讨论一类广义常微分方程边值问题dx=d[A]x+dg,x(a)+μ∫b a x(s)ds=x(b)解的存在性和惟一性,其中x:[a,b→]Rn是[a,b]上的向量值函数,A是定义在[a,b]上的m×n阶矩阵值函数,g是n维向量实值函数并且μ∈R.借助伴随方程,给出了这类广...讨论一类广义常微分方程边值问题dx=d[A]x+dg,x(a)+μ∫b a x(s)ds=x(b)解的存在性和惟一性,其中x:[a,b→]Rn是[a,b]上的向量值函数,A是定义在[a,b]上的m×n阶矩阵值函数,g是n维向量实值函数并且μ∈R.借助伴随方程,给出了这类广义常微分方程边值问题解的存在性和惟一性.展开更多
伴随方法是一种高效的敏感性分析方法,在大型非线性复杂系统的敏感性计算中有着显著的优势。依据伴随理论,基于大气化学模式GRAPES-CUACE(global-regional assimilation and prediction system coupled with the CMA unified atmospheri...伴随方法是一种高效的敏感性分析方法,在大型非线性复杂系统的敏感性计算中有着显著的优势。依据伴随理论,基于大气化学模式GRAPES-CUACE(global-regional assimilation and prediction system coupled with the CMA unified atmospheric chemistry environment forecasting system),建立了气溶胶模块和气体模块的伴随模式,并对其进行了正确性测试。结合黑碳气溶胶(black carbon aerosol,BC)及臭氧(O3)浓度观测数据,分别利用气溶胶和气体伴随模块进行了数值模拟及源-浓度的敏感性实验。结果表明:CUACE模式能较好地模拟BC浓度的日变化过程。利用气溶胶伴随模式模拟分析了目标函数(观测浓度与模拟浓度差值)关于BC排放源的敏感性,发现敏感性与浓度差值成正比关系。气体伴随模型的敏感性分析表明,若要减小2015年7月7日08:00至8日07:00北京顺义站O3模拟浓度与观测浓度的差异,需要对NOx和VOCs排放源分布进行调整,即在当前状态减小区域内的NOx排放源以及增大对应网格点的VOCs排放源,再结合优化算法即可得到合理的排放源分布。本文开发的GRAPES-CUACE气溶胶伴随和气体伴随模块能够有效地针对气溶胶和气体进行敏感性分析,为下一步构建完整的GRAPES-CUACE大气化学四维变分同化系统以及污染源反演工作奠定了基础。展开更多
The strong nonlinearity of boundary layer parameterizations in atmospheric and oceanic models can cause difficulty for tangent linear models in approximating nonlinear perturbations when the time integration grows lon...The strong nonlinearity of boundary layer parameterizations in atmospheric and oceanic models can cause difficulty for tangent linear models in approximating nonlinear perturbations when the time integration grows longer. Consequently, the related 4—D variational data assimilation problems could be difficult to solve. A modified tangent linear model is built on the Mellor-Yamada turbulent closure (level 2.5) for 4-D variational data assimilation. For oceanic mixed layer model settings, the modified tangent linear model produces better finite amplitude, nonlinear perturbation than the full and simplified tangent linear models when the integration time is longer than one day. The corresponding variational data assimilation performances based on the adjoint of the modified tangent linear model are also improved compared with those adjoints of the full and simplified tangent linear models.展开更多
文摘讨论一类广义常微分方程边值问题dx=d[A]x+dg,x(a)+μ∫b a x(s)ds=x(b)解的存在性和惟一性,其中x:[a,b→]Rn是[a,b]上的向量值函数,A是定义在[a,b]上的m×n阶矩阵值函数,g是n维向量实值函数并且μ∈R.借助伴随方程,给出了这类广义常微分方程边值问题解的存在性和惟一性.
文摘伴随方法是一种高效的敏感性分析方法,在大型非线性复杂系统的敏感性计算中有着显著的优势。依据伴随理论,基于大气化学模式GRAPES-CUACE(global-regional assimilation and prediction system coupled with the CMA unified atmospheric chemistry environment forecasting system),建立了气溶胶模块和气体模块的伴随模式,并对其进行了正确性测试。结合黑碳气溶胶(black carbon aerosol,BC)及臭氧(O3)浓度观测数据,分别利用气溶胶和气体伴随模块进行了数值模拟及源-浓度的敏感性实验。结果表明:CUACE模式能较好地模拟BC浓度的日变化过程。利用气溶胶伴随模式模拟分析了目标函数(观测浓度与模拟浓度差值)关于BC排放源的敏感性,发现敏感性与浓度差值成正比关系。气体伴随模型的敏感性分析表明,若要减小2015年7月7日08:00至8日07:00北京顺义站O3模拟浓度与观测浓度的差异,需要对NOx和VOCs排放源分布进行调整,即在当前状态减小区域内的NOx排放源以及增大对应网格点的VOCs排放源,再结合优化算法即可得到合理的排放源分布。本文开发的GRAPES-CUACE气溶胶伴随和气体伴随模块能够有效地针对气溶胶和气体进行敏感性分析,为下一步构建完整的GRAPES-CUACE大气化学四维变分同化系统以及污染源反演工作奠定了基础。
基金Acknowledgments. The authors would like to thank Prof. Z. Yuan for her numerous suggestions in the writing of this paper. This work is supported by the National Natural Science Foundation of China (Grant No.40176009), the National Key Programme for Devel
文摘The strong nonlinearity of boundary layer parameterizations in atmospheric and oceanic models can cause difficulty for tangent linear models in approximating nonlinear perturbations when the time integration grows longer. Consequently, the related 4—D variational data assimilation problems could be difficult to solve. A modified tangent linear model is built on the Mellor-Yamada turbulent closure (level 2.5) for 4-D variational data assimilation. For oceanic mixed layer model settings, the modified tangent linear model produces better finite amplitude, nonlinear perturbation than the full and simplified tangent linear models when the integration time is longer than one day. The corresponding variational data assimilation performances based on the adjoint of the modified tangent linear model are also improved compared with those adjoints of the full and simplified tangent linear models.
基金Supported by National Natural Science Foundation for Distinguished Young Scholars of China(61025014)the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(61021002)
