Transcript Lecture 4.ppt

As you move down a watershed, the drainage area increases and the
discharge increases
Q=r*DA
Since Q ↑ as DA↑
downstream
x1
x2
x3
Stream cross-section
x4
x1 x2x3
x4
and Q=w*v*d
Then d, w, and v all
tend to increase
downstream as WA
increases.
w=nQa
v=pQb
d=qQc
n*p*q=1
a+b+c=1
Q=wvd=(nQa)*(pQb)*(qQc)=npqQa+b+c
which can only be true if npq=a+b+c=1
These relationships can tell us how the width, velocity and depth of a river will
change as its discharge increases or decreases.
We can also write w,v and d as functions of DA
since Q=rDA
rDA=wvd=(n(rDA)a)*(p(rDA)b)*(q(rDA)c)
So that
w=nrDAa, v=prDAb, and d=qrDAc
How stream width increases with Drainage Area in the Upper Oldman R
100
1
0
Log10 Drainage Area
2
3
oo
Width (m)
o
10
o
2
oo
Log10 width
Slope =0.55
1
o
o
0
1.0
1
10
100
1000
Drainage Area (km2)
Log w =0.23 + 0.55 Log DA
w= 1.7DA0.55
W
DA
How stream velocity and depth increase with drainage area in the Upper Oldman R
Slope velocity line =0.2
o
o o
o
o
o
o
1.0
o
Slope of depth line=0.25 o o o
o
o
o o
1.0
Depth m
Velocity m/sec
o
0.1
0.1
1
10
100
1000
Drainage Area (km2)
v=0.24 DA0.2
d=0.22 DA0.25
The exponents for width, velocity and depth add up to 1
Since w=nQa and v=pQb and d=qQc
We can write
Log w=Log (nQa)=Log n + Log Qa = Log n + aLogQ
Or since Q=rDA
Log w=Log (nrDAa)=Log n + Log r + Log DAa
= Log n + Log r + aLogDA
And similarly
Log v=Log p + Log r + bLogDA, and
Log d=Log q + Log r + qLogDA, and
Log Q=Log r + LogDA
These relationships are useful since they allow us to plot the non-linear functions as
linear graphs, and to establish exponent values using linear techniques.
v= 0.24 DA 0.2
2
1.8
1.6
1.4
Mean 1.2
velocity 1
(m/s) 0.8
0.6
0.4
0.2
0
0
500
1000
1500
2000
2500
Drainage Area (km2)
•The bell curves rising out of the plane of the graph depict the variability of the river’s flow
regime at a series of points along the drainage—the bell curves get wider toward the right,
illustrating the increasing range of variability downstream
Cumulative
Frequency (percentiles)
frequency
velocity
(m/s)
50%
100% 100%
About 90% of the river has
velocity less than this
value
50% of the river has velocity
less than this value
Only about 10% of the river
has velocity less than this
value
Two different ways of depicting variability
2
1.8
1.6
1.4
Mean 1.2
velocity 1
(m/s) 0.8
0.6
0.4
0.2
0
The % of the river <1.2 m/s
decreases downstream
At lower velocity (eg 0.6 m/s) the
downstream decrease in % occurs
more rapidly
0
500
1000
1500
Drainage Area (km2)
2000
2500
The distance between these two lines represents the proportion of the river with
velocity between 0.8 – 1.0 m/s at the point where DA = 1000 km2
1
0.9
0.8
0.7
0.6
0.5
Proportion
< given velocity 0.4
0.3
0.2
0.1
0
1.2 m/s
1.0 m/s
0.8 m/s
0.6 m/s
0.4m/s
0.2m/s
500
0
1000
1500
2000
2500
o
% of habitat
o
50
o
40
o o
o
20
10
o
o
o
30
o
o
>1m/s very large adults
0.6-1m /sec adult trout
0.2-0.6m/sec juvenile trout
o
o
o
o
o
o
o
o 0-0.2m/sec trout fry
500
o
o
o
1000
1500
2000
2500
Drainage area (km2)
Low velocity habitats predominate in the upstream sections and medium and high
velocity habitats become more predominant downstream
Fish and other aquatic biota that live in rivers and
streams have to contend with the variability of the
flow regime.
How variable is runoff/discharge?
From year to year?
From month to month
From day to day
Runoff is highly variable from year to year
Fig 5-14 from your text