Simulated 2D residual velocity fields in the inner German Bight were

subjected to Principal Component Analysis (PCA). Residual currents

were obtained from coastDat2 barotropic 2D simulations with the

hydrodynamic model TRIM-NP V2.1.22 in barotropic 2D mode on a Cartesian grid (1.6km spatial resolution)

stored on an hourly basis for the years 1948 - 2012

(doi:10.1594/WDCC/coastDat-2_TRIM-NP-2d) and later extended until

August 2015.

The present analysis refers to the period Jan 1958 - Aug 2015. The spatial

domain considered is the region to the east of 6 degrees east and to

the south of 55.6 degrees north. All grid nodes with a bathymetry of

less than 10m were excluded.

Residual velocities were calculated in two different ways:

1.) as 25h means,

2.) as monthly means.

Both types of residual current data are available from

* RESIDUAL_CURRENTS_195801_201508

The directory contains sub-directories for years and months. Daily

residual currents for the 13th of September 1974, for instance,

are stored in

* RESIDUAL_CURRENTS_195801_201508/YEAR_1974/MONTH_09/TRIM2D_1974_09_13_means.nc

while monthly mean residual currents for September 1974 are stored in:

* RESIDUAL_CURRENTS_195801_201508/YEAR_1974/TRIM2D_1974_09_means.nc

All current fields provided were interpolated from the original

Cartesian model grid to a more convenient regular geographical grid

(116x76 nodes).

Mean residual currents are stored in:

* mean_residual_currents.nc

This data set contains residual velocities both on original Cartesian

grid nodes and interpolated to the geographical grid. An example plot

is provided:

* mean_residual_currents.png

For PCA, two residual velocity components from each of 12133 Cartesian

grid nodes were combined into one data vector (length 2x12133),

referring to 21061 daily or 692 monthly time levels. Results of two

independent PCAs for either daily or monthly mean fields are stored

in:

* PCA_daily_residual_currents.nc

* PCA_monthly_residual_currents.nc

Files contain three leading Principal Components (PCs) and

corresponding Emipirical Orthogonal Functions (EOFs). Again EOFs

were also interpolated to a regular geographical grid.

PC time series are also stored in plain ASCII format:

* PCs_daily.txt

* PCs_monthly.txt

For monthly fields the number N of variables (N=2x12133) is much

larger than the number T of time levels (T=692). Therefore, to reduce

computational demands, the roles of time and space were formally

interchanged. Having conducted the PCA the EOFs were then transformed

back to the original spatial coordinates (cf. Section 12.2.6 in von

Storch and Zwiers (1999), Statistical Analysis in Climate Research,

Cambridge University Press).

A much larger number of time levels made even this approach

prohibitive for the full set of daily data. Therefore, PCAs were

performed for six sub-periods (1958-1965, 1966-1975, 1976-1985,

1986-1995, 1996-2005, 2006-2015(Aug)) independently. EOFs obtained from

these six sub-periods were then averaged to obtain EOFs representative

for the whole period. Corresponding PCs were calculated by

projecting daily fields onto these average EOFs.

IMPORTANT: In contrast with PCA of monthly data, the PCA of daily

data INVOLVES SOME APPROXIMATIONS!

EOFs on the original nodes were normalized to have unit lengths. The

following figures,

* daily_EOF1.png

* daily_EOF2.png

* daily_EOF3.png

show the first three EOFs obtained from daily data, assuming that

corresponding PCs have the value of one standard deviation. The

following two plots,

* monthly_EOF1.png

* monthly_EOF2.png

show the leading EOFs for monthly mean data. EOF3 is omitted as it

represents just a very small percentage of overall variance (1.7%).