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 (&tgr;*) collapses model parameters and the active proportion of the streambed of individual rivers into general trends. An exponential relation between model parameters and &tgr;* 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. ¿ 1999 American Geophysical Union