条件非线性最优扰动（CNOP）：简介与数值求解
Conditional Nonlinear Optimal Perturbation: Introduction and Numerical Computation
中文摘要：
介绍了条件非线性最优扰动（Conditional Nonlinear Optimal Perturbation，CNOP）的定义及其在大气和海洋等可预报性研究中的应用。根据研究对象不同，CNOP分为与初始扰动有关的CNOP（CNOP-I）方法、与模式参数扰动有关的CNOP（CNOP-P）方法和同时考虑初始扰动和模式参数扰动的CNOP方法。目前，CNOP-I方法已经应用于ENSO、黑潮和阻塞可预报性以及热盐环流和草原生态系统稳定性的研究。此外，CNOP-I方法也被应用于探讨台风目标观测的研究，利用CNOP-I方法能够识别出台风预报的初值敏感区，通过观测系统模拟试验表明在初值敏感区增加观测能够有效改进台风的预报技巧。CNOP-P方法也在ENSO和黑潮可预报性以及热盐环流和草原生态系统稳定性研究中得到了应用。为了将CNOP方法应用于更多的领域，本文利用一个简单的Burgers方程，介绍了如何通过建立Burgers方程的切线性模式和伴随模式，从而利用非线性最优化算法计算获得CNOP。这一数值试验为将CNOP方法应用于更多的领域提供了借鉴。
中文关键词：
条件非线性最优扰动方法（CNOP），可预报性，目标观测
KeyWords：
conditional nonlinear optimal perturbation (CNOP), predictability, adaptive observations
Abstract：
This paper introduces the definition of conditional nonlinear optimal perturbation (CNOP), and the applications of the CNOP in atmosphere and ocean studies. The CNOP approach is expanded as that related to initial perturbation (CNOP-I), related to parameter perturbation (CNOP-P), and the combined both of CNOP-I and CNOP-P, according to the different perturbation types. The CNOP-I approach has been applied to the predictability studies of ENSO events, Kuroshio path anomalies, blocking, nonlinear stabilities of thermohaline circulation and grassland ecosystem. The CNOP-I has been further employed to explore the target observation of typhoon. The sensitive region could be identified by using the CNOP-I approach. The forecast skill may be improved by adding more adaptive observations in the sensitive region. The CNOP-P approach has been applied also to Kuroshio path anomalies, nonlinear stabilities of thermohaline circulation and grassland ecosystem. Here, we carried out a numerical simulation how to obtain the CNOP with the Burgers equation through building the tangent linear model and adjoint model. The result shows that the CNOP can be calculated by using the Burgers equation, the tangent linear model and the adjoint model with nonlinear optimization algorithm; It supplies a guide to a beginner to learn the CNOP and a reference for employing the CNOP to other applicable subjects.