mcgf (version 1.1.1)

cor_lagr_askey: Calculate Lagrangian correlation of the Askey form

Description

Calculate Lagrangian correlation of the Askey form

Usage

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

Value

Correlations of the same dimension as h1.

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.

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

References

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

See Also

Other correlation functions: cor_cauchy(), cor_exp(), cor_fs(), cor_lagr_exp(), cor_lagr_tri(), cor_sep(), cor_stat(), cor_stat_rs()

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)