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It is possible to express a watershed by the assembly of the 1st order basins when the interbasin area is attached to the 1st orber basins. Then, the channel system of a watershed is analogically expressed by a tree system in which a trunk is a main channel, a branch is a tributary and a leaf is a 1st orber basin.
The following laws are found as to the topologically random channel network.
I) Law of bifurcation of channel
i)R_b=4
ii)_υN_u=3/4(1/4)^υ-u-1·Nu
iii)N(_iC_u)=(1/2)ⁱ·N_u
II) Law of channel length
i)R_l=2
III) Law of basin area
i)R_a=4
in which R_b is bifurcation ratio, N_u is number of u - th order channel, _υN_u is number of u - th order channel which joins υ - th order channel, N(_iC_u) is number of υ - th order channel which has i pieaces of (u - 1) - th order channel. R_l and R_a are channel length ratio and basin area ratio respectively.
In addition, the following equation is applicable to the longitudinal profile of ordered channel system in dynamic equilibrium (Fig. 3).Y1/Y2=…=Yu/Yu+1=1
in which Y_u is the average fall of the altitude of u - th order channel.
It is possible to make a synthetic channel network which has the subsystem as in Table 1, if it is assumed that the above subsystem is connected at random which is the basic law of topology model of channel network. In this way, ten samples of synthetic channel network are composed, which has 1024 pieces of 1st order basin and 6 th order channel at the end of the watershed. When the law of equality of the average fall of ordered channel system is taken into account, the altitude of each 1st order basin of the synthetic channel network can be calculated.
Then, a/A and h/H of a hypsometric curve are estimable under the assumption that the 1st order basin has unit area. Ten hypsometric curves of hypothetical watershed composed of synthetic channel networks are depicted in Fig. 4. As is Fig. 5, a mean hypsometric curve of the synthetic channel net-work is almost completely identical with that of STRAHLER.
As to the transformation of a watershed landform, the following explanation would be valid from the viewpoint of the topological model of channel network. The structure of u - th order channel network is topologically identical with that of (u+1) - th order. And the longitudinal profil of channel system of u - th order basin is also similiar to that of (u+1) - th order basin. So it would be correct that the

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