Using a high degree of parallelism is essential to perform data assimilation efficiently. The state formulation of the incremental weak constraint four-dimensional variational data assimilation method allows parallel calculations in the time dimension. In this approach, the solution is approximated by minimising a series of quadratic cost functions using the conjugate gradient method. To use this method in practice, effective preconditioning strategies that maintain the potential for parallel calculations are needed. We examine approximations to the control variable transform (CVT) technique when the latter is beneficial. The new strategy employs a randomised singular value decomposition and retains the potential for parallelism in the time domain. Numerical results for the Lorenz 96 model show that this approach accelerates the minimisation in the first few iterations, with better results when CVT performs well.
翻译:使用高度的平行法对于高效率地进行数据同化至关重要。 递增弱限制四维变异数据同化方法的状态配方允许在时间尺度上进行平行计算。 在这种方法中,解决方案的近似方法是使用共振梯度法,将一系列二次成本函数最小化。 要在实践中使用这种方法,需要有效的先决条件战略来保持平行计算的可能性。 当控制变量变异(CVT)技术对后者有利时,我们检查控制变量变异技术的近似值。新战略使用随机化的单值分解法,并保留时间域中的平行法潜力。 Lorenz 96 模型的数值结果显示,这一方法加速了最初几个迭代的最小化,当CVT运行良好时,效果会更好。