Derivate: Derivate a discrete variable using finite differences

In eliocamp/meteoR: Tools for Easier Analysis of Meteorological Fields

Derivate a discrete variable using finite differences

Description

Derivate a discrete variable using finite differences

Usage

Derivate(
  formula,
  order = 1,
  cyclical = FALSE,
  fill = FALSE,
  data = NULL,
  sphere = FALSE,
  a = 6371000,
  equispaced = TRUE
)

Laplacian(
  formula,
  cyclical = FALSE,
  fill = FALSE,
  data = NULL,
  sphere = FALSE,
  a = 6371000,
  equispaced = TRUE
)

Divergence(
  formula,
  cyclical = FALSE,
  fill = FALSE,
  data = NULL,
  sphere = FALSE,
  a = 6371000,
  equispaced = TRUE
)

Vorticity(
  formula,
  cyclical = FALSE,
  fill = FALSE,
  data = NULL,
  sphere = FALSE,
  a = 6371000,
  equispaced = TRUE
)

Arguments

formula	a formula indicating dependent and independent variables
order	order of the derivative
cyclical	logical vector of boundary condition for each independent variable
fill	logical indicating whether to fill values at the boundaries with forward and backwards differencing
data	optional data.frame containing the variables
sphere	logical indicating whether to use spherical coordinates (see details)
a	radius to use in spherical coordinates (defaults to Earth's radius)
equispaced	logical indicating whether points are equispaced or not.

Details

Each element of the return vector is an estimation of \frac{\partial^n x}{\partial y^{n}} by centred finite differences.

If sphere = TRUE, then the first two independent variables are assumed to be longitude and latitude (in that order) in degrees. Then, a correction is applied to the derivative so that they are in the same units as a.

Using fill = TRUE will degrade the solution near the edges of a non-cyclical boundary. Use with caution.

Laplacian(), Divergence() and Vorticity() are convenient wrappers that call Derivate() and make the appropriate sums. For Divergence() and Vorticity(), formula must be of the form vx + vy ~ x + y (in that order).

Value

If there is one independent variable and one dependent variable, a numeric vector of the same length as the dependent variable. If there are two or more independent variables or two or more dependent variables, a list containing the directional derivatives of each dependent variables.

See Also

Other meteorology functions: EOF(), GeostrophicWind(), WaveFlux(), thermodynamics, waves

Examples

data.table::setDTthreads(2)
theta <- seq(0, 360, length.out = 20)*pi/180
theta <- theta[-1]
x <- cos(theta)
dx_analytical <- -sin(theta)
dx_finitediff <- Derivate(x ~ theta, cyclical = TRUE)[[1]]

plot(theta, dx_analytical, type = "l")
points(theta, dx_finitediff, col = "red")

# Curvature (Laplacian)
# Note the different boundary conditions for each dimension
variable <- expand.grid(lon = seq(0, 360, by = 3)[-1],
                        lat = seq(-90, 90, by = 3))
variable$z <- with(variable, cos(lat*pi/180*3) + sin(lon*pi/180*2))
variable <- cbind(
     variable,
     as.data.frame(Derivate(z ~ lon + lat, data = variable,
                          cyclical = c(TRUE, FALSE), order = 2)))
library(ggplot2)
ggplot(variable, aes(lon, lat)) +
    geom_contour(aes(z = z)) +
    geom_contour(aes(z = z.ddlon + z.ddlat), color = "red")

# The same as
ggplot(variable, aes(lon, lat)) +
    geom_contour(aes(z = z)) +
    geom_contour(aes(z = Laplacian(z ~ lon + lat, cyclical = c(TRUE, FALSE))),
                 color = "red")

eliocamp/meteoR documentation built on Feb. 19, 2024, 1:11 p.m.