The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
184 
alone, point D is the best choice. But, apparently stream AB 
accords to the main orientation of the river in greater degree 
than stream AC or AD, further more it has greater amount of 
water than others too. So, Stream AB is the best choice for 
mainstream and Point B should be the best choice for 
mainstream and Point B should be the headwater of the river. 
When identifying the mainstream and headwater for a river, we 
should bring the three factors together and the length principle 
can’t be adopted alone. The orientation and the amount of water 
are important as well. 
4.2 Finding the Mainstream headwater using the Multiple 
Criteria Decision approach 
As discussed before, a river often has many tributaries and we 
have to select which is the appropriate mainstream from them 
using the three principles. We use the multiple criteria decision 
approach to help us make decision. In chapter 3, we have 
constructed a tree-like rive network by replacing lakes and wide 
rivers with their centerlines, and we calculated its topology that 
provided enough information to trace the river. We trace the 
tree-like river network from the embouchure of the river (the 
embouchure can be easily found in the topographic data), and 
find all the routes that starts from the embouchure and ends at 
the leaf nodes of the river network. These routes are the objects 
set from which we choose the mainstream. We record the length 
of the route, average value of angles, number of three-arcs 
nodes of the routes, and put them into the following object 
matrix O: 
o = 
^ len\,len2,...,lenn ^ 
ang\, ang 2,..., angn 
K num\, numl,..., numn y 
Figure6. The multiformity of river and complexity on 
identifying mainstream 
4.1.2 Orientation: In the tree-like river network, the rivers are 
presented by nodes and arcs linked to them. The orientation of a 
river can be represented by the angles between arcs and their 
former arcs. When identifying mainstream, we don’t need to 
consider those nodes that have two arcs linked to them, for this 
means the river here have only one tributary. When the node has 
three arcs linked to it, the river here has two tributaries and we 
must compare which one is more suitable to form the 
mainstream. As illustrate by the figure, the smaller the angle is, 
the better the tributary accord to the mainstream. As a is 
smaller than p, stream AB is a better choice than stream AC. 
When identifying the mainstream from the river network we 
treat the mainstream as a whole, and we use the average value 
of all the angles formed by arcs that are connected by the 
three-arcs nodes to make choice. 
4.1.3. Amount of water: When there are many tributaries to be 
selected, the amount of water they contain is an important factor. 
In topographic data, there are no attributes giving the 
information of the amount of water. We can obtain the water 
amount of a river by calculating the amount of the tributaries a 
river has. The amount of the tributaries is equal to the amount of 
three-arcs nodes, so the number of three-arcs nodes a river has 
shall be a factor effecting the identifying of mainstream. 
Where lent = length of the route, 
angi = the average value of angles, 
and numj = the number of the three-arcs nodes in route; 
As the three factors have different unit we can’t compare them 
directly, so we turn the matrix into the relative matrix R: 
'r\ 1, r\2,.. 
.,r\j ' 
R = 
r2\,r22,. 
~,r2j 
^7*3 1,7*32,. 
j j 
Where 
and 
Next we should set the weight of the three factors. The weights 
of different factors represent their importance when selecting 
the mainstream. We put their weights into the weight vector W: 
W = (wj, w 2 , w 3 ). Where 0<Wj<l and w 1 +w 2 +w 3 : =l. Then we 
can get the decision vector D: D = R*W= (di, d 2 , ... , d 3 ). 
Where d; =w 1 *r li +w 2 *r 2i +w 3 *r 3 i. 
The weight vector has significant affect on the selection result. 
It is difficult to set the exact value of every factor, and 
considerable experiments are essential to set the weight vector.