The eddy covariance (EC) technique was used to measure half hourly fluxes of energy and evaporation from 15 December 2007 to 30 November 2008 at the Scott Research Farm, located 7 km east of Hamilton. Many other supporting measurements of climate and soil variables were also made. The research addressed three objectives: 1. To examine the accuracy of the eddy covariance measurement technique. 2. Understand the surface partitioning of energy and water vapour on a diurnal to annual timescale. 3. Compare measurements of evaporation to methods of estimation. Average energy balance closure at Scott Farm was deficient by 24%, comparable to published studies of up to 30%. Three lysimeter studies were carried out to help verify eddy covariance data. These resulted in the conclusions that; 1) lysimeter pots needed to be deeper to allow for vegetation rooting depths to be encompassed adequately; 2) forcing energy balance closure was not supported by two of the studies (summer and winter); 3) latent heat flux (λE) gap filling of night time EC data during winter over estimated values by about 10 W m-2; and 4) the spring lysimeter study verified eddy covariance measurements including the closure forcing method. Some uncertainty still exists as to the accuracy of both lysimeter and EC methods of evaporation measurement because both methods still have potential biases, however for the purpose of this study, it would appear data are sufficiently accurate to have confidence in results. Energy and water vapour fluxes varied on both a diurnal and seasonal timescale. Diurnally, fluxes were small or negative at night and were highest during the day, usually at solar noon. Seasonally, spring and summer had the highest energy and evaporation fluxes and winter rates were small but tended to exceed available energy supply. Evaporation was constrained by soil moisture availability during summer and by energy availability during winter. Estimated annual evaporation at Scott Farm was 755 mm, 72% of precipitation. Two evaporation models were compared to eddy covariance evaporation (EEC) measurements; the FAO56 Penman-Monteith model (Eo) and the Priestley-Taylor model (EPT). Both models over estimated evaporation during dry conditions and slightly under estimated during winter. The α coefficient that is applied to EPT was not constant and a seasonally adjusted value would be most appropriate. A crop coefficient of 1.13 is needed for Eo measurements during moist conditions. Eo began over estimating evaporation when soil moisture contents dropped below ~44%. A water stress adjustment was applied to both models which improved evaporation estimates, however early onset of drying was not able to be adjusted for. The adjusted Eo model is the most accurate overall, when compared to EEC.

This dissertation focuses on the further development of creating accurate numerical models of complex dynamical systems using the holistic discretisation technique [Roberts, Appl. Num. Model., 37:371-396, 2001]. I extend the application from second to fourth order systems and from only one spatial dimension in all previous work to two dimensions (2D). We see that the holistic technique provides useful and accurate numerical discretisations on coarse grids. We explore techniques to model the evolution of spatial patterns governed by pdes such as the Kuramoto-Sivashinsky equation and the real-valued Ginzburg-Landau equation. We aim towards the simulation of fluid flow and convection in three spatial dimensions. I show that significant steps have been taken in this dissertation towards achieving this aim. Holistic discretisation is based upon centre manifold theory [Carr, Applications of centre manifold theory, 1981] so we are assured that the numerical discretisation accurately models the dynamical system and may be constructed systematically. To apply centre manifold theory the domain is divided into elements and using a homotopy in the coupling parameter, subgrid scale fields are constructed consisting of actual solutions of the governing partial differential equation(pde). These subgrid scale fields interact through the introduction of artificial internal boundary conditions. View the centre manifold (macroscale) as the union of all states of the collection of subgrid fields (microscale) over the physical domain. Here we explore how to extend holistic discretisation to the fourth order Kuramoto-Sivashinsky pde. I show that the holistic models give impressive accuracy for reproducing the steady states and time dependent phenomena of the Kuramoto-Sivashinsky equation on coarse grids. The holistic method based on local dynamics compares favourably to the global methods of approximate inertial manifolds. The excellent performance of the holistic models shown here is strong evidence in support of the holistic discretisation technique. For shear dispersion in a 2D channel a one-dimensional numerical approximation is generated directly from the two-dimensional advection-diffusion dynamics. We find that a low order holistic model contains the shear dispersion term of the Taylor model [Taylor, IMA J. Appl. Math., 225:473-477, 1954]. This new approach does not require the assumption of large x scales, formerly absolutely crucial in deriving the Taylor model. I develop holistic discretisation for two spatial dimensions by applying the technique to the real-valued Ginzburg-Landau equation as a representative example of second order pdes. The techniques will apply quite generally to second order reaction-diffusion equations in 2D. This is the first study implementing holistic discretisation in more than one spatial dimension. The previous applications of holistic discretisation have developed algebraic forms of the subgrid field and its evolution. I develop an algorithm for numerical construction of the subgrid field and its evolution for 1D and 2D pdes and explore various alternatives. This new development greatly extends the class of problems that may be discretised by the holistic technique. This is a vital step for the application of the holistic technique to higher spatial dimensions and towards discretising the Navier-Stokes equations.

There are many different types of non-alcoholic beverages (NAB) available in the United States today compared to a decade ago. Additionally, the needs of beverage consumers have evolved over the years centering attention on functionality and health dimensions. These trends in volume of consumption are a testament to the growth in the NAB industry. Our study pertains to ten NAB categories. We developed and employed a unique cross-sectional and time-series data set based on Nielsen Homescan data associated with household purchases of NAB from 1998 through 2003. First, we considered demographic and economic profiling of the consumption of NAB in a two-stage model. Race, region, age and presence of children and gender of household head were the most important factors affecting the choice and level of consumption. Second, we used expectation-prediction success tables, calibration, resolution, the Brier score and the Yates partition of the Brier score to measure the accuracy of predictions generated from qualitative choice models used to model the purchase decision of NAB by U.S. households. The Yates partition of the Brier score outperformed all other measures. Third, we modeled demand interrelationships, dynamics and habits of NAB consumption estimating own-price, cross-price and expenditure elasticities. The Quadratic Almost Ideal Demand System, the synthetic Barten model and the State Adjustment Model were used. Soft drinks were substitutes and fruit juices were complements for most of non-alcoholic beverages. Investigation of a proposed tax on sugar-sweetened beverages revealed the importance of centering attention not only to direct effects but also to indirect effects of taxes on beverage consumption. Finally, we investigated factors affecting nutritional contributions derived from consumption of NAB. Also, we ascertained the impact of the USDA year 2000 Dietary Guidelines for Americans associated with the consumption of NAB. Significant factors affecting caloric and nutrient intake from NAB were price, employment status of household head, region, race, presence of children and the gender of household food manager. Furthermore, we found that USDA nutrition intervention program was successful in reducing caloric and caffeine intake from consumption of NAB. The away-from-home intake of beverages and potential impacts of NAB advertising are not captured in our work. In future work, we plan to address these limitations.

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