A Probability model of scour and fill depths in gravel‐bed channels

The exponential density function was fitted to frequency distributions of scour and fill depths derived from six single‐threaded gravel‐bed channels. Scour chains and monitors were used to record the depth of bed activity in the 6 to 20 m wide channels. Goodness‐of‐fit analyses indicate that the exponential function is a plausible model. Introduction of dimensionless shear stress (т*) collapses model parameters and the active proportion of the streambed of individual rivers into general trends. An exponential relation between model parameters and т* suggests a means to derive scour and fill depths to a first approximation based only on flow and channel characteristics. Exponentially distributed depths require over 400 observations to estimate the mean to within 10% with 95% confidence.