UBC Theses and Dissertations
Multivariate statistical models for seasonal climate prediction and climate downscaling Cannon, Alex Jason
This dissertation develops multivariate statistical models for seasonal forecasting and downscaling of climate variables. In the case of seasonal climate forecasting, where record lengths are typically short and signal-to-noise ratios are low, particularly at long lead-times, forecast models must be robust against noise. To this end, two models are developed. Robust nonlinear canonical correlation analysis, which introduces robust cost functions to an existing model architecture, is outlined in Chapter 2. Nonlinear principal predictor analysis, the nonlinear extension of principal predictor analysis, a linear model of intermediate complexity between multivariate regression and canonical correlation analysis, is developed in Chapter 3. In the case of climate downscaling, the goal is to predict values of weather elements observed at local or regional scales from the synoptic-scale atmospheric circulation, usually for the purpose of generating climate scenarios from Global Climate Models. In this context, models must not only be accurate in terms of traditional model verification statistics, but they must also be able to replicate statistical properties of the historical observations. When downscaling series observed at multiple sites, correctly specifying relationships between sites is of key concern. Three models are developed for multi-site downscaling. Chapter 4 introduces nonlinear analog predictor analysis, a hybrid model that couples a neural network to an analog model. The neural network maps the original predictors to a lower-dimensional space such that predictions from the analog model are improved. Multivariate ridge regression with negative values of the ridge parameters is introduced in Chapter 5 as a means of performing expanded downscaling, which is a linear model that constrains the covariance matrix of model predictions to match that of observations. The expanded Bernoulli-gamma density network, a nonlinear probabilistic extension of expanded downscaling, is introduced in Chapter 6 for multi-site precipitation downscaling. The single-site model is extended by allowing multiple predictands and by adopting the expanded downscaling covariance constraint.
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