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《Acta Geographica Sinica》 1991-04

## MATHEMATICAL MODELLING OF HYDROGEOMORPHO-LOGY AND ITS APPLICATION IN THE KARST OF GUIZHOU, CHINA

Tan Ming (Department of Geography, Guizhou Normal University)
In karst areas it is often difficult to define catchment areas; as two Kinds of boundaries may exist: the surface and subsurface boundaries. Karstic catchment is actually opened, so a model is hoped to be established not concerning bowndaries of a catchment but runoff. Also there are no flow nets which can be analysed in terms of Horton's laws. If the direction of runoff is clear, a section of the catchment where lithology and structure do not change can be selected for analysis. Karst features which are produced by movement of water can hen be measured along with their distance from the outlet of the basin, and relationships, i.e the model of hydrogeomorphology can be established between them.Selection of landform characteristics for measurement One km2 units were used to divide the sample area into n grid squares. For each square the parameters were measured from 1: 50000 topographical maps produced by aerial photography, namely: a) Minimum height in metres Lm (above mean sea level). This figure may refer to a point, but generally signifies the bottom of a depression on the landform surface. b) Average absolute height of cols Ca in metres. c) Average relative height of cols Cr in metres. Thus Cr = Ca-Lm d) Average absolute height of conical peaks Pa in metres. This was approximated from the average absolute height of the highest contours of cones. e) Average relative height of conical peaks Pr in metres. Thus Pr = Pa - Lm f) Average height of cones Ph in metres. g) Average half long axis of cones PI in metres. h) Area ratio Rp of flat land as a percentage. This indicates the proportion of flat land with a slope of less than 5?in a sample grid square. In order to study how runoff variations influence karst landform development, as many other factors as possible should be held constant. In practice this is difficult to achieve, but three sample areas were selected in the headwaters of the Wujiang basin, the largest river in Guizhou province, that approximately fulfil the requirement. Selection and characteristics of the sample areas a) Sample area I (near the Liuchong River) is located on a truncated, gently dipping anticline of lower Permian limestones. The landscape comprises cone karst interspersed with dry valleys, termed fengcong-valley. Runoff is subsurface to the Liuchong River. b) Sample Area II (near the Sancha River) is located in a gently dipping syncline of middle Triassic dolomites and dolomitic limestones. The locality is near the town of Puding. The morphology of karst in this region changes in the general direction of runoff from fenglin-plain to fengcong-basin to fengcong-valley. Drainage is from south to north to the Sancha River. c) Sample Area III (near the Boyu River) is also located in the Puding syncline, but in its southern part. Lithology and structure are similar to that in sample area II. The morphology of karst in this region changes in the general direction of runoff from fengcong-de" pression to fenglin-plain and then to monadnoek plain with relatively thick residual red clay cover. Drainage is from east to west to the Boyu River, a tributary of the Sancha River. Analysis of the trends of Pa, Ca, and Lm in the direction of runoff Kilometre square quadrats were placed over each of the three sample areas. The average valuts of Pa, Ca and Lm were calculated for cones in each square- and these were each regressed against distance to basin 6*utlet as the independent variable. The three trend lines in each sample area show that the relief in a karstic catchmenf is made up of two tiers: Ph and Cr. The essentially parallel trends of Pa and Ca imply that the upper relief tier (Ph = Pa-Ca) is of unvarying amplitude regardless of distance from the catchment outlet. By contrast, the minimum height (Lm) trend converged or diverged with respect to the Ca trend. This suggests that whereas the upper tier may possess the character of dynamic equilibrium, Cr = Ca - Lm, the lower tier appears to be undergoing evolution. The thickness of the Ph tier remains steady in all sample ar
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