sl.rot.vec: Rotate velocity vectors on a sphere

In FESOM/spheRlab: Spherical Geometry, Analysis, and Plotting of Geoscientific Data on Arbitrary Grids

Rotate velocity vectors on a sphere

Description

Use this function to rotate velocity vectors (given as local u-v-components) on a sphere with Euler angles in z-x-z convention.

Usage

  sl.rot.vec <- function(al, be, ga, lon, lat, urot, vrot, flag)

Arguments

al, be, ga	three numeric scalars defining the Euler angles (in degrees).
lon, lat	a numeric vector specifying the longitudes and latitudes of the points, either the rotated or geographical coordinates (see parameter 'flag' and section 'Details' for clarification).
urot, vrot	numeric vectors, the u- and v-component of the velocity vectors that shall be rotated.
flag	an integer scalar, either 0 or 1, defining how the input coordinates are interpreted. For flag=0, the input longitude and latitude are considered as the "true" coordinates of the input velocities, and for flag=1 the input longitude and latitude are considered as coordinates that are already rotated with the given Euler angles.

Details

If for example the velocities are given on longitude and latitude in geographical coordinates, but the vector orientation is still corresponding to the rotated coordinate system, you need to use flag=1 and set the Euler angles to the values that transform the geographic to the rotated coordinates (Example 1 below). If lon and lat are the coordinates of the rotated system, you need to set flag=0.

Value

A list with the following elements:

u	rotated velocity component (in new eastward direction)
v	rotated velocity components (in new northward direction)

Note

The provided example #1 is also the necessary post-processing for FESOM velocity output.

Author(s)

Simon Reifenberg, translated from Python and adapted from FESOM/pyfesom (under MIT license)

See Also

sl.assemble.eulermatrix, sl.uvw2uv, sl.uv2uvw

Examples

  ### Example 1: rotated vectors  ->  geographical coordinate system
  #   velocity vectors u, v, are oriented with respect to a North Pole over Greenland (40°W 75°N)
  #   this coordinate rotation was obtained by the Euler angles (50,15,-90)
  #   lon, lat are here the geographical ("real") coordinates
  
  lon = c(0, 30, 60, 90, 180, -10)    # geogr. coord.
  lat = c(0, 30, 45, 60, 80, 85)      # geogr. coord.
  u.rot   = 1.5 * cos(lat*pi/180)     # rotated velocity 
  v.rot   = rep(0, 6)                 # rotated velocity
  
  U.geo <- sl.rot.vec(50, 15, -90, lon, lat, u.rot, v.rot, 1)  # velocity for geogr. coordinate system
  
  ### Example 2: <provided in near future>
  

FESOM/spheRlab documentation built on July 13, 2024, 7 a.m.