q=r*da
DESCRIPTION
As you move down a watershed, the drainage area increases and the discharge increases. Q=r*DA. Since Q ↑ as DA↑ downstream and Q=w*v*d Then d, w , and v all tend to increase downstream as WA increases. x 1. x 2. x 3. w=nQ a v=pQ b d=qQ c n*p*q=1 a+b+c=1. Stream cross-section. - PowerPoint PPT PresentationTRANSCRIPT
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Q=r*DA
As you move down a watershed, the drainage area increases and the discharge increases
x4
x3
x2
x1
Since Q ↑ as DA↑ downstream
and Q=w*v*dThen d, w, and v all tend to increase downstream as WA increases.
x1x3
x4x2
Stream cross-section
w=nQa
v=pQb
d=qQc
n*p*q=1a+b+c=1
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Q=wvd=(nQa)*(pQb)*(qQc)=npqQa+b+c
which can only be true if npq=a+b+c=1
rDA=wvd=(n(rDA)a)*(p(rDA)b)*(q(rDA)c)
So that w=nrDAa, v=prDAb, and d=qrDAc
We can also write w,v and d as functions of DA
since Q=rDA
These relationships can tell us how the width, velocity and depth of a river will change as its discharge increases or decreases.
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Drainage Area (km2)
10
1.0
100
o
ooo
o
ooo
Slope =0.55Width (m)
1 10 100 10000
1
2
Log10 width
0 1 2 3
Log10 Drainage Area
Log w =0.23 + 0.55 Log DAw= 1.7DA0.55
How stream width increases with Drainage Area in the Upper Oldman R
W
DA
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Drainage Area (km2)
oo
oo
Slope of depth line=0.25
o
o
o
o oSlope velocity line =0.2
Depth m
1.0
0.1
0.1
1.0
Velocity m/sec
o
o
o
o
o
o
o
1 10 100 1000
v=0.24 DA0.2
d=0.22 DA0.25The exponents for width, velocity and depth add up to 1
How stream velocity and depth increase with drainage area in the Upper Oldman R
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Since w=nQa and v=pQb and d=qQc
We can writeLog w=Log (nQa)=Log n + Log Qa = Log n + aLogQOr since Q=rDALog w=Log (nrDAa)=Log n + Log r + Log DAa = Log n + Log r + aLogDA
And similarlyLog v=Log p + Log r + bLogDA, andLog d=Log q + Log r + qLogDA, andLog 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.
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0
0.2
0.40.6
0.8
1
1.2
1.41.6
1.8
2
0 500 1000 1500 2000 2500
Drainage Area (km2)
Mean velocity (m/s)
v= 0.24 DA 0.2
•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
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frequency
velocity (m/s)
Cumulative Frequency (percentiles)
100%50%
About 90% of the river has velocity less than this value
100%
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
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0
0.2
0.40.6
0.8
1
1.2
1.41.6
1.8
2
0 500 1000 1500 2000 2500
Mean velocity (m/s)
Drainage Area (km2)
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
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0
0.1
0.20.3
0.4
0.5
0.6
0.70.8
0.9
1
0 500 1000 1500 2000 2500
Proportion< given velocity
1.2 m/s
1.0 m/s
0.8 m/s0.6 m/s
0.2m/s0.4m/s
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
Drainage area (km2)
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10
20
30
50
40
500 15001000 2000 2500
oo
o
oo
o
o
o
o
o
o
oo
o
o
o
o
o
0.6-1m /sec adult trout0.2-0.6m/sec juvenile trout
0-0.2m/sec trout fry
% of habitat
Drainage area (km2)
o
o
o
o >1m/s very large adults
Low velocity habitats predominate in the upstream sections and medium and high velocity habitats become more predominant downstream
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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
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Runoff is highly variable from year to year
Fig 5-14 from your text