A simple quasi-geostrophic barotropic vorticity equation model is used as the dynamic frame of the model in this paper.Considering that there are many random errors in model's initial values of meteorolo- gical da...A simple quasi-geostrophic barotropic vorticity equation model is used as the dynamic frame of the model in this paper.Considering that there are many random errors in model's initial values of meteorolo- gical data,and that it is not perfectly complete about model's physical processes (for example,take no ac- count of the interaction between atmosphere and underlying surface,radiation,etc.),we add the random for- ced term to the model and use the Monte-Carlo method with random initial values.A statistical-dynamic integrated model is thus built up,and a numerical forecasting experiment of 500hPa monthly mean height field of January 1983 has been carried out.The experiment result proves that the forecasting result of the model, considering random forcing and random initial values at the same time,is better than that by the pure dynamic model,the random initial value model and the random forced model.展开更多
This paper is devoted to constructing a globally rough solution for the higher order modified Camassa-Holm equation with randomization on initial data and periodic boundary condition.Motivated by the works of Thomann ...This paper is devoted to constructing a globally rough solution for the higher order modified Camassa-Holm equation with randomization on initial data and periodic boundary condition.Motivated by the works of Thomann and Tzvetkov(Nonlinearity,23(2010),2771–2791),Tzvetkov(Probab.Theory Relat.Fields,146(2010),4679–4714),Burq,Thomann and Tzvetkov(Ann.Fac.Sci.Toulouse Math.,27(2018),527–597),the authors first construct the Borel measure of Gibbs type in the Sobolev spaces with lower regularity,and then establish the existence of global solution to the equation with the helps of Prokhorov compactness theorem,Skorokhod convergence theorem and Gibbs measure.展开更多
文摘A simple quasi-geostrophic barotropic vorticity equation model is used as the dynamic frame of the model in this paper.Considering that there are many random errors in model's initial values of meteorolo- gical data,and that it is not perfectly complete about model's physical processes (for example,take no ac- count of the interaction between atmosphere and underlying surface,radiation,etc.),we add the random for- ced term to the model and use the Monte-Carlo method with random initial values.A statistical-dynamic integrated model is thus built up,and a numerical forecasting experiment of 500hPa monthly mean height field of January 1983 has been carried out.The experiment result proves that the forecasting result of the model, considering random forcing and random initial values at the same time,is better than that by the pure dynamic model,the random initial value model and the random forced model.
基金supported by the National Natural Science Foundation of China(Nos.11901302,11401180)the Natural Science Foundation from Jiangsu province BK20171029the Academic Discipline Project of Shanghai Dianji University(No.16JCXK02)。
文摘This paper is devoted to constructing a globally rough solution for the higher order modified Camassa-Holm equation with randomization on initial data and periodic boundary condition.Motivated by the works of Thomann and Tzvetkov(Nonlinearity,23(2010),2771–2791),Tzvetkov(Probab.Theory Relat.Fields,146(2010),4679–4714),Burq,Thomann and Tzvetkov(Ann.Fac.Sci.Toulouse Math.,27(2018),527–597),the authors first construct the Borel measure of Gibbs type in the Sobolev spaces with lower regularity,and then establish the existence of global solution to the equation with the helps of Prokhorov compactness theorem,Skorokhod convergence theorem and Gibbs measure.
