Below is a plot of channel width versus drainage area from $1947$ and again in $1999$ for a stream in New Jersey whose watershed has been heavily urbanized between $1947$ and $1999.$

Given what you know about the effects of urbanization on runoff generation, can you speculate about why the change that is apparent in the figure from $1947-1999$ occurred?

Leopold and Maddock $(1953)$ suggest that the downstream scaling of channel width and drainage area is given by $\backslash ($ W$=$c Q$^\{1/2\}\backslash ),$ where $\backslash ($ c $\backslash )$ is a constant and $\backslash ($ Q $\backslash )$ is discharge $(\backslash (\backslash$mathrm$\{$m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash )).$ For a drainage area of $\backslash (100\backslash$mathrm$\{$~km$\}^\{2\}\backslash ),$ the ratio of $1999$ channel width to $1947$ channel width is about $10/7$ or $\backslash (\backslash$sim $1\mathrm{.}4\backslash ).$ Using the relationship for channel width scaling above, determine the ratio of $1999$ discharge to $1947$ discharge for the reference channel section at the $\backslash (100\backslash$mathrm$\{$~km$\}^\{2\}\backslash )$ mark.