兰州大学机构库 >数学与统计学院
大尺度环流相互作用研究与模式下边界条件估计研究
Alternative TitleTHE INTERACTION BETWEEN LARGE-SCALECIRCULATIONS AND ESTIMATION OF BOUNDARYCONDITIONS FOR NUMERICAL MODEL
李宽
Thesis Advisor胡淑娟
2014-05-29
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword大尺度环流相互作用 三型环流分解模型 模式下边界条件估计 微分方程反问题 最优控制问题
Abstract本文的研究内容由两部分构成.首先,全球范围内的大尺度大气环流系统对于全球气候演变具有重要影响,其相互间的作用往往伴随着全球气候的变化,因此,研究大尺度水平型环流、经圈型环流以及纬圈型环流之间的相互作用问题显得十分重要.此外,现有的数值天气预报模式总存在模式误差,模式误差是导致预报不准确的主要原因之一.关于模式误差的订正已有许多方法,但现有方法多数是建立在边界条件准确给定的假设基础之上,而实际中,数值模式的下边界条件是很难准确获得的.因此,若能利用我们所积累的历史观测资料,有效解决数值模式下边界条件的估计问题,必然能够有效改进数值模式的预报效果. 在第一部分研究中,我们将已有的大尺度三型环流分解模型与球坐标系下大气运动的原始方程组相结合,建立了大尺度水平型环流、经圈型环流以及纬圈型环流动力学方程组,并在保持方程组主要物理性质不变的基础上,对绝热无耗散条件下的动力学方程组进行化简,得到了一个大尺度环流相互作用的简化模型.针对此简化模型,本文给出了它的数值求解方法,通过计算模拟此简化模型,期望揭示水平型环流、经圈型环流以及纬圈型环流之间的相互关系,为气候预测提供理论依据. 在第二部分工作中,考虑到大气运动具有连续演变性,因此,数值模式的下边界信息必然包含在近期的历史观测资料中.如果我们将数值模式下边界条件看做未知项,则近期历史观测资料就可看做是满足准确边界条件的数值模式的特解,那么,确定数值模式边界条件的问题就变成了已知方程的特解反过来求解方程中的未知项的问题,它本质上是偏微分方程反问题.本文利用反问题思路,引入反问题正则化思想,将确定数值模式下边界条件的问题提为最优控制问题,再通过优化方法对其求解,并开展了相关数值实验.实验结果表明,利用历史观测资料,将估计数值模式下边界问题提为偏微分方程反问题,进而通过优化方法进行求解是改进数值预报的一个有效方法.
Other AbstractThis paper consists of two parts. Firstly, the large-scale circulation system plays an important role in global climate changing and the mutual effect is often accompanied by climate change. So, the research of the interactions between the large-scale horizontal circulation, the meridianal circulation and the zonal circulation is significant. In addition, the model error is unavoidable under the existing numerical forecast model. The model error is one of the main causes of the inaccurate prediction. There are many ways to revise the model error. But most of them are based on the assumption of that the boundary conditions are satisfied rigorously. But the fact is that it really difficult to obtain the accurate data of the boundary conditions. So if we could solve the estimation problem of lower boundary conditions effectively by using the historical observations. It must be helpful to improve the prediction effect. In the first part of this study, our method is to combine the three-dimensional circulation decomposition model with the primitive equations of motion in spherical coordinates and build the large-scale horizontal circulation, the meridional circulation and the zonal circulation dynamic equations. Then on the basis of that the physical properties are invariant, these equations are simplified under the assumption of non-dissipative and heat insulation. Finally, we obtain a simplified model of the interactions of large-scale circulation and expect to reveal the correlations between the large-scale horizontal circulation, the meridianal circulation and the zonal circulation, provide theoretical basis for climate prediction. In another piece of this work, according to the continuous evolution of atmospheric motion, the lower boundary conditions of numerical model must be embedded in the latest observation data. If we regard the lower conditions as unknown terms, then the latest observation data could be regarded as the particular solution of the numerical model which satisfied the accurate boundary conditions. So, the problem of confirming the numerical model’s boundary conditions turns into finding the unknown term of the equation under the condition of knowing the particular solution. It is essentially an inverse partial differential equation(PDE). In this paper, we use the idea of inverse problem, introduce the regularization theory, transform the numerical model’s boundary problem into optimal control problem. Then we could solve the probl...
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225573
Collection数学与统计学院
Recommended Citation
GB/T 7714
李宽. 大尺度环流相互作用研究与模式下边界条件估计研究[D]. 兰州. 兰州大学,2014.
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