### Description

In the interior of the matrix, centred second-order differences are used to infer the components of the grad. Along the edges, first-order differences are used.

### Arguments

 h a matrix x x values y y values

### Value

A list containing gx and gy, matrices of the same dimension as h.

### Author(s)

Dan Kelley, based on advice of Clark Richards, and mimicking a matlab function.

Other functions relating to vector calculus: curl

### Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ## Geostrophic flow around an eddy library(oce) dx <- 5e3 dy <- 10e3 x <- seq(-200e3, 200e3, dx) y <- seq(-200e3, 200e3, dy) R <- 100e3 h <- outer(x, y, function(x, y) 500*exp(-(x^2+y^2)/R^2)) grad <- grad(h, x, y) par(mfrow=c(2,2), mar=c(3, 3, 1, 1), mgp=c(2, 0.7, 0)) contour(x,y,h,asp=1, main=expression(h)) f <- 1e-4 gprime <- 9.8 * 1 / 1024 u <- -(gprime / f) * grad\$gy v <- (gprime / f) * grad\$gx contour(x, y, u, asp=1, main=expression(u)) contour(x, y, v, asp=1, main=expression(v)) contour(x, y, sqrt(u^2+v^2), asp=1, main=expression(speed))

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