河道の勾配と流域の地形特性量との関係-国土数値情報を用いた計測-

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タイトル別名
  • Relationship between Channel Slopes and Topographic Parameters of Drainage Basins
  • カドウ ノ コウバイ ト リュウイキ ノ チケイ トクセイリョウ ト ノ カン

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In this study topographic measurements of channels and drainage basins were performed to clarify the quantitative relationships between channel slope and drainage basin topography, characterized by two distinct parameters, drainage area (A) and mean drainage height (H). The latter was defined as the mountain volume of a catchment divided by the former.<br> Digital elevation data prepared by the Geographical Survey Institute of Japan were utilized for automated and nationwide measurement. Before calculating the drainage area and the mean drainage height at an arbitrary grid point of the digital elevation data, grid drainage networks composed of flow direction lines, which point to the lowest grid point among the eight neighbors, were made.<br> The channel slope can be obtained as the fall of a flow direction line; however, it is not expected to show the actual channel slope because the grid interval is too short to estimate gradient. Thus the channel reach, composed of several steps in the flow direction lines, was defined according to the condition that in each reach the integer values of the logarithm of the associated drainage area are equal to each other. The base of the logarithm must be 2 for the consistent ordering of the channel reaches.<br> The relationship among the drainage area (A), the mean drainage height (H), and the slope of the channel reach (I) was defined by the following equation:<br> I=kHAm, <br>where k and m are constants. The values of m were computed by least-square regression for 84 basins in Japan whose drainage areas were ranked between 1, 024 km2 and 2, 047 km2. The values of m ranged from -0.6 to -0.7 with very high correlation coefficients, and the average was -0.66. Although the investigated river basins have various climatic and geologic conditions, the deviations of m did not indicate any regional trends.<br> Presuming m as -0.5 in the previous equation, the following equation:<br> I=βH/√A, <br>was also examined, where, β is a dimensionless constant. The variable H/-√A, which represents the drainage relief number, indicates the aspect ratio or relief ratio of the drainage basin. The average value of β derived from the 84 basins mentioned above was 0.38, and the standard deviation was 0.045. The constancy of β among various basins shows that the channel slope is more strongly regulated by relief characteristics than by other conditions such as climate and lithology.

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