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
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