关键词: 流域地貌演化阶段, 沟壑密度, 切割深度, 理论极值建模

Abstract: According to the geographical cycle theory, drainage landform evolution process is divied into three periods—young, mature and old period. In defferent evolution periods, the relation between gully density and cutting depth is various. However, it is sure that landforms are the most tattered and gully density reaches the maximum in the later young—early mature period. By presuming that the drainage landform is evoluted into hills in the period, the maths equation of the theoretical maximum of gully density was established, which is D=ctgθ^h∫_h0^maxdh/(hctga+c)² (1) where:D: gully density;θ: slope;h: cutting depth;c: gully bed average width;h₀: cutting depth minimum;h_max: cutting depth maximum On the above presuming base, the maths function on relation between gully density and cutting depth were established for the defferent development periods. The maths function shows that:①in the early young period, the gully density and cutting depth increase at the same time; ②in the later young—early mature preiod, gully density reaches the maximum and it decreases as cutting depth imcreases; ③ in the later mature—old preiod, gully density decreases as cutting depth decreases. Two example calculations demonstrate that the maths equation of the theoretical maximum of gully density may be used in practice. It can infer drainage landform evolution period and predict soil erosion developing tendency. It supplements quantitative anslysis on landforms shape elements with drainage landform evolution in defferent periods.

Key words: drainage landform evolution periods, gully density, cutting depth, the theoretical maximum of gully density