Basic Concepts and Management Issues of Rivers - River Dynamics and Integrated River Management - page 6

(a)
(b)
Fig. 1.7 C-type channel networks in the upper reaches of the Yangtze River in Yunnan Province: (a) Developing
network; (b) Developed network (See color figure at the end of this topic)
Random growth model —Leopold and Langbein (1962) proposed a random walk model, in which a
matrix or grid coordinate scheme is used within which the network grows. Each grid element represents a
unit length of possible growth. Figure 1.8 shows the homework of a student with the random growth
model. The length of a stream from initiation to its joining with another stream has a minimum limit, which
is dependent on separation or cell size, and the actual length of an individual link is, therefore, a function
of the cell size in the matrix. The square cell represents the unit area required to support a unit length of
channel. Rainfall over each unit area creates the minimum runoff, the direction of the runoff is determined
by a random number. According to the topography of China the probabilities of the flow direction are
selected as follows:
West-East P = 0.5; East-West P = 0.1; North-South P = 0.2 and South-North P = 0.2
In Fig. 1.8 an arrow represents the flow direction on each cell. The arrow direction is determined with
random numbers generated by the computer. For instance, if the random number is in the range of 0-5,000,
the flow direction is from west to east; if the number is in the range of 5,001-7,000, the flow direction is
from north to south; if the number is in the range of 7,001-8,000, the flow direction is from east to west;
and if the number is in the range of 8,001-9,999, the flow direction is from south to north. Two neighboring