6.6.2. EOF Analysis¶
6.6.2.1. Operation¶
Operation name: | EOF Analysis |
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Algorithm reference: | |
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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 |
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description: | decide if EOF analysis should be rotatated |
settings: | no rotation, varimax, … |
name: | matrix |
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description: | decide to use correlation or covariance matrix |
settings: | correlation matrix or covariance matrix |
6.6.2.3. Input data¶
name: | longitude (lon, x) |
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type: | floating point number |
range: | [-180.; +180.] respectively [0.; 360.] |
dimensionality: | vector |
description: | grid information on longitudes |
name: | latitude (lat, y) |
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type: | floating point number |
range: | [-90.; +90.] |
dimensionality: | vector |
description: | grid information on latitudes |
name: | height (z) |
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type: | floating point number |
range: | [-infinity; +infinity] |
dimensionality: | vector |
description: | grid information on height/depth |
name: | variable(s) |
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type: | floating point number |
range: | [-infinity; +infinity] |
dimensionality: | cube or 4D |
description: | values of (a) certain variable(s) |
name: | time (steps) |
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type: | integer or double |
range: | [0; +infinity] |
dimensionality: | vector |
description: | days/months since … |
6.6.2.4. Output data¶
name: | principal components (PCs) |
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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) |
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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 |
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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) |
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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) |
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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) |
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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) |
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type: | floating point number |
valid values: | [-90.; +90.] |
default value: | maximum latitude of input data |
description: | latitudinal coordinate limiting rectangular area of interest |