Morphological Systems in a Drainage Basin
A. The Drainage Basin Cycle:
A drainage basin may be defined as that area of land from which precipitation feeds a
measuring point on a river system. In the simplest case, the drainage basin includes all the area
drained by the river and its tributaries. The drainage basin is bounded by the watershed,
separating it from adjacent basins.
In a drainage basin precipitation is converted to runoff by a series of processes that store
and transmit water over the ground surface, within the soil or within the underlying parent
material. Some part of that water may be stored near the surface and evaporated or taken up into
the vegetation and transpired.
Runoff that flows down the slopes of the land in more or less broadly distributed films,
sheets, or rills is referred to as overland flow in distinction with channel flow, or stream flow, in
which the water occupies a narrow trough confined by lateral banks.
Within this broad definition, overland flow can take many forms. It may be a continuous
thin film, called sheet flow, where the soil or rock surface is extremely smooth, or a series of tiny
rivulets connecting one water-filled hollow with another, where the ground is rough or pitted. On
a grass-covered slope, overland flow is subdivided into countless tiny threads of water, passing
around the stems. Even in a heavy and prolonged rain, overland flow in full progress on a sloping
lawn may not be visible to the causal observer. On heavily forested slopes bearing a thick mat of
decaying leaves and many fallen branches and tree trunks, overland flow may pass almost
entirely concealed beneath this cover.
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At the base of a hill slope, overland flow is disposed or by passing into a stream channel
or lake, or by sinking into the ground, should a highly permeable layer of sand, gravel, or blocky
slide rock be encountered.
Overland flow is measured in inches or centimeters of water per hour, just as for
precipitation and infiltration. Therefore, a simple formula expresses the rate at which a given unit
of ground surface will produce overland flow as follows:
Rate of production of overland flow = Rate of (precipitation - infiltration)
Seeking to escape to progressively lower levels and eventually to the sea, runoff becomes
organized into drainage systems. In a typical stream network, each fingertip tributary receives
runoff from a small area of land surface surrounding the channel. This area may be regarded as
the unit cell of the drainage system. The entire surface within the outer divide of the drainage
basin constitutes the watershed for overland flow. Thus, a drainage system is a converging
mechanism funneling and integrating the weaker and more diffuse forms of runoff into
progressively deeper and more intense paths of activity.
B. Stream Characteristics:
1. Stream channel:
The channel of a stream may be thought of as a long, narrow trough, shaped by the
forces of moving water to be most effective in moving the quantity of water and sediment
supplied from the drainage basin or watershed. Channels may be so narrow that a person can
jump across them, or as wide as 1.5 km for great rivers such as the Mississippi or Changjaing.
Taking the entire range of natural channel widths as between one foot and one mile, a
5000-fold difference in size.
Hydraulic engineers who must measure stream dimensions and flow rates have
adopted a set of terms to describe channel geometry. Depth, in feet or metres, is measured at
any specified point in the stream as the vertical distance from the surface to bed. Width is the
distance across the stream from one water edge to the other. Cross sectional area "A" is the
area in square metres or square feet. Wetted perimeter "P" is the length of the line of contact
between the water and the channel, as measured from the cross section.
Channel slope "S" (gradient), is the angle between the water surface and the
horizontal plane. Slope can be started in feet per mile or metres per kilometre. Thus a slope of
5 ft/ml. means that the stream surface undergoes a vertical drop of 5 ft. for each mile of
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horizontal distance downstream. Slope can also be given in terms of percent grade. A grade
of 3 percent, or 0.03, means that the stream drops 3 feet for every 100 feet of horizontal
distance.
2. Stream flow:
Gravity acts upon the water of a stream to exert pressure against the confining walls.
A small part of the gravitational force is aimed downstream parallel with the surface and bed,
causing flow. Resisting the force of downstream flow is the force of resistance, or friction,
between the water and the floor and sides of the channel. As a result, water close to the bed
and banks moves slowly that in the deepest and most centrally located zone flows faster.
Because the average velocity at a given point in a stream differs greatly according to
whether it is being measured close to the banks and bed, or out in the middle line, a single
figure, the mean velocity, is computed for the entire cross section to express the activity of
the stream as a whole. Mean velocity in streams is commonly equal to about 60% of the
maximum velocity.
Another measure of stream flow is discharge (Q), defined as volume of water passing
through a given cross section of the stream in a given unit of time. Commonly, discharge is
stated in cubes metres per second. Discharge may be obtained by taking the mean velocity
(V), and multiplying it by cross sectional area (A). This relationship is stated by the import
equation - 'the equation of continuity of flow':
" Q = VA"
Stream channels differ in the amount of resistance offered to flow. Resistance is large
in abroad but shallow channel, and is much less in a deep, narrow channel. The optimum
channel would be semi-circular in cross section. However, streams are often required to have
broad, shallow channels because of the load to mineral matter that must be carried, or
because the banks are weak and will not hold a steep attitude.
It is intuitively obvious that water will flow faster in a channel of steep gradient than
one of low gradient, since the component of gravity acting parallel with the bed is stronger
for the steep gradient.
Velocity increases quickly where a stream passes from a pool of low gradient to a
steep stretch of rapids. As velocity increases, cross-sectional area "A" must also decrease, for
otherwise their product, "AV" could not be held constant. In a pool, where velocity is low,
cross-sectional area is correspondingly increased.
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Stream flow, as measured by the hydrologist, is recorded in the form of a hydrograph
which shows the variation of discharge with time at a certain location of a river. It is possible
to distinguish the level of base flow, resulting from runoff supplied by ground water from that
of flood flow, which produces a series of sawtooth-shaped fluctuations in the hydrograph.
The peak of discharge is usually obtained sometime after the most intense rain has ceased
(Basin Lag).
A hydrograph has several components:
a. Discharge is the amount of water flow in the river. It varies from time to time, and from
place to place along a river.
b. Base flow is much more constant in amount and the water level is nearly the same. Even if
there is long drought, a large river system still has a certain base flow. The water in base
flow is discharged from delayed ground water flow in soil during ordinary time. Usually
the base flow is highest just after the flood.
c. Rainfall always occurs before the greatest flood reaches a section of a river. Its intensity is
partly responsible for the magnitude of the peak.
d. The rising limb has its steepness determined by the rate of surface runoff. The higher the
peak, and the shorter the basin lag, the steeper will be the rising limb. The gradient of the
profile reflects the rate of rising flood.
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e. The peak shows the maximum flood level. Peak usually occurs sometime after the most
intense rain. There may be more than one peak.
f. Time indicates when the peak of flood level occurs.
g. Basin lag is the time between the heaviest rain in a thunderstorm and the peak. The lag is
determined by the nature of soil moisture, the structure and relief of the basin and the
intensity of the thunderstorm.
h. Storm runoff occurs during flood. It is really flood water, collected from surface runoff
and quick subsurface flow during heavy rain.
i. The recession limb indicates the rate of passing flood.
From such hydrographs, much information about the magnitude and frequency of
discharge peaks can be gleaned which is of great use to engineers and hydrologists in the
planning of irrigation and power development, drainage system, water supply and flood
forecasting. The flood hydrograph is also of particular interest to geomorphologists because
the variation of the hydrograph shape from basin to basin shows the dependence of the
discharge on geological and morphological characteristics of a drainage basin. A flast stream
has a hydrograph with a sharp peak, resulting from high immediate surface runoff, with little
absorption and storage of water in the basin.
In many parts of the world, spring is a time of floods because the flow of rivers is
augmented not only by spring rains but also by snow-melt. Although some rivers flood quite
regularly, the recurrence interval (time between floods) varies from basin to basin and varies
with the magnitude of the flood.
C. Fluvial Morphology
Measurement of shape, geometry of any natural form - be it plant, animal or relief feature
- is termed morphometry. Fluvial morphometry denotes the measurement of geometrical
properties of the land surface of a fluvial erosion system.
1. Basic form elements of a fluvial erosion landscape:
a. Linear Properties of the Stream Channel System:
A branching system of lines is analyzed regardless of differences in channel widths,
all streams are considered as pure lines, have infinitely small width. Linear properties are
therefore limited to the numbers, lengths and arrangements of sets of line segments.
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b. Areal Properties of Drainage Basin:
These include the surface areas of drainage basins as well as descriptions of the
shapes of those basins. Area is a two-dimensional properties, the product of both length
and width whereas lines have only the one dimension of length. As a generalization, it
can be stated that areas perform best the function of intercepting precipitation and of
supplying rock debris, whereas lines (channels) perform best the function of transporting
water and debris out of the area.
c. Relief Properties of the Fluvial System:
These refer to the relative heights of points on surfaces and lines with respect to the
horizontal base of reference. In other words, relief expresses the magnitude of the vertical
dimension of the landform and also the gradient of ground surfaces and stream channels.
Such measurement tells the rate of drop of the runoff and are measures of the intensity of
the processes of erosion and transportation.
2. Measurements:
a. Stream Orders:
Given a map of a complete stream channel network, we can subdivide the network
into individual lengths of channel, or channel segments, assigning a sequence of numbers
to the orders. Each fingertip channel is designated as a segment of the first order. At the
junction of any two first-order segments, a channel of the second order is produced and
extends down to the point where it joins another second-order channel, where upon a
segment of third-order results and so forth. The trunk stream of any watershed bears the
highest order number of the entire system. Channels of the first and second order usually
carry flowing streams only in wet weather.
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If a large numbers of channel network in a given region are divided into segments,
each assigned an order according to the above rules. It will be possible to make some
generalizations about the form and dimensions of the drainage network characteristics of
that region. Consider first the distribution of numbers of segments of each order in a
single watershed. For example, the following table shows the number of stream segments
of each stream order in the drainage basin of the Big Badlands of South Dakota.
Stream Order (u)
No. of Stream Segments (Nu)
Bifurcation Ratio (Rb)
--------------------------------------------------------------------------------------------------1
139
---2
46
3.02
3
11
4.18
4
3
3.66
5
1
3.00
==========================================================
The order of a stream segment is designated by the symbol 'u'; the ratio between the
number of stream segments of any given order to the number of segments of the next
higher order, a proportion designated the bifurcation ratio (Rb). The bifurcation ratio
between successive orders is then defined as:
" Rb = Nu / (N(u+1)) "
Studies of many stream networks confirm the principle that in a region of uniform
climate, rock type, and stage of development, the bifurcation ratio tends to remain
constant from one order to the next. Values of bifurcation ratio between 3 and 5 are
characteristics of natural stream analysis.
b. Stream Numbers:
R.E. Horton had formulated a law of stream numbers:
"The numbers of stream segments of successively lower orders in a given basin tend
to form a geometric series, beginning with a single segment of the highest order and
increasing according to a constant bifurcation ratio."
For example, if the bifurcation ratio is 3, and the trunk segment is the sixth order, the
number of segments will be 1, 3, 9, 27, 81 and 243.
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The formalized statement of Horton's law of stream numbers is then as follow:
" Nu = Rb(k-u) "
Where Nu = number of stream segment
Rb = bifurcation ratio
k = order of the main trunk stream, i.e. the segment of highest order
u = stream order
Horton further observed that the total number of stream segments of the entire
drainage basin can be expressed as follows:
" Nu = (Rbk - 1) / (Rb - 1) "
c. Stream Length:
It is apparent that the first-order channel segments have, on the average, the shortest
length, and that the segments become longer as order increases. The mean length of
stream segments, in kilometres, increases by a ratio of roughly 3 times with each increase
in stream order. This proportion of length increase is known as the length ratio (R1 = 3),
and tend to be approximately constant for a given drainage system. Chance variations to
be expected in the configuration of any drainage system will produce inequalities of
observed length ratio from one order to the next.
Definition of length ratio resembles that of bifurcation ratio:
" R1 = Lu / (L(u-1)) "
where Lu = mean length of all stream segments of order u.
Horton's law of stream length: "The cumulative lengths of stream segments of
successive orders tend to form a geometric series beginning with the mean length of the
first-order segments and increasing according to a constant length ratio."
d. Stream Slopes:
Channel slope is defined as the ratio of vertical drop to horizontal distance, measured
from the upper end to the lower end of a single stream segment of a given order. Slope is
stated as a ratio. Thus a slope of 0.01 is a ratio of 1:100. i.e. a drop of 1 metre vertically in
100 metres horizontally.
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e. Basin Areas:
Horton's law of basin areas: " The mean basin areas of successive stream orders tend
to form a geometric series beginning with mean area of the first-order basins and
increasing according to a constant area ratio."
" Ra = Au / A(u-1) "
where Ra = area ratio
Au = mean area of basins of order u
Therefore, the law of basin areas is:
" Au = A1 * Ra (u-1) "
Usually, the discharge of a stream increases with increasing drainage area.
f. Drainage Density and Texture of Topography
Suppose that a drainage density value of 12 is obtained; this number is interpreted as
meaning that there are 12 km of channel for every sq. km. of land surface. Because area
and length are measured from a map, which projects the sloping surfaces and somewhat
less than the true values, to a degree depending upon the amount of slope. The equation of
drainage density is
" D = S(LK) / AK "
where D = drainage density
LK = total length of streams (km)
AK = area of the basin (sq. km.)
There are several factors controlling drainage density, but the most important control
factor is exerted by the infiltration capacity:
Geology (Rock Type): Hard, resistant rocks, such as intrusive granitic rock, sandstone,
conglomerate and quartzite, tend to give low drainage density (coarse texture).
This is because stream erosion is difficult and only a relatively large channel
can maintain itself. Therefore, the first-order basins are large and provide large
amount of runoff to the channels. In weak rock such as shales and clays, even
a small watershed can supply enough runoff for channel erosion, and tend to
give high drainage density.
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Highly permeable materials, such as sand or gravel, tend to give low drainage
density because infiltration is great and little water is available as surface
runoff to maintain the channels. Clays and shales, on the other hand, have a
high proportion of surface runoff and this combines with their weakness to
give high drainage density.
Topography: Runoff tends to be encouraged on steep slopes, and having a high
drainage density. However, it is reduced where the land is flat because water is
ease to infiltrate into the ground.
Vegetation: Dense vegetation helps to intercept rainfall, to increase the infiltration
capacity of the soil and to prevent overland flow. Where vegetation is sparse,
drainage densities are much higher. For example, badlands are characteristics
of arid climates and the drainage density there tends to be markedly higher on
all rock types.
Climate: Generally, the drainage density is highest in areas of high rainfall. But it is
not invariably so; for three reasons.
i. Balance between rainfall and evapotranspiration. Where evapotranspiration is
high, less rainfall is available for erosion and channel formation.
ii. Rainfall and vegetation tend to be closely related, so that areas of high rainfall
are often characterised by a dense vegetation cover; as we have seen, the
vegetation encourages infiltration and reduces runoff.
iii. Intense storms lead to more overland flow than prolonged, light rain.
Thus the relationships between climate and drainage density are often
complex.
g. Conclusion:
The mathematical laws of Horton, governing stream numbers, lengths, areas and
slopes, taken together, form a modern extension of Playfair's law of stream. Playfair's law,
a purely qualitative expression, states that:
" The branches of a stream run in valleys proportional to their sizes and that they have
a nice adjustment of their decluilies (slopes)."
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3. Drainage patterns:
The patterns which stream systems exhibit are largely governed by two factors:
i. the initial slopes of the area in which they develop and
ii. local differences in the resistance of the rocks.
http://www.il-st-acad-sci.org/kingdom/geo1005.html
a. Dendritic Pattern:
A dendritic pattern of drainage is a tree-like, random
branching pattern developed in a region of uniform or
homogeneous rock. There is no strong local variation in rock
resistance.
b. Rectangular Pattern:
A rectangular pattern of drainage is a rectilinear or grid-like stream pattern developed
in a region with strong marked joint systems or faults intersecting at approximately right
angles. The tributaries develop along the joints or faults along which erosion is more
effective. Thus this pattern is largely controlled by structural weakness.
c. Trellised Pattern:
A trellised pattern of drainage is a rectilinear stream pattern
developed in a region of alternate layers of resistant and less
resistant rocks which dip in the same direction. The rock layers
lie at right angles to the general slope down which the main
stream, called consequent stream, flows. The streams join one
another at right angles. The first set of tributaries which join the consequent stream are
called subsequent streams. It is common in scarpland regions and regions of folded rocks.
d. Radial Pattern:
A radial pattern of drainage is a stream pattern developed on
a structure dome, a volcanic cone, and uplifted fault block, or a
conical hill. The streams radiated from the crest or common core
as the uplift.
e. Centripetal Pattern:
A centripetal drainage pattern consists of streams drainage from different directions
towards the centre of a depression or basin. This pattern is common in inland basins
where streams terminate in a lake at the centre, and do not drain into the sea. Streams in
intermontane basins or desert basins often develop this pattern.
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