地球表层形态分析的定量注记

SOME THEORETICAL CONCLUSIONS OF MORPHOLOGICAL SYSTEMS ON THE EARTH'S SURFACE

地球的表面形态结构,是一种随机型的空间分布格局。本文企图以某种定量的、预测的方式,对于此种格局加以理论上的归纳。分别应用力能学分析和统计学分析两种完全不同的思考方法,获得了地球表层的海拔高度上限约21km。这一基本理论问题的合理解决,将使地球表层的一系列基本特性如动力学参数、热力学参数、行为学参数、系统学参数等有更加精确和更加严谨的表达。在此基础上,作者又从理论上推演了地球表层高度-面积分布的宏观趋势,并将其计算的结果与实际统计的结果进行对比分析,取得了比较满意的总体检验。

As a theoretical assumption, morphological structure of Earth's surface can be considered as a 'stochastic' spatial pattern at some transient state. It should be particularily pointed out that the pattern reflects intrinsic height-size correlation. The attempt of the author is to approach the subject from different theoretical frameworks in order to obtain some quantitative models through which forecast of the distribution possibility of random altitude statistics over sea level would become possible. 1. In this paper, the author has developed a specific theory, called Nonlinear Descending Principle (NDP), to calculate the altitude's limit on the Earth's surface. In fact, NDP is based on a fundamental consideration assuming that the distributed frequency of height-size relation over the see level can be expressed as following: logS_i=f(a,b,c,...)+B sum from △H=1 to i H_i where: S_i——the area over the height i f(a,b,c,...)——a function related. with Earth's size (a),shape (b), movement (c), and so forth H——the altitude over the see level (△H=1 km) i——1,2,3,… B——constant In the paper, by using Scheidegger's data in 1982 (Scheidegger, 1982), the author has obtained through NDP the two coefficients as: f(a, b, c,...)=2.2834; and B=-0.3905. If we find a height at which the amount of the Earth's mass is just equal to or greater than the average net denudation of global scale per year, i. e. the amount=28.2×10~9 t/a, the corresponding height is regarded as the altitude's limit on the Earth's surface. This limit has been determined in the paper using NDP as 20.5 km. This figure is well coincident with Weskov's result (21.7 km). However, we know that Weskov used a totally different method which I named the method 'Energetics's Analysis'. The determination of the altitude's limit on the Earth's surface is very beneficial for the precise estimation of the Earth's fundamental properties such as kinetic parameter, thermodynamic parameter, and behavior parameter. 2. Using Equilibrium Law of River's Profile, the author also has derived another interesting result. From which a macroscopic expression of distribution possibility of height-size relation over sea level can be obtained as: P(h)=T/exp(hT) where: P(h)——the possibiiity distribution of height h, T——a constant depending on a statistical model related unit height and unit holizontal distance. The result illustrates that the theoretical calculation is well coincident with practical measurement. 3. Morphological systems of the Earth's surface are determined only from the associated physical properties of phenomena i. e. their shape, slope, relief, geometry, composition, strength etc. and have to be seen as a transient scene in the whole proceeding of geological cycle. Also, the structure of morphological systems is considered as a comprehensive result of mutual action between different forces at all scales of magnitude. Microscopically, they are irregular, stochastic, and disordering. But macroscopically, they are determined, regular, and distinguishable. So, the most valuable tools for the description of morphological systems on the Earth's surface are those which derive from mathematical regression and correlation techniques. It is likely possible to develop some statistical models for construction of the systems just like those in Quantum Mechanics.