The N4220 copula (Nelsen, 2006, p. 118; eq. 4.2.20) is named by the author (Asquith) for the copBasic package and is defined as
$$\mathbf{C}_{\mathrm{N4220}}(u,v; \Theta) = \biggl[\mathrm{log}\biggl( \mathrm{exp}\bigl(u^{-\Theta}\bigr) +
\mathrm{exp}\bigl(v^{-\Theta}\bigr) -
\mathrm{exp}(1)\biggr)\biggr]^{-1/\Theta}\mbox{.}$$
The \(\mathbf{N4220}(u,v)\) copula is not comprehensive because for \(\Theta = 0^{+}\) the copula becomes the independence \(\mathbf{P}(u,v)\) copula (P) and as \(\Theta \rightarrow \infty\) the copula becomes \(\mathbf{M}(u,v)\) (M). The copula is undefined for \(\Theta < 0\). This copula has lower-tail dependency, which is the reverse of the \(\mathbf{rN4220}(u,v)\) that has uppr-tail dependency. Hence, a reflected (refer to COP, reflect=2) version of this copula is natively supported as the rN4220cop to put the tail dependency into the upper-right corner and more “hydrologic-system like.”