立方抛物线形断面收缩水深的计算需求解含已知参数的单变量高次方程，理论上无解析解。首次提出高次方程近似求解的迭代逼近－逐次优化拟合方法，基于迭代理论建立合适的拟合函数模型，选取适当的参数对其进行逐次优化拟合，得到一套高精度的直接计算公式，为明渠特征水深的精确计算提供了一条新的途径。误差分析及实例计算结果表明，在工程适用范围内，该公式的最大相对误差绝对值小于0.118%，精度高于现有的各类直接计算公式，具有较大的工程实用价值。

High-order equations including one variable and known parameters have to be solved for the calculation of contracted water depth in cubic parabolic cross-sections, which have no analytic solutions. The iterative approximation-gradually optimal fitting method was first established for approximate solutions of high-order equations. An appropriate model function was proposed for curve fitting based on the iteration theory. Proper parameters were selected for gradually optimal fitting and a direct calculation formula with high accuracy was derived, thus providing a new approach to the accurate calculation of characteristic depths in open channels. Results of error analysis and practical example indicated that within the practical scope of engineering, the maximum absolute relative error of the proposed formula was less than 0.118%, which was more accurate than all the presently available formulae. The proposed formula was of great val-ue for practical engineering