A wavelet based approach for combining the outputs of different rainfall–runoff models

The rainfall–runoff modelling being a stochastic process in nature is dependent on various climatological variables and catchment characteristics and therefore numerous hydrological models have been developed to simulate this complex process. One approach to modelling this complex non-linear rainfall–runoff process is to combine the outputs of various models to get more accurate and reliable results. This multi-model combination approach relies on the fact that various models capture different features of the data, and hence combination of these features would yield better result. This study for the first time presented a novel wavelet based combination approach for estimating combined runoff The simulated daily output (Runoff) of five selected conventional rainfall–runoff models from seven different catchments located in different parts of the world was used in current study for estimating combined runoff for each time period. Five selected rainfall–runoff models used in this study included four data driven models, namely, the simple linear model, the linear perturbation model, the linearly varying variable gain factor model, the constrained linear systems with a single threshold and one conceptual model, namely, the soil moisture accounting and routing model. The multilayer perceptron neural network method was used to develop combined wavelet coupled models to evaluate the effect of wavelet transformation (WT). The performance of the developed wavelet coupled combination models was compared with their counterpart simple combination models developed without WT. It was concluded that the presented wavelet coupled combination approach outperformed the existing approaches of combining different models without applying input WT. The study also recommended that different models in a combination approach should be selected on the basis of their individual performance.     

Rainfall‐runoff modelling using artificial neural networks technique: a Blue Nile catchment case study

A rainfall‐runoff model based on an artificial neural network (ANN) is presented for the Blue Nile catchment. The best geometry of the ANN rainfall‐runoff model in terms of number of hidden layers and nodes is identified through a sensitivity analysis. The Blue Nile catchment (about 300 000 km²) in the Nile basin is selected here as a case study. The catchment is classified into seven subcatchments, and the mean areal precipitation over those subcatchments is computed as a main input to the ANN model. The available daily data (1992–99) are divided into two sets for model calibration (1992–96) and for validation (1997–99). The results of the ANN model are compared with one of physical distributed rainfall‐runoff models that apply hydraulic and hydrologic fundamental equations in a grid base. The results over the case study area and the comparative analysis with the physically based distributed model show that the ANN technique has great potential in simulating the rainfall‐runoff process adequately. Because the available record used in the calibration of the ANN model is too short, the ANN model is biased compared with the distributed model, especially for high flows. Copyright © 2005 John Wiley & Sons, Ltd.     

APPROXIMATING RAINFALL-RUNOFF MODELLING RESPONSE USING A STOCHASTIC INTEGRAL EQUATION

Rainfall-runoff modelling uncertainty can be analysed by the use of a stochastic integral formulation. The stochastic integral equation can be based on the rainfall–runoff model input of model rainfall or model rainfall excess. Similarly, the stochastic integral equation can be based on the rainfall–runoff model output of the modelled runoff hydrograph. The residual between actual measured runoff data and modelled runoff (from the rainfall–runoff model) is analysed here by the use of a stochastic integral equation. This approach is used to develop a set of convolution integral transfer function realizations that represent the chosen rainfall–runoff modelling error. The resulting stochastic integral component is a distribution of possible residual outcomes that may be directly added to the rainfall–runoff model's deterministic outcome, to develop a distribution of probable runoff hydrograph realizations from the chosen rainfall–runoff model.     

Modeling scale-dependent runoff generation in a small semi-arid watershed accounting for rainfall intensity and water depth

Observed scale effects of runoff on hillslopes and small watersheds derive from complex interactions of time-varying rainfall rates with runoff, infiltration and macro- and microtopographic structures. A little studied aspect of scale effects is the concept of water depth-dependent infiltration. For semi-arid rangeland it has been demonstrated that mounds underneath shrubs have a high infiltrability and lower lying compacted or stony inter-shrub areas have a lower infiltrability. It is hypothesized that runoff accumulation further downslope leads to increased water depth, inundating high infiltrability areas, which increases the area-averaged infiltration rate. A model was developed that combines the concepts of water depth-dependent infiltration, partial contributing area under variable rainfall intensity, and the Green–Ampt theory for point-scale infiltration. The model was applied to rainfall simulation data and natural rainfall–runoff data from a small sub-watershed (0.4 ha) of the Walnut Gulch Experimental Watershed in the semi-arid US Southwest. Its performance to reproduce observed hydrographs was compared to that of a conventional Green–Ampt model assuming complete inundation sheet flow, with runon infiltration, which is infiltration of runoff onto pervious downstream areas. Parameters were derived from rainfall simulations and from watershed-scale calibration directly from the rainfall–runoff events. The performance of the water depth-dependent model was better than that of the conventional model on the scale of a rainfall simulator plot, but on the scale of a small watershed the performance of both model types was similar. We believe that the proposed model contributes to a less scale-dependent way of modeling runoff and erosion on the hillslope-scale.     

Regional scale rainfall–runoff modeling using VARX–MGARCH approach

Multivariate time series modeling approaches are known as useful tools for describing, simulating, and forecasting hydrologic variables as well as their changes over the time. These approaches also have temporal and cross-sectional spatial dependence in multiple measurements. Although the application of multivariate linear and nonlinear time series approaches such as vector autoregressive with eXogenous variables (VARX) and multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) models are commonly used in financial and economic sciences, these approaches have not been extensively used in hydrology and water resources engineering. This study employed VARX and VARX–MGARCH approaches in modeling mean and conditional heteroscedasticity of daily rainfall and runoff records in the basin of Zarrineh Rood Dam, Iran. Bivariate diagonal VECH (DVECH) model, as a main type of MGARCH, shows how the conditional variance–covariance and conditional correlation structure vary over the time between residuals series of the fitted VARX. For this purpose, five model fits, which consider different combinations of twofold rainfall and runoff, including both upstream and downstream stations, have been investigated in the present study. The VARX model, with different orders, was applied to the daily rainfall–runoff process of the study area in each of these model fits. The Portmanteau test revealed the existence of conditional heteroscedasticity in the twofold residuals of fitted VARX models. Therefore, the VARX–DVECH model is proposed to capture the heteroscedasticity existing in the daily rainfall–runoff process. The bivariate DVECH model indicated both short-run and long-run persistency in the conditional variance–covariance matrix related to the twofold innovations of rainfall–runoff processes. Furthermore, the evaluation criteria for the VARX–DVECH model revealed the improvement of VARX model performance.     

A stochastic framework to assess the performance of flood warning systems based on rainfall‐runoff modeling

Nowadays, Flood Forecasting and Warning Systems (FFWSs) are known as the most inexpensive and efficient non‐structural measures for flood damage mitigation in the world. Benefit to cost of the FFWSs has been reported to be several times of other flood mitigation measures. Beside these advantages, uncertainty in flood predictions is a subject that may affect FFWS's reliability and the benefits of these systems. Determining the reliability of advanced flood warning systems based on the rainfall–runoff models is a challenge in assessment of the FFWS performance which is the subject of this study. In this paper, a stochastic methodology is proposed to provide the uncertainty band of the rainfall–runoff model and to calculate the probability of acceptable forecasts. The proposed method is based on Monte Carlo simulation and multivariate analysis of the predicted time and discharge error data sets. For this purpose, after the calibration of the rainfall–runoff model, the probability distributions of input calibration parameters and uncertainty band of the model are estimated through the Bayesian inference. Then, data sets of the time and discharge errors are calculated using the Monte Carlo simulation, and the probability of acceptable model forecasts is calculated by multivariate analysis of data using copula functions. The proposed approach was applied for a small watershed in Iran as a case study. The results showed using rainfall–runoff modeling based on real‐time precipitation is not enough to attain high performance for FFWSs in small watersheds, and it seems using weather forecasts as the inputs of rainfall–runoff models is essential to increase lead times and the reliability of FFWSs in small watersheds. Copyright © 2013 John Wiley & Sons, Ltd.     

Study of discontinuities in hydrological data using catastrophe theory

Abstract

Modelling and prediction of hydrological processes (e.g. rainfall–runoff) can be influenced by discontinuities in observed data, and one particular case may arise when the time scale (i.e. resolution) is coarse (e.g. monthly). This study investigates the application of catastrophe theory to examine its suitability to identify possible discontinuities in the rainfall–runoff process. A stochastic cusp catastrophe model is used to study possible discontinuities in the monthly rainfall–runoff process at the Aji River basin in Azerbaijan, Iran. Monthly-averaged rainfall and flow data observed over a period of 20 years (1981–2000) are analysed using the Cuspfit program. In this model, rainfall serves as a control variable and runoff as a behavioural variable. The performance of this model is evaluated using four measures: correlation coefficient, log-likelihood, Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results indicate the presence of discontinuities in the rainfall–runoff process, with a significant sudden jump in flow (cusp signal) when rainfall reaches a threshold value. The performance of the model is also found to be better than that of linear and logistic models. The present results, though preliminary, are promising in the sense that catastrophe theory can play a possible role in the study of hydrological systems and processes, especially when the data are noisy.

Citation Ghorbani, M. A., Khatibi, R., Sivakumar, B. & Cobb, L. (2010) Study of discontinuities in hydrological data using catastrophe theory. Hydrol. Sci. J. 55(7), 1137–1151.     

Fuzzy computing based rainfall–runoff model for real time flood forecasting

This paper analyses the skills of fuzzy computing based rainfall–runoff model in real time flood forecasting. The potential of fuzzy computing has been demonstrated by developing a model for forecasting the river flow of Narmada basin in India. This work has demonstrated that fuzzy models can take advantage of their capability to simulate the unknown relationships between a set of relevant hydrological data such as rainfall and river flow. Many combinations of input variables were presented to the model with varying structures as a sensitivity study to verify the conclusions about the coherence between precipitation, upstream runoff and total watershed runoff. The most appropriate set of input variables was determined, and the study suggests that the river flow of Narmada behaves more like an autoregressive process. As the precipitation is weighted only a little by the model, the last time‐steps of measured runoff are dominating the forecast. Thus a forecast based on expected rainfall becomes very inaccurate. Although good results for one‐step‐ahead forecasts are received, the accuracy deteriorates as the lead time increases. Using the one‐step‐ahead forecast model recursively to predict flows at higher lead time, however, produces better results as opposed to different independent fuzzy models to forecast flows at various lead times. Copyright © 2004 John Wiley & Sons, Ltd.     

Reservoir rainfall–runoff geomorphological model. I: application and parameter analysis

This article describes and formulates a model designed to simulate runoff in wet weather events, called reservoir rainfall–runoff geomorphological model (R³GeM). In these wetlands, soil saturation is the main mechanism for the generation of surface runoff. To determine the saturated areas, the model applies a relationship based on the topographic index, between watershed storage and saturated surface. Precipitation is separated into surface runoff by saturation, subsurface runoff and losses; then, the flow of surface and subsurface runoff is performed. This hydrological model has five parameters and has been implemented in 37 events in Aixola watershed and 15 in Oiartzun watershed, both located on the Cantabrian coast of Spain. We analysed the influence of these five parameters in their behaviour, and we have proven, noting the efficiency gains, that the proposed model is valid to simulate the rainfall–runoff process. Copyright © 2012 John Wiley & Sons, Ltd.     

A simple rainfall–runoff model based on hydrological units applied to the Teba catchment (south‐east Spain)

A hydrological model (YWB, yearly water balance) has been developed to model the daily rainfall–runoff relationship of the 202 km² Teba river catchment, located in semi‐arid south‐eastern Spain. The period of available data (1976–1993) includes some very rainy years with intensive storms (responsible for flooding parts of the town of Malaga) and also some very dry years. The YWB model is in essence a simple tank model in which the catchment is subdivided into a limited number of meaningful hydrological units. Instead of generating per unit surface runoff resulting from infiltration excess, runoff has been made the result of storage excess. Actual evapotranspiration is obtained by means of curves, included in the software, representing the relationship between the ratio of actual to potential evapotranspiration as a function of soil moisture content for three soil texture classes. The total runoff generated is split between base flow and surface runoff according to a given baseflow index. The two components are routed separately and subsequently joined. A large number of sequential years can be processed, and the results of each year are summarized by a water balance table and a daily based rainfall runoff time series. An attempt has been made to restrict the amount of input data to the minimum. Interactive manual calibration is advocated in order to allow better incorporation of field evidence and the experience of the model user. Field observations allowed for an approximate calibration at the hydrological unit level. Copyright © 2001 John Wiley & Sons, Ltd.     

Response analysis of rainfall–runoff processes using wavelet transform: a case study of the alpine meadow belt

Rainfall–runoff processes appear to be highly nonlinear in Bayinbluk watersheds of the northwestern China. In this study, the time‐scale wavelet transform has been used for the analysis of this nonstationary system. The Haar and Morlet wavelet transform were used to analyse the rainfall–runoff conversion relationship. Wavelet power spectrum and change point methods are also employed to analyse rainfall rates and runoffs measured at daily to half‐hourly sampling rate. The four experimental sites (Luoto, Haer, Kuce and Shengl) are located in the Tianshan Mountains (Xinjiang province, China). Correlation analysis and wavelet transform are first applied to runoff process in different underlying surfaces. Wavelet analyses of rainfall rates and runoffs also give meaningful information on the temporal variability of the rainfall–runoff relationship. Change point and wavelet power spectrum analysis provide simple interpretation of energy distribution between different scales. The results indicate that wavelet transform is a good method for analysing the nonlinear relationship of temporal–spatial responses between rainfall and runoff. This method allowed quantification of the processes affecting runoff and provided an insight into their implications in surface water management. Copyright © 2011 John Wiley & Sons, Ltd.     

The Runoff Declining Process and Water Quality in Songhuajiang River Catchment,China under Global Climatic Change

The runoff in Songhuajiang River catchment has experienced a decreasing trend during the second half of the 20th century. Serially complete daily rainfall data of 42 rainfall stations from 1959 to 2002 and daily runoff data of five meteorological stations from 1953 to 2005 were obtained. The Mann–Kendall trend test and the sequential version of Mann–Kendall test were employed in this study to test the monthly and annual trends for both rainfall and runoff, to determine the start point of abrupt runoff declining, and to identify the main driving factors of runoff decline. The results showed an insignificant increasing trend in rainfall but a significant decreasing trend in runoff in the catchment. For the five meteorological stations, abrupt runoff decline occurred during 1957–1963 and the middle 1990s. Through Mann–Kendall comparisons for the area‐rainfall and runoff for the two decreasing periods, human activity, rather than climatic change, is identified as the main driving factor of runoff decline. Analysis of land use/cover shows that farmland is most related with runoff decline among all the land use/cover change in Nenjiang catchment. From 1986 to 1995, the area of farmland increased rapidly from 6.99 to 7.61 million hm². Hydraulic engineering has a significant influence on the runoff decline in the second Songhuajiang catchment. Many large‐scale reservoirs and hydropower stations have been built in the upstream of the Second Songhuajiang and lead to the runoff decline. Nenjiang and the Second Songhuajiang are the two sources of mainstream of Songhuajiang. Decreased runoff in these two sub‐catchments then results in runoff decrease in mainstream of Songhuajiang catchment. It is, therefore, concluded that high percent agricultural land and hydraulic engineering are the most probable driving factors of runoff decline in Songhuajiang River catchment, China.     

Short‐term flood inundation prediction using hydrologic‐hydraulic models forced with downscaled rainfall from global NWP

A short‐term flood inundation prediction model has been formulated based on the combination of the super‐tank model, forced with downscaled rainfall from a global numerical weather prediction model, and a one‐dimensional (1D) hydraulic model. Different statistical methods for downscaled rainfall have been explored, taking into account the availability of historical data. It has been found that the full implementation of a statistical downscaling model considering physically‐based corrections to the numerical weather prediction model output for rainfall prediction performs better compared with an altitudinal correction method. The integration of the super‐tank model into the 1D hydraulic model demonstrates a minimal requirement for the calibration of rainfall–runoff and flood propagation models. Updating the model with antecedent rainfall and regular forecast renewal has enhanced the model's capabilities as a result of the data assimilation processes of the runoff and numerical weather prediction models. The results show that the predicted water levels demonstrate acceptable agreement with those measured by stream gauges and comparable to those reproduced using the actual rainfall. Moreover, the predicted flood inundation depth and extent exhibit reasonably similar tendencies to those observed in the field. However, large uncertainties are observed in the prediction results in lower, flat portions of the river basin where the hydraulic conditions are not properly analysed by the 1D flood propagation model. Copyright © 2013 John Wiley & Sons, Ltd.     

A Bayesian method for missing rainfall estimation using a conceptual rainfall–runoff model

The estimation of missing rainfall data is an important problem for data analysis and modelling studies in hydrology. This paper develops a Bayesian method to address missing rainfall estimation from runoff measurements based on a pre-calibrated conceptual rainfall–runoff model. The Bayesian method assigns posterior probability of rainfall estimates proportional to the likelihood function of measured runoff flows and prior rainfall information, which is presented by uniform distributions in the absence of rainfall data. The likelihood function of measured runoff can be determined via the test of different residual error models in the calibration phase. The application of this method to a French urban catchment indicates that the proposed Bayesian method is able to assess missing rainfall and its uncertainty based only on runoff measurements, which provides an alternative to the reverse model for missing rainfall estimates.     

Assessment of Climate Change Impact on the Gharesou River Basin Using SWAT Hydrological Model

The evaluation of climate change and its side effects on the hydrological processes of the basin can increasingly help in dealing with the challenges that water resource managers and planners face in future courses. These side effects are investigated using the simulation of hydrological processes with the help of physical rainfall‐runoff model. Hydrological models provide a framework for examining the relationship between climate and water resources. This research aims at the investigation of the effect of climate change on the runoff of Gharesou, which is one of the main branches of the “Karkheh” River in Iran during the periods 2040–2069. To achieve this, the distributed hydrological model Soil and Water Assessment Tool (SWAT) – a model that is sensitive to the changes in land, water, and climate – has been used with the aim of evaluating the impact of climate change on the hydrology of the Gharesou Basin. For this reason, first, the continuous distributed model of rainfall‐runoff SWAT for the period 1971–2000 has been calibrated and validated. Next, with the aim of evaluating the impact of climate change and global warming on the basin hydrology for the period 2040–2069, HadCM3‐AR4 global climate model data under the A2 scenario – from the SRES scenario set‐haves been downscaled. Eventually, the downscaled climate data haves been introduced in the SWAT model, and the future runoff changes have been studied. The results showed that the temperature increases in most of the months, and the precipitation rate exhibits a change in the range of ±30%. Moreover, the produced runoff in this period changes from ?90 to 120% during different months.     

A Modified Neural Network for Improving River Flow Prediction/Un Réseau de Neurones Modifié pour Améliorer la Prévision de L'Écoulement Fluvial

Abstract

Artificial neural network (ANN) models provide huge potential for simulating nonlinear behaviour of hydrological systems. However, the potential of ANN is yet to be fully exploited due to the problems associated with improving the model generalization performance. Generalization refers to the ability of a neural network to correctly process input data that have not been used for calibrating the neural network model. In the hydrological context, better generalization performance implies higher precision of forecasting. The primary objectives of this study are to explore new measures for improving the generalization performance of an ANN-based rainfall–runoff model, and to evaluate the applicability of the new measures. A modified neural network model (entitled goal programming (GP) neural network) for modelling the rainfall–runoff process has been developed, in which three enhancements are made as compared to the widely-used backpropagation (BP) network. The three enhancements are (a) explicit integration of hydrological prior knowledge into the neural network learning; (b) incorporation of a modified training objective function; and (c) reduction of network sensitivity to input errors. Seven watersheds across a range of climatic conditions and watershed areas in China were selected for examining the alternative networks. The results demonstrate that the GP consistently outperformed the BP both in the calibration and verification periods and three proposed measures yielded improvement of performance.     

Rainfall–runoff simulation using a normalized antecedent precipitation index

Abstract

The normalized antecedent precipitation index (NAPI) model by Heggen for the prediction of runoff yield is analytically derived from the water balance equation. Heggen's model has been simplified further to a rational form and its performance verified with the Soil Conservation Service Curve Number (SCS-CN) model. The simplified model has three coefficients specific to a watershed, and requires two inputs: rainfall and the derived parameter, NAPI. The characteristic behaviour of the NAPI has resonance with the curve number (CN) of the SCS model. The proposed NAPI model was applied to three watersheds in the semi-arid region of India to simulate runoff yield. The model showed improved correlation between the observed and predicted runoff data compared to the SCS-CN model. The F test and paired t test also confirmed the reliability of the model with significance levels of 0.01 and 0.001%, respectively. The proposed model could be used successfully for rainfall–runoff modelling in a watershed.

Citation Ali, S., Ghosh, N. C. & Singh, R. (2010) Rainfall–runoff simulation using a normalized antecedent precipitation index. Hydrol. Sci. J. 55(2), 266–274.     

LINEAR RAINFALL–RUNOFF SYSTEM IDENTIFICATION WITH RAMIFICATIONS FOR MODELLING CATCHMENT PROCESSES

The convolution assumption between excess rainfall and runoff provides a framework in which catchment runoff can be predicted with reasonable accuracy and moderate computational cost. Associated with it, the deconvolution problem of estimating unitgraph ordinates from rainfall–runoff events involves a matrix with a particularly simple structure. This matrix structure is used here as a basis on which the ill-posed nature of deconvolution is analysed. As a result, based on a simple transform of the excess rainfall data, a very simple criterion is derived to test the degree to which deconvolution may yield a unit hydrograph estimate displaying spurious oscillations of large magnitude. This has practical implications as the solution to an ill-posed problem can be very sensitive to errors in the model and the data and therefore may need to be stabilized. Illustration of these issues is provided using published rainfall–runoff data.     

Use of the Connectivity of Runoff Model (CRUM) to investigate the influence of storm characteristics on runoff generation and connectivity in semi‐arid areas

Much attention has been given to the surface controls on the generation and transmission of runoff in semi‐arid areas. However, the surface controls form only one part of the system; hence, it is important to consider the effect that the characteristics of the storm event have on the generation of runoff and the transmission of flow across the slope. The impact of storm characteristics has been investigated using the Connectivity of Runoff Model (CRUM). This is a distributed, dynamic hydrology model that considers the hydrological processes relevant to semi‐arid environments at the temporal scale of a single storm event. The key storm characteristics that have been investigated are the storm duration, rainfall intensity, rainfall variability and temporal structure. This has been achieved through the use of a series of defined storm hydrographs and stochastic rainfall. Results show that the temporal fragmentation of high‐intensity rainfall is important for determining the travel distances of overland flow and, hence, the amount of runoff that leaves the slope as discharge. If the high‐intensity rainfall is fragmented, then the runoff infiltrates a short distance downslope. Longer periods of high‐intensity rainfall allow the runoff to travel further and, hence, become discharge. Therefore, storms with similar amounts of high‐intensity rainfall can produce very different amounts of discharge depending on the storm characteristics. The response of the hydrological system to changes in the rainfall characteristics can be explained using a four‐stage model of the runoff generation process. These stages are: (1) all water infiltrating, (2) the surface depression store filling or emptying without runoff occurring, (3) the generation and transmission of runoff and (4) the transmission of runoff without new runoff being generated. The storm event will move the system between the four stages and the nature of the rainfall required to move between the stages is determined by the surface characteristics. This research shows the importance of the variable‐intensity rainfall when modelling semi‐arid runoff generation. The amount of discharge may be greater or less than the amount that would have been produced if constant rainfall intensity is used in the model. Copyright © 2006 John Wiley & Sons, Ltd.     

Performance of a conceptual and physically based model in simulating the response of a semi‐urbanized watershed in San Antonio,Texas

The need for accurate hydrologic analysis and rainfall–runoff modelling tools has been rapidly increasing because of the growing complexity of operational hydrologic and hydraulic problems associated with population growth, rapid urbanization and expansion of agricultural activities. Given the recent advances in remote sensing of physiographic features and the availability of near real‐time precipitation products, rainfall–runoff models are expected to predict runoff more accurately. In this study, we compare the performance and implementation requirements of two rainfall–runoff models for a semi‐urbanized watershed. One is a semi‐distributed conceptual model, the Hydrologic Engineering Center‐Hydrologic Modelling System (HEC‐HMS). The other is a physically based, distributed‐parameter hydrologic model, the Gridded Surface Subsurface Hydrologic Analysis (GSSHA). Four flood events that took place on the Leon Creek watershed, a sub‐watershed of the San Antonio River basin in Texas, were used in this study. The two models were driven by the Multisensor Precipitation Estimator radar products. One event (in 2007) was used for HEC‐HMS and GSSHA calibrations. Two events (in 2004 and 2007) were used for further calibration of HEC‐HMS. Three events (in 2002, 2004 and 2010) were used for model validation. In general, the physically based, distributed‐parameter model performed better than the conceptual model and required less calibration. The two models were prepared with the same minimum required input data, and the effort required to build the two models did not differ substantially. Copyright © 2012 John Wiley & Sons, Ltd.