Bias in topographic thresholds for gully heads

Abstract

The topographic threshold for overland flow gully head represents a promising tool for both research development and users. Nevertheless, some of the basic assumptions that were used to derive the threshold equation are also at the base for errors, including systematic ones, which introduce bias in the evaluations. Particularly, the assumption that the gully head catchment (GHC) area is a synonym for runoff causes is often false. This cause errors when calculating the threshold equation parameters (i.e. exponent and coefficient of the power equation linking critical slope gradient near the gully head to the GHC area). The assumption implies that every part of the GHC is connected via continuous overland flow paths to the outlet at the moment of peak discharge. Larger areas require larger concentration times, hence longer rainfall duration. This makes the occurrence of a rainfall intensity of the right duration to allow the total connectivity of the GHC less frequent (i.e. less probable). Also the land use (characterized by a specific vegetation type) and the soil conditions could have an effect on the probability that the previous assumption is verified. In order to show this, a distributed model developed in R was used to analyse where the conditions for gully erosion are actually verified. The hydrological part was developed based on the curve number (CN) approach, including the simulation of peak discharge with a few modifications/adaptations to a spatially distributed environment. A small routine was added to simulate concentrated flow erosion and condition for gully head formation. Then, a set of simulations were run using a series of daily rainfall amount and different land use/soil scenarios. Results show a clear effect of the vegetation distribution and patterns on gully head position in the simulated landscapes. From these results, it becomes evident that CN-weighted average in composite catchments needs to be replaced by a different averaging procedures, where the fraction of catchment area as CN weight is completed by an additional weight based on distances to the catchment outlets of the different land uses.