EH PA]: Res 
fige7e Description picture of DEM cent- 
ral part before "structurization" 
  
fig.8. The picture after "structurization" 
(1) - heights isolines 
(2) - edges of graph 
(3) - roots FAA boundaries, 
drainage network /NMDN/. 
On fige10.1-10.6 we have shown in black 
nodes where S(i,j)>S, and on fige11.1- 
11.6 nodes where K(i,j)>K, corresponding- 
ly for S =0,1,50,100,200,500 and for 
K =1,2,3,5,10,20. R means ratio of marked 
nodes to their common number in per centse 
The present pictures show that the more a 
threshold is the higher is a level of dra- 
inage network generalization, Hence, if 
we Say "thalveg of first order" we have to 
point input data scale, discretization 
step and tolerance of DEM points measuring 
K and S values in initial points /leaf no- 
des/ of drainage network. 
4 
a number of holes 
240 
220, 
200, 
180, 
140 | 
  
   
number of passes 
   
  
20 40 60 80 100 {20 440 480 
fig.9. "Structurization procedure" con- 
vergence graphe 
Values of the surface describing functi- 
ons may serve as measure of drainage net - 
work stability and drainage basins in the 
whole as closed hierarchical systems. Pre- 
liminary analysis of the functions distri- 
bution allows to evaluate the level of the 
development of the earth surface and its 
washing up of water erosion. 
The pictures can be interpreted as tempo- 
ral images of the drainage network forms- 
tion process. In this case the functions 
values can determine the distinction mea- 
sure of the substrat properties which the 
drainage network has been formed one. If 
we consider these images in the reverse 
order we can interpret them as process of 
the network developmente The K/S ratio de- 
termines the measure of the flowlines mer- 
ging accumulated from the definite area 
and characterizes the internal surface 
geometry. 
4e SOME APPLICATIONS OF THE MODEL 
It seems obvious that in the.frame of the 
suggested mathematical model the most of 
tasks of the morphometrical analysis can 
be reduced to the simple algorithms on 
trees. For example, to define the lengths 
of thalvegs sections it's sufficient to 
calculate the paths lengths between the 
corresponding nodes, The corresponding 
slopes square value is determined as the 
difference of S values on these nodes mi- 
nus the path length. The same procedure 
of the K-values gives the approximate 
length of the slopes limiting watersheds. 
The definition of the Strahler's orders of 
thalvegs is reduced to the definition of 
the nodes ranks and arcs orders in the 
NMDNe As we can define the DB boundaries 
for any point of DEM, so we can construct 
the complete map of the drainage basins 
boundaries of any order. The hierarchy of 
these boundaries is the same as the one 
of the drainage network. Now we can easily