Syllabus
1. Introduction - need to analyze huge datasets - examples of tasks leading to the use of multivariate methods: classification, regionalization, reduction of datasets, removal of linear dependency, ...
2. Multiple linear regression - basic notions and definitions - methods of selection of predictors
3. Principal component analysis - definitions - derivation, basic properties - selection of the input data matrix (modes of decomposition) - selection of similarity matrix - concept of simple structure, rotation, selection of the number of components - interpretation of results - Buell's map sequences
4. Cluster analysis - basic definitions - (dis)similarity measures - algorithms, their properties - fuzzy methods - principal component analysis as a cluster analysis method
5. Canonical correlation analysis - basic derivation - interpretation of results - relations among multiple regression, principal component analysis, and canonical correlation analysis
6. Examples of treating specific tasks - definition of climate areas (regionalization) - teleconnections (modes of variability) in geopotential height fields - incl. comparison with correlation method - classification of circulation patterns - classification of air masses (weather types) - relationships between circulation and surface climate elements (temperature, precipitation) - statistical downscaling - identification and removal of ?non-meteorological" signal - Model Output Statistics
Annotation
Introduction to multivariate statistical methods currently used in meteorology and climatology, with emphasis on their practical applications