mcgf (version 1.1.1)

.cor_lagr_tri: Calculate Lagrangian correlation of the triangular form

Description

Calculate Lagrangian correlation of the triangular form

Usage

.cor_lagr_tri(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 triangular form with parameters \(\boldsymbol v = (v_1, v_2)^\top\in\mathbb{R}^2\) has the form $$C(\mathbf{h}, u)=\left(1-\dfrac{1}{k\|\boldsymbol v\|} \left|\dfrac{\mathbf{h}^\top\boldsymbol v}{\|\boldsymbol v\|}- u\|\boldsymbol v\|\right|\right)_+,$$ 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.