Tool Name	Focal PCA on a Grid
Tool ID	15
Library ID	statistics_grid
Version	1.0
Author(s)	A.Thomas, O.Conrad (c) 2016

Description

This tool uses the difference in cell values of a center cell and its neighbours (as specified by the kernel) as features for a Principal Component Analysis (PCA). This method has been used by Thomas and Herzfeld (2004) to parameterize the topography for a subsequent regionalization of climate variables with the principal components as predictors in a regression model.

References

Benichou, P., Lebreton, O. (1987): Prise en compte de la topographie pour la cartographie des champs pluviometriques statistiques. Meteorologie 7. Serie, no. 19.

Thomas, A., Herzfeld, U.C. (2004): REGEOTOP: New Climatic Data Fields for East Asia Based on Localized Relief Information and Geostatistical Methods. International Journal of Climatology, 24(10), 1283-1306. DOI:10.1002/joc.1058. Wiley Online Library

Parameters

Name	Type	Identifier	Description	Constraints
Input
Grid	grid, input	GRID
Output
Base Topographies	grid list, output, optional	BASE
Principal Components	grid list, output	PCA
Eigen Vectors	table, output, optional	EIGEN
Options
Number of Components	integer number	COMPONENTS	number of first components in the output; set to zero to get all	Minimum: 1 Default: 7
Output of Base Topographies	boolean	BASE_OUT		Default: 0
Overwrite Previous Results	boolean	OVERWRITE		Default: 1
Kernel Type	choice	KERNEL_TYPE		Available Choices: [0] Square [1] Circle Default: 1
Kernel Radius	integer number	KERNEL_RADIUS	Kernel radius in cells.	Minimum: 1 Default: 2
Method	choice	METHOD		Available Choices: [0] correlation matrix [1] variance-covariance matrix [2] sums-of-squares-and-cross-products matrix Default: 1