dot-cor_lagr_tri: Calculate Lagrangian correlation of the triangular form

In mcgf: Markov Chain Gaussian Fields Simulation and Parameter Estimation

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)

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.

Value

Correlations of the same dimension as h1.

mcgf documentation built on June 29, 2024, 9:09 a.m.