Sensitivity analysis of EUROSEM using Monte Carlo simulation I: hydrological,soil and vegetation parameters

Knowledge about model uncertainty is essential for erosion modelling and provides important information when it comes to parameterizing models. In this paper a sensitivity analysis of the European soil erosion model (EUROSEM) is carried out using Monte Carlo simulation, suitable for complex non‐linear models, using time‐dependent driving variables. The analysis revealed some important characteristics of the model. The variability of the static output parameters was generally high, with the hydrologic parameters being the most important ones, especially saturated hydraulic conductivity and net capillary drive followed by the percentage basal area for the hydrological and vegetation parameters and detachability and cohesion for the soil erosion parameters. Overall, sensitivity to vegetation parameters was insignificant. The coefficient of variation for the sedigraph was higher than for the hydrograph, especially from the beginning of the rainstorm and up to the peak, and may explain difficulties encountered when trying to match simulated hydrographs and sedigraphs with observed ones. The findings from this Monte Carlo simulation calls for improved within‐storm modelling of erosion processes in EUROSEM. Information about model uncertainty will be incorporated in a new EUROSEM user interface. Copyright © 2000 John Wiley & Sons, Ltd.     

Random Monte Carlo simulation analysis and risk assessment for ammonia concentrations in wastewater effluent disposal

High concentrations of ammonia in a river can cause fish kills and harms to other aquatic organisms. A simple water quality model is needed to predict the probability of ammonia concentration violations as compared to the US Environmental Protection Agencys ammonia criteria. A spreadsheet with Random Monte Carlo (RMC) simulations to model ammonia concentrations at the mixing point (between a river and the effluent of a wastewater treatment plant) was developed with the use of Microsoft Excel and Crystal Ball add-in software. The model uses effluent and river ammonia, alkalinity, and total carbonate data to determine the probability density functions (PDFs) for the Monte Carlo simulations. Normal, lognormal, exponential and uniform probability distributions were tested using the Chi-square method and p-value associated with it to choose the best fit to the random data selected from the East Burlington wastewater treatment plant in North Carolina and the Clinch River in Tennessee. It is suggested that different options be tested with a minimum of three classes and a maximum of n/5 classes (n = number of data points) and the highest probability (p-value) for the PDF being tested be chosen. The results indicted that six violations to the EPA criterion for maximum concentration (CMC) were predicted when using 2000 RMC simulations and PDFs fitted to the available data, which violate the current criterion of no more than one violation over 3 years. All violations occur when the pH of the blend ranges from 8.0 to 9.0. No violations were found to the criteria of chronic concentration (CCC) using RMC.     

Probabilistic evaluation of flood hazard in urban areas using Monte Carlo simulation

The goal of the presented research was the derivation of flood hazard maps, using Monte Carlo simulation of flood propagation at an urban site in the UK, specifically an urban area of the city of Glasgow. A hydrodynamic model describing the propagation of flood waves, based on the De Saint Venant equations in two‐dimensional form capable of accounting for the topographic complexity of the area (preferential outflow paths, buildings, manholes, etc.) and for the characteristics of prevailing imperviousness typical of the urban areas, has been used to derive the hydrodynamic characteristics of flood events (i.e. water depths and flow velocities). The knowledge of the water depth distribution and of the current velocities derived from the propagation model along with the knowledge of the topographic characteristics of the urban area from digital map data allowed for the production of hazard maps based on properly defined hazard indexes. These indexes are evaluated in a probabilistic framework to overcome the classical problem of single deterministic prediction of flood extent for the design event and to introduce the concept of the likelihood of flooding at a given point as the sum of data uncertainty, model structural error and parameterization uncertainty. Copyright © 2011 John Wiley & Sons, Ltd.     

GPU加速的水体辐射传输Monte Carlo模拟模型研究

水体辐射传输方程是复杂的微积分方程,只能利用数值方法求解,如Monte Carlo光线追踪法、不变嵌入法、离散坐标法等,其中,Monte Carlo方法是目前解决水体水下光场三维问题的唯一有效方法.根据辐射传输理论,开发了水下光场的Monte Carlo模拟模型,主要包含大气、水-气界面、层化水体和水底边界4个模块.实现了模拟任意太阳角度、不同水体固有光学属性和任意深度条件下,考虑大气、粗糙水面和水底边界的水下光场,能够获取辐亮度、辐照度等辐射量的空间分布.该模型暂不考虑Raman散射、偏振、内部光源的影响.实现了GPU加速水下光场Monte Carlo模拟,并用Mobley等提出的海洋光学标准问题中的问题1~6进行验证.在两种计算环境下,通过对不同边界条件下的CPU、GPU运行时间及加速比的对比,发现GPU计算可以达到几百至上千倍的加速比.     

Effects of rock fragment cover on hydrological processes under rainfall simulation in a semi‐arid region of China

Rock fragment cover has long been an important agricultural crop production technique on the Loess Plateau, China. Although this approach plays an important role in controlling hydrological processes and preventing soil erosion, inconsistent results have been recovered in this field. In this study, we investigated the effects of rock fragment cover on infiltration, run‐off, soil erosion, and hydraulic parameters using rainfall simulation in the field in a semi‐arid region of China. Two field plots encompassing 6 rock fragment coverages (0%, 10%, 20%, 25%, 30%, and 40%), as well as 2 rock fragment positions and sizes were exposed to rainfall at a particular intensity (60 mm h^?1). The results of this study showed that increasing the rock fragment coverage with rock fragments resting on the soil surface increased infiltration but decreased run‐off generation and sediment yield. A contrasting result was found, however, when rock fragments were partially embedded into the soil surface; in this case, a positive relationship between rock fragment coverage and run‐off rate as well as a nonmonotonic relationship with respect to soil loss rate was recovered. The size of rock fragments also exerted a positive effect on run‐off generation and sediment yield but had a negative effect on infiltration. At the same time, both mean flow velocity and Froude number decreased with increasing rock fragment coverage regardless of rock fragment position and size, whereas both Manning roughness and Darcy–Weisbach friction factor were positively correlated. Results show that stream power is the most sensitive hydraulic parameter affecting soil loss. Combined with variance analysis, we concluded that the order of significance of rock fragment cover variables was position followed by coverage and then size. We also quantitatively incorporated the effects of rock fragment cover on soil loss via the C and K factors in the Revised Universal Soil Loss Equation. Overall, this study will enable the development of more accurate modelling approaches and lead to a better understanding of hydrological processes under rock fragment cover conditions.     

Evaluation of typhoon‐induced rainfall using nonparametric Monte Carlo simulation and locally weighted polynomial regression

Typhoons in Korea are the major causes of natural disasters in the Korean peninsula. In this study, rainfall generated by typhoons was quantitatively analysed using various statistical methods. First, the frequency analysis of rainfall induced by typhoons was carried out to calculate the design rainfall. Second, the frequency analysis of simulated rainfall derived by nonparametric Monte Carlo simulation (NMCS) was performed to evaluate the uncertainty of rainfall caused by typhoons. Third, the regression relationship between the physical characteristic factors of typhoons and rainfall was established by locally weighted polynomial regression (LWPR), and the characteristic factors of typhoons were simulated. The simulated characteristic factors were then used to estimate rainfall and to calculate the design rainfall by typhoons. Comparative analyses of design rainfalls as estimated using various statistical methods were performed. The LWPR showed good performance in terms of reproducing typhoon characteristics. Therefore, the combined NMCS and LWPR method suggested in this study can be used as a supplementary technique for assessing extreme rainfall with climate change and reflected variability. Copyright © 2010 John Wiley & Sons, Ltd.     

Development of probability distributions for urban hydrologic model parameters and a Monte Carlo analysis of model sensitivity

This paper proposes an approach to estimating the uncertainty related to EPA Storm Water Management Model model parameters, percentage routed (P_R) and saturated hydraulic conductivity (K_sat), which are used to calculate stormwater runoff volumes. The methodology proposed in this paper addresses uncertainty through the development of probability distributions for urban hydrologic parameters through extensive calibration to observed flow data in the Philadelphia collection system. The established probability distributions are then applied to the Philadelphia Southeast district model through a Monte Carlo approach to estimate the uncertainty in prediction of combined sewer overflow volumes as related to hydrologic model parameter estimation. Understanding urban hydrology is critical to defining urban water resource problems. A variety of land use types within Philadelphia coupled with a history of cut and fill have resulted in a patchwork of urban fill and native soils. The complexity of urban hydrology can make model parameter estimation and defining model uncertainty a difficult task. The development of probability distributions for hydrologic parameters applied through Monte Carlo simulations provided a significant improvement in estimating model uncertainty over traditional model sensitivity analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimating the effects of spatial variability of infiltration on the output of a distributed runoff and soil erosion model using Monte Carlo methods

Monte Carlo procedures were used to evaluate the effects of spatial variations in the values of the infiltration parameter on the results of the ANSWERS distributed runoff and erosion model. Simulation results obtained were compared with measured values. Field infiltration measurements indicated spatial correlation at much smaller distances than the size of an element. Therefore, at first only the error of the mean had to be taken into consideration for block infiltration rates. Consequently, not only single hydrographs were produced, but also error bands. Secondly, nine other hypothetical spatial correlation structures were also evaluated using Monte Carlo methods. in particular at low nugget variances, increasing spatial correlation of infiltration resulted in increasing coefficients of variation in model outputs. In general, rainstorms with low rainfall intensities were more difficult to simulate accurately than extreme events with high rainfall intensities. This is explained by the greater influence of the infiltration uncertainties at low rainfall intensities.     

Standardized uncertainty analysis for hydrometry: a review of relevant approaches and implementation examples

Abstract

The water-centric community has continuously made efforts to identify, assess and implement rigorous uncertainty analyses for routine hydrological measurements. This paper reviews some of the most relevant efforts and subsequently demonstrates that the Guide to the expression of uncertainty in measurement (GUM) is a good candidate for estimation of uncertainty intervals for hydrometry. The demonstration is made by implementing the GUM to typical hydrometric applications and comparing the analysis results with those obtained using the Monte Carlo method. The results show that hydrological measurements would benefit from the adoption of the GUM as the working standard, because of its soundness, the availability of software for practical implementation and potential for extending the GUM to hydrological/hydraulic numerical simulations.

Editor D. Koutsoyiannis

Citation Muste, M., Lee, K. and Bertrand-Krajewski, J.-L., 2012. Standardized uncertainty analysis for hydrometry: a review of relevant approaches and implementation examples. Hydrological Sciences Journal, 57 (4), 643–667.     

Sensitivity and uncertainty analysis of a sediment transport model: a global approach

Computerized sediment transport models are frequently employed to quantitatively simulate the movement of sediment materials in rivers. In spite of the deterministic nature of the models, the outputs are subject to uncertainty due to the inherent variability of many input parameters in time and in space, along with the lack of complete understanding of the involved processes. The commonly used first-order method for sensitivity and uncertainty analyses is to approximate a model by linear expansion at a selected point. Conclusions from the first-order method could be of limited use if the model responses drastically vary at different points in parameter space. To obtain the global sensitivity and uncertainty features of a sediment transport model over a larger input parameter space, the Latin hypercubic sampling technique along with regression procedures were employed. For the purpose of illustrating the methodologies, the computer model HEC2-SR was selected in this study. Through an example application, the results about the parameters sensitivity and uncertainty of water surface, bed elevation and sediment discharge were discussed.     

Effects of spatially structured vegetation patterns on hillslope erosion in a semiarid Mediterranean environment: a simulation study

A general trend of decreasing soil loss rates with increasing vegetation cover fraction is widely accepted. Field observations and experimental work, however, show that the form of the cover‐erosion function can vary considerably, in particular for low cover conditions that prevail on arid and semiarid hillslopes. In this paper the structured spatial distribution of the vegetation cover and associated soil attributes is proposed as one of the possible causes of variation in cover–erosion relationships, in particular in dryland environments where patchy vegetation covers are common. A simulation approach was used to test the hypothesis that hillslope discharge and soil loss could be affected by variation in the spatial correlation structure of coupled vegetation cover and soil patterns alone. The Limburg Soil Erosion Model (LISEM) was parameterized and verified for a small catchment with discontinuous vegetation cover at Rambla Honda, SE Spain. Using the same parameter sets LISEM was subsequently used to simulate water and sediment fluxes on 1 ha hypothetical hillslopes with simulated spatial distributions of vegetation and soil parameters. Storms of constant rainfall intensity in the range of 30–70 mm h^?1 and 10–30 min duration were applied. To quantify the effect of the spatial correlation structure of the vegetation and soil patterns, predicted discharge and soil loss rates from hillslopes with spatially structured distributions of vegetation and soil parameters were compared with those from hillslopes with spatially uniform distributions. The results showed that the spatial organization of bare and vegetated surfaces alone can have a substantial impact on predicted storm discharge and erosion. In general, water and sediment yields from hillslopes with spatially structured distributions of vegetation and soil parameters were greater than from identical hillslopes with spatially uniform distributions. Within a storm the effect of spatially structured vegetation and soil patterns was observed to be highly dynamic, and to depend on rainfall intensity and slope gradient. Copyright © 2005 John Wiley & Sons, Ltd.     

The representation of sediment source group tracer distributions in Monte Carlo uncertainty routines for fingerprinting: An analysis of accuracy and precision using data for four contrasting catchments

Previous studies comparing sediment fingerprinting un-mixing models report large differences in their accuracy. The representation of tracer concentrations in source groups is perhaps the largest difference between published studies. However, the importance of decisions concerning the representation of tracer distributions has not been explored explicitly. Accordingly, potential sediment sources in four contrasting catchments were intensively sampled. Virtual sample mixtures were formed using between 10 and 100% of the retrieved samples to simulate sediment mobilization and delivery from subsections of each catchment. Source apportionment used models with a transformed multivariate normal distribution, normal distribution, 25th–75th percentile distribution and a distribution replicating the retrieved source samples. The accuracy and precision of model results were quantified and the reasons for differences were investigated. The 25th–75th percentile distribution produced the lowest mean inaccuracy (8.8%) and imprecision (8.5%), with the Sample Based distribution being next best (11.5%; 9.3%). The transformed multivariate (16.9%; 17.3%) and untransformed normal distributions (16.3%; 20.8%) performed poorly. When only a small proportion of the source samples formed the virtual mixtures, accuracy decreased with the 25th–75th percentile and Sample Based distributions so that when <20% of source samples were used, the actual mixture composition infrequently fell outside of the range of uncertainty shown in un-mixing model outputs. Poor performance was due to combined random Monte Carlo numbers generated for all tracers not being viable for the retrieved source samples. Trialling the use of a 25th–75th percentile distribution alongside alternatives may result in significant improvements in both accuracy and precision of fingerprinting estimates, evaluated using virtual mixtures. Caution should be exercised when using a normal type distribution, without exploration of alternatives, as un-mixing model performance may be unacceptably poor.     

Effects of rock fragments incorporated in the soil matrix on concentrated flow hydraulics and erosion

Rock fragments can act as a controlling factor for erosional rates and patterns in the landscape. Thus, the objective of this study is to better understand the role that rock fragments incorporated into the soil matrix play in concentrated flow hydraulics and erosion. Laboratory flume experiments were conducted with soil material that was mixed with rock fragments. Rock fragment content ranged from 0 to 40 per cent by volume. Other treatments were slope (7 and 14%) and flow discharge (5·7 and 11·4 l min^?1). An increase in rock fragment content resulted in lower sediment yield, and broader width of flow. Rock fragment cover at the soil surface, i.e. surface armour, increased with time in experiments with rock fragments. Flow energy was largely dissipated by rock fragment cover. For more turbulent flow conditions, when roughness elements were submerged in the flow, hydraulic roughness was similar for different rock fragment contents. In experiments with few or no rock fragments a narrow rill incised. Flow energy was dissipated by headcuts. Total sediment yield was much larger than for experiments with rock fragments in the soil. Adding just a small number of rock fragments in the soil matrix resulted in a significant reduction of sediment yield. Copyright © 2007 John Wiley & Sons, Ltd.     

Comprehensive evaluation of regional flood frequency analysis by L- and LH-moments. II. Development of LH-moments parameters for the generalized Pareto and generalized logistic distributions

As part II of a sequence of two papers, previously developed L-moments by Hosking (1990), and the LH-moments by Wang (1997) are further investigated. The LH-moments (L to L₄) are used to develop the regional parameters of the generalized extreme value distribution, generalized Pareto (GPA) distribution and the generalized logistic (GLO) distributions. These respective probability distribution functions (PDFs) are evaluated in terms of their performances. Flood peaks by the corresponding PDFs are compared with those generated by Monte Carlo simulation of randomized data, considering the respective LH-moments. The influence of the LH-moments on estimated PDFs are studied by evaluating the relative bias (RBIAS) in quantile estimation due to variability of the k parameter. Karkhe watershed located in western Iran was used as a case study area. Part I of this study identified the study area as regions A and B. The minimum calculated relative root mean square error (RRMSE) and RBIAS between simulated flood peaks and flood peaks by the corresponding PDFs were used in PDF selection, considering the respective LH-moments. The boxplots of the RRMSE tests identified the L₃ level of the GPA distribution as the suitable PDF for sample sizes 20 and 80; for region A. Similar results were found for the RBIAS test. As for region B, the boxplots of the RRMSE tests indicated similar results for the three PDFs. However, the boxplots of the RBIAS tests identified the L₄ level of the GLO most suitable for sample sizes 20 and 80. Relative efficiencies of the LH-moments were investigated, measured as RRMSE ratios of L-moments over the respective LH-moments. For the most parts the findings of this part of the study were similar to those of part I.     

Sensitivity analyses of a distributed catchment model to verify the model structure

Sensitivity analyses are valuable tools for identifying important model parameters, testing the model conceptualization, and improving the model structure. They help to apply the model efficiently and to enable a focussed planning of future research and field measurement. Two different methods were used for sensitivity analyses of the complex process-oriented model TAC^D (tracer aided catchment model, distributed) that was applied to the meso-scale Brugga basin (40 km²) and the sub-basin St Wilhelmer Talbach (15.2 km²). Five simulations periods were investigated: two summer events, two snow melt induced events and one summer low flow period. The model was applied using 400 different parameter sets, which were generated by Monte Carlo simulations using latin hypercube sampling. The regional sensitivity analysis (RSA) allowed determining the most significant parameters for the complete simulation periods using a graphical method. The results of the regression-based sensitivity analysis were more detailed and complex. The temporal variability of the simulation sensitivity could be observed continuously and the significance of the parameters could be determined in a quantitative way. A dependency of the simulation sensitivity on initial- and boundary conditions and the temporal and spatial variability of the sensitivity to some model parameters was revealed by the regression-based sensitivity analysis. Thus, the difficulty of transferring the results to different time periods or model applications in other catchments became obvious. The analysis of the temporal course of the simulation sensitivity to parameter values in conjunction with simulated and measured additional data sets (precipitation, temperature, reservoir volumes etc.) gave further insight into the internal model behaviour and demonstrated the plausibility of the model structure and process conceptionalizations.     

Seismic performance sensitivity and uncertainty analysis of gravity dams

Uncertainties in structural engineering are often arising from the modeling assumptions and errors, or from variability in input loadings. A practical approach for dealing with them is to perform sensitivity and uncertainty analysis in the framework of stochastic and probabilistic methods. These analyses can be statically and dynamically performed through nonlinear static pushover and IDA techniques, respectively. Of the existing structures, concrete gravity dams are infrastructures which may encounter many uncertainties. In this research, probabilistic analysis of the seismic performance of gravity dams is presented. The main characteristics of the nonlinear tensile behavior of mass concrete, along with the intensity of earthquake excitations are considered as random variables in the probabilistic analysis. Using the tallest non‐overflow monolith of the Pine Flat gravity dam as a case study, its response under static and dynamic situations is reliably examined utilizing different combinations of parameters in the material and the seismic loading. The sensitivity analysis reveals the relative importance of each parameter independently. It will be shown that the undamaged modulus of elasticity and tensile strength of mass concrete have more significant roles on the seismic resistance of the dam than the ultimate inelastic tensile strain. In order to propagate the parametric uncertainty to the actual seismic performance of the dam, probabilistic simulation methods such as Monte Carlo simulation with Latin hypercube sampling, and approximate moment estimation techniques will be used. The final results illustrate the possibility of using a mean‐parameter dam model to estimate the mean seismic performance of the dam. Copyright © 2014 John Wiley & Sons, Ltd.     

中国西部湖泊水量对未来气候变化的响应--蒙特卡罗概率法在气候模拟输出的应用

基于CGCM2对未来100年气候的9个模拟试验,对中国半干旱地区青海湖、岱海和呼伦湖及其流域,运用蒙特卡罗分析法模拟湖泊水量对气候变化的响应以及相应的概率.结果表明,从2020s,2050s和2080s三个时期温度增加的发生频率高于75%的分布看,温度将稳定增加2-5℃.未来的年平均温度增幅将超过了过去50年的观测记录,与过去一万年期间高温期的变化幅度相当.三个时期75%以上发生频率的温度和降水变化将会分别引起青海湖流域为-5%至 10%,呼伦湖流域为-7%至 5%,岱海流域为 2%至 12%的降水变化.虽然未来年降水总量的变幅没有超过过去50年器测记录变幅,更不及全新世的降水变化量,但湖泊水量对气候变化的反映变率较变幅要大.模拟的气候变化在75%概率的情况下,未来3个湖泊水量将有累计30%-45%的变化,变幅在±10%之间.快速的湖泊水量变化不能不引起对不远未来的水资源状况的重视和警备.     

A simulation study to examine the sensitivity of the Pettitt test to detect abrupt changes in mean

Abstract

The Pettitt test is a non-parametric test that has been used in a number of hydroclimatological studies to detect abrupt changes in the mean of the distribution of the variable of interest. This test is based on the Mann-Whitney two-sample test (rank-based test), and allows the detection of a single shift at an unknown point in time. This test is often used to detect shifts in extremes because of the lack of distributional assumptions. However, the downside of not specifying a distribution is that the Pettitt test may be inefficient in detecting breaks when dealing with extremes. Here we adopt a Monte Carlo approach to examine the sensitivity of the Pettitt test in detecting shifts in the mean under different conditions (location of the break within the series, magnitude of the shift, record length, level of variability in the data, extreme vs non-extreme records, and pre-assigned significance level). These simulation results show that the sensitivity of this test in detecting abrupt changes increases with the increase in the magnitude of the shift and record length. The number of detections is higher when the time series represents the central part of the distribution (e.g. changes in the time series of medians), while the skill decreases as we move toward either low or high extremes (e.g. changes in the time series of maxima). Furthermore, the number of detections decreases as the variability in the data increases. Finally, abrupt changes are more easily detected when they occur toward the center of the time series.

Editor D. Koutsoyiannis Associate editor K. Hamed     

Cancer risk analysis and assessment of trihalomethanes in drinking water

This study conducts risk assessment for an array of health effects that may result from exposure to disinfection by-products (DBPs). An analysis of the relationship between exposure and health-related outcomes is conducted. The trihalomethanes (THMs) species have been verified as the principal DBPs in the drinking water disinfection process. The data used in this study was collected from the Taiwan Water Corporation (TWC) from 1998 to 2002. Statistical analysis, multistage of Benchmark model, Monte Carlo simulation (MCS) and sensitive analysis were used to estimate the cancer risk analysis and assessment. This study included the statistical data analysis, epidemiology investigation and cancer risk assessment of THMs species in drinking water in Taiwan. It is more significant to establish an assessment procedure for the decision making in policy of drinking water safety predominantly.     

Quantifying fine‐grained sediment sources in the River Axe catchment,southwest England: application of a Monte Carlo numerical modelling framework incorporating local and genetic algorithm optimisation

Increasing recognition of the deleterious environmental effects of excessive fine sediment delivery to watercourses means that reliable sediment source assessment represents a fundamental component of catchment planning targeting the protection of freshwater resources and their ecological integrity. Sediment tracing or fingerprinting approaches have been increasingly used to provide catchment scale sediment source information, but there is a need to continue refining existing procedures especially with respect to uncertainty analysis during mass balance modelling. Consequently, an updated Monte Carlo numerical modelling framework was devised and tested, incorporating both conventional and robust statistics coupled with random and Latin Hypercube Sampling (LHS) together with local and genetic algorithm (GA) optimisation. A sediment sourcing study undertaken in the River Axe catchment, southwest England, suggested that the use of robust statistics and LHS with GA optimisation generated the best performance with respect to predicting measured bed sediment geochemistry in six out of eight model applications. On this basis, the catchment‐wide average median sediment source contributions were predicted to be 38 ± 1% (pasture topsoils), 3 ± 1% (cultivated topsoils), 37 ± 1% (damaged road verges) and 22 ± 1% (channel banks/subsurface sources). Using modelling frameworks which provide users with flexibility to compare local and global optimisation during uncertainty analysis is recommended for future sediment tracing studies. Copyright © 2011 John Wiley & Sons, Ltd.