利用时空协同克里金方法时空估算中国新疆降水量（英文）
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摘要
在对地观测中,所研究的地学变量不仅具有时间、空间特征,还受其它变量的影响,采用多元时空相关数据,可以提高时空估值的精度。以新疆区域为试验区,利用1960—2013年气象站的降水量观测数据的月平均值,采用时空克里金和时空协同克里金插值方法,估计试验区2013年1—12月降水量的时空分布情况。在使用时空协同克里金插值过程中,建立时空直接变异函数和协变异函数是时空CoKriging插值的关键一步。以该地区1960—2013年月平均降水量为主变量,引入同时间同位置的月平均空气相对湿度作为协变量,对降水量和空气相对湿度进行时空直接变异函数和时空交叉协变异函数建模。实验结果表明,引入空气相对湿度作为协变量的时空协同克里金的插值方法比时空普通克里金的插值方法的均方根误差降低了31.46%;引入空气相对湿度作为协变量的时空协同克里金的插值方法的估计值与观测值的相关系数比时空普通克里金的插值方法的相关系数提高了5.07%。因此,引入空气湿度作为协变量的时空协同克里金插值方法提高了插值精度。
In various environmental studies, geoscience variables not only have the characteristics of time and space,but also are influenced by other variables. Multivariate spatiotemporal variables can improve the accuracy of spatiotemporal estimation. Taking the monthly mean ground observation data of the period 1960–2013 precipitation in the Xinjiang Uygur Autonomous Region, China, the spatiotemporal distribution from January to December in 2013 was respectively estimated by space-time Kriging and space-time CoKriging. Modeling spatiotemporal direct variograms and a cross variogram was a key step in space-time CoKriging. Taking the monthly mean air relative humidity of the same site at the same time as the covariates, the spatiotemporal direct variograms and the spatiotemporal cross variogram of the monthly mean precipitation for the period 1960–2013 were modeled. The experimental results show that the space-time CoKriging reduces the mean square error by 31.46% compared with the space-time ordinary Kriging.The correlation coefficient between the estimated values and the observed values of the space-time CoKriging is 5.07%higher than the one of the space-time ordinary Kriging. Therefore, a space-time Co Kriging interpolation with air humidity as a covariate improves the interpolation accuracy.
In various environmental studies, geoscience variables not only have the characteristics of time and space,but also are influenced by other variables. Multivariate spatiotemporal variables can improve the accuracy of spatiotemporal estimation. Taking the monthly mean ground observation data of the period 1960–2013 precipitation in the Xinjiang Uygur Autonomous Region, China, the spatiotemporal distribution from January to December in 2013 was respectively estimated by space-time Kriging and space-time CoKriging. Modeling spatiotemporal direct variograms and a cross variogram was a key step in space-time CoKriging. Taking the monthly mean air relative humidity of the same site at the same time as the covariates, the spatiotemporal direct variograms and the spatiotemporal cross variogram of the monthly mean precipitation for the period 1960–2013 were modeled. The experimental results show that the space-time CoKriging reduces the mean square error by 31.46% compared with the space-time ordinary Kriging.The correlation coefficient between the estimated values and the observed values of the space-time CoKriging is 5.07%higher than the one of the space-time ordinary Kriging. Therefore, a space-time Co Kriging interpolation with air humidity as a covariate improves the interpolation accuracy.
引文
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[2]JIAPAER G,LIANG Shun-lin,YI Qiu-xiang,LIU Jin-ping.Vegetation dynamics and responses to recent climate change in Xinjiang using leaf area index as an indicator[J].Ecological Indicators,2015,58:64-76.DOI:10.1016/j.ecolind.2015.05.036.
[3]YANG Yue,QIU Wen-sheng,ZENG Wei,XIE Huan,XIESu-chao.A prediction method of rail grinding profile using non-uniform rational B-spline curves and Kriging model[J].Journal of Central South University,2018,25(1):230-240.DOI:https://doi.org/10.1007/s11771-018-3732-9.
[4]SHU Hong.A unification of gaillangran’s spatio-temporal data models[J].Geomatics and Information Science of Wuhan University,2007,32(8):723-726.DOI:10.13203/j.whugis2007.08.015.(in Chinese)
[5]KYRIAKIDIS P,JOURNEL A.Geostatistical space-time models:A review[J].Mathematical Geology,1999,31(6):651-684.DOI:10.1023/A:1007528426688.
[6]SUBBA R T,TERDIK G,SUBBA R T,TERDIK G.A new covariance function and spatio-temporal prediction(Kriging)for a stationary spatio-temporal random process[J].Journal of Time Series Analysis,2017,38(6):936-959.DOI:10.1111/jtsa.12245.
[7]BAHRAMI J E,HOSSEINI S M,BAHRAMI J E,HOSSEINI S M.Predicting saltwater intrusion into aquifers in vicinity of deserts using spatio-temporal Kriging[J].Environ Monit Assess,2017,189(2):81.DOI:10.1007/s10661-017-5795-8.
[8]RAJA N B,AYDIN O,TURKOGLU N,CICEK L.Space-time kriging of precipitation variability in Turkey for the period 1976-2010[J].Theoretical and Applied Climatology,2016,129(1,2):293-304.DOI:10.1007/00704-016-1788-8.
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[10]MITCHELL M W,GUMPERTZ M G G M L.Testing for separability of space-time covariances[J].Environmetrics,2005,16:819-831.DOI:10.1002/env.737.
[11]PORCU E P,GREGORI,MATEU J.Nonseparable stationary anisotropic space-time covariance functions.Stochastic Environmental Research and Risk Assessment,2006,21(2):113-122.DOI:10.1007/s00477-006-0048-3.
[12]MASTRANTONIO G G,JONA L,GELFAND A E,MASTRANTONIO G,LASINIO G J,GELFAND A E.Spatio-temporal circular models with non-separable covariance structure[J].Test,2015,25(2):331-350.DOI:10.1007/s11749-015-0458-y.
[13]GNEITING T.Nonseparable,stationary covariance functions for space-time data[J].Journal of the American Statistical Association,2002,97:590-600.DOI:10.1198/016214502760047113.
[14]de IACO S,MYERS D E,POSA D.On strict positive definiteness of product and product-sum covariance models[J].Journal of Statistical Planning and Inference,2011,141(3):1132-1140.DOI:10.1016/j.jspi.2010.09.014.
[15]de CESARE L,MYERS D E,POSA D.Product-sum covariance for space-time modeling:An environmental application[J].Environmetrics,2001,12(1):11-23.DOI:10.1002/1099-095x(200102)12:1<11::aid-env426>3.0.co;2-p.
[16]MYERS D E.Space-time correlation models and contaminant plumes[J].Environmetrics,2002,13(5,6):535-553.DOI:10.1002/env.536.
[17]HEUVELINK G B M,GRIFFITH D A.Space-time geostatistics for geography:A case study of radiation monitoring across parts of germany.geographical analysis[J].2010.42(2):161-179.DOI:10.1111/j.1538-4632.2010.00788.x.
[18]PEBESMA E.Spacetime:Spatio-temporal data in R[J].Journal of Statistical Software,2012,51(7):1-30.https://www.jstatsoft.org/article.
[19]XU J,SHU H.Spatio-temporal kriging based on the product-sum model:Some computational aspects[J].Earth Science Informatics,2014,8(3):639-648.DOI:10.1007/s12145-014-0195-x.
[20]GAO Sheng-guo,ZHU Zhong-li,LIU Shao-min,JIN Rui,YANG Guang-chao,TAN Lei.Estimating the spatial distribution of soil moisture based on Bayesian maximum entropy method with auxiliary data from remote sensing[J].International Journal of Applied Earth Observation and Geoinformation,2014,32:54-66.DOI:10.1016/j.jag.2014.03.003.
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[24]CHEN F,ZHANG M,WANG S,QIU X,DU M.Environmental controls on stable isotopes of precipitation in Lanzhou,China:An enhanced network at city scale[J].Sci Total Environ,2017,609:1013-1022.DOI:10.1016/j.scitotenv.2017.07.216.
[25]JESúS R,CESAR A M,ESTEBAN A G,ALBA S V,FRANCISCO N S,IBAI R,JUAN I L M.Meteorological and snow distribution data in the Izas Experimental Catchment(Spanish Pyrenees)from 2011 to 2017[J].Earth Syst Sci Data,2017,9:993-1005.DOI:10.5194/essd-9-993-2017.
[26]WANG Yan.Applied time series analysis[M].3rd ed.Beijing:Renmin University of China Press,2013.(in Chinese)
[27]de IACO S,PALMA M,POSA D.Modeling and prediction of multivariate space-time random fields[J].Computational Statistics&Data Analysis,2005,48(3):525-547.DOI:10.1016/j.csda.2004.02.011.
[28]MATEU J,PORCU E,GREGORI P.Recent advances to model anisotropic space-time data[J].Statistical Methods and Applications,2007,17(2):209-223.DOI:10.1007/s10260-007-0056-6.
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[30]MYERS D E.Matrix formulation of Co-Kriging[J].Mathematical Geology,1982,14(3):249-257.DOI:10.1007/BF01032887.
[31]DENBY B,SCHAAP M,SEGERS A,BUILTJES P,HORáLEK J.Comparison of two data assimilation methods for assessing PM10 exceedances on the European scale[J].Atmospheric Environment,2008,42(30):7122-7134.DOI:10.1016/j.atmosenv.2008.05.058.
[32]KEARNS M,RON D.Algorithmic stability and sanity-check bounds for leave-one-out cross-validation[J].Neural Computation,1999,11(6):1427-1453.DOI:10.1162/089976699300016304.
[33]MEHDIZADEH S,BEHMANESH J,KHALILI K.Acomparison of monthly precipitation point estimates at 6locations in Iran using integration of soft computing methods and GARCH time series model[J].Journal of Hydrology,2017,554:721-742.DOI:10.1016/j.jhydrol.2017.09.056.