Nonparametric statistical downscaling for the fusion of in-lake and remote sensing data

摘要

Lakes are vital components of the global biosphere, supporting complex ecosystems and playing important roles in the global biogeochemical cycle. However, they are vulnerable to the threat from climate change and their responses to climate forcing, eutrophication and other pressures, and their possibly confounding interactions, are not yet well understood. Monitoring lake health is therefore essential, in order to understand the changing patterns over space and time.ududTraditionally, in-situ data, which are collected directly from within lakes and analysed in laboratories, have been available for analysis. However, although these data are assumed to be accurate within measurement error, they are expensive to collect, so that few, if any, in-situ sampling locations are available for each lake, often with infrequent sampling at each location. On the other hand, remotely-sensed data, which are derived from reflectance measurements of the Earth's surface, obtained from satellites, have recently become widely available. These data have good spatial coverage of up to 300 metre resolution, covering entire lakes, often with a monthly-average time-scale, but they must firstly be calibrated with the in-situ data to ensure accuracy, before inferences are made.ududThe data for this research were provided by the GloboLakes project (www.globolakes.ac.uk), which is a consortium research project that is investigating the state of lakes and their responses to environmental drivers on a global scale. The research primarily focusses on log(chlorophyll-a) data for Lake Balaton, in Hungary, and for the Great Lakes of North America.ududThe key question of interest for this research is: ``How can data fusion be performed for in-situ and remotely-sensed lake water quality data, accounting for the spatiotemporal change of support between the point-location, point-time in-situ data and the grid-cell-scale, monthly-averaged remotely-sensed data, producing a fused dataset that takes accuracy from the in-situ data and spatial and temporal information from the remotely-sensed data?"ududIn order to answer this question, this thesis presents the following work:ududAn initial analysis of the data for Lake Balaton motivates the following work, by demonstrating the spatial and temporal patterns in the data, using mixed-effects models, generalised additive models, kriging and principal components analysis.ududFollowing the identification of statistical downscaling as an appropriate method for fusion of the data, statistical downscaling models are developed, specifically in the framework of Bayesian hierarchical models with spatially-varying coefficients, for the novel application to data for log(chlorophyll-a), producing fully calibrated maps of fused data across lake surfaces, with associated comprehensive uncertainty measures.ududBivariate and multiple-lakes statistical downscaling models are developed and applied, motivated by the assumption that sharing information between variables and between lakes can improve the accuracy of model predictions.ududThe statistically novel method of nonparametric statistical downscaling is developed, to account for both the spatial and temporal aspects of the change of support between the in-situ and remotely-sensed data. Using methodology from both functional data analysis and statistical downscaling, the model treats in-situ and remotely-sensed data at each location as observations of smooth functions over time, estimated using bases, with the basis coefficients related via a spatially-varying coefficient regression. This is computed within a Bayesian hierarchical model, enabling the calculation of comprehensive uncertainties.ududThis thesis presents the background, motivation, model development and application of the novel method of nonparametric statistical downscaling, filling the gap in the literature of accounting for changing temporal support in statistical downscaling modelling. Results are presented throughout this thesis, to demonstrate the utility of the method for real lake water quality data.