A Preliminary Assessment of a Newly-Defined Multispectral Hue Space for Retrieving River Depth with Optical Imagery and In Situ Calibration Data

Abstract

Bathymetry is a key element in the modeling of river systems for flood mapping, geomorphology, or stream habitat characterization. Standard practices rely on the interpolation of in situ depth measurements obtained with differential GPS or total station surveys, while more advanced techniques involve bathymetric LiDAR or acoustic soundings. However, these high-resolution active techniques are not so easily applied over large areas. Alternative methods using passive optical imagery present an interesting trade-off: they rely on the fact that wavelengths composing solar radiation are not attenuated at the same rates in water. Under certain assumptions, the logarithm of the ratio of radiances in two spectral bands is linearly correlated with depth. In this study, we go beyond these ratio methods in defining a multispectral hue that retains all spectral information. Given n coregistered bands, this spectral invariant lies on the (n−2)-sphere embedded in Rn−1, denoted Sn−2 and tagged ‘hue hypersphere’. It can be seen as a generalization of the RGB ‘color wheel’ (S1) in higher dimensions. We use this mapping to identify a hue-depth relation in a 35 km reach of the Garonne River, using high resolution (0.50 m) airborne imagery in four bands and data from 120 surveyed cross-sections. The distribution of multispectral hue over river pixels is modeled as a mixture of two components: one component represents the distribution of substrate hue, while the other represents the distribution of ‘deep water’ hue; parameters are fitted such that membership probability for the ‘deep’ component correlates with depth.

Keywords

• bathymetry
• depth
• rivers
• multispectral hue
• spectral invariant
• directional statistics