Laplacian Eigenvectors

The eigenvectors of the Laplace operator form an orthogonal set of spatial patterns that can be ordered by a measure of length scale. These vectors are attractive in statistics and data compression if one wants to reduce the dimension of a data set by filtering out small scale variability. Climate scientists often need such basis vectors to study data on subdomains on a sphere, such as over continents only. Unfortunately, computing Laplacian eigenfunctions in domains with irregular boundaries is numerically challenging. Recent advances in machine learning have lead to new algorithms for computing Laplacian eigenfunctions. On this page, we provide links to interesting applications and numerical codes of these new methods.

If you use these algorithms and find bugs or improvements, then please let us know.

Main references

Laplacian Eigenfunctions for Climate Analysis

T. DelSole and M. K. Tippett, 2015

Data analysis and representation on a general domain using eigenfunctions of Laplacian

N. Saito, 2008

Software

1. R Codes

   1. R function

   2. Example (North Atlantic Domain)

2. Matlab Codes

   1. Matlab function

   2. Examples

Laplacians for Some Standard Grids

Main Page

IRI Data Library, Tippett Home Page

NCEP Grid

NMME Grid