SVD input normalisation

In climate science, the term SVD (Singular vector Decomposition) is
used for the procedure to find a decomposition of two time-varying
fields into a sum of maps (the SVDs) times time series (confusing referred to as Prinicpal Components, PCs):
*E*(*x*,*t*) = ∑_{i=1N
Ei(x) pi(t)
}

The SVDs (maps) and PCs are chosen such that for small *N* the
difference with the full field is as small as possible.

In this field you can choose how many SVDs (and PCs) you want to have computed, and how the difference should be evaluated.

More SVDs only take slightly more time to compute, so feel free to give a large number.

The SVD decomposition can be defined in two ways. The first is to minimise the difference in absolute units, for instance in mb or mm/dy. The second is to minimse the fraction of the variability at each point that is explained by the SVD decomposition, i.e., diagonalise the cross-correlation matrix instead of the covariance matrix. This is also known as Canonical Correlation analysis (CCA). The first method emphasises the areas in which the variability is large, the second one treats all areas equally.