Application of Gridless Method in Data Assimilation

In general, data assimilation systems analyze values on regularly distributed grids according to the irregularly distributed observations. As long as a data assimilation system was established on a certain grid, it cannot adapt to another grid. In this study, the gridless method was introduced into the three-dimensional variation (3DVar) system. Compared with grid-based method, the gridless method uses discrete points for calculation and does not require grid division, thus being immune to grid distribution. Therefore, the data assimilation system based on gridless method can adapt to most model grid structures without the need to write new code. In the data assimilation system based on gridless method, the Cressman analysis technique is adopted as observation operator and the physical transformation matrix is handled using the Taylor expansion method. The idealized experiments based on the Rankine vortex demonstrate that the 3DVar system based on gridless method can handle structured grid, unstructured grid, and mixed (structured and unstructured) grid. Furthermore, the study showed that data assimilation can be performed simultaneously for different grid resolutions, resulting in higher consistency between the grids than when data assimilation is performed separately.