Testing uncertainty in a model of stream bank erosion

Sediment and nutrient loads in Australian rivers are a significant management concern. The National Land and Water Audit (2002) identified bank erosion as a major source of sediment, particularly in southern Australian systems. This paper tests a method of incorporating uncertainty into and the up-scaling of a cross-section scale stream bank erosion model. The cross-section scale model is based on an understanding of fluvial erosion and mass failure processes in which fluvial erosion is estimated using an excess shear stress approach while mass failure is estimated using a limit equilibrium analysis at the cross-section scale. Figure 1 shows a schematic of the model. A Monte-Carlo framework is used to propagate input uncertainty to output uncertainty in the model and to scale up to the reach scale. Widely available databases are used to estimate variables for the two model components. A range of spatial information (GIS layers) is used to describe spatial variations in general properties such as soil type and catchment area. These are considered to be relatively well known (compared with cross-section geometry, geotechnical properties of the bank materials, riparian tree density, and hydrologic variables), although spatially coarse. A variety of empirical models and assumptions are used to transform the spatial information into model parameters, which are considered to be relatively poorly known. Two major challenges, which are related, involve incorporating the effects of natural variability along a river reach and estimating the uncertainty in the model inputs and the effect that this has on uncertainty in the model prediction. A Monte Carlo framework is used to achieve this. This involves developing a series of statistical models to predict the erosion model inputs and their (co)variability. A hierarchical approach is used to develop these input models. An attempt is first made to construct a statistical model that predicts each model parameter from available spatial information using multiple regressions. Uncertainty in these parameters is incorporated using the regression error statistics. Where cross-correlations were found to be important, these were incorporated in the generation models. Where it was not possible to develop empirical relationships with available spatial data sets, a suitable parametric distribution is fitted for those input variables for which some data is available. Where no data were available for fitting a distribution, a distribution was assumed with a shape and parameters based on heuristic consideration of the relevant processes. Once both the erosion model and the various input models were established, the Monte Carlo technique was applied. This involves generating sets of the input variables of the model from the respective stochastic input models and the running the erosion model. This allows the probability distribution for the model output to be estimated for a location in the stream network. The model is tested using historical records of plan form change from a 40km reach of the Goulburn River downstream of Eildon Dam in Victoria, Australia. The results obtained from the model are promising; with bank erosion rates being predicted within a factor of two without calibration. A series of sensitivity analyses (detail sensitivity analysis, scenario analysis, and advance sensitivity analysis) were conducted to identify key variables for predicting bank erosion rates using this particular bank erosion model. This suggested that bank angle, bank material physical characteristics, stream bed slope, and the high-flow flow regime (bankfull duration) control the behaviour of the model for loam bank materials