This problem is aimed at helping you understand the pga

Question

1.  For a domain defined between

-5 ≤ x ≤ 5

-5 ≤ y ≤ 5

0 ≤ t ≤ 10

Generate a dataset with variability in space and time following:

f(x, y, t) =  f₁(x, y, t)+ f₂(x, y, t) + f₃(x, y, t)

where,

• Standing wave oscillating in time:

f₁(x, y, t) = Sin(0.2πy) * Cos(0.5πx) * (1+Cos(2πt))

• Trend (increasing magnitude in time) with random component:

 f₂(x, y, t) = 0.09 * t + ε    where ε= N(0, 0.01)

• Spike in space at different times:

This problem is aimed at helping you understand the PGA method using an idealized dataset Since you know the data you are generating. it should help you understand the capability of the method.

a. Perform a principal component analysis on the dataset you have generated.

b. What is the total variability in the dataset?

c. What is the percent of the total variability explained by the first three components?

d. How many components should be retained?

e. Plot the spatial representation of each of the PCs you retained.

f. Reconstruct (back transform) your original data after reducing the dimensionality of the data Plot the scores of each of the PCs you retained Discuss your results.

2. Using a precipitation dataset provided to you (angle\homework\PW.txt), perform a PCA analysis and interpret the results. Answer the same questions as in Problem 1

The file PW.tct file contains monthly precipitation in U.S. from:

• January 1979- December 2000 (264 months).
• It extends from 140 W to 60 W (33 longitude points or rows) and
• 20N to 60 N (171atingle points or columns)

It covers the conterminous United States. The file is read first by longitude, then by latitude and that by time.

When you are doing the PCA, remove the means for each month. For example: Jan_i -average(Jan(1979 - 2001)), so that the dominant mode will not capture the intra-annual cycle (not very interesting).

Attachment:- Assignment.rar