| 基于矩阵补全的气象数据推测 |
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| 引用本文： | 史加荣,李雪霞.基于矩阵补全的气象数据推测[J].气象科技,2019,47(3):420-425. |
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| 作者姓名： | 史加荣 李雪霞 |
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| 作者单位： | 1 省部共建西部绿色建筑国家重点实验室/西安建筑科技大学，西安 710055; 2 西安建筑科技大学理学院，西安 710055,西安建筑科技大学理学院，西安 710055 |
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| 基金项目： | “十三五”国家重点研发计划专项（2018YFC0704500）、中国博士后科学基金(批准号：2017M613087)、国家自然科学基金青年科学基金(批准号：61403298)资助 |
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| 摘 要： | 传统的气象数据推测大多基于插值方法,而此方法需要近邻台站的完整观测数据,这在很大程度上限制了插值方法的应用。为此,本文提出了一种基于矩阵补全的气象数据推测方法,该方法根据气象数据的近似低秩性来推测缺失数据。首先,选取我国662个气象台站2004—2013年的逐日平均温度和日照时数两种气象要素作为研究对象,通过矩阵奇异值的累积贡献率来检验数据集的近似低秩性。然后设计了两组试验,第1组试验考虑了不同采样概率下各年份的数据推测,第2组试验随机选取某些台站,考虑所选台站数据连续缺测时的推测。最后,使用矩阵补全方法推测缺失数据,采用10a的平均误差作为评价指标。试验结果表明:矩阵补全方法能很好地推测缺失数据,且具有一定的鲁棒性。
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| 关 键 词： | 气象数据推测 矩阵补全 低秩 奇异值分解 鲁棒 |
| 收稿时间： | 2018/6/26 0:00:00 |
| 修稿时间： | 2018/10/16 0:00:00 |
Meteorological Data Estimation Based on Matrix Completion |
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| Shi Jiarong and Li Xuexia.Meteorological Data Estimation Based on Matrix Completion[J].Meteorological Science and Technology,2019,47(3):420-425. |
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| Authors: | Shi Jiarong and Li Xuexia |
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| Abstract: | The traditional meteorological data estimation is mostly based on the interpolation methods, which require the complete observation data of the nearest neighbor stations and largely limit the application of the interpolation methods. This paper proposes a method for estimating meteorological data based on matrix completion. The proposed method estimates missing data based on the approximate low rankness of meteorological data. The daily average temperature and sunshine hours of 662 meteorological stations in China from 2004 to 2013 are selected as the research objects. The approximate low rankness of the data set is validated by the cumulative contribution rate of matrix singular values. Then two groups of experiments are designed. The first group of experiments considers the data estimation for different years with different sampling probabilities. The second group randomly chooses some stations and considers the data estimation when the data of the selected stations are continuously missing. Finally, the matrix completion method is employed to estimate the missing data, and the 10 year average error is used as the evaluation index. Experimental results show that the matrix completion method has good estimation performance and certain robustness. |
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