This is a study of the factors that affect face shapes, and the techniques that can be used to measure variations in two dimensional representations of faces. The materials included thirty photographs of people in natural poses and thirty portraits that were based on the pose photographs. Visual assessors were asked to score the photographs and portraits in terms of pose (cant, turn and pitch) and also to compare the portraits to the photographs and score them in terms of likeness in the depiction of the face and its component features. Anthropometric indices were derived and used to score the images for the pose variables as well as for aspects of individual variation in external face shape and the spatial arrangement of the features. Geometric morphometric analysis was also used to determine the shape variation occurring in the photographs, the variation within the portraits, and to specifically discern where the portraits differ from the photographs in the depiction of head pose and individual differences in facial morphology. For the analysis of pose it was found that visual assessors were best at discerning the extent of head turning and poorest at discerning head pitch. These tendencies occurred in the visual assessments of both the photographs and the portrait drawings. For the analysis of the individual variation in face shapes it was found that external face shape varies according to upper face dimensions and the shape of the chin, and that vertical featural configurations are strongly linked to external face shape. When the portrait and photograph data were placed in the same geometric morphometric analysis the inaccuracies in the portrait drawings became evident. When these findings were compared to the visual assessments it transpired that, on average, visual assessment was generally congruent with the geometric morphometric analysis, but were possibly confounded by patterns of dysmorphology in the portraits that were contrary to what this study suggests are normal patterns of face shape variation. Overall this study has demonstrated that while anthropometric and visual assessments of facial differences are quite good, both were comparatively poor at assessing head pitch and tended to be confounded by the dysmorphologies arising in the portrait drawings. Geometric morphometric analysis was found to be very powerful in discerning complex shape variations associated with head pose and individual differences in facial morphology, both within and between the photographs and portraits.

Mawson Lakes is a new suburban housing development, situated 12 kms from the city of Adelaide in South Australia. The developers, the Mawson Lakes Joint Venture (MLJV), and the local council, the City of Salisbury, intend to capture all stormwater entering the site and recondition all wastewater. The water will then be supplied to residents and businesses for non-potable usage. Modelling the behaviour of the Mawson Lakes catchment under extreme conditions such as drought and prolonged periods of high rainfall will allow the project team to determine optimal water management strategies for the catchment. One of the problems facing the team is the prediction of future rainfall patterns and the typical form of extreme events. In this thesis I have used historical records to construct synthetic rainfall data that will allow the project team to investigate a wide range of typical behaviour. The Gamma distribution has been widely used to approximate the probability density function (PDF) of monthly rainfall totals. However, there is no natural way to extend this method directly to obtain a joint PDF for rainfall densities associated with two or more months, unless the monthly totals are independent. I propose a modified method to construct a suitable PDF using parameters from the maximum likelihood estimate for a marginal Gamma distribution and a series of associated Laguerre polynomials. This series of special functions allows us to match the correlation between monthly totals and to match the observed moments with any level of precision needed. The joint PDF for two months is constructed using a sum of products of associated Laguerre polynomials. In order to get an analytic expression for the marginal distributions and the associated cumulative probabilities, it is convenient to use a weighted total and a weighted proportion contributed from the first month. The method makes extensive use of well-known formulae from the theory of special functions. The cumulative marginal probability density for the weighted total and the cumulative conditional probability density for the weighted proportion are used to generate simulated rainfall totals for each month in a two month period. In theory the simulated data is statistically identical to the observed data. In practice we apply standard statistical methods to check that the simulated data is consistent with the observed data. This method can be extended to the general case of any number of months, but computationally is restricted to only three. For this reason an alternative method is proposed to generate synthetic data for more than three months, which uses groups and subgroups of months, but still retains the characteristics of the original PDF. Although the series method could also be used to model a sequence of days, I propose an alternative method using Markov processes. This method will match a sequence of daily totals, generated from a probability transition matrix, to the monthly total generated by the series method. This methodology allows the research team to simulate certain special cases such as droughts and prolonged periods of high rainfall. These unusual events are of great interest in catchment planning and management. / thesis (PhDMathematics)--University of South Australia, 2004.

Diss. (sammanfattning) Uppsala : Sveriges lantbruksuniv., 2007. / Härtill 4 uppsatser.

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Diss. (sammanfattning). Uppsala : Sveriges lantbruksuniv., 2003. / Härtill 4 uppsatser.

Diss. (sammanfattning) Uppsala : Sveriges lantbruksuniv. / Härtill 5 uppsatser.

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Diss. (sammanfattning). Uppsala : Sveriges lantbruksuniversitet, 2004. / Härtill 5 uppsatser.

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Diss. (sammanfattning) Uppsala : Sveriges lantbruksuniversitet, 2006. / Härtill 4 uppsatser.