.cor_lagr_askey | R Documentation |
Calculate Lagrangian correlation of the Askey form
.cor_lagr_askey(v1, v2, k = 2, h1, h2, u)
v1 |
Prevailing wind, u-component. |
v2 |
Prevailing wind, v-component. |
k |
Scale parameter of |
h1 |
Horizontal distance matrix or array. |
h2 |
Vertical distance matrix or array, same dimension as |
u |
Time lag, same dimension as |
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.
Correlations of the same dimension as h1
.
Askey, R. (1973). Radial characteristic functions, Tech. Report No. 1262, Math. Research Center, University of Wisconsin-Madison.
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