cor_lagr_askey() R function from [mcgf]

Calculate Lagrangian correlation of the Askey form


cor_lagr_askey(v1, v2, k = 2, h1, h2, u)

Arguments

v1: Prevailing wind, u-component.
v2: Prevailing wind, v-component.
k: Scale parameter of $\|\boldsymbol v\|$ , $k>0$ . Default is 2.
h1: Horizontal distance matrix or array.
h2: Vertical distance matrix or array, same dimension as h1.
u: Time lag, same dimension as h1.

Returns

Correlations of the same dimension as h1.

Details

The Lagrangian correlation function of the Askey form with parameters $\boldsymbol v = (v_1, v_2)^\top\in\mathbb{R}^2$ has the form

C(\mathbf{h}, u)=\left(1-\dfrac{1}{k\|\boldsymbol v\|}\left\|\mathbf{h}-u\boldsymbol v\right\|\right)^{3/2}_+,

where $\|\cdot\|$ is the Euclidean distance, c(" $x_+=\\max(x,0),\n$ ", " $\\mathbf{h} = (\\mathrm{h}_1, \\mathrm{h}_2)^\\top\\in\\mathbb{R}^2$ "), and $k > 0$ is the scale parameter controlling the magnitude of asymmetry in correlation.

Examples


h1 <- matrix(c(0, -5, 5, 0), nrow = 2)
h2 <- matrix(c(0, -8, 8, 0), nrow = 2)
u <- matrix(0.1, nrow = 2, ncol = 2)
cor_lagr_askey(v1 = 5, v2 = 10, h1 = h1, h2 = h2, u = u)

h1 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3))
h2 <- array(c(0, -10, 10, 0), dim = c(2, 2, 3))
u <- array(rep(-c(1, 2, 3), each = 4), dim = c(2, 2, 3))
cor_lagr_askey(v1 = 10, v2 = 10, h1 = h1, h2 = h2, u = u)

References

Askey, R. (1973). Radial characteristic functions, Tech. Report No. 1262, Math. Research Center, University of Wisconsin-Madison.

cor_lagr_askey function