Liangsheng Shi

Uncertainty quantification of contaminant transport and risk assessment with conditional stochastic collocation method

Solute transport prediction is always subject to uncertainty due to the scarcity of observation data. The data worth of limited measurements can be explored by conditional simulation. This paper presents an efficient approach for the conditional simulation of solute transport in a randomly heterogeneous aquifer. The conditioning conductivity field is parameterized by the Karhunen–Loève (KL) expansion, and the concentration field is represented by Lagrange polynomials of random variables in the KL expansion. After employing the stochastic collocation method (SCM), stochastic governing advection–dispersion equations are reduced to a series of uncoupled deterministic equations. The concentration realizations can be obtained by sampling the established Lagrange polynomials instead of solving governing equations repeatedly. We assess the accuracy and computational efficiency of this method in comparison to the conditional Monte Carlo simulation. The influence of conditioning to hydraulic conductivity measurements on transport is analyzed. Numerical results demonstrate that the SCM can efficiently derive the conditional statistics of concentration as well as the probability of the aquifer to be contaminated. It is shown that the contamination risk is significantly influenced by measurements conditioning.

Qualification of Uncertainty for Simulating Solute Transport in the Heterogeneous Media with Sparse Grid Collocation Method

The sparse grid collocation method is discussed to qualify the uncertainty of solute transport. The Karhunen-Loeve (KL) expansion is employed to decompose the log transformed hydraulic conductivity. The head, velocity and concentration fields are represented by the Lagrange polynomial expansion. A sparse grid collocation method is then used to reduce the original stochastic partial differential equations to a set of deterministic equations which is collocated at selected interpolation (collocation) points. The collocation points are constructed by the Smolyak algorithm. The accuracy, efficiency and convergence property of sparse grid collocation method are investigated by numerical experiments. The analysis shows that stochastic collocation strategy helps to decouple stochastic computations, and all the numerical computation is possible to be implemented by existing deterministic finite element codes. The proposed method provides an efficient way to evaluate the uncertainty of the solute transport in the heterogeneous media.

Deriving adaptive operating rules of hydropower reservoirs using time‐varying parameters generated by the EnKF

Operating rules have been used widely to decide reservoir operations because of their capacity for coping with uncertain inflow. However, stationary operating rules lack adaptability; thus, under changing environmental conditions, they cause inefficient reservoir operation. This paper derives adaptive operating rules based on time-varying parameters generated using the ensemble Kalman filter (EnKF). A deterministic optimization model is established to obtain optimal water releases, which are further taken as observations of the reservoir simulation model. The EnKF is formulated to update the operating rules sequentially, providing a series of time-varying parameters. To identify the index that dominates the variations of the operating rules, three hydrologic factors are selected: the reservoir inflow, ratio of future inflow to current available water, and available water. Finally, adaptive operating rules are derived by fitting the time-varying parameters with the identified dominant hydrologic factor. Chinas Three Gorges Reservoir was selected as a case study. Results show that (1) the EnKF has the capability of capturing the variations of the operating rules, (2) reservoir inflow is the factor that dominates the variations of the operating rules, and (3) the derived adaptive operating rules are effective in improving hydropower benefits compared with stationary operating rules. The insightful findings of this study could be used to help adapt reservoir operations to mitigate the effects of changing environmental conditions.

Comparison of Noniterative Algorithms Based on Different Forms of Richards’ Equation

Through linearizing an implicit differencing scheme, several noniterative numerical solutions of Richards’ equation in different forms are derived here. Paniconi et al. (Water Resources Research, 27(6), 1147–1163, 1991) have developed a first-order accurate linearization of the head-based Richards’ equation (RE) and a second-order accurate linearization of the implicit-factored head-based RE. Considering other forms of RE, we propose a second-order accurate linearization of the moisture-based RE and a second-order accurate linearization of the mixed form RE combined with the primary variable switching technique. Extensive comparisons between the noniterative solutions are conducted through three numerical experiments. Their accuracies, efficiencies, and mass balance behaviors are analyzed. The results indicate that the first-order accurate scheme is not efficient compared to iterative models. The noniterative schemes of head-based RE suffer from the mass imbalance problem without iteration. The linearized moisture-based RE can obtain mass conservative, accurate results effectively, while it may confront numerical problems when the soil approaches saturation. Among these noniterative schemes, the linearized mixed form RE combined with the primary variable switching technique is superior in terms of accuracy, mass balance, and efficiency compared to traditional iterative methods.

STOCHASTIC ANALYSIS OF GROUNDWATER FLOW SUBJECT TO RANDOM BOUNDARY CONDITIONS

A stochastic model was developed to simulate the flow in heterogeneous media subject to random boundary conditions. Approximate partial differential equations were derived based on the Karhunen-Loeve (KL) expansion and perturbation expansion. The effect of random boundary conditions on the two-dimensional flow was examined. It is shown that the proposed stochastic model is efficient to include the random boundary conditions. The random boundaries lead to the increase of head variance and velocity variance. The influence of the random boundary conditions on head uncertainty is exerted over the whole simulated region, while the randomness of the boundary conditions leads to the increase of the velocity variance in the vicinity of boundaries.

A Reduced‐Order Successive Linear Estimator for Geostatistical Inversion and its Application in Hydraulic Tomography

National Natural Science Foundation of China [51779179, 51609173, 51479144, 51522904]; CRDF [DAA2-15-61224-1]; Tianjin Normal University from the Thousand Talents Plan of Tianjin City; Special Fund for Public Industry Research from Ministry of Land and Resources of China [201511047]

Effect of low‐concentration rhamnolipid biosurfactant on Pseudomonas aeruginosa transport in natural porous media

The effect of low-concentrations of monorhamnolipid biosurfactant on transport of Pseudomonas aeruginosa ATCC 9027 in natural porous media (silica sand and a sandy soil) was studied with miscible-displacement experiments using artificial groundwater as the background solution. Transport of two types of cells was investigated, glucose- and hexadecane-grown cells with lower and higher cell surface hydrophobicity (CSH), respectively. The effect of hexadecane presence as a residual non-aqueous phase liquid (NAPLs) on transport was also examined. A clean-bed colloid deposition model was used to calculate deposition rate coefficients (k) for quantitative assessment. Significant cell retention was observed in the sand (81% and 82% for glucose- and hexadecane-grown cells, respectively). Addition of a low-concentration rhamnolipid solution enhanced cell transport, with 40 mg/L of rhamnolipid reducing retention to 50% and 60% for glucose- and hexadecane-grown cells, respectively. The k values for both glucose- and hexadecane-grown cells correlate linearly with rhamnolipid-dependent CSH represented as bacterial-adhesion-to-hydrocarbon rate of cells. Retention of cells by the soil was nearly complete (>99%). Addition of 40 mg/L rhamnolipid solution reduced retention to 95%. The presence of NAPLs in the sand increased the retention of hexadecane-grown cells with higher CSH. Transport of cells in the presence of the NAPL was enhanced by rhamnolipid at all concentrations tested, and the relative enhancement was greater than in was in the absence of NAPL. This study shows the importance of hydrophobic interaction on bacterial transport in natural porous media and the potential of using low-concentration rhamnolipid for facilitating the transport in subsurface for bioaugmentation efforts.

A New ArcGIS-Based Software of Uncertainty Analysis for Nitrate Load Estimation

Domestic waste water treatment using Onsite Sewage Treatment and Disposal Systems (OSTDS) (also known as septic systems) is a source of nitrogen contamination in groundwater and surface water. Estimating nutrient load from septic systems as a storm water source to surface water bodies is important to reduce nutrient load in support of Total Maximum Daily Load (TMDL) programs. Software packages of nitrate load estimation using geographic information systems (GIS) have gained popularity, not only because a GIS is efficient to process and integrate spatial data but also because skills required for applying GIS-based software are widely available. Recently, Rios et al. (2013a) developed an ArcGIS-Based Nitrate Load Estimation Toolkit (ArcNLET) to simulate nitrate transport in groundwater and to estimate nitrate load from septic systems to surface water bodies. However, the load estimates are inherently uncertain, and impacts of the uncertainty on TMDLrelated decision making have not been well studied. Uncertainty analysis for GIS-simulated results is of particular importance, because GIS is frequently used as a decision support system. Conducting uncertainty analyses within GIS environments has become popular, owing to recent development of GIS tools and technologies for coupling GIS with methods and tools of uncertainty analysis. This paper presents a new software package, ArcNLET-MC (MC stands for Monte Carlo), developed by Rios et al. (2013b) to analyze uncertainty in nitrate

Data assimilation of soil water flow by considering multiple uncertainty sources and spatial–temporal features: a field-scale real case study

Accurate estimates of soil moisture and soil hydraulic parameters via data assimilation largely depend on the quality of the model structure, input data and observations. Often, however, all of this information is subject to uncertainty under real circumstances. This real-case study seeks to understand the effects of different uncertainty sources and observation scales on data assimilation performance. Ensemble Kalman filter method based on the soil water-flow model, a sub-module of soil–water–atmosphere–plant model, is established to simultaneously estimate the model states and parameters. The soil hydraulic parameters are extensively measured or calibrated to examine the parameter estimation accuracy. Furthermore, considering the high spatial and temporal variability of soil moisture observation in the field-scale problem, an analysis of spatiotemporal characteristics is combined with data assimilation. Results indicated that simultaneously considering parameter and initial conditions uncertainty leads to a better soil moisture and parameter estimation than that ignoring initial uncertainty in realistic practice. Unlike the other error sources, an inadequate description to the meteorological forcing has a negative influence on surface soil moisture estimation, which might be attributed to the persistent disturbances of evaporation uncertainty and the lack of observations at shallow soil depth. Moreover, a prior knowledge of spatiotemporal features of soil moisture observation is beneficial to efficiently improve data assimilation performance. It is possible to implement field-scale data assimilation with a few representative points, instead of using the spatial average of all observations at a high cost. The assimilation results highlight the possibly positive outcomes of accounting for the multi-source of uncertainties and emphasize the significant importance of characterizing the spatial–temporal feature of soil moisture for a field-scale application.

Impact of kinetic mass transfer on free convection in a porous medium

We investigate kinetic mass transfer effects on unstable density-driven flow and transport processes by numerical simulations of a modified Elder problem. The first-order dual-domain mass transfer model coupled with a variable-density-flow model is employed to describe transport behavior in porous media. Results show that in comparison to the no-mass-transfer case, a higher degree of instability and more unstable system is developed in the mass transfer case due to the reduced effective porosity and correspondingly a larger Rayleigh number (assuming permeability is independent on the mobile porosity). Given a constant total porosity, the magnitude of capacity ratio (i.e., immobile porosity/mobile porosity) controls the macroscopic plume profile in the mobile domain, while the magnitude of mass transfer timescale (i.e., the reciprocal of the mass transfer rate coefficient) dominates its evolution rate. The magnitude of capacity ratio plays an important role on the mechanism driving the mass flux into the aquifer system. Specifically, for a small capacity ratio, solute loading is dominated by the density-driven transport, while with increasing capacity ratio local mass transfer dominated solute loading may occur at later times. At significantly large times, however, both mechanisms contribute comparably to solute loading. Sherwood Number could be a nonmonotonic function of mass transfer timescale due to complicated interactions of solute between source zone, mobile zone and immobile zone in the top boundary layer, resulting in accordingly a similar behavior of the total mass. The initial assessment provides important insights into unstable density-driven flow and transport in the presence of kinetic mass transfer.