史加荣. 2020. 基于奇异值分解的气象数据推测[J]. 气象学报, (0):-, doi:10.11676/qxxb2020.005
基于奇异值分解的气象数据推测
Meteorological Data Estimation Based on Singular Value Decomposition
投稿时间:2017-06-22  修订日期:2018-02-18
DOI:10.11676/qxxb2020.005
中文关键词:  气象数据推测  奇异值分解  低秩性  基向量
英文关键词:meteorological data prediction  singular value decomposition  low-rankness  base vector
基金项目:国家自然科学基金;中国博士后基金
作者单位E-mail
史加荣 西安建筑科技大学 jiarongs3@163.com 
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中文摘要:
      以中国662个气象台站的2004-2013年逐日平均温度、平均相对湿度、日照时数和气温日较差等4个气象要素为研究对象,使用奇异值分解方法来推测缺失气象数据。为了减弱随机性的不利影响,将10年的逐日气象数据取平均值。分别采用奇异值分解的相对误差和相似度矩阵来证实气象数据的近似低秩性,并探讨了气象要素之间的相关性。分析了主要的基向量,设计了三组推测实验。第一组实验随机选取6个气象台站的数据用于测试,其余台站用于训练,以获得5个最佳的基向量。随机选取每个测试台站的12个观测值,再由所选取的基向量来推测未知值。平均温度、平均相对湿度、日照时数和气温日较差的平均推测误差分别为8.00%、7.83%、17.17%和10.82%。在第二组实验中,随机选取70%的气象台站用于训练,其余气象台站用于验证推测性能。实验结果表明基向量的数目可选为5-15,随着基向量或观测值数目的增加,推测性能也随之改善。第三组实验根据10个台站1952年下半年的气象观测数据,推测上半年的未观测值,实验结果合理可靠。
英文摘要:
      Based on the daily average temperature, average relative humidity, sunshine hours and diurnal temperature range of 662 meteorological stations in China from 2004 to 2013, the method of singular value decomposition is employed to estimate the missing meteorological data. To reduce negative influence of randomness, the daily meteorological data of 10 years are averaged. Both the relative error of singular value decomposition and the similarity matrix are adopted to verify the approximate low-rankness of meteorological data, and the correlations between different meteorological elements are discussed. After expounding the principal base vectors, three groups of estimation experiments are designed. The first group chooses randomly the data of 6 meteorological stations for testing, and the remaining stations for training to obtain five best base vectors. For each testing station, 12 observations are stochastically selected and other unknown elements are estimated according to the chosen base vectors. The means of estimation errors of average temperature, average relative humidity, sunshine hours and diurnal temperature range are 8.00%, 7.83%, 17.17% and 10.82%, respectively. In the second group of experiments,70% of the meteorological stations were randomly selected for training, the remaining for validating the estimation performance. The experimental results show that the number of base vectors can be chosen in the range from 5 to 15, and the estimation performance can be improved with the increase of the number of base vectors or the number of observations.The third group of experiments estimate the unobserved meteorological observation data of 10 stations in the first half of 1952 according to the corresponding observed data in the second half, and the estimation results are reasonable and reliable.
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