Exploring the Relations between Riverbank Erosion and Geomorphological Controls Using Geographically Weighted Logistic Regression
Atkinson, Peter M., German, Sally E., Sear, David A., Clark, Michael J., Geographical Analysis
The relations between riverbank erosion and geomorphological variables that are thought to control or influence erosion are commonly modelled using regression. For a given river, a single regression model might be fitted to data on erosion and its geomorphological controls obtained along the river's length. However, it is likely that the influence of some variables may vary with geographical location (i.e., distance upstream). For this reason, the spatially stationary regression model should be replaced with a non-stationary equivalent. Geographically weighted regression (GWR) is a suitable choice. In this paper, GWR is extended to predict the binary presence or absence of erosion via the logistic model. This extended model was applied to data obtained from historical archives and a spatially intensive field survey of a length of 42 km of the Afon Dyfi in West Wales. The model parameters and the residual deviance of the model varied greatly with distance upstream. The practical implication of the result is th at different management practices should be implemented at different locations along the river. Thus, the approach presented allowed inference of spatially varying management practice as a consequence of spatially varying geomorphological process.
The evolution of river planform is an important area of research in fluvial geomorphology, and is of significance to river managers and owners of riparian land. Bank erosion, a key process of planform change, continues to be a focus for process and applied research. The erosion of river banks not only causes change in channel planform and cross-section but is a key process whereby floodplain sediments are remobilised to become a part of the basin sediment yield (Bull 1997).
The literature associated with channel planform change is now extensive, with research largely focusing at two scales: (i) mesoscale analysis of channel planform and bank retreat rates over periods of up to 200 years (Gurnell 1997) and (ii) more detailed site-specific studies of the processes of bank retreat (Hooke 1995; Lawler, Thorne, and Hooke 1997; Bull 1997). Relatively few studies attempt to link such different scales of analysis, and even fewer attempt this at the basin scale. Notable exceptions include the work of Lawler (1992) who identified theoretical process domains for bank erosion, and Abernathy and Rutherford (1998) who attempted a similar analysis including the additional influence of vegetation. However, even these studies involve fragmentary information and make no explicit attempt to link historical channel activity with the full suite of contemporary controls on the physical processes of bank erosion.
Recent geomorphological investigations into the processes of bank erosion have been undertaken through the use of erosion pins and PEEPS (Lawler 1993; Lawler, Thorne, and Hooke 1997), investigations into bank stability (Thorne 1982; Simon and Hupp 1992; Simon and Darby 1995), and the use of bank reconnaissance methods (Thorne, Allen, and Simon 1996). However, these investigations tend to focus on particular banks and specific erosion issues, and the detailed data sets required preclude investigation of the entire catchment. Further, the multivariate nature of the controls and the variability of these in space can prevent identification of the actual processes of bank erosion. In particular, geomorphologists are frequently challenged to explore relationships that may vary in their nature from place to place (they require spatially non-stationary models) and that involve categorical data.
Bank erosion is a significant problem for many people who derive income from, or live on, land next to rivers. Bank erosion management has typically been site-specific (tending to treat the problem where it arises) and simplistic (using techniques centred on the assumption that the erosion is caused by fluvial scour) (Sear, Newson, Brookes 1995; Thorne 1997). …