Watershed Geomorphology
9/15 Agenda
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Plot water balance components from each site
Wrap-up similarity discussion
Introduce project
Watershed delineation with DEMs
Hillslope erosional processes
Homework Due 9/19
• Obtain the values of annual Q, P, ET, and PET
from each of the three watersheds.
• Plot each watershed on a Budyko Curve (if
possible)
• Discuss similarities and differences in the
annual water balance between the three sites.
Watershed Similarity
• “Although the river and hillside do not resemble each other at first sight,
they are only extreme members of a continuous series and when this
generalization is appreciated one may fairly extend the river all over its
asin and up to is very divde. Ordinarily treated, the river is like the veins of
a leaf, broadly viewed it is the entire leaf.” (Davis, 1899)
– Recognizes the continuous series and repeating patterns of networks
– Implies infinite dissection, which is not likely true.
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Distinct process thresholds in the landscape, which create distinct pattern breaks
Watershed Similarity
• Multiple examples of self-similarity in watersheds
– Patterns at one scale are repeated across “all”
scales
– Consider the koch curve:
http://www.jimloy.com/fractals/koch.htm
– And the self-similar tree
Watershed Similarity
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Self-similar patterns exist throughout nature
Self-similar patterns exist throughout watersheds
Why?
Shreeve (1956) showed that random channel
networks evolve to self-similar states
• Rodriguez-Iturbe (199x) suggested that chance
and the tendency to evolve to least-energy
patterns leads to self-similarity
– Once an “efficient” pattern is found, it repeats itself
Process and Pattern
• Least energy patterns are non-unique
• Channels and watersheds continually adjust
their inputs
– Dynamic equilibrium
• A balanced state maintained by dynamic adjustments
as fluctuations occur in the energy flow over the short
term or as the system continuously changes its
condition over the long term
– Watersheds are open systems
• Continuous flux of mass and energy
Open Systems
• A continuous flux of mass and energy
• In physics, open systems are self-regulatory
– Adjust shape to minimize entropy, or least-energy
expenditure
• It is hypothesized that river channels adjust shape
so that energy expenditure is minimized
– Potential energy is converted to kinetic energy,
dissipated as friction at the boundaries
– Watersheds likely behave similarly
• Responsible for self-similar patterns
Patterns in Fluvial Geomorph
• Pools and riffles
– sequence is approximately x times the river width
– Self-adjusting mechanism to balance energy
expenditure along a stream
Patterns in Fluvial Geomorph
• Meandering
– Langbein and Lepold 1966: Meandering pattern
represents a least work tendency
-Yang 1971: The meandering pattern expresses the
constraints on a river so that ther is a least time rate
of energy expenditure
• Bedforms, braids, channel network…
The search for closure
• Numerous attempts have been made to derive
these “universal” properties by taking into
consideration energy dissipation
– Consider the hydraulic geometry problem
Watershed Similarity
• Not as well established as fluvial similarity
• 90’s hydrologic literature full of fractals
– Promised to “solve” the runoff generation
problem
Fractal Dimension
• The exponent in a power law function that
describes how objects change with scale
– L = CA0.6
– Consider the dimensions
• Line D=1
• Area D=2
• Volume D=3
– Fractal is somewhere in between
Dimension
• Consider a square with a side length L=1
Dimension
• Divide each side into 3 segments
N = bD
b = divisions
D = dimension
N = total segments
9 = 32
Dimension
• D = 2 regardless of divider size
N
9
16
25
b D
3 2
4 2
5 2
Dimension
• Lines, squares, and cubes are self-similar
objects
– We can break a line into x pieces and then
magnify each pieces by x to obtain the original
image
N = bD
LogN = DLogB
D = (LogN)/(LogB)
N is the number of self similar pieces
B is a magnification factor
Fractal Dimension
Replace each line with 4 lines, each with a length
of 1/3 the original.
This can be done infinitely, producing a line of
infinite length. If you were to attempt to measure
the length of this line, your result would depend
on the size of the ruler.
D = (LogN)/LogB) = Log4/log3 = 1.26
=log 16/log9= 1.26
=log64/log27 = 1.26
The Koch curve is self-similar in the 1.26
dimension
Fractals and Watersheds
• An irregular geometric object with an infinite
nesting of structure at all scales.
• Many fractals have been identified in
watershed geomorphology.
• What does the existence of self-similar
patterns and fractals mean for hydrology?
Watershed Delineation
• Digital Elevation Models revolutionized geomorphologic AND hydrologic
analysis
• 1990’s literature full of “how to” papers describing methods to extract
geomorphologic information from DEM’s
• Commercial software companies grab free, unsupported code from papers
• Commonly used programs
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ArcGIS Hydrology tools - uses some out of date concepts, incomplete
TauDEM – Doesn’t work in ArcGIS 10, works from dos prompt
RiverTools – independent, expensive but works
Many hydrologic model packages have their own GIS programs
None do everything, user must have skill and knowledge
DEM Basics
• A digital elevation model is a digital file containing
x,y,z data (i.e. long, lat, elev)
• 2 types of surface models – I will discuss the 2nd
– TIN (triangular Irregular Network)
• Irregularly spaced points linked to form a network of triangles
– Raster
• Regularly spaced grid of x,y,z
DEM Basics
• A grid file in ascii format specificies
– Arrangement of data
– Corner coordinates
– Resolution
DEM Basics
• x,y,z numbers underlie the image
DEM basics
• All GIS hydrology programs perform some
common tasks
– Fill pits
– Compute slopes
– Compute flow directions
– Compute flow accumulation
• Nearly all other operations are based on these
Grids
DEM Basics
• Basic operations produce information at each
x,y including elevation, corrected elevation,
slope, flow direction, flow accumulation
• Many hydrologic and geomorphologic metrics
are based on grids and features derived from
above grids
DEM basics
• Fill command “fills” false pits by adding
elevation to terminal sinks
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DEM Basics
Slope in cardinal direction: S= (z1-z2)/resolution
Slope in diagonal directions: S – (z1-z2)/(1.414*resolution)
-can be reported in degrees, radians, ratio, pecent…
DEM Basics
• Flow direction command assigns each pixel with a
flow direction code
DEM Basics
• Flow direction command assigns each pixel with a
flow direction code
– D8 method
• 8 flow direction choices
• Calculates slope to 8 possible neighbors
• Assigns code in direction of steepest slope
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What code would the red pixel receive?
Any potential problems?
DEM Basics
• Flow direction command assigns each pixel with a
flow direction code
– Dinf method
• Allows flow to emerge from a point in any radial direction
• Far superior, but not commonly implemented
• See TauDEM:
http://hydrology.usu.edu/taudem/taudem5.0/index.html
DEM Basics
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Flow accumulation command calculates how many pixels flow through a point by
connecting the flow direction arrows
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What is the flow accumulation of
the red pixel?
If the resolution is 10m, what is the
drainage area of the red pixel?
DEM Basics
• Flow accumulation looks like a channel network, but it’s not
DEM Basics
• Distinguishing hillslope flow paths from
streams
– Where do channels begin?
• Most programs require user to enter a threshold
drainage area
• Importance for hydrology?
– Not a straightforward problem
• Errors in connectivity create stream errors