Geography Reference
In-Depth Information
depth and grain size measurements. In traditional flow
modelling methods, water depth and bed roughness are
iteratively solved based on flow and continuity (i.e. con-
servation of mass) equations. However many researchers
have considered the problem of the hydraulic roughness
exerted by the bed and its relationship to flow depth and
bed particle size. For example, Richards (1982) present a
classic form (equation 9.1) of the 'law of the wall' where
the logarithmic velocity profile is integrated over the flow
depth in order to give an equation where dimensionless
velocity (mean column velocity V/shear velocity u
∗
)is
calculated as a function of water depth, H, and D
65
(the
65th percentile of the local grain size distribution). Such
equations have long been difficult to apply in flow mod-
elling because the detailed maps of depth and grain size
were simply not available.
V
u
∗
presented in Figure 9.15 is well suited to juvenile salmonid
habitat models since they can detect areas of slow flow
which are well known to be preferred by juvenile salmon
(Armstrong et al., 2003).
The use of precision as the standard quality met-
ric in this case is inappropriate. An alternate validation
approach can be found in geostatistical methods. In such
methods, the quality of a dataset is estimated not by the
likely error of a single point but by the overall properties of
the dataset. For example, Carbonneau et al. (2003) used
the scaling properties of photogrammetrically derived
digital elevation models (DEMs) as part of the qual-
ity assessment procedure. The scaling properties of the
DEM were compared to the established scaling prop-
erties of natural surfaces in order to demonstrate that
the DEMs were not dominated by error (which also has
clear scaling properties). A similar approach is applicable
to the simplified velocity estimation method presented
above. Lamouroux et al. (1995) present an alternative
type of velocity prediction. These authors show that with
the readily available reach scale parameters of discharge,
mean roughness, mean depth and mean width, the shape
of the velocity distribution can be accurately predicted.
Rather than predicting single point, localised, velocities,
Lamouroux et al. (1995) show that we can predict the
probability distribution of velocities.
The approach of Lamouroux et al. (1995) was there-
fore used to validate the data presented in Figure 9.15.
The required discharge data was obtained. Mean depth,
mean roughness and mean width were derived from
the image data and from the image processing methods
described above. When applied to the model of Lam-
ouroux et al. (1995), this resulted in a prediction envelope
shown in Figure 9.16. This figure shows the prediction of
Lamouroux et al. (1995), in green, for the reach in
Figure 9.15 overlain on the actual calculated velocity
5
.
75 log
H
D
65
=
+
6
(9.1)
With the grain size and depth data discussed earlier in this
chapter, and with a simple continuity assumption that
in a given river cross-section, the discharge will partition
itself laterally in proportion to the depth and rough-
ness, it is possible to make estimates of local velocities.
Figure 9.15 shows an example of such velocity estimates
for a 1 km stretch of the St-Marguerite River using the
rectified projection where the river is represented as a
rectangle. Figure 9.15 provides reasonable estimates of
velocity which quite clearly captures the fast flowing areas
associated with flow constriction and the slow flowing
areas associated with an increase in cross-sectional area.
Clearly such a simplified estimation of velocity will not be
as precise or accurate as a fully calibrated and validated
computer fluid dynamics model. However, this lower
precision is offset by the potential to function over large
areas and even entire rivers. Furthermore, the type of data
1.5
100
1.0
200
300
0.5
400
0.0
100
200
300
400
500
600
700
800
900
1000
V [m/s]
Distance downstream [m]
Figure 9.15
Flow velocity (V) map estimated from bed material grain size, discharge and water depth for a 1000m reach of the
Sainte-Marguerite River (Quebec, Canada).
Search WWH ::
Custom Search