Environmental Engineering Reference
In-Depth Information
occurrence and finally summed for 'm' discharge
classes to yield a time-integrated value of excess
stream power,
V
e
:
The result of Equation 5.2 is given as stream
power with units of watts (per unit channel
length) but can be expressed as an 'annualized'
quantity of excess energy (for an average year in the
period of flow record), or Annual Geomorphic
Energy (AGE), in units of kilowatt-hours (kWh),
where one kWh is the quantity of energy equiva-
lent to a steady power of 1 kW running for 1 hour
(or 3.6 megajoules of energy consumed). By mak-
ing this adjustment, the final value represents
energy consumption rather than rate and is com-
parable to the more conventional measure of an-
nual sediment yield.
Further details of the development and a pre-
liminary application of REAS are provided by Soar
et al. (in press).
"
#
V
e
¼
m
j
F
j
W
j
X
n
i
P
i
v
j
v
ci
ð
5
:
2
Þ
¼
1
¼
1
where F
j
¼
decimal frequency of occurrence of each
discharge class, j, W
j
refers to the channel width for
each discharge class,
v
j
¼
corresponding specific
stream power (W/m
2
) as defined in Equation 5.1,
v
ci
¼
critical specific stream power (W/m
2
) for ini-
tiating transport of the median grain size of each
size class, i, in the particle size distribution of n
classes, and P
i
¼
decimal frequency of occurrence
of each size class in the particle size distribution.
The critical specific stream power is estimated
usingFerguson's (2005) expression, below, basedon
a reanalysis of Bagnold's original equation (1980):
Data requirements and outputs
The input variables required for each reach in
REAS (Fig. 5.6) are:
1 bed material particle size or size distribution;
2 flow duration curve;
3 channel cross-section;
4 channel slope;
5 channel and floodplain roughness coefficients
(Manning n values).
"
#
D
i
D
b
0
:
4
0
:
6
0
:
73
S
D
i
D
b
v
ci
¼
0
:
113D
1
:
b
log
ð
5
:
3
Þ
where D
b
¼
median particle size found in the bed
material (mm); D
i
¼
median particle size found in
size class i (mm), and S
¼
channel slope.
Fig. 5.6
Input data required for
each sediment reach when using
REAS (River Energy Audit
Scheme) to analyse the spatial
distribution of Annual
Geomorphic Energy (AGE) in a
river network.
