Abstract: The iterative algorithm for calculating the Monin-Obukhov (M-O) length in the aerodynamic method is transformed into the problem of finding the fixed points of a one-dimension mapping in nonlinear theory. By adopting the nondimensional functions of the profile-flux relationships summarized by Dyer, the analytical solution of M-O length is derived for the stable surface layer, which is applicable to Richardson number (Ri) less than 0.2. The consistence between analytical and iterative solutions is validated through the computations of 4 calculation cases for the stable surface layer in typical summer and winter time. According to the theory of fixed-point stability in nonlinear sciences, the convergence property is discussed. It is concluded that the analytical solutions can be figured out by iteration in principle, though iterative solutions exhibit significant errors when Ri approaches 0.2.

Key words: Monin-Obukhov length, surface layer, analytical solution, one-dimension mapping, Floquet multiplier

摘要： 将空气动力学方法迭代求解Monin-Obukhov（M-O）长度的过程，转化为非线性理论中求解映射不动点的问题，获得稳定近地面层M-O长度的解析解。求解过程中采用了Dyer归纳的通量廓线关系的无量纲函数形式，并给出解析解的适用范围是Richardson数（Ri）小于0.2。通过对中国夏、冬两季各2种典型稳定层结条件算例的计算，验证了解析解与迭代解的一致性。根据非线性科学中关于映射不动点稳定性的理论，讨论了迭代算法的收敛性，表明迭代算法在理论上可以收敛到解析解，但在 Ri 接近0.2时误差较大。

关键词: Monin-Obukhov长度, 近地面层, 解析解, 一维映射, Floquet乘子