation. This analysis represents a first step in the estimation of the safety with respect to the failure of a turbine in the fatigue limit state.     

Divergence of solutions to perturbation-based advection-dispersion moment equations

Moment equation methods are popular and powerful tools for modeling transport processes in randomly heterogeneous porous media, but the application of these methods to advection-dispersion equations often leads to erroneous oscillations. Perturbative methods, required to close systems of moment equations, become inaccurate for large perturbations; however, little quantitative theory exists for determining when this occurs for advection-dispersion equations. We consider three different methods (asymptotic approximation, Eulerian truncation, and iterative solution) for closing and solving advection-dispersion moment equations describing transport in stratified porous media with random permeability. We obtain approximate analytical expressions for time above which the asymptotic approximation to the mean diverges, in particular quantifying the impact that dispersion has on delaying—but not eliminating—divergence. We demonstrate that Eulerian truncation and iterative solution methods do not eliminate divergent behavior either. Our divergence criteria provide a priori estimates that signal a warning to the practitioner of stochastic advection-dispersion equations to carefully consider whether to apply perturbative approaches.     

An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty

In this study, an interval-parameter multi-stage stochastic linear programming (IMSLP) method has been developed for water resources decision making under uncertainty. The IMSLP is a hybrid methodology of inexact optimization and multi-stage stochastic programming. It has three major advantages in comparison to the other optimization techniques. Firstly, it extends upon the existing multi-stage stochastic programming method by allowing uncertainties expressed as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. Secondly, penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. Thirdly, it cannot only handle uncertainties through constructing a set of scenarios that is representative for the universe of possible outcomes, but also reflect dynamic features of the system conditions through transactions at discrete points in time over the planning horizon. The developed IMSLP method is applied to a hypothetical case study of water resources management. The results are helpful for water resources managers in not only making decisions of water allocation but also gaining insight into the tradeoffs between environmental and economic objectives.     

On the modelling of sand bedforms using the semivariogram

This study shows the usefulness of the semivariogram for modelling sand ripples created by water flows of varied flow intensity. A combination of two mathematical functions is fitted to each sample semivariogram, that is an exponential (or stochastic) component and a periodic component. The parameters of each of these components have direct physical meaning. A non-dimensional ratio combining the two parameters of the exponential model is interpreted as a regularity index (which increases with the degree of regularity of bedform arrangement). This regularity index is inversely related to the Froude number of the flow. The non-dimensional wavelength, estimated from the dominant periodic function, is also inversely and closely related to the Froude number. The wave height, accurately estimated from properties of the two fitted components, is a direct function of flow velocity and is also proportional to the standard deviation of bed elevations. The bedform shape introduces a considerable discrepancy between the generally assumed normal frequency distribution and the empirical distributions of bed height. The series of bed elevations are generally characterized by a mixture of normal distributions having the same variance but different means. The calculation of a covariance assuming a constant and single mean (as in spectral analysis) can therefore be misleading and the problem may be avoided by using the semivariogram.     

A stochastic model of surface contaminant releases to support assessment of site contamination at a former industrial site

An industrial site is usually contaminated by accidental (and occasionally intentional) releases of pollutants to the environment from various operations carried out on that site. Consequently, the pattern of contamination created during the life of the site depends in part, at least, on the pattern of operations. Thus, the assessment of the pattern of contamination over the site should be improved: if it is possible to identify the pattern of operations on the site, the duration of the different activities and the perceived likelihood of releases from the different operations. A stochastic model has been developed that can be used to simulate alternative realizations of contaminant releases (duration, extent and timing). The model employs release zones associated with particular activities or groups of activities on the site and the areas of each of the zones may be independent or overlapping. The period of activity in each zone is obtained from the site records, while the likelihood and extent of contamination in each zone is inferred from an analysis of the contamination data obtained by point sampling. The form of the model, the method of inference of the model parameter values from the site data and the application of the model to the study site are presented. The release model has been developed as part of a suite of stochastic models for site ground contamination analysis. The stochastic soil and transport models and the application of the integrated modelling system are described in separate papers.     

FLOW FIELD IN SCOURED ZONE OF CHANNEL CONTRACTIONS

Experiments were conducted in a laboratory flume to measure the two-dimensional turbulent flow field in the scoured zone of channel contractions under a clear-water scour condition. The Acoustic Doppler Velocimeter (ADV) was used to detect the flow field at different vertical lines along the centerline of uncontracted (main channel) and contracted zones of the channel. The distributions of time-averaged velocity components, turbulent intensity, turbulent kinetic energy, and Reynolds stresses are presented in nondimensional graphical form. The bed shear stresses are computed from the measured Reynolds stresses being in threshold condition within the zone of contraction where bed was scoured. The data presented in this paper would be useful to the investigators for the development of kinematic flow model and morphological model of scour at a channel or river contraction.     

Seismic ground motion relationship in southern China based on stochastic finite-fault model

The characteristics of seismic ground motions in southern China are difficult to determine statistically due to a lack of strong ground motion data. In this study, a stochastic finite-fault ground motion model was adopted to simulate the seismic ground motions at bedrock for southern China, based on parameters derived from small and medium earthquakes that have occurred in the region. From these, the response spectra was estimated. A set of ground motion attenuation relations hipswas then developed based on simulated peak ground motions and response spectral parameters through regression, which would be applicable for use in engineering practice. Through comparisons, it was demonstrated that the proposed ground motion relationships are generally consistent with those obtained from other reported ground motion attenuation models for southern China.     

Inverse modeling of lichen growth curves and implications for lichenometric dating

Lichenometric dating represents a quick and affordable surface exposure dating method that has been widely used to provide a minimum age constraint on tectonic and geomorphic landscape changes as well as buildings and anthropogenic landscape changes in various settings during the late Holocene. Despite its widespread usage, this method has several limitations. Major problems relate to the sampling of lichen population on any given rock surface and the modeling of growth curves. In order to overcome these issues, it has been suggested to subdivide the rock surface into some areas and measure the largest lichen thallus on each one. However, how to express the data in terms of a probability distribution function and link it to an age of last exposure of the rock surface are still a matter of debate. Here, we propose a novel approach to the modeling of lichen growth curves by treating lichen growth as a continuous-time Markov process with a time-varying rate and additive Brownian noise. Given the growth rates, the probability distribution of the lichen population at any time can then be obtained by solving the Fokker–Planck equation. This method is illustrated using a dataset from the Huashan area of eastern China, which consists of measurements of the largest thalli on 12 rock surfaces of known age. We first build up the probability distribution of the lichen population for each rock surface based on extreme value theory and then use these to optimize the growth curve by minimizing the Jensen–Shannon divergence. A new method is also proposed to use the growth curve to map a sample of size data from an undated rock surface to the calendar age domain so as to yield a fully probabilistic estimate of the exposure age of the undated rock surface rather than a point estimate.