基于矩阵优化填充和结构性先验统计信息的气象数据恢复

Meteorological Data Restoration Based on Matrix Completion and Prior Features

摘要: 由于观测手段和观测背景的限制，再加上环境复杂，很多时候只有部分气象观测资料可用，为了在这种背景下进行气象预报，充分完备的气象资料是重要基础，因此基于零散的部分观测数据、先验数据的统计特征和矩阵优化填充技术的气象资料恢复研究具有重要的工程价值和数学意义，其研究在国内外尚属空白。本文旨在通过部分观测资料，充分利用矩阵的低秩性和气象观测数据的内在结构性先验统计信息，应用矩阵填充的奇异值阈值化SVT算法，优化分析得到欠缺数据，从而获得填充的补全数据。实验结果表明，基于结构性先验信息和矩阵优化填充方法得到的数据准确率明显取决于矩阵格式选择和气象数据本身特性，而且本文通过理论和实验分析出最佳的矩阵优化填充模型，表明当可利用的资料占比高于临界采样率时，数据填充误差可控制在10%以内，可以有效地解决预报和分析时的观测资料数据缺失不全的问题。

Abstract: Because of the limitation of observation means and background, combined with the complex environment, only some observation data are available. For the sake of better weather forecast, the research of meteorological data restoration based on part of observation data and matrix completion would have important scientific significance. This paper aims to, through part of real-time observation data, according to the low rank of a matrix, with applying SVT (Singular Value Thresholding) algorithm of matrix completion, obtain the deficient data so that one can make weather forecast better. The experimental result shows that the accuracy of forecast with matrix completion method is obviously higher than that with classical statistical method. When available data proportion is higher than the critical sampling proportion, errors of data filling can be controlled within 10%, which meet the requirements of meteorological data.