Flood frequency analysis by a bivariate model based on copulas

La adecuada estimación de avenidas de diseño asociadas a altos periodos de retorno es necesaria para el diseño y gestión de estructuras hidráulicas como presas. En la práctica, la estimación de estos cuantiles se realiza normalmente a través de análisis de frecuencia univariados, basados en su mayoría en el estudio de caudales punta. Sin embargo, la naturaleza de las avenidas es multivariada, siendo esencial tener en cuenta características representativas de las avenidas, tales como caudal punta, volumen y duración del hidrograma, con el fin de llevar a cabo un análisis apropiado; especialmente cuando el caudal de entrada se transforma en un caudal de salida diferente durante el proceso de laminación en un embalse o llanura de inundación. Los análisis de frecuencia de avenidas multivariados han sido tradicionalmente llevados a cabo mediante el uso de distribuciones bivariadas estándar con el fin de modelar variables correlacionadas. Sin embargo, su uso conlleva limitaciones como la necesidad de usar el mismo tipo de distribuciones marginales para todas las variables y la existencia de una relación de dependencia lineal entre ellas. Recientemente, el uso de cópulas se ha extendido en hidrología debido a sus beneficios en relación al contexto multivariado, permitiendo superar los inconvenientes de las técnicas tradicionales. Una copula es una función que representa la estructura de dependencia de las variables de estudio, y permite obtener la distribución de frecuencia multivariada de dichas variables mediante sus distribuciones marginales, sin importar el tipo de distribución marginal utilizada. La estimación de periodos de retorno multivariados, y por lo tanto, de cuantiles multivariados, también se facilita debido a la manera en la que las cópulas están formuladas. La presente tesis doctoral busca proporcionar metodologías que mejoren las técnicas tradicionales usadas por profesionales para estimar cuantiles de avenida más adecuados para el diseño y la gestión de presas, así como para la evaluación del riesgo de avenida, mediante análisis de frecuencia de avenidas bivariados basados en cópulas. Las variables consideradas para ello son el caudal punta y el volumen del hidrograma. Con el objetivo de llevar a cabo un estudio completo, la presente investigación abarca: (i) el análisis de frecuencia de avenidas local bivariado centrado en examinar y comparar los periodos de retorno teóricos basados en la probabilidad natural de ocurrencia de una avenida, con el periodo de retorno asociado al riesgo de sobrevertido de la presa bajo análisis, con el fin de proporcionar cuantiles en una estación de aforo determinada; (ii) la extensión del enfoque local al regional, proporcionando un procedimiento completo para llevar a cabo un análisis de frecuencia de avenidas regional bivariado para proporcionar cuantiles en estaciones sin aforar o para mejorar la estimación de dichos cuantiles en estaciones aforadas; (iii) el uso de cópulas para investigar tendencias bivariadas en avenidas debido al aumento de los niveles de urbanización en una cuenca; y (iv) la extensión de series de avenida observadas mediante la combinación de los beneficios de un modelo basado en cópulas y de un modelo hidrometeorológico. Accurate design flood estimates associated with high return periods are necessary to design and manage hydraulic structures such as dams. In practice, the estimate of such quantiles is usually done via univariate flood frequency analyses, mostly based on the study of peak flows. Nevertheless, the nature of floods is multivariate, being essential to consider representative flood characteristics, such as flood peak, hydrograph volume and hydrograph duration to carry out an appropriate analysis; especially when the inflow peak is transformed into a different outflow peak during the routing process in a reservoir or floodplain. Multivariate flood frequency analyses have been traditionally performed by using standard bivariate distributions to model correlated variables, yet they entail some shortcomings such as the need of using the same kind of marginal distribution for all variables and the assumption of a linear dependence relation between them. Recently, the use of copulas has been extended in hydrology because of their benefits regarding dealing with the multivariate context, as they overcome the drawbacks of the traditional approach. A copula is a function that represents the dependence structure of the studied variables, and allows obtaining the multivariate frequency distribution of them by using their marginal distributions, regardless of the kind of marginal distributions considered. The estimate of multivariate return periods, and therefore multivariate quantiles, is also facilitated by the way in which copulas are formulated. The present doctoral thesis seeks to provide methodologies that improve traditional techniques used by practitioners, in order to estimate more appropriate flood quantiles for dam design, dam management and flood risk assessment, through bivariate flood frequency analyses based on the copula approach. The flood variables considered for that goal are peak flow and hydrograph volume. In order to accomplish a complete study, the present research addresses: (i) a bivariate local flood frequency analysis focused on examining and comparing theoretical return periods based on the natural probability of occurrence of a flood, with the return period associated with the risk of dam overtopping, to estimate quantiles at a given gauged site; (ii) the extension of the local to the regional approach, supplying a complete procedure for performing a bivariate regional flood frequency analysis to either estimate quantiles at ungauged sites or improve at-site estimates at gauged sites; (iii) the use of copulas to investigate bivariate flood trends due to increasing urbanisation levels in a catchment; and (iv) the extension of observed flood series by combining the benefits of a copula-based model and a hydro-meteorological model.

Gray's model of personality and aggregate level factor analysis

Previous research shows that correlations tend to increase in magnitude when individuals are aggregated across groups. This suggests that uncorrelated constellations of personality variables (such as the primary scales of Extraversion and Neuroticism) may display much higher correlations in aggregate factor analysis. We hypothesize and report that individual level factor analysis can be explained in terms of Giant Three (or Big Five) descriptions of personality, whereas aggregate level factor analysis can be explained in terms of Gray's physiological based model. Although alternative interpretations exist, aggregate level factor analysis may correctly identify the basis of an individual's personality as a result of better reliability of measures due to aggregation. We discuss the implications of this form of analysis in terms of construct validity, personality theory, and its applicability in general. Copyright (C) 2003 John Wiley Sons, Ltd.

An advanced regularization methodology for use in watershed model calibration

A calibration methodology based on an efficient and stable mathematical regularization scheme is described. This scheme is a variant of so-called Tikhonov regularization in which the parameter estimation process is formulated as a constrained minimization problem. Use of the methodology eliminates the need for a modeler to formulate a parsimonious inverse problem in which a handful of parameters are designated for estimation prior to initiating the calibration process. Instead, the level of parameter parsimony required to achieve a stable solution to the inverse problem is determined by the inversion algorithm itself. Where parameters, or combinations of parameters, cannot be uniquely estimated, they are provided with values, or assigned relationships with other parameters, that are decreed to be realistic by the modeler. Conversely, where the information content of a calibration dataset is sufficient to allow estimates to be made of the values of many parameters, the making of such estimates is not precluded by preemptive parsimonizing ahead of the calibration process. White Tikhonov schemes are very attractive and hence widely used, problems with numerical stability can sometimes arise because the strength with which regularization constraints are applied throughout the regularized inversion process cannot be guaranteed to exactly complement inadequacies in the information content of a given calibration dataset. A new technique overcomes this problem by allowing relative regularization weights to be estimated as parameters through the calibration process itself. The technique is applied to the simultaneous calibration of five subwatershed models, and it is demonstrated that the new scheme results in a more efficient inversion, and better enforcement of regularization constraints than traditional Tikhonov regularization methodologies. Moreover, it is argued that a joint calibration exercise of this type results in a more meaningful set of parameters than can be achieved by individual subwatershed model calibration. (c) 2005 Elsevier B.V. All rights reserved.

A fuzzy AHP based integer linear programming model for the multi-criteria transshipment problem

Purpose – The purpose of this research is to develop a holistic approach to maximize the customer service level while minimizing the logistics cost by using an integrated multiple criteria decision making (MCDM) method for the contemporary transshipment problem. Unlike the prevalent optimization techniques, this paper proposes an integrated approach which considers both quantitative and qualitative factors in order to maximize the benefits of service deliverers and customers under uncertain environments. Design/methodology/approach – This paper proposes a fuzzy-based integer linear programming model, based on the existing literature and validated with an example case. The model integrates the developed fuzzy modification of the analytic hierarchy process (FAHP), and solves the multi-criteria transshipment problem. Findings – This paper provides several novel insights about how to transform a company from a cost-based model to a service-dominated model by using an integrated MCDM method. It suggests that the contemporary customer-driven supply chain remains and increases its competitiveness from two aspects: optimizing the cost and providing the best service simultaneously. Research limitations/implications – This research used one illustrative industry case to exemplify the developed method. Considering the generalization of the research findings and the complexity of the transshipment service network, more cases across multiple industries are necessary to further enhance the validity of the research output. Practical implications – The paper includes implications for the evaluation and selection of transshipment service suppliers, the construction of optimal transshipment network as well as managing the network. Originality/value – The major advantages of this generic approach are that both quantitative and qualitative factors under fuzzy environment are considered simultaneously and also the viewpoints of service deliverers and customers are focused. Therefore, it is believed that it is useful and applicable for the transshipment service network design.

A gloss composition and context clustering based distributed word sense representation model

In recent years, there has been an increasing interest in learning a distributed representation of word sense. Traditional context clustering based models usually require careful tuning of model parameters, and typically perform worse on infrequent word senses. This paper presents a novel approach which addresses these limitations by first initializing the word sense embeddings through learning sentence-level embeddings from WordNet glosses using a convolutional neural networks. The initialized word sense embeddings are used by a context clustering based model to generate the distributed representations of word senses. Our learned representations outperform the publicly available embeddings on half of the metrics in the word similarity task, 6 out of 13 sub tasks in the analogical reasoning task, and gives the best overall accuracy in the word sense effect classification task, which shows the effectiveness of our proposed distributed distribution learning model.

Evaluating Effects of Everglades Restoration on American Crocodile Populations in South Florida Using a Spatially-Explicit, Stage-Based Population Model

The distribution and abundance of the American crocodile (Crocodylus acutus) in the Florida Everglades is dependent on the timing, amount, and location of freshwater flow. One of the goals of the Comprehensive Everglades Restoration Plan (CERP) is to restore historic freshwater flows to American crocodile habitat throughout the Everglades. To predict the impacts on the crocodile population from planned restoration activities, we created a stage-based spatially explicit crocodile population model that incorporated regional hydrology models and American crocodile research and monitoring data. Growth and survival were influenced by salinity, water depth, and density-dependent interactions. A stage-structured spatial model was used with discrete spatial convolution to direct crocodiles toward attractive sources where conditions were favorable. The model predicted that CERP would have both positive and negative impacts on American crocodile growth, survival, and distribution. Overall, crocodile populations across south Florida were predicted to decrease approximately 3 % with the implementation of CERP compared to future conditions without restoration, but local increases up to 30 % occurred in the Joe Bay area near Taylor Slough, and local decreases up to 30 % occurred in the vicinity of Buttonwood Canal due to changes in salinity and freshwater flows.

Parametric CAD model based shape optimization using adjoint functions

Adjoint methods have proven to be an efficient way of calculating the gradient of an objective function with respect to a shape parameter for optimisation, with a computational cost nearly independent of the number of the design variables [1]. The approach in this paper links the adjoint surface sensitivities (gradient of objective function with respect to the surface movement) with the parametric design velocities (movement of the surface due to a CAD parameter perturbation) in order to compute the gradient of the objective function with respect to CAD variables.
For a successful implementation of shape optimization strategies in practical industrial cases, the choice of design variables or parameterisation scheme used for the model to be optimized plays a vital role. Where the goal is to base the optimization on a CAD model the choices are to use a NURBS geometry generated from CAD modelling software, where the position of the NURBS control points are the optimisation variables [2] or to use the feature based CAD model with all of the construction history to preserve the design intent [3]. The main advantage of using the feature based model is that the optimized model produced can be directly used for the downstream applications including manufacturing and process planning.
This paper presents an approach for optimization based on the feature based CAD model, which uses CAD parameters defining the features in the model geometry as the design variables. In order to capture the CAD surface movement with respect to the change in design variable, the “Parametric Design Velocity” is calculated, which is defined as the movement of the CAD model boundary in the normal direction due to a change in the parameter value.
The approach presented here for calculating the design velocities represents an advancement in terms of capability and robustness of that described by Robinson et al. [3]. The process can be easily integrated to most industrial optimisation workflows and is immune to the topology and labelling issues highlighted by other CAD based optimisation processes. It considers every continuous (“real value”) parameter type as an optimisation variable, and it can be adapted to work with any CAD modelling software, as long as it has an API which provides access to the values of the parameters which control the model shape and allows the model geometry to be exported. To calculate the movement of the boundary the methodology employs finite differences on the shape of the 3D CAD models before and after the parameter perturbation. The implementation procedure includes calculating the geometrical movement along a normal direction between two discrete representations of the original and perturbed geometry respectively. Parametric design velocities can then be directly linked with adjoint surface sensitivities to extract the gradients to use in a gradient-based optimization algorithm.
The optimisation of a flow optimisation problem is presented, in which the power dissipation of the flow in an automotive air duct is to be reduced by changing the parameters of the CAD geometry created in CATIA V5. The flow sensitivities are computed with the continuous adjoint method for a laminar and turbulent flow [4] and are combined with the parametric design velocities to compute the cost function gradients. A line-search algorithm is then used to update the design variables and proceed further with optimisation process.

Constructing stability landscapes to identify alternative states in coupled social-ecological agent-based models

The resilience of a social-ecological system is measured by its ability to retain core functionality when subjected to perturbation. Resilience is contextually dependent on the state of system components, the complex interactions among these components, and the timing, location, and magnitude of perturbations. The stability landscape concept provides a useful framework for considering resilience within the specified context of a particular social-ecological system but has proven difficult to operationalize. This difficulty stems largely from the complex, multidimensional nature of the systems of interest and uncertainty in system response. Agent-based models are an effective methodology for understanding how cross-scale processes within and across social and ecological domains contribute to overall system resilience. We present the results of a stylized model of agricultural land use in a small watershed that is typical of the Midwestern United States. The spatially explicit model couples land use, biophysical models, and economic drivers with an agent-based model to explore the effects of perturbations and policy adaptations on system outcomes. By applying the coupled modeling approach within the resilience and stability landscape frameworks, we (1) estimate the sensitivity of the system to context-specific perturbations, (2) determine potential outcomes of those perturbations, (3) identify possible alternative states within state space, (4) evaluate the resilience of system states, and (5) characterize changes in system-scale resilience brought on by changes in individual land use decisions.

Modeling the impact of potential vaccines on epidemics of sexually transmitted chlamydia trachomatis infection

Background. We investigated the likely impact of vaccines on the prevalence of and morbidity due to Chlamydia trachomatis (chlamydia) infections in heterosexual populations. Methods.An individual‐based mathematical model of chlamydia transmission was developed and linked to the infection course in chlamydia‐infected individuals. The model describes the impact of a vaccine through its effect on the chlamydial load required to infect susceptible individuals (the “critical load”), the load in infected individuals, and their subsequent infectiousness. The model was calibrated using behavioral, biological, and clinical data. Results.A fully protective chlamydia vaccine administered before sexual debut can theoretically eliminate chlamydia epidemics within 20 years. Partially effective vaccines can still greatly reduce the incidence of chlamydia infection. Vaccines should aim primarily to increase the critical load in susceptible individuals and secondarily to decrease the peak load and/or the duration of infection in vaccinated individuals who become infected. Vaccinating both sexes has a beneficial impact on chlamydia‐related morbidity, but targeting women is more effective than targeting men. Conclusions.Our findings can be used in laboratory settings to evaluate vaccine candidates in animal models, by regulatory bodies in the promotion of candidates for clinical trials, and by public health authorities in deciding on optimal intervention strategies.

The applicability of biased estimation in model and model order selection

Biased estimation has the advantage of reducing the mean squared error (MSE) of an estimator. The question of interest is how biased estimation affects model selection. In this paper, we introduce biased estimation to a range of model selection criteria. Specifically, we analyze the performance of the minimum description length (MDL) criterion based on biased and unbiased estimation and compare it against modern model selection criteria such as Kay's conditional model order estimator (CME), the bootstrap and the more recently proposed hook-and-loop resampling based model selection. The advantages and limitations of the considered techniques are discussed. The results indicate that, in some cases, biased estimators can slightly improve the selection of the correct model. We also give an example for which the CME with an unbiased estimator fails, but could regain its power when a biased estimator is used.

Port of Brisbane stormwater quality : stage 2 development of a port specific water quality model

Background: The quality of stormwater runoff from ports is significant as it can be an important source of pollution to the marine environment. This is also a significant issue for the Port of Brisbane as it is located in an area of high environmental values. Therefore, it is imperative to develop an in-depth understanding of stormwater runoff quality to ensure that appropriate strategies are in place for quality improvement, where necessary. To this end, the Port of Brisbane Corporation aimed to develop a port specific stormwater model for the Fisherman Islands facility. The need has to be considered in the context of the proposed future developments of the Port area. ----------------- The Project: The research project is an outcome of the collaborative Partnership between the Port of Brisbane Corporation (POBC) and Queensland University of Technology (QUT). A key feature of this Partnership is that it seeks to undertake research to assist the Port in strengthening the environmental custodianship of the Port area through ‘cutting edge’ research and its translation into practical application. ------------------ The project was separated into two stages. The first stage developed a quantitative understanding of the generation potential of pollutant loads in the existing land uses. This knowledge was then used as input for the stormwater quality model developed in the subsequent stage. The aim is to expand this model across the yet to be developed port expansion area. This is in order to predict pollutant loads associated with stormwater flows from this area with the longer term objective of contributing to the development of ecological risk mitigation strategies for future expansion scenarios. ----------------- Study approach: Stage 1 of the overall study confirmed that Port land uses are unique in terms of the anthropogenic activities occurring on them. This uniqueness in land use results in distinctive stormwater quality characteristics different to other conventional urban land uses. Therefore, it was not scientifically valid to consider the Port as belonging to a single land use category or to consider as being similar to any typical urban land use. The approach adopted in this study was very different to conventional modelling studies where modelling parameters are developed using calibration. The field investigations undertaken in Stage 1 of the overall study helped to create fundamental knowledge on pollutant build-up and wash-off in different Port land uses. This knowledge was then used in computer modelling so that the specific characteristics of pollutant build-up and wash-off can be replicated. This meant that no calibration processes were involved due to the use of measured parameters for build-up and wash-off. ---------------- Conclusions: Stage 2 of the study was primarily undertaken using the SWMM stormwater quality model. It is a physically based model which replicates natural processes as closely as possible. The time step used and catchment variability considered was adequate to accommodate the temporal and spatial variability of input parameters and the parameters used in the modelling reflect the true nature of rainfall-runoff and pollutant processes to the best of currently available knowledge. In this study, the initial loss values adopted for the impervious surfaces are relatively high compared to values noted in research literature. However, given the scientifically valid approach used for the field investigations, it is appropriate to adopt the initial losses derived from this study for future modelling of Port land uses. The relatively high initial losses will reduce the runoff volume generated as well as the frequency of runoff events significantly. Apart from initial losses, most of the other parameters used in SWMM modelling are generic to most modelling studies. Development of parameters for MUSIC model source nodes was one of the primary objectives of this study. MUSIC, uses the mean and standard deviation of pollutant parameters based on a normal distribution. However, based on the values generated in this study, the variation of Event Mean Concentrations (EMCs) for Port land uses within the given investigation period does not fit a normal distribution. This is possibly due to the fact that only one specific location was considered, namely the Port of Brisbane unlike in the case of the MUSIC model where a range of areas with different geographic and climatic conditions were investigated. Consequently, the assumptions used in MUSIC are not totally applicable for the analysis of water quality in Port land uses. Therefore, in using the parameters included in this report for MUSIC modelling, it is important to note that it may result in under or over estimations of annual pollutant loads. It is recommended that the annual pollutant load values given in the report should be used as a guide to assess the accuracy of the modelling outcomes. A step by step guide for using the knowledge generated from this study for MUSIC modelling is given in Table 4.6. ------------------ Recommendations: The following recommendations are provided to further strengthen the cutting edge nature of the work undertaken: * It is important to further validate the approach recommended for stormwater quality modelling at the Port. Validation will require data collection in relation to rainfall, runoff and water quality from the selected Port land uses. Additionally, the recommended modelling approach could be applied to a soon-to-be-developed area to assess ‘before’ and ‘after’ scenarios. * In the modelling study, TSS was adopted as the surrogate parameter for other pollutants. This approach was based on other urban water quality research undertaken at QUT. The validity of this approach should be further assessed for Port land uses. * The adoption of TSS as a surrogate parameter for other pollutants and the confirmation that the <150 m particle size range was predominant in suspended solids for pollutant wash-off gives rise to a number of important considerations. The ability of the existing structural stormwater mitigation measures to remove the <150 m particle size range need to be assessed. The feasibility of introducing source control measures as opposed to end-of-pipe measures for stormwater quality improvement may also need to be considered.

Assessing the leanness in product design : a model for planned design reuse

Shrinking product lifecycles, tough international competition, swiftly changing technologies, ever increasing customer quality expectation and demanding high variety options are some of the forces that drive next generation of development processes. To overcome these challenges, design cost and development time of product has to be reduced as well as quality to be improved. Design reuse is considered one of the lean strategies to win the race in this competitive environment. design reuse can reduce the product development time, product development cost as well as number of defects which will ultimately influence the product performance in cost, time and quality. However, it has been found that no or little work has been carried out for quantifying the effectiveness of design reuse in product development performance such as design cost, development time and quality. Therefore, in this study we propose a systematic design reuse based product design framework and developed a design leanness index (DLI) as a measure of effectiveness of design reuse. The DLI is a representative measure of reuse effectiveness in cost, development time and quality. Through this index, a clear relationship between reuse measure and product development performance metrics has been established. Finally, a cost based model has been developed to maximise the design leanness index for a product within the given set of constraints achieving leanness in design process.

Inciting the social imagination to realising the dream : An unfolding story of reform in a low-socioeconomic school

This paper presentation addresses design-based research that became a catalyst for social change among a disadvantaged school community. The aim of the longitudinal research was to protoype an evidence-based model for whole school digital and print literacy pedagogy renewal among students from low socioeconomic, Indigenous, and migrant backgrounds. Applying Anthony Gidden’s principle of the “duality of structure”, the paper presentation interprets how the collective agency of researchers and the school community began to transform the structural properties of the institution in a two-way dynamism, so that the structural properties of the school were not outside of individual action, but were implicated in its reproduction and transformation.

Nurses driving change to improve access to education and quality in lcinical teaching : A partnership between Australia and Viet Nam

In Viet Nam, standards of nursing care fail to meet international competency standards. This increases risks to patient safety (eg. hospital acquired infection), consequently the Ministry of Health identified the need to strengthen nurse education in Viet Nam. This paper presents experiences of a piloted clinical teaching model developed in Ha Noi, to strengthen nurse led institutional capacity for in-service education and clinical teaching. Historically 90% of nursing education was conducted by physicians and professional development in hospitals for nurses was limited. There was minimal communication between hospitals and nursing schools about expectations of students and assessment and quality of the learning experience. As a result when students came to the clinical sites, no-one understood how to plan their learning objectives and utilise teaching and learning approaches appropriate to their level. Therefore student learning outcomes were variable. They focussed on procedures and techniques and “learning how to do” rather than learning how to plan, implement and evaluate patient care. This project is part of a multi-component capacity building program designed to improve nurse education in Viet Nam. The project was funded jointly by Queensland University of Technology (QUT) and the Australian Agency for International Development. Its aim was to develop a collaborative clinically-based model of teaching to create an environment that encourages evidence-based, student-centred clinical learning. Accordingly, strategies introduced promoted clinical teaching of competency based nursing practice utilising the regionally endorsed nurse core competency standards. Thirty nurse teachers from Viet Duc University Hospital and Hanoi Medical College participated in the program. These nurses and nurse teachers undertook face to face education in three workshops, and completed three assessment items. Assessment was applied, where participants integrated the concepts learned in each workshop and completed assessment tasks related to planning, implementing and evaluating teaching in the clinical area. Twenty of these participants were then selected to undertake a two week study tour in Brisbane, Australia where the clinical teaching model was refined and an action plan developed to integrate into both organisations with possible implementation across Viet Nam. Participants on this study tour also experienced clinical teaching and learning at QUT by attending classes held at the university, and were able to visit selected hospitals to experience clinical teaching in these settings as well. Effectiveness of the project was measured throughout the implementation phase and in follow up visits to the clinical site. To date changes have been noted on an individual and organisational level. There is also significant planning underway to incorporate the clinical teaching model developed across the organisation and how this may be implemented in other regions. Two participants have also been involved in disseminating aspects of this approach to clinical teaching in Ho Chi Minh, with further plans for more in-depth dissemination to occur throughout the country.

Engineering-based modelling experiences in the elementary classroom

Introducing engineering-based model-eliciting experiences in the elementary curriculum is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results indicate that engineering model-eliciting activities can be introduced effectively into the elementary curriculum, providing rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.