We have two objectives 1. Demonstrate how **SpatPCA**
captures the most dominant spatial pattern of variation based on
different signal-to-noise ratios. 2. Represent how to use
**SpatPCA** for one-dimensional data

The underlying spatial pattern below indicates realizations will vary dramatically at the center and be almost unchanged at the both ends of the curve.

We want to generate 100 random sample based on - The spatial signal for the true spatial pattern is distributed normally with \(\sigma=20\) - The noise follows the standard normal distribution.

We can see simulated central realizations change in a wide range more frequently than the others.

There are two comparison remarks 1. Two estimates are similar to the
true eigenfunctions 2. **SpatPCA** can perform better at
the both ends.