6.6.2. EOF Analysis¶

6.6.2.1. Operation¶

Operation name:	EOF Analysis

Algorithm reference:
	Wikipedia entry on Principal Component Analysis <https://en.wikipedia.org/wiki/Principal_component_analysis>, Blog entry on step by step PCA implementation in Python <http://sebastianraschka.com/Articles/2014_pca_step_by_step.html>,
Description:	This Operations serves for the application of Empricial Orthogonal Function (EOF) Analysis, also known as Principal Component Analysis (PCA), for data analysis regarding spatial patterns/modes. EOF Analysis implies the removal of redundancy.
Utilised in:	Use Case #6 Workflow

name:	rotated
description:	decide if EOF analysis should be rotatated
settings:	no rotation, varimax, …

name:	matrix
description:	decide to use correlation or covariance matrix
settings:	correlation matrix or covariance matrix

name:	longitude (lon, x)
type:	floating point number
range:	[-180.; +180.] respectively [0.; 360.]
dimensionality:	vector
description:	grid information on longitudes

name:	latitude (lat, y)
type:	floating point number
range:	[-90.; +90.]
dimensionality:	vector
description:	grid information on latitudes

name:	height (z)
type:	floating point number
range:	[-infinity; +infinity]
dimensionality:	vector
description:	grid information on height/depth

name:	variable(s)
type:	floating point number
range:	[-infinity; +infinity]
dimensionality:	cube or 4D
description:	values of (a) certain variable(s)

name:	principal components (PCs)
type:	floating point number
range:	[-infinity.; +infinity]
dimensionality:	vector
description:	temporal evolution of variance belonging to spatial pattern, number of

name:	empirical orthogonal functions (EOFs)
type:	floating point number
range:	[-infinity.; +infinity]
dimensionality:	array
description:	also named eigenvectors; tendency and strength of dominant spatial pattern of variance. All eigenvectors are orthogonal to one another.

name:	eigenvalues
type:	floating point number
range:	[0; 1] for correlation matrix, [0; +infinity] for covariance matrix
dimensionality:	scalar
description:	ith eigenvalue constitutes measure for the portion of variance explained by the ith PC/EOF

name:	lon1, x1 (longitudinal position)
type:	floating point number
valid values:	[-180.; +180.] respectively [0.; 360.]
default value:	minimum longitude of input data
description:	longitudinal coordinate limiting rectangular area of interest

name:	lon2, x2 (longitudinal position)
type:	floating point number
valid values:	[-180.; +180.] resp. [0.; 360.]
default value:	maximum longitude of input data
description:	longitudinal coordinate limiting rectangular area of interest

name:	lat1, y1 (latitudinal position)
type:	floating point number
valid values:	[-90.; +90.]
default value:	minimum latitude of input data
description:	latitudinal coordinate limiting rectangular area of interest

name:	lat2, y2 (latitudinal position)
type:	floating point number
valid values:	[-90.; +90.]
default value:	maximum latitude of input data
description:	latitudinal coordinate limiting rectangular area of interest