随机力是气候系统变化本身固有的属性，气候系统的随机动力学已成为重要的前沿课题。然而多尺度的气候变化具有显著的长期记忆性或持续性，分数阶导数和分数噪声的引入是刻画气候变化的自然选择，而这方面的研究尚未开展或需要更多深入的研究。该项目首先开展Hurst参数H分别属于(0.5，1)和(0，0.5)的加性分数噪声驱动力强迫作用下时间分数阶随机非线性大气动力方程组的定性理论和长期行为的对比研究；进一步分析乘性分数噪声驱动力强迫作用下具有时间分数阶导数的随机非线性大气动力方程组的数值计算方法，并给出相应的离散系统随机吸引子的存在性，以及离散系统与原系统吸引子之间距离的估计；最后考察人为因素作为一个随机力时，利用分数噪声驱动力强迫作用下具有时间分数阶导数的随机脉冲Lorenz系统的适定性和长期行为的理论研究及数值模拟，为气候异常演变的物理机制问题和极端事件预测研究探索新的思路和方法。

The random force is an inherent attribute of climate systems, so the stochastic dynamics of climate systems has become a leading issue. Multi-scale climate change has significant long-term memory or persistence. The introduction of fractional time derivative and fractional noise is a natural choice to characterize climate change, however there is little reference in this field. The purpose of this project is to investigate stochastic dynamic equations describing the large scale motion of the atmosphere with fractional time derivative and fractional noise. Firstly, the existence of global solutions and random attractors of such systems with additive fractional noise will be studied when Hurst parameter H belongs to (0.5, 1) or (0, 0.5). We then present numerical calculation method for such systems with multiplicative fractional noise. In particular, the error estimates of random attractors of discrete equations will be obtained. Finally, we investigate that human factor is a random force. The existence of global solutions and random attractors for stochastic impulsive Lorenz systems with fractional time derivative and fractional noise will be established, and numerical simulation will be used to explore new ideas and methods for the physical mechanism of the abnormal evolution of the climate and the prediction of extreme events.