A geostatistical framework for quantifying the reach-scale spatial structure of river morphology: 1. Variogram models, related metrics, and relation to channel form

Fluvial geomorphology is fundamentally concerned with the association between form and process in rivers. Examining these interactions in complex, natural channels requires a means of quantifying the variability and organization of bed topography—this paper introduces a geostatistical framework for characterizing reach-scale spatial structure. Transformation to a channel-centered coordinate system allows topographic variations to be resolved into along- and across-stream components. Dimensionless variables, obtained by scaling distances by the mean channel width and de-trended elevations by the mean bankfull depth, account for channel size and allow spatial patterns to be compared over time or among sites. These patterns are effectively described by the variogram, a spatial statistic that expresses dissimilarity as a function of distance. Fitting a parametric model to the sample variogram provides a rich description of channel form. For example, multiple, nested structures can be combined to account for anisotropy, with varying degrees of spatial variability observed over different length scales along and across the channel. Integral metrics derived from the variogram model yield a more compact summary, and variogram maps a useful visualization. To guide interpretation of these metrics, I used a simple ‘channel builder’ to isolate the effects of specific aspects of river morphology on the variogram. This analysis indicated that geostatistical models were sensitive to changes in the size, shape, and orientation of channel features, but not to a pure translation of the morphology. The results also highlighted the importance of considering streamwise and transverse components jointly rather than in isolation.