二维潮波模式底摩擦效应参数化方案同化研究

基于伴随同化方法对二维潮波模式底摩擦效应的线性与非线性参数化方案进行了比较研究。采用拉格朗日乘子法推导了底摩擦效应两种参数化方案的伴随表达式,并借助孪生实验对所述方法的参数反演能力进行了验证.通过同化高度计资料和验潮站资料,分别使用线性和非线性参数化方案,以及常数底摩擦系数与空间分布底摩擦系数设置的两两组合,对模拟结果进行了比较和分析。经过同化,模拟结果与观测数据的差异均有了明显下降。结果表明,如果将底摩擦系数设置为全区常数,则非线性参数化方案的模拟结果远优于线性方案;然而,在空间分布设置下,两者模拟得到的水位场与潮流场仅有细微差别,并尝试从底摩擦引起的能量耗散角度对其原因进行了分析。

Study on bottom friction parameterizations for two-dimensional tidal models using data assimilation

Adjoint method is applied to study the similarities and the differences of the Ekman (linear) and the Quadratic (nonlinear) bottom friction parameterizations for a two-dimensional regional tidal model.The adjoint expressions for the linear and the nonlinear parameterizations are derived based on the Largrangian multiplier method.By assimilating the model-generated observations,identical twin experiments are performed to test the inversion ability of the presented methodology.Four experiments which employ the linear parameterization,the nonlinear parameterizations,the constant bottom friction coefficient (BFC) and the spatially varying BFC are carried out to simulate the M₂ tide in the Bohai and Yellow Seas by assimilating TOPEX/Poseidon altimetry and tidal gauge data.After the assimilation,the misfit between model-produced and observed data is significantly decreased.The simulation results indicate that the simulation results using the nonlinear Quadratic parameterization is more accurate than the linear Ekman parameterization if the traditional constant BFC is used.However,when the spatially varying BFCs are used,the difference between two approaches diminished.The reason is analyzed from the dissipation rate caused by bottom friction.