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In order to improve the prediction of numerical tidal model in continental shelf, the open boundary conditions are optimized by assimilating the observed data into the model in which the adjoint method, based on optimal control theory, is used. The nonlinear shallow water equations are considered in which horizontal kinematic nonlinearities, nonlinear bottom friction and horizontal eddy diffusion are included. The adjoint model is obtained by using Leqrange multipliers. This study contains two parts: Part I... In order to improve the prediction of numerical tidal model in continental shelf, the open boundary conditions are optimized by assimilating the observed data into the model in which the adjoint method, based on optimal control theory, is used. The nonlinear shallow water equations are considered in which horizontal kinematic nonlinearities, nonlinear bottom friction and horizontal eddy diffusion are included. The adjoint model is obtained by using Leqrange multipliers. This study contains two parts: Part I (this paper)-the establishment of the adjoint model and twin-experiment, and part Ⅱ (another paper)-the numerical results which are incorporated the data from tide stations with/without TOPEX/POSEIDON altimeter data for optimizing the open boundary conditions of the model. 本研究采用基于最优控制理论的伴随法,把观测资料同化到陆架海域潮汐 数值模型中去,优化开边界条件,提高数值预报的精度.潮汐模型的控制方程为考虑 平流项、非线性底摩擦和侧向涡动粘性项的非线性浅水方程组;采用Lagrange乘子 法建立了伴随模型.研究分两部分:第一部分即本文,建立非线性浅水方程模型的伴 随方程、给出目标函数的梯度,并实现“孪生”数值试验;第二部分另文给出. In order to improve the prediction of numerical tidal model in continental shelf, the open boundary conditions are optimized by assimilating the observed data into the model in which the adjoint method, based on optimal control theory, is used. The non linear shallow water equations are considered in which the horizontal kinematic nonlinearities, nonlinear bottom friction and horizontal eddy diffusion are included. On the basis of the establishment of adjoint model and twin experiment (Part Ⅰ), the variational... In order to improve the prediction of numerical tidal model in continental shelf, the open boundary conditions are optimized by assimilating the observed data into the model in which the adjoint method, based on optimal control theory, is used. The non linear shallow water equations are considered in which the horizontal kinematic nonlinearities, nonlinear bottom friction and horizontal eddy diffusion are included. On the basis of the establishment of adjoint model and twin experiment (Part Ⅰ), the variational assimilation results obtained by incorporating the data from tide stations with/without TOPEX/Poseidon altimeter data in the Huanghai Sea and the East China Sea for optimizing the open boundary conditions of the model are reported. The deviations of the model results before and after assimilation from the observed demonstrate the applicability of the variational assimilation. 本研究基于最优控制理论 ,采用变分数据同化法 ,通过建立伴随模型 ,把观测资料同化到陆架海域潮汐数值模型中去 ,优化开边界条件 ,以便提高数值预报的精度 .潮汐模型的控制方程为考虑平流项、非线性底摩擦和侧向涡动粘性项的非线性浅水方程组 .在第Ⅰ部分建立伴随模型和进行“孪生”数值试验的基础上 ,给出利用验潮站的水位资料以及TOPEX/Poseidon卫星测高数据在黄海、东海进行变分数据同化试验的数值结果 .试验表明利用上述资料对模型进行变分同化校正是可行的 Under the spherical coordinate,the boundary value method using the along track estimates of(T/P) satellite as open boundary conditions is applied to establish tide models in the Yellow Sea.The results prove the applicability of the method.While testing bottom friction coefficient,the comparisons show that its effect is small.Thus,its value can be taken as 0.0022 without testing process. 利用球坐标系中的二维潮波方程组,以T/P卫星沿迹分析结果为开边界条件的边值法,计算了黄海中的一个四边形区域。结果证明了此方法的可行性。同时在调试底摩擦系数时,发现其对本方法的影响甚小,说明本方法计算不同区域的潮汐数值模型时,底摩擦系数都可以取为0.0022,省去对底摩擦系数的调试过程。
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