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The Normalised Area Function is one of the network geomorphology tools used by Justin Robinson, Murugesu Sivapalan and John Snell in their paper ‘On the relative roles of hillslope processes, channel routing, and network geomorphology in the hydrologic response of natural catchments’ published in Water Resources Research in 1995. It reflects the spatial distribution of flow paths lengths to the outlet for a catchment.

 

The Normalised Area Function is usually represented by a chart of flow path length vs probability and can be parameterised by mean flow path length, maximum flow path length and flow path length variance or standard deviation. An example Normalised Area Function for two subcatchments is presented below.

 

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