数据同化中的伴随方法的有关问题的研究

关于伴随方法应用中只能利用模式的伴随的观点，被认为是有疑问的．所作的数值模拟实验表明，对于潮波模型而言，方程的伴随能够得到与模式的伴随同样的结果:调和常数的实测值与模拟值的振幅差的绝对值的平均小于5.0 cm，迟角差的绝对值的平均小于5.0°．这些结果都能够体现渤、黄海M2分潮的基本特征．作为对比，也利用前人的方法对渤、黄海的M2分潮潮波进行了数值模拟，首先借助于历史资料和观测资料得到开边界的初始猜测，然后对开边界的初始猜测值进行调整，以得到与高度计资料之差尽可能小的模拟结果．但由于开边界的值共有72个，究竟有哪些值需要调整，需要如何调整，只有经过不断的调试，才能部分地解决这些问题．工作量大且很难得到令人满意的结果．该文实现了确定开边界条件的自动化过程，这与前人的方法相比，有无可比拟的优势．需要特别强调的是如果利用方程的伴随，可以避免繁琐而冗长的数学推导．因而说明方程的伴随也应该引起足够的重视．

Study on the Adjoint Method in Data Assimilation and the Related Problems

It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observed M₂ tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulate M₂ tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. The satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.