Climate Research

TInnovative Framework for High-Dimensional Error Modeling in Meteorological Data Assimilation: Fusion of TOENS-Q and Hierarchical Matrices with Spatial Error Correlation Optimization

Authors: Yueshui Lin
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

High-dimensional modeling of spatially correlated observation errors in meteorological data assimi- lation faces computational complexity (O(n3 )) and precision loss (truncation noise >8 × 10³). This paper proposes an innovative framework integrating quaternion algebra (TOENS-Q) with hierarchi- cal matrices: (1) Spatial topology encoding via geographic quaternion Qobs = ϕ + λi + θj + hk ;(2) Precision error control with intensity parameter s achieving ε = 2- s error bound (δ < 10-9 when s > 1024); (3) Hierarchical acceleration reducing complexity to O(nlog n) with 16 × mem- ory compression. Experiments demonstrate 98% reduction in truncation noise and assimilation time compression from 42 minutes to 2.2 minutes for SEVIRI data assimilation.
Category: Climate Research