Applying of Gridless Method in Data Assimilation System

Data assimilation integrates irregularly distributed observations into model grid points to provide initial values for numerical models. Once a data assimilation system is established on a chosen grid type, it cannot be easily adapted to another grid type. In this paper, we introduce a gridless method for the three-dimensional variation assimilation (3DVar) system. Unlike grid-based methods, the gridless method uses arbitrarily distributed points for calculation and does not require pre-defined grid cells; thus, it can switch to any grid distribution, namely the data assimilation system based on a gridless method can be adapted to most model grid structures without the need to add new codes. In the data assimilation system based on the gridless method presented here, the Cressman analysis technique is adopted as the observation operator and the physical transformation matrix is handled using the Taylor expansion method. We use idealized experiments based on the Rankine vortex to demonstrate the 3DVar system based on the gridless method; we show that the system can handle structured, unstructured, and mixed (structured and unstructured) grids. Furthermore, we show that the gridless data assimilation method can perform data assimilation on grids of different resolutions and structural types simultaneously using a single cost function.