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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
  
    
zug p ILI 
200 400 600 800 1000 
400 420 440 460 480 
Aititudes (m) Altitudes (m) 
Figure 5 : statistical representation of the relationship between 
altitudes and slope in two zones located in Oklahoma (left) and 
the Ferro basin in Italy (right) (Depraetere 1984). 
On the graph, zones where the average slope profile is positive 
helps to identify the distribution of altitudes in concave zones, 
while convex zones are identified by negative slope sectors of 
the average sector. The dominant statistical tendencies in the 
profiles of the slope faces can thus be quantitatively estimated. 
3.3 The orientation 
The orientation of a slope determines the quantity of solar 
radiation received on its surface. Associated with the slope, it 
plays a fundamental role in differenciating the contrasts 
between the slopes, also subject to the geographical latitude of 
the site (this latter intervenes through the manner in which the 
shadows are cast onto the ground). The radiative contrasts 
generated can vary very quickly and substantially, emphasizing 
the effects of external processes and influencing the vegetation 
on ground level. The expression of the orientation with a 
polynomial model seen previously is given below (4). 
-a ) 
arccos di ii a<i) 
a +h ) 
4) 
-arccos m if-q-0 
Yo p^ 
The northern and southern slope faces of a valley are exposed 
differently ; they are not subjected to the same conditions of sun 
exposure and therefore of erosion. In temperate climates, 
regions thus develop differently provoked dissymetries. The 
orientation is an indicator that can distinguish between these 
two slope faces (figure 5). 
        
   
148 
1, 
E a A” : d P 
Figure 6 : shaded DMT of Briançon (left), data from IGN’s BD 
TOPO® (step=25m) ; orientation representation thresholded at 
90? and 270? (right) , in black, orientation to the north; in white, 
orientation to the south. 
    
813 
This kind of image can be used to study the fine structure of the 
surface; the white zones in the middle of the black slope faces 
(and vice-versa) can easily be seen ; the slope contains the relief 
oriented differently from its general orientation, these are thus 
clues to understanding its structure. 
3.4 Vertical convexity 
The vertical convexity of the ground surface plays a role in the 
acceleration of transport speed of matter as slope values, whose 
variations it reflects, increase. In brief, the increase in 
competence and capacity of superficial runoff in convex zones 
can thus be described , as well as their slowing down in concave 
zones, with all the consequences implied with these phenomena 
such as the deposit of sedimentary loads. This given leads to a 
preliminary association between preferential zones of terrain 
erosion and convex zones of the terrain, and those runoffs 
coming together in concave zones without neglecting the effects 
of other factors such as the roughness of the ground. The 
expression of the vertical curvature with a polynomial model 
seen previously is given below (5). 
s ea 4 20bd+ eb? ; 
du US ©) 
(1+a +6?) 
The sign of the vertical curvature of slope lines reveals the 
convex or concave nature of the terrain, just like the horizontal 
curvature line of level lines. 
3.5 The horizontal curvature of contour lines 
The horizontal convexity of the ground surface is associated 
with the solid contributions to a zone due to the convergence or 
divergence of runoff. This curvature of the surface is a 
characteristic element of the type and evolution of a relief zone 
and will often be closely associated with zones of thalwegs or 
ridges. If the vertical curvature can be modelled into two 
dimensional profiles, it becomes absolutely essential to study 
surfaces before horizontal curvatures. It takes on very strong 
and negative values in the thalwegs, remaining weak in the 
regular slope faces and becoming very strong and positive along 
ridges. The expression of horizontal curvature of contour lines 
with a polynomial model seen previously is given below. 
_ 2abd — cb” — ea” 
Ae (6) 
The calculation of the curvatures of level lines is one approach 
to the modelling of the thalweg network and the ridge network 
which are the sites of extreme negative and positive values in 
the curvature of the level line. The final network is not 
compact, points not belonging to the network appear after all. It 
is thus merely an informative result, which is logical given the 
simplicity of the method used.