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
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
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.
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
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
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.
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
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
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
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)
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
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