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1974 ; Wang and Shen 1980 ; Haque and Mahmood 1985 ; Moll et al. 1987 ; Robert
and Richards 1988 ; Coleman 1996 ; Nikora et al. 1997 ; McElroy et al. 2008 ; van der
Mark et al. 2008 ; Tuijnder et al. 2009 ).
In contrast to analyses of linear sections of bed surfaces, the discussion of this
section focuses on recent three- and four-dimensional (3D and 4D) measurements
of bed surfaces, where the need to quantify the 3D form is recognised from detailed
studies of fixed beds (e.g. Maddux et al. 2003a , b ; Venditti 2007 ) and is even more
apparent for considerations of deformable mobile beds of waves that vary markedly
in space and time (e.g. Inglis 1949 ; ASCE 1966 ; Parsons et al. 2005 ; Henning et al.
2009 ; Aberle et al. 2010 ).
Early analyses of bedform three-dimensionality were based on viewing the
crestlines or contours of individual bedforms in plan. Allen ( 1968 ) initially quanti-
fied three-dimensionality for an individual discrete bedform through the ratio of the
streamwise extent of its crestline to its cross-stream crest width. He later adopted an
alternative ratio of streamwise crest spacing to cross-stream crest width (Allen
1969 ). Venditti et al. ( 2005b ) present a further form of this approach, quantifying
three dimensionality for an individual bedform as the ratio of curved crest length to
cross-stream crest width.
Recently, riverbed surfaces have been analysed as 3D random fields in contrast
to combinations of discrete bed elements (e.g. Nikora et al. 1998 ; Goring et al.
1999 ; Butler et al. 2001 ; Nikora and Walsh 2004 ; Aberle and Nikora 2006 ). Sand-bed
investigations along this line are presented below, along with comments on the
approaches, example results, and discussions of implications.
3.1 Bedform Three-Dimensionality and Laser Scanning
Recognising the increasing use of lasers to profile sediment surfaces (e.g. Nairn
1998 ; Coleman et al. 2003 ; Aberle and Nikora 2006 ; Tuijnder et al. 2009 ), the
measurement of bed surfaces using a 3D scanner was investigated. The Polhemus
FastSCAN system utilised compiles measurements of 3D surfaces obtained by
sweeping the scanning wand over the surface in a manner similar to spray painting.
The handheld wand projects a narrow line of laser light onto the surface, with the
intersection of the laser line and the surface in 3D space being recorded using the
two cameras of the SCORPION wand used in the present tests (Fig. 4c ). During
scanning, the relative location and orientation of the wand is determined using an
electromagnetic tracking system, enabling the 3D surface to be accurately recon-
structed from the handheld scanner measurements as the scanner moves throughout
space. The system is fast, flexible, portable, and easy to use and has been adopted
in biomedical imaging, recording of archaeological artefacts, industrial design,
and the production of movies and video games. Of particular relevance to the
present study, the FastSCAN system was used by Smart et al. ( 2004 )toanalyse
the roughness of alluvial beds in the field. Owing to its electromagnetic operation,
the system is limited in the presence of large metal objects, which became a significant
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