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

6.6.2.2. Options


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

6.6.2.3. Input data


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:time (steps)
type:integer or double
range:[0; +infinity]
dimensionality:vector
description:days/months since …

6.6.2.4. Output data


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

6.6.2.5. Parameters


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