dot-cor_lagr_askey function

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

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.

References

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