International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
DO 530600000
mo
4
Altitudes in meters
Figure 2 : theoretical case of an altitudinal spectrum
representing a system of terraces with several surfaces
(Depraetere 1984)
As for any discrete random variable, it is possible to define the
distribution function of the altitude from the law of distribution
defined above. The accumulated probabilities are copied onto
the Y-axis, the altitudes still being represented on the X-axis.
Altitude values are usually standardized along the X-axis, as
well as an interchange between the two axes; the curve
produced is called an hypsometric curve (fugure 3). It is a
descriptive statistical figure well adapted to the study of a slope.
Its shape provides a standard description of the organization of
rock volumes and reflects the evolution of the landscape. The
calculation of the area located beneath the curve gives a value
called an hypsometric integral. For a given altitudinal
magnitude, the potential energy contained in the rock mass in
relation to the base level can be estimated. This estimation is
important for the evaluation of transport processes. Like
pressure and temperature in chemistry, hypsometric curves and
integrals can be considered as variables of state.
Percentage Hypsometric Plot for After Dolo Set
Relative Height. (h/H)
o 2
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e
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0.0
0.0 0.2 0.6 0.8 1.0
ees Area, (o/h)
Figure 3 : hypsometric curve (right) of Mount Saint Helens
after the eruption. The calculated value of the hypsometric
integral indicates a change from 0.58 to 0.64 after the eruption.
A convex curve signifies a young landscape with an important
energy potential of rock mass in relation to base level,
suggesting tendancies like perching throughout the region, the
presence of entrenchment valleys, sharp slopes with probable
active transport processes. Inversely, a concave curve signifies
the development of surface erosion adjusted to the base level of
the zone. The energy potential is transformed into mechanical
and kinetic energy leading for example to the erosion of
interfluve zones.
3.2 The slope
1
ULLALLALALARI
The vector is represented by the equation P= |
grad(Z)
812
; a+ex+dy+e' .
whose coordinates are thus for the
b+dx+ey+e"
polynomial model proposed. If the norm on the surface of the
terrain and the vertical at this site form an angle a, the module
of the slope vector ,usually called slope, is equal to the tangent
of the angle a which can be considered equal to a^ - b^ . The
slope can be assimilated to a force field, whose exploitation is
fundamental in order to model the dynamics of the sloped basin.
As for altitude, certain representations can be fruitful, especially
to study dynamic factors of the local geomorphology. By the
study of representational modes on the clinographic curve
(figure 4) and the equivalent of hypsometric curve slope angles
for altitudes, identification of the process functioning threshold
is possible. The estimation of lower limit, characteristic and
higher limit angles of the modes are potentially associated with
the nature of each dominant rock in the zone studied. The
superimposition of clinographic curves characteristic of each of
these rocks with the general clinographic curve of the zone can
be used to estimate the role of each of the rocks in the relay
process which exists between them, and therefore, on the
general dynamics of the zone; however, taking the morpho-
structural context, structural stage of evolution and the
vegetation cover into account can make this type of study rather
complex.
Slope equilibrium
^ "n of shales
25
f Slope equilibrium
of weathered sand stones
20
\ / : Slope equilibrium
15 A A) of marls
P
e
r
C N / \
e i m ur
n NA NUN Slope equilibrium
t ! \ of sand stones
a 10 4 N
g in pe Colluvions
e A ds SS if Scarps
5 d re Y 2 $2 . Ap
^ Sy S À e i Te S4
J o v AL
0 z 1 Y SC £ >. u“ ew y 1 >
0 10 20 30 40 50
Angles in degrees
Figure 4 : theoretical case of a clinographic curve in a
lithologically contrasted region (Depraetere 1984)
The spectral distribution of slopes can also be calculated, as is
the case for orientations. It must be recalled that the quantitative
diagnosis made is not necessarily the determining factor in
relation to other elements of the landscape such as the type of
rocks, the vegetation cover, man-made modifications... The
combined study of hypsometric and clinographic curves
provides a better understanding of links between the shapes and
processes in a given zone. A comparison with studies made on
the characteristic elements of the relief is easy.
The fusion between the two indicators of altitude and slope
provides effective statistical data on the curvature of the slope
faces, by the representation of the clino-hypsometric curve
(figure 6) ; altitudes are traditionally represented on the X-axis
and slopes on the Y-axis. The cloud of points thus produced
makes variable densities typical of curvature in the zone
visually appear. The cloud of points reveals the profile of an
average slope face indicative of the general layout of curvatures
in the zone.
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