Cluster Analysis of AMSR-E Brightness Temperatures

Danny Braswelland

Roy Spencer

23 September 2014

Defining cluster analysis• In a general sense, cluster analysis is the grouping of a set of

items into subsets of items with similar characteristics. For example, in a restaurant you could group (cluster) patrons based what they ordered, or whether or not they added salt to their food, or even the color of their clothes. Another way would be to cluster them based on separation distance, e.g. those sitting together at each table.

• Separation distance is one of the more common ways of clustering items. This can be in a 2 or 3 dimensional real space or in a higher order multi-dimensional space.

• Accounting for the distance is usually done in one of two ways: absolute distance or squared distance.

• Squared distance places progressively greater weights on larger separations, and is the more commonly used.

Defining cluster analysis (cont)

• For our purposes, we use “cluster analysis” to mean the dividing of M points in N dimensions into K clusters so that the within-cluster sum of squares is minimized.

• Each cluster is defined by the coordinates of its centroid.

• As a simple example in 2-D, consider random points on a square grid.

• Each point is defined by its (x,y) coordinates.

Random points on a square grid

10,000 points

Random points on a square grid classified into 4 clusters

Cluster centroids marked in red

Cluster centroids marked in red

Random points on a square grid classified into 6 clusters

Clustering of AMSR-E Tbs• For AMSR-E, a point is defined by 9 simultaneous AMSU channel

differences computed from the 10 channels: - 10V, 10H - 18V, 18H - 23V, 23H - 36V, 36H - 89V, 89H

• Reference channel for differences: 18V• 9 dimensions - each channel difference is considered a dimension• Differences used to remove temperature signal• 10 clusters• Used K-means algorithm by Hartigan and Wong (ref at end) to perform

clustering

AMSR-E Data Used

• AMSR-E Level 2A (v12)• Land only• ASC/DSC orbits combined• Days: 1/15/2008, 6/15/2008

10 land clusters

Tb (K

)

Channel

Average Tbs for each cluster

1

2

3

4

5

6

7

8

9

10

Clusters 1, 2

2 - snow1 - dense veg

Clusters 3, 4

4 – snow/storms3 – glacial ice

Clusters 5, 6

6 – sparse veg5 – deep snow

Clusters 7, 8

8 - snow7- marginal desert/sea ice

Clusters 9, 10

10 – glacial ice9 – desert/glacial ice

Reference for:K-means Clustering Algorithm

• Hartigan, J. A.; Wong, M. A. (1979). "Algorithm AS 136: A K-Means Clustering Algorithm". Journal of the Royal Statistical Society, Series C 28 (1): 100–108.

• Fortran 77 subroutine asa_136.f available from: http://lib.stat.cmu.edu/apstat/136