Lower bound estimation of the maximum allowable initial error and its numerical calculation

摘要

TIn the numerical prediction of weather or climate events, the uncertainty of the initial values and/or prediction models can bring the forecast result’s uncertainty. Due to the absence of true states, studies on this problem mainly focus on the three subproblems of predictability, i.e., the lower bound of the maximum predictable time, the upper bound of the prediction error, and the lower bound of the maximum allowable initial error. Aimed at the problem of the lower bound estimation of the maximum allowable initial error, this study first illustrates the shortcoming of the existing estimation, and then presents a new estimation based on the initial observation precision and proves it theoretically. Furthermore, the new lower bound estimations of both the two-dimensional ikeda model and lorenz96 model are obtained by using the cnop (conditional nonlinear optimal perturbation) method and a pso (particle swarm optimization) algorithm, and the estimated precisions are also analyzed. Besides, the estimations yielded by the existing and new formulas are compared; the results show that the estimations produced by the existing formula are often incorrect.摘要本文基于观测误差限，针对可预报性问题中第三个子问题最大允许初始误差，分析了前人给出的下界估计的不足，给出了一个下界估计并从理论上证明了该估计的正确性。利用条件非线性最优扰动方法并结合粒子群优化算法，在二维Ikeda模式和Lorenz96模式上进行了数值试验，进一步检验了原有的下界估计并不是真正的下界估计，新估计是正确的下界估计。