点源时间序列数据缺失值的估值方法比较——以小流域气象和水文数据为例
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摘要
对点源时间序列数据缺失值进行有效估值能提升其数据质量。为探究不同估值方法对点源时间序列数据缺失值的估值效果及其影响因素,以亚热带典型小流域长期定位观测的每日气象和水文数据(最高气温、最低气温、太阳辐射量、降雨量及地表径流量)为例,以均方根误差(RMSE)、绝对平均误差(MAE)和Pearson相关系数(r)为性能验证指标,比较了线性内插法(LIM)、K-最近邻插值法(KNNM)、样条插值法(SIM)、多项式插值法(PIM)和核密度估值法(KDEM)5种估值方法的估值性能差异及其主要影响因素。结果表明:(1)LIM、SIM和KDEM的估值性能总体上优于其它2种方法;(2)5种估值方法对气象数据(最高气温、最低气温和太阳辐射量)缺失值估值的RMSE为1.81~6.35,MAE为1.30~4.20,r为0.70~0.98(P<0.05),而对水文数据(降雨量和地表径流量)缺失值估值的RMSE为12.54~26.28,MAE为3.60~14.21,r为0.07~0.72。可见,各估值方法对气象数据的估值性能强于对水文数据;(3)上述数据集的变异系数(CV)与估值评估指标(RMSE、MAE及r)线性相关(P<0.05),是影响估值性能的重要因素。
The effective estimation of the missing values of time series data at the scale of point process could improve its data quality.The meteorological and hydrological data sets(daily maximum air temperature,daily minimum air temperature,daily solar radiation,daily rainfall and daily stream flow) were collected through the long-term field experiments in a typically small subtropical watershed in subtropical zone.The performance differences within five interpolation methods of linear interpolation method(LIM),K-Nearest neighbor interpolation method(KNNM),spline interpolation method(SIM),polynomial interpolation method(PIM) and kernel density estimation method(KDEM) were analyzed on the above-mentioned five data sets.The root mean square error(RMSE),absolute mean error(MAE) and Pearson correlation coefficient(r) were selected to evaluate the advantages and disadvantages of the five methods.The results showed that:(1) The estimation performance of LIM,SIM and KDEM was generally superior to the other two methods.(2) The estimation of the missing values of meteorological data(maximum temperature,minimum temperature and solar radiation) produced the varying values of the three evaluation indices with RMSE values of 1.81-6.35,MAE values of 1.30-4.20 and r values of 0.70-0.98(P<0.05),respectively.In contrast,the estimation of missing values of hydrological data(rainfall and stream flow) had relatively high values of RMSE and MAE which were 12.51-26.28 and 3.60-14.21,respectively,and low values of r(0.07-0.72).So the above-mentioned interpolation methods generally produced better estimation of missing values of meteorological data sets than those of hydrological data.(3) Additionally,the coefficient of variation(CV) of the above data sets linearly correlated with the evaluation indices(RMSE,MAE and r)(P<0.05),and played an important role in affecting the valuation performance of the above-mentioned interpolation methods.
The effective estimation of the missing values of time series data at the scale of point process could improve its data quality.The meteorological and hydrological data sets(daily maximum air temperature,daily minimum air temperature,daily solar radiation,daily rainfall and daily stream flow) were collected through the long-term field experiments in a typically small subtropical watershed in subtropical zone.The performance differences within five interpolation methods of linear interpolation method(LIM),K-Nearest neighbor interpolation method(KNNM),spline interpolation method(SIM),polynomial interpolation method(PIM) and kernel density estimation method(KDEM) were analyzed on the above-mentioned five data sets.The root mean square error(RMSE),absolute mean error(MAE) and Pearson correlation coefficient(r) were selected to evaluate the advantages and disadvantages of the five methods.The results showed that:(1) The estimation performance of LIM,SIM and KDEM was generally superior to the other two methods.(2) The estimation of the missing values of meteorological data(maximum temperature,minimum temperature and solar radiation) produced the varying values of the three evaluation indices with RMSE values of 1.81-6.35,MAE values of 1.30-4.20 and r values of 0.70-0.98(P<0.05),respectively.In contrast,the estimation of missing values of hydrological data(rainfall and stream flow) had relatively high values of RMSE and MAE which were 12.51-26.28 and 3.60-14.21,respectively,and low values of r(0.07-0.72).So the above-mentioned interpolation methods generally produced better estimation of missing values of meteorological data sets than those of hydrological data.(3) Additionally,the coefficient of variation(CV) of the above data sets linearly correlated with the evaluation indices(RMSE,MAE and r)(P<0.05),and played an important role in affecting the valuation performance of the above-mentioned interpolation methods.
引文
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[10]邵晓梅,严昌荣,魏红兵.基于Kriging插值的黄河流域降水时空分布格局[J].中国农业气象,2006,27(2):65-69.Shao X M,Yan C R,Wei H B.Spatial and temporal structure of precipitation in the Yellow River Basin based on Kriging method[J].Chinese Journal of Agrometeorology,2006,27(2):65-69.(in Chinese)
[11]Liu Y,Chen P Q,Zhang W.A spatial interpolation method for surface air temperature and its error analysis[J].Chinese Journal of Atmospheric Sciences,2006,30(1):146-152.
[12]杜东升,廖玉芳,赵福华.湖南复杂地形下日平均气温空间插值方法探讨[J].中国农业气象,2011,32(4):607-614.Du D S,Liao Y F,Zhao F H.Study on the spatial interpolation method for daily mean air temperature over complex terrain in Hunan province[J].Chinese Journal of Agrometeorology,2011,32(4):607-614.(in Chinese)
[13]郭建茂,王锦杰,吴越,等.基于卫星遥感与气象站数据的水稻高温热害监测和评估模型研究:以江苏、安徽为例[J].农业现代化研究,2017,38(2):298-306.Guo J M,Wang J J,Wu Y,et al.Research on monitoring and modeling of rice heat injury based on satellite and meteorological station data:case study of Jiangsu and Anhui[J].Research of Agricultural Modernization,2017,38(2):298-306.(in Chinese)
[14]任利利,殷淑燕.汉江上游近50多年来气温变化特征与区域差异[J].农业现代化研究,2013,34(3):348-352.Ren L L,Yin S Y.Air temperature variation of the upper reaches of Hanjiang River in recent 50 years and its regional differences[J].Research of Agricultural Modernization,2013,34(3):348-352.(in Chinese)
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[18]Saleem M U,Ahmed S R.Missing data imputations for upper air temperature at 24 standard pressure levels over pakistan collected from Aqua satellite[J].Journal of Data Analysis and Information Processing,2016,4(3):132.
[19]郑小波,罗宇翔,于飞,等.西南复杂山地农业气候要素空间插值方法比较[J].中国农业气象,2008,29(4):458-462.Zheng X B,Luo Y X,Yu F,et al.Comparisons of spatial interpolation methods for agro-climate factors in complex mountain areas of southwest China[J].Chinese Journal of Agrometeorology,2008,29(4):458-462.(in Chinese)
[20]孟岑,李裕元,吴金水,等.亚热带典型小流域总氮最大日负荷(TMDL)及影响因子研究:以金井河流域为例[J].环境科学学报,2016,36(2):700-709.Meng C,Li Y Y,Wu J S,et al.Study on total nitrogen TMDL and its contributing factors in typical subtropical watersheds:a case study of Jinjinghe watershed[J].Acta Scientiae Circumstantiae,2016,36(2):700-709.(in Chinese)
[21]李新,程国栋,卢玲.空间内插方法比较[J].地球科学进展,2000,15(3):260-265.Li X,Cheng G D,Lu L.Comparison of spatial interpolation methods[J].Advance Earth Sciences,2000,15(3):260-265.(in Chinese)
[22]张晓琴,王敏.基于主成分分析的成分数据缺失值插补法[J].应用概率统计,2016,32(1):101-110.Zhang X Q,Wang M.Imputation of missing values for compositional data based on principal component analysis[J].Chinese Journal of Applied Probability and Statistics,2016,32(1):101-110.(in Chinese)
[23]陈林.基于GIS的流域水文数据的时空分析:以格兰德河流域径流数据为例[D].青岛:山东科技大学,2010.Chen L.GIS-based spatial-temporal analysis of watershed hydrological data[D].Qingdao:Shandong University of Science and Technology,2010.(in Chinese)
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[25]殷杰,石锐.SAS中处理数据集缺失值方法的对比研究[J].计算机应用,2007,27(b6):438-439.Yin J,Shi R.A comparative study on the method of missing value of data set in SAS[J].Computer Applications,2007,27(b6):438-439.(in Chinese)
[26]花琳琳,施念,杨永利,等.不同缺失值处理方法对随机缺失数据处理效果的比较[J].郑州大学学报(医学版),2012,47(3):315-318.Hua L L,Shi N,Yang Y L,et al.Comparison of different methods in dealing with missing values of missing at random[J].Journal of Zhengzhou University(Medical Sciences),2012,47(3):315-318.(in Chinese)
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