改进的牛顿法确定大气消光系数边界值

Using improved Newton method to determine the boundary value of atmospheric extinction coefficient

在用激光雷达方程反演大气消光系数时,大气消光系数边界值对反演精度影响较大,而在低层大气中该值较难确定。文中提出了一种基于改进牛顿法的大气消光系数边界值确定方法,其核心思想是,把确定大气消光系数边界值的问题转化为求非线性方程的数值解。首先,根据大气消光系数边界值与激光雷达回波信号功率以及大气光学厚度之间的关系,假设大气消光系数边界值为x,构建一个非线性方程。其次,采用改进的牛顿法求非线性方程的数值解,得到大气消光系数边界值。使用香港天文台装置在香港国际机场的多普勒激光雷达回波信号数据,对该方法的可行性和可靠性进行了验证。结果表明:利用该方法确定边界值,可以较为准确地反演出低层大气消光系数。该方法收敛速度快,迭代次数少,并且不需要计算导数值,极大地减少了运算量,具有较强的实际应用价值。

When using lidar equation to inverse the extinction coefficient of atmosphere, its boundary value has a great influence on the inversion precision, however, it is hard to be determined in the lower atmosphere. A method was proposed to determine the boundary value of the extinction coefficient of atmosphere based on improved Newton; the core idea was to transform the problem of determining boundary value of the extinction coefficient of atmosphere to get numerical solution of the nonlinear equation. First of all, according to the relationship between the boundary value of extinction coefficient of atmosphere and the power of laser radar echo as well as optical thickness of atmosphere, it was supposed the boundary value of the extinction coefficient of atmosphere was x, a nonlinear equation could be constructed. Secondly, by using the improved Newton method to get the numerical solution of the nonlinear equation, the boundary value of the extinction coefficient of atmosphere can be got. By means of the echo signal dataof Doppler laser radar in the Hong Kong international airport received by Hong Kong observatory devices, the feasibility and reliability of this method was verified. The results show that by using this method to determine the boundary value, the extinction coefficient of atmosphere can be inversed more accurately in lower atmosphere. This approach has fast convergence and fewer iteration times, and need not calculate the derivative value so that the amount of calculation is reduced greatly, consequently it has great application value.