Browsing by Subject "Spatial Modelling"

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    Open Access
    Development of a land use-based spatial water requirements model for the Berg Water Management Area
    (2017) Van Der Walt, Marthinus; Smit, Julian
    This study was conducted to investigate the requirements for the spatial modelling of current and future water demand in the Berg River Water Management Area in the Western Cape of South Africa in order to produce a prototype model from which annual water requirements could be computed and spatially visualised. To accomplish this the spatial distribution of water demand within the study area was first investigated. The data required to perform spatial water demand modelling of diverse land uses and socio-economic activities were evaluated. Finally, the question of improving spatial water demand modelling at the catchment scale was considered from both a systems design and a technical perspective. The resulting model consists of two main modules; one performing a rudimentary monthly soil water balance to obtain monthly and annual irrigation requirements, and another applying preconfigured determinant layers derived from land use to town zone layers in order to determine annual urban water use intensities per areal unit. The resulting model prototype follows a sequential workflow based on a series of components that combine to produce a spatial overview of water use intensity within the study area. Water demand was found to be predominantly irrigated agriculture in the upper reaches of the Berg (mainly wine grape) and was found to be dominated by intensive industrial users in the central and lower reaches. The model was designed so that new data could be introduced in order to expand the system where required, as well as allowing for updated datasets to be incorporated as they become available. Due to the uncertainties inherent in the modelling and approximation of real world phenomena, the importance of establishing a set of structured, stable, predefined user requirements and system specifications were noted as a fundamental requirement for improving model development and design efficiency and ensuring model validity. It was further found that incorporating additional datasets, covering parameters related to the system, may serve to improve model accuracy, but could easily lead to compounded errors if not correctly parameterised or adequately validated.
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    Open Access
    Efficient Bayesian analysis of spatial occupancy models
    (University of Cape Town, 2020) Bleki, Zolisa; Clark, Allan
    Species conservation initiatives play an important role in ecological studies. Occupancy models have been a useful tool for ecologists to make inference about species distribution and occurrence. Bayesian methodology is a popular framework used to model the relationship between species and environmental variables. In this dissertation we develop a Gibbs sampling method using a logit link function in order to model posterior parameters of the single-season spatial occupancy model. We incorporate the widely used Intrinsic Conditional Autoregressive (ICAR) prior model to specify the spatial random effect in our sampler. We also develop OccuSpytial, a statistical package implementing our Gibbs sampler in the Python programming language. The aim of this study is to highlight the computational efficiency that can be obtained by employing several techniques, which include exploiting the sparsity of the precision matrix of the ICAR model and also making use of Polya-Gamma latent variables to obtain closed form expressions for the posterior conditional distributions of the parameters of interest. An algorithm for efficiently sampling from the posterior conditional distribution of the spatial random effects parameter is also developed and presented. To illustrate the sampler's performance a number of simulation experiments are considered, and the results are compared to those obtained by using a Gibbs sampler incorporating Restricted Spatial Regression (RSR) to specify the spatial random effect. Furthermore, we fit our model to the Helmeted guineafowl (Numida meleagris) dataset obtained from the 2nd South African Bird Atlas Project database in order to obtain a distribution map of the species. We compare our results with those obtained from the RSR variant of our sampler, those obtained by using the stocc statistical package (written using the R programming language), and those obtained from not specifying any spatial information about the sites in the data. It was found that using RSR to specify spatial random effects is both statistically and computationally more efficient that specifying them using ICAR. The OccuSpytial implementations of both ICAR and RSR Gibbs samplers has significantly less runtime compared to other implementations it was compared to.