CALCULATING RIVER LENGTH BASED ON TOPOGRAPHIC DATA 
ZHANG Lijuan 1 ' 2 HUANG Wei 2 JIANG Jie 2 
’China University of Mining and technology, Xueyuan road, Haidian district,Beijing,China 
2 National Geomatics Center of China, Baishengcun, Zizhuyuan, Beijing, China - 
zhanglijuan_ngcc@ 163 .com 
KEYWORDS: River Length, Topographic Data, Identifying Mainstream, Centerline, Multiple Criteria Decision 
ABSTRACT: 
River length has been the particular interest of people. Topographic data, which are obtained from field survey or digitizing from 
topographies, can serve as ideal data source for river length calculating. The topographic data are vector-based data, which represent 
river entities as polygonal line. Depending on data scale, rivers are represented in topographic data as single-line (narrow) or 
double-line (wide). Unlike single-line rivers, double-line rivers can’t be used to computing length directly. So we constructed a 
tree-like single-line river network by replacing double-line rivers and lakes with their centerlines. The exact river length is 
determined by the position of the headwater and the position of the embouchure. The headwater is difficult to be located in the 
topographic data, for relatively large rivers usually have numerous tributaries. There are presently three principles to accord when 
determining the mainstream and the main headwater: a) Length; b) Orientation; c) Amount of water. We use the multiple criteria 
decision approach, which is a well-known general approach, to determine the best one from many choices based on the three factors 
and their weights. 
1. INTRODUCTION 
River length has been the particular interest of people, for 
rivers are the ecological chain on which human and other life 
rely and they play an important role in human civilization 
development. Considerable work has been done by geographers 
tring to find out the exact river length. The traditional way is 
surveying the river length from the topographies. The 
topographies are derived through field survey by surveyors. 
This method is time and labor wasting, and often fails to get 
precision result. Since topographic data are obtained from field 
survey or digitizing from topographies, they can serve as ideal 
data source for river length calculating. 
The start and end point of a river are referred to headwater and 
embouchure. Headwater is the water from which a river rises, 
and it can be fountain, lake or glacier. The headwater differs 
due to variable situations. Embouchure is the end of a river 
where it flows into the sea, other river (tributary flows into 
mainstream), lake, etc. The exact river length is determined by 
the following factors: the position of the headwater; the 
position of the embouchure and the source data used. Unlike 
the embouchure, which can be easily found out, the headwater 
is difficult to be made certain in the topographic data. 
Generally speaking, relatively large rivers usually have more 
than one headwater stream, so we have to select an appropriate 
headwater stream as the mainstream while leave others as 
tributaries. There are presently three principles to accord when 
determining the mainstream and the main headwater: a) Length: 
The headwater stream from which the river has the longest 
length can be the mainstream; b) Orientation: The headwaters 
stream which accord to the main orientation of the whole river 
can be the mainstream; c) Amount of water: The headwater 
stream which has the largest amount of water can be the 
mainstream. The multiple criteria decision approach is a 
well-known general framework to determine the best one from 
many choices based on multiple factors and their weights. This 
optimization technique is well founded in mathematics, 
operations research, and in decision making. This general 
concept allows for the solution of an overall, complex problem. 
This paper proposes to use multiple criteria decision approach 
for mainstream selection based on the three factors discussed 
above. 
The topographic data are vector-based data, which represent 
river entities as polygonal line. Depending on data scale, rivers 
are classified as single-line (narrow) or double-line (wide). 
Unlike single-line rivers, the double-line rivers can’t be used to 
computing length directly. So a single-line river network and its 
topology structure must be constructed before performing 
further analysis. 
The paper is organized as follows: after a review of related 
work, the construction of single-line river network using the 
centerline replacing the double-line river is presented, together 
with some examples showing the possibilities of wide rivers 
and lakes. Then the approach for mainstream selection based on 
multiple criteria decision is shown, giving the theoretical 
background. Finally, a summary concludes the paper. 
2. RELATED WORK 
Centerlines are traditionally used to generalize river and road 
systems (Nickerson, 1998), and it is well studied both in image 
analysis (Duda and Hart 1973) and computational geometry 
(Aggarwal et al. 1989). It can be extracted by computing 
Voronoi diagrams (Boissonnat et al. 1993; Fortune 1987) or 
constrained Delaunay triangulations (chew 1989). McAllister 
and Snoeyink present the medial axis generalization of river 
networks to get the benefit of calculating surface area. 
There are mainly three factors affecting the identifying of the 
mainstream (LIU 2001; QU 2004). Qu (2004) studies the 
XIUHE upriver situation and compares three large tributaries 
using the three factors to determine the headwaters of XIUHE 
river. WU (1995) present an approach that constructs the river 
system and selects the mainstream of a river mainly based on 
the length principle. GUO (2003) organizes river data as graph 
structure and determines the mainstream using its depth and 
orientation in the graph.