# Bed form tracking

## Principles and calculation of bed form tracking

The basic principle of bed form tracking is the computation of the bed load transport from bed form profiles measured at successive time intervals under similar flow conditions (Figure 1). Assuming steady flow conditions and undisturbed bed form migration, the bed load transport rate can be computed from the bed form dimensions (Engel and Lau, 1980, 1981, De Boer, 1996).

The bed load transport (in kg/sm) can be determined as:

$S_b=\alpha\,_s\rho\,_s(1-p)fa\Delta\,$

in which:

$\alpha\,_s$ = coefficient (0.5 to 0.6),
p = porosity factor (= 0.4),
$\rho\,_s$= density of sediment particles (= 2650 kg/m3),
$\Delta\,$= average bed form height (m)
f = shape factor = $2V/(\Delta\,L))$ with: V = volume of bed form per unit width, L= bed form length.
a = average migration velocity (m/s),

To apply this equation, the migration velocity and the bed form height must be determined from the bed profiles. The bed load transport rate can also be computed directly from the (successive) profile data using all data instead of selecting the characteristic parameters such as the average migration velocity and the bed-form height (see Havinga, 1982). To collect the bed profile data along a prefixed course, an accurate three-dimensional measuring system must be available consisting of a two-dimensional horizontal positioning system and a one-dimensional vertical sounding system. In (isolated) field conditions, where an accurate positioning system is too complicated, a much simpler method can be used. By means of an analogue echo sounder two or more successive bed-profile registrations can be made in a longitudinal section between two well-defined cross-sections (bank marker). Using a simple hand method, the average migration velocity and bed-form height can be determined quite easily, as shown in Figure 1A. Engel and Wiebe (1979) report an overall inaccuracy of about 40 to 50% for flume conditions. Figure 1B shows measured and computed transport rates for flume conditions (Simons et al, 1965). For field conditions the inaccuracy may be as large as 100%. De Boer (1996) has developed a dune-track computer program to estimate the bed load transport from successive bed profile measurements. The k-factor was found to be 0.64 for the Dutch IJssel river. The length of each profile should at least be between 1 and 3 km. The local bed load transport may vary between 50% and 200% of the average value for one profile.