A GIS‐based variable source area hydrology model

Effective control of nonpoint source pollution from contaminants transported by runoff requires information about the source areas of surface runoff. Variable source hydrology is widely recognized by hydrologists, yet few methods exist for identifying the saturated areas that generate most runoff in humid regions. The Soil Moisture Routing model is a daily water balance model that simulates the hydrology for watersheds with shallow sloping soils. The model combines elevation, soil, and land use data within the geographic information system GRASS, and predicts the spatial distribution of soil moisture, evapotranspiration, saturation‐excess overland flow (i.e., surface runoff), and interflow throughout a watershed. The model was applied to a 170 hectare watershed in the Catskills region of New York State and observed stream flow hydrographs and soil moisture measurements were compared to model predictions. Stream flow prediction during non‐winter periods generally agreed with measured flow resulting in an average r² of 0·73, a standard error of 0·01 m³/s, and an average Nash‐Sutcliffe efficiency R² of 0·62. Soil moisture predictions showed trends similar to observations with errors on the order of the standard error of measurements. The model results were most accurate for non‐winter conditions. The model is currently used for making management decisions for reducing non‐point source pollution from manure spread fields in the Catskill watersheds which supply New York City's drinking water. Copyright © 1999 John Wiley & Sons, Ltd.     

An analysis of the impact of spatial variability in rainfall on runoff and sediment predictions from a distributed model

This paper investigates the effect of introducing spatially varying rainfall fields to a hydrological model simulating runoff and erosion. Pairs of model simulations were run using either spatially uniform (i.e. spatially averaged) or spatially varying rainfall fields on a 500‐m grid. The hydrological model used was a simplified version of Thales which enabled runoff generation processes to be isolated from hillslope averaging processes. Both saturation excess and infiltration excess generation mechanisms were considered, as simplifications of actual hillslope processes. A 5‐year average recurrence interval synthetic rainfall event typical of temperate climates (Melbourne, Australia) was used. The erosion model was based on the WEPP interrill equation, modified to allow nonlinear terms relating the erosion rate to rainfall or runoff‐squared. The model results were extracted at different scales to investigate whether the effects of spatially varying rainfall were scale dependent. A series of statistical metrics were developed to assess the variability due to introducing the spatially varying rainfall field. At the catchment (approximately 150 km²) scale, it was found that particularly for saturation excess runoff, model predictions of runoff were insensitive to the spatial resolution of the rainfall data. Generally, erosion processes at smaller sub‐catchment scales, particularly when the sediment generation equation had non linearity, were more sensitive to spatial rainfall variability. Introducing runon infiltration reduced the total runoff and sediment yield at all scales, and this process was also most sensitive to the rainfall resolution. Copyright © 2011 John Wiley & Sons, Ltd.     

Predicting saturation‐excess runoff distribution with a lumped hillslope model: SWAT‐HS

Saturation‐excess runoff is the major runoff mechanism in humid well‐vegetated areas where infiltration rates often exceed rainfall intensity. Although the Soil and Water Assessment Tool (SWAT) is one of the most widely used models, it predicts runoff based mainly on soil and land use characteristics, and is implicitly an infiltration‐excess runoff type of model. Previous attempts to incorporate the saturation‐excess runoff mechanism in SWAT fell short due to the inability to distribute water from one hydrological response unit to another. This paper introduces a modified version of SWAT, referred to as SWAT‐Hillslope (SWAT‐HS). This modification improves the simulation of saturation‐excess runoff by redefining hydrological response units based on wetness classes and by introducing a surface aquifer with the ability to route interflow from “drier” to “wetter” wetness classes. Mathematically, the surface aquifer is a nonlinear reservoir that generates rapid subsurface stormflow as the water table in the surface aquifer rises. The SWAT‐HS model was tested in the Town Brook watershed in the upper reaches of the West Branch Delaware River in the Catskill region of New York, USA. SWAT‐HS predicted discharge well with a Nash‐Sutcliffe Efficiency of 0.68 and 0.87 for daily and monthly time steps. Compared to the original SWAT model, SWAT‐HS predicted less surface runoff and groundwater flow and more lateral flow. The saturated areas predicted by SWAT‐HS were concentrated in locations with a high topographic index and were in agreement with field observations. With the incorporation of topographic characteristics and the addition of the surface aquifer, SWAT‐HS improved streamflow simulation and gave a good representation of saturated areas on the dates that measurements were available. SWAT‐HS is expected to improve water quality model predictions where the location of the surface runoff matters.     

Do not only connect: a model of infiltration‐excess overland flow based on simulation

The paper focusses on connectivity in the context of infiltration‐excess overland flow and its integrated response as slope‐base overland flow hydrographs. Overland flow is simulated on a sloping surface with some minor topographic expression and spatially differing infiltration rates. In each cell of a 128 × 128 grid, water from upslope is combined with incident rainfall to generate local overland flow, which is stochastically routed downslope, partitioning the flow between downslope neighbours. Simulations show the evolution of connectivity during simple storms. As a first approximation, total storm runoff is similar everywhere, discharge increasing proportionally with drainage area. Moderate differences in plan topography appear to have only a second‐order impact on hydrograph form and runoff amount. Total storm response is expressed as total runoff, runoff coefficient or total volume infiltrated; each plotted against total storm rainfall, and allowing variations in average gradient, overland flow roughness, infiltration rate and storm duration. A one‐parameter algebraic expression is proposed that fits simulation results for total runoff, has appropriate asymptotic behaviour and responds rationally to the variables tested. Slope length is seen to influence connectivity, expressed as a scale distance that increases with storm magnitude and can be explicitly incorporated into the expression to indicate runoff response to simple events as a function of storm size, storm duration, slope length and gradient. The model has also been applied to a 10‐year rainfall record, using both hourly and daily time steps, and the implications explored for coarser scale models. Initial trails incorporating erosion continuously update topography and suggest that successive storms produce an initial increase in erosion as rilling develops, while runoff totals are only slightly modified. Other factors not yet considered include the dynamics of soil crusting and vegetation growth. Copyright © 2014 John Wiley & Sons, Ltd.     

Local‐ and field‐scale infiltration into vertically non‐uniform soils with spatially‐variable surface hydraulic conductivities

We studied the problem of local‐ and field‐scale infiltration over a particular class of heterogeneous soils. At the local scale, the soils are described as being vertically non‐uniform, with the saturated hydraulic conductivity continuously decreasing with depth according to a power law function. Analogous to the Green–Ampt model, analytical expressions are first developed for local‐scale infiltration using a sharp front approximation, and model results are compared with numerical solutions of the Richards equation. These results show that saturation does not occur from below in soils with such vertical non‐uniformity, thereby allowing for the use of a sharp front approximation. Because of vertical non‐uniformity, ponding conditions are achieved locally even for rainfall rates less than the surface saturated hydraulic conductivity. Furthermore, infiltration rates asymptotically approach zero at long times. To determine field‐scale infiltration properties, the spatial variability in the surface saturated hydraulic conductivity is represented by a log‐normal random field. Using cumulative infiltration as the independent variable, expressions are developed for the ensemble mean of field‐scale infiltration and the expected time for a given depth of water to infiltrate over the field. Surface horizontal heterogeneity is found to control field‐scale infiltration at small times, whereas local vertical non‐uniformity exerts a strong control at long times. Copyright © 2011 John Wiley & Sons, Ltd.     

A combined rainfall infiltration model based on Green–Ampt and SCS‐curve number

The Green–Ampt infiltration equation is an incomplete governing equation for rainfall infiltration due to the absence of an inertia term. The estimation of the capillary pressure head at the wetting front is difficult to determine. Thus, a major limitation of the Green–Ampt model is the constant, non‐zero surface ponding depth. This paper proposes an integrated rainfall infiltration model based on the Green–Ampt model and the SCS‐CN model. It achieves a complete governing equation for rainfall infiltration by momentum balance and the water budget based on the Green–Ampt assumption, and uses the curve number from the SCS‐CN method to calculate the initial abstraction, which is used as a basic parameter for the governing equation of the intensity of rainfall loss during the runoff period. The integrated rainfall infiltration model resolves the dilemma for capillary pressure head estimation, overcomes the limitation of constant, non‐zero surface ponding depth, and facilitates the calculation of runoff for individual flood simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Identifying and linking source areas of flow and P transport in dairy‐grazed headwater catchments,North Island,New Zealand

We examined the applicability of the critical‐source area (CSA) concept to the dairy‐grazed 192‐ha Upper Toenepi catchment and its 8·7‐ha Kiwitahi sub‐catchment, New Zealand. We evaluated if phosphorus (P) transport from land into stream is dominated by saturation‐excess (SE) and infiltration‐excess (IE) runoff during stormflow and by sub‐surface (<1·5 m depth) flows during baseflow. We measured stream flow and shallow groundwater levels, collected monthly stream, tile drain (TDA) and groundwater samples, and flow‐proportional stream samples from the Kiwitahi sub‐catchment, and determined their dissolved reactive phosphorus (DRP) and total phosphorus (TP) concentrations. In the Kiwitahi sub‐catchment, during storm events, IE contributions were significant. Contributions from SE appeared significant in the Upper Toenepi catchment. However, in both catchments, sub‐surface contributions dominated stormflow and baseflow periods. Absence of water table at the surface and the water table gradient towards the stream indicated that P transport during events was not limited to surface runoff. The dynamics of the groundwater table and the occurrence of SE areas were influenced by proximity to the stream and hillslope positions. Baseflow accounted for 42% of the annual flow in the Kiwitahi sub‐catchment, and contributed 37 and 52% to the DRP and TP loads, respectively. The P transport during baseflow appeared equally important as P losses from CSAs during stormflow. The close resemblance in P levels between groundwater and stream samples during baseflow demonstrates the importance of shallow groundwater for stream flow. In the Upper Toenepi catchment, contributions from effluent ponds (EFFs) dominated P loads. Management strategies should focus on controlling P release from EFFs, and on decreasing Olsen P concentrations in soil to minimize leaching of P via sub‐surface flow to streams. Research is needed to quantify the role of sub‐surface flow as well as to expand management strategies to minimize P transfers during stormflow and baseflow conditions. Copyright © 2010 John Wiley & Sons, Ltd.     

Development of a soil moisture‐based distributed hydrologic model for determining hydrologically based critical source areas

A simple grid cell‐based distributed hydrologic model was developed to provide spatial information on hydrologic components for determining hydrologically based critical source areas. The model represents the critical process (soil moisture variation) to run‐off generation accounting for both local and global water balance. In this way, it simulates both infiltration excess run‐off and saturation excess run‐off. The model was tested by multisite and multivariable evaluation on the 50‐km² Little River Experimental Watershed I in Georgia, U.S. and 2 smaller nested subwatersheds. Water balance, hydrograph, and soil moisture were simulated and compared to observed data. For streamflow calibration, the daily Nash‐Sutcliffe coefficient was 0.78 at the watershed outlet and 0.56 and 0.75 at the 2 nested subwatersheds. For the validation period, the Nash‐Sutcliffe coefficients were 0.79 at the watershed outlet and 0.85 and 0.83 at the 2 subwatersheds. The per cent bias was less than 15% for all sites. For soil moisture, the model also predicted the rising and declining trends at 4 of the 5 measurement sites. The spatial distribution of surface run‐off simulated by the model was mainly controlled by local characteristics (precipitation, soil properties, and land cover) on dry days and by global watershed characteristics (relative position within the watershed and hydrologic connectivity) on wet days when saturation excess run‐off was simulated. The spatial details of run‐off generation and travel time along flow paths provided by the model are helpful for watershed managers to further identify critical source areas of non‐point source pollution and develop best management practices.     

考虑降雨空间变化的随机产汇流模型

引入两个负指数型差值函数,估计降雨量的概率分布,以此描述流域降雨空间变异性问题.将降雨量空间统计分布与垂向混合产流模型耦合进行产流量计算,即对地表径流,采用超渗产流模式,根据降雨与土壤下渗能力的联合分布推求其空间分布;对地面以下径流,采用蓄满产流模式,以地表渗入量的均值作为输入,进行简化处理以提高其实用性;最终推导出总产流量概率分布函数计算公式.将流域概化成一个线性水库,并根据随机微分方程理论,推导任一计算时段洪水流量的概率分布,从而构建了一个完整的随机产汇流模型.以淮河支流黄泥庄流域为例进行应用研究,结果表明,该模型可提供洪水过程的概率预报,可用于防洪风险分析,若以概率分布的期望值作为确定性预报,亦具有较高精度.     

A field‐scale infiltration model accounting for spatial heterogeneity of rainfall and soil saturated hydraulic conductivity

This study first explores the role of spatial heterogeneity, in both the saturated hydraulic conductivity K_s and rainfall intensity r, on the integrated hydrological response of a natural slope. On this basis, a mathematical model for estimating the expected areal‐average infiltration is then formulated. Both K_s and r are considered as random variables with assessed probability density functions. The model relies upon a semi‐analytical component, which describes the directly infiltrated rainfall, and an empirical component, which accounts further for the infiltration of surface water running downslope into pervious soils (the run‐on effect). Monte Carlo simulations over a clay loam soil and a sandy loam soil were performed for constructing the ensemble averages of field‐scale infiltration used for model validation. The model produced very accurate estimates of the expected field‐scale infiltration rate, as well as of the outflow generated by significant rainfall events. Furthermore, the two model components were found to interact appropriately for different weights of the two infiltration mechanisms involved. Copyright © 2005 John Wiley & Sons, Ltd.     

A rainfall‐runoff model parameterized from GIS and runoff data

A guiding principle in hydrological modelling should be to keep the number of calibration parameters to a minimum. A reduced number of parameters to be calibrated, while maintaining the accuracy and detail required by modern hydrological models, will reduce parameter and model structure uncertainty and improve model diagnostics. In this study, the dynamics of runoff are derived from the distribution of distances from points in the catchments to the nearest stream. This distribution is unique for each catchment and can be determined from a geographical information system. The distribution of distances, will, when a celerity of (subsurface) flow is introduced, provide a distribution of travel times, or a unit hydrograph (UH). For spatially varying levels of saturation deficit, we have different celerities and, hence, different UHs. Runoff is derived from the superposition of the different UHs. This study shows how celerities can be estimated if we assume that recession events represent the combined UHs for different levels of saturation deficit. A new soil moisture routine which estimates saturated and unsaturated volumes of subsurface water and with only one parameter to calibrate is included in the new model. The performance of the new model is compared with that of the Swedish HBV model and is found to perform equally well for eight Norwegian catchments although the number of parameters to be calibrated in the module concerning soil moisture and runoff dynamics is reduced from seven in the HBV model to one in the new model. It is also shown that the new model has a more realistic representation of the subsurface hydrology. Copyright © 2013 John Wiley & Sons, Ltd.     

Influence of soil‐surface types on the overall runoff of the Tabernas badlands (south‐east Spain): field data and model approaches

The Tabernas desert, an extensive badlands area in Almeria province (south‐east Spain), is characterized by a high variability in soil surface cover and soil properties along with important topographical contrasts giving rise to a wide range of hydrological behaviour. A double approach through field monitoring and modelling has been used to ascertain the influence of soil‐surface variability on the overall hydrological response. Small plots were monitored for 3 years to assess runoff from the different surface types. Data provided by the long‐term monitoring of three small catchments formed by different soil surfaces were used to find out the specific contribution of each soil surface to the catchment runoff. A simple spatially distributed model was built to predict runoff generation based on the infiltration rate of each soil‐surface type (defined as terrain units with the same cover, the same soil type and on the same landform). Plot results prove that the soil surface units within the study area behave differently in terms of hydrological response to natural rainfall. These responses are explained by the types of cover, topographical characteristics and soil properties. When runoff events are simple (with one or two runoff peaks), the modelled hydrographs reproduce the hydrographs observed reasonably well, but in complex events (with several runoff peaks) the adjustment is not as good. The model also shows the influence of the spatial distribution of soil surfaces on the overall runoff, aiding exploration of the spatial hydrological relationships among different landscape units. Copyright © 2002 John Wiley & Sons, Ltd.     

Understanding subgrid variability of snow depth at 1‐km scale using Lidar measurements

It is well known that snow plays an important role in land surface energy balance; however, modelling the subgrid variability of snow is still a challenge in large‐scale hydrological and land surface models. High‐resolution snow depth data and statistical methods can reveal some characteristics of the subgrid variability of snow depth, which can be useful in developing models for representing such subgrid variability. In this study, snow depth was measured by airborne Lidar at 0.5‐m resolution over two mountainous areas in south‐western Wyoming, Snowy Range and Laramie Range. To characterize subgrid snow depth spatial distribution, measured snow depth data of these two areas were meshed into 284 grids of 1‐km × 1‐km. Also, nine representative grids of 1‐km × 1‐km were selected for detailed analyses on the geostatistical structure and probability density function of snow depth. It was verified that land cover is one of the important factors controlling spatial variability of snow depth at the 1‐km scale. Probability density functions of snow depth tend to be Gaussian distributions in the forest areas. However, they are eventually skewed as non‐Gaussian distribution, largely due to the no‐snow areas effect, mainly caused by snow redistribution and snow melt. Our findings show the characteristics of subgrid variability of snow depth and clarify the potential factors that need to be considered in modelling subgrid variability of snow depth.     

A semi‐distributed parallel‐type linear reservoir rainfall‐runoff model and its application in Taiwan

The main purpose of this paper is to introduce a semi‐distributed parallel surface rainfall‐runoff conceptual model. In this paper, a general solution of the instantaneous unit hydrograph (IUH) has been derived successfully for N linearly connected reservoirs, each having a different storage constant. The solution is a function of geomorphologic parameters, meteorologic factors and roughness coefficients. The model also takes into account the hydrologic response which is influenced by outflow downstream of a reservoir. For calibration, the shuffled complex evolution (SCE) algorithm is used to search for the global optimal parameters of the model. Because of the parallel structure, the mean roughness parameter of the channel becomes a “conceptual” parameter without a real physical meaning. To evaluate the adaptability of the model adopted, three watersheds around the city of Taipei in Taiwan were chosen to test the effectiveness of the model. The study provides an appropriate rainfall‐runoff model for planning flood mitigation in Taiwan. Copyright © 1999 John Wiley & Sons, Ltd.     

A kinematic‐wave‐based distributed watershed model using FEM,GIS and remotely sensed data

For the appropriate management of water resources in a watershed, it is essential to calculate the time distribution of runoff for the given rainfall event. In this paper, a kinematic‐wave‐based distributed watershed model using finite element method (FEM), geographical information systems (GIS) and remote‐sensing‐based approach is presented for the runoff simulation of small watersheds. The kinematic wave equations are solved using FEM for overland and channel flow to generate runoff at the outlet of the watershed concerned. The interception loss is calculated by an empirical model based on leaf area index (LAI). The Green‐Ampt Mein Larson (GAML) model is used for the estimation of infiltration. Remotely sensed data has been used to extract land use (LU)/land cover (LC). GIS have been used to prepare finite element grid and input files such as Manning's roughness and slope. The developed overland flow model has been checked with an analytical solution for a hypothetical watershed. The model has been applied to a gauged watershed and an ungauged watershed. From the results, it is seen that the model is able to simulate the hydrographs reasonably well. A sensitivity analysis of the model is carried out with the calibrated infiltration parameters, overland flow Manning's roughness, channel flow Manning's roughness, time step and grid size. The present model is useful in predicting the hydrograph in small, ungauged watersheds. Copyright © 2007 John Wiley & Sons, Ltd.     

Two‐dimensional physically based finite element runoff model for small agricultural watersheds: II. Model testing and field application

Mathematical models are useful analysis tools to understand problems in watersheds associated with runoff, and to find solutions through land use changes and best management practices. However, before a model is applied in the field, it must be tested and checked to ensure that the model represents the real world adequately. In this paper, a two‐dimensional physically based finite element runoff model ROMO2D has been verified and validated by comparing the model output with analytic solution under simplified conditions, published data, and field measurements. Calibration of the model was done manually through a multi‐objective calibration procedure, using observed field data. Before going for field validation/application of ROMO2D, analysis was carried out to determine the optimum number of finite elements into which the watershed should be discretized and the size of the time step. A sensitivity analysis of the model was performed using the observed values of watershed parameters. The model was applied to a 1·45 ha agricultural watershed located in the Shiwalik foothills (India) to simulate runoff. The results demonstrated the potential of the model to simulate runoff from small agricultural watersheds for individual storm events with reasonable accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

Scale effects of Hortonian overland flow and rainfall‐runoff dynamics: laboratory validation of a process‐based model

Hortonian runoff was measured in the laboratory from uniform slopes of lengths of 1·5, 3·0, and 6·0 m for steady, high‐intensity rainstorms with durations of 1·0 to 7·5 min. A clear reduction in runoff per unit slope length was found as slope lengths were increased. This effect becomes more pronounced with decreasing storm duration. The runoff data were used to validate a simple process‐based model that combines the Philip‐two‐term infiltration equation with the kinematic wave overland flow principle. The predicted and experimental results agreed well. Laboratory findings were extrapolated with the aid of the model to slopes and rainfall durations similar to those found under West African conditions. The calculated reduction of runoff per unit length is similar to reported observations. Thus, this process‐based model can largely explain the phenomenon of runoff reduction with increasing slope length. Copyright © 2002 John Wiley & Sons, Ltd.     

A physically based distributed subsurface–surface flow dynamics model for forested mountainous catchments

This study was designed to develop a physically based hydrological model to describe the hydrological processes within forested mountainous river basins. The model describes the relationships between hydrological fluxes and catchment characteristics that are influenced by topography and land cover. Hydrological processes representative of temperate basins in steep terrain that are incorporated in the model include intercepted rainfall, evaporation, transpiration, infiltration into macropores, partitioning between preferential flow and soil matrix flow, percolation, capillary rise, surface flow (saturation‐excess and return flow), subsurface flow (preferential subsurface flow and baseflow) and spatial water‐table dynamics. The soil–vegetation–atmosphere transfer scheme used was the single‐layer Penman–Monteith model, although a two‐layer model was also provided. The catchment characteristics include topography (elevation, topographic indices), slope and contributing area, where a digital elevation model provided flow direction on the steepest gradient flow path. The hydrological fluxes and catchment characteristics are modelled based on the variable source‐area concept, which defines the dynamics of the watershed response. Flow generated on land for each sub‐basin is routed to the river channel by a kinematic wave model. In the river channel, the combined flows from sub‐basins are routed by the Muskingum–Cunge model to the river outlet; these comprise inputs to the river downstream. The model was applied to the Hikimi river basin in Japan. Spatial decadal values of the normalized difference vegetation index and leaf area index were used for the yearly simulations. Results were satisfactory, as indicated by model efficiency criteria, and analysis showed that the rainfall input is not representative of the orographic lifting induced rainfall in the mountainous Hikimi river basin. Also, a simple representation of the effects of preferential flow within the soil matrix flow has a slight significance for soil moisture status, but is insignificant for river flow estimations. Copyright © 2005 John Wiley & Sons, Ltd.     

Field investigation and modelling of coupled stream discharge and shallow water‐table dynamics in a small Mediterranean catchment (Sardinia)

In the semi‐arid Mediterranean environment, the rainfall–runoff relationships are complex because of the markedly irregular patterns in rainfall, the seasonal mismatch between evaporation and rainfall, and the spatial heterogeneity in landscape properties. Watersheds often display considerable non‐linear threshold behavior, which still make runoff generation an open research question. Our objectives in this context were: to identify the primary processes of runoff generation in a small natural catchment; to test whether a physically based model, which takes into consideration only the primary processes, is able to predict spatially distributed water‐table and stream discharge dynamics; and to use the hydrological model to increase our understanding of runoff generation mechanisms. The observed seasonal dynamics of soil moisture, water‐table depth, and stream discharge indicated that Hortonian overland‐flow was negligible and the main mechanism of runoff generation was saturated subsurface‐flow. This gives rise to base‐flow, controls the formation of the saturated areas, and contributes to storm‐flow together with saturation overland‐flow. The distributed model, with a 1D scheme for the kinematic surface‐flow, a 2D sub‐horizontal scheme for the saturated subsurface‐flow, and ignoring the unsaturated flow, performed efficiently in years when runoff volume was high and medium, although there was a smoothing effect on the observed water‐table. In dry years, small errors greatly reduced the efficiency of the model. The hydrological model has allowed to relate the runoff generation mechanisms with the land‐use. The forested hillslopes, where the calibrated soil conductivity was high, were never saturated, except at the foot of the slopes, where exfiltration of saturated subsurface‐flow contributed to storm‐flow. Saturation overland‐flow was only found near the streams, except when there were storm‐flow peaks, when it also occurred on hillslopes used for pasture, where soil conductivity was low. The bedrock–soil percolation, simulated by a threshold mechanism, further increased the non‐linearity of the rainfall–runoff processes. Copyright © 2013 John Wiley & Sons, Ltd.