Skip to main content
SpringerLink
Log in

Spatiotemporal interpolation of precipitation across Xinjiang, China using space-time CoKriging

利用时空协同克里金方法时空估算中国新疆降水量

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

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 CoKriging interpolation with air humidity as a covariate improves the interpolation accuracy.

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。

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. HU Dan-gui, SHU Hong, HU Hong-da, XU Jian-hui. Spatiotemporal regression Kriging to predict precipitation using time-series MODIS data [J]. Cluster Computing, 2017, 20(1): 347–357. DOI: https://doi.org/10.1007/s10586-016-0708-0.

    Article  Google Scholar 

  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: https://doi.org/10.1016/j.ecolind.2015.05.036.

    Article  Google Scholar 

  3. YANG Yue, QIU Wen-sheng, ZENG Wei, XIE Huan, XIE Su-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.

    Article  Google Scholar 

  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: https://doi.org/10.13203/j.whugis2007.08.015. (in Chinese)

    Google Scholar 

  5. KYRIAKIDIS P, JOURNEL A. Geostatistical space-time models: A review [J]. Mathematical Geology, 1999, 31(6): 651–684. DOI: https://doi.org/10.1023/A:1007528426688.

    Article  MathSciNet  MATH  Google Scholar 

  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: https://doi.org/10.1111/jtsa.12245.

    Article  MathSciNet  MATH  Google Scholar 

  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: https://doi.org/10.1007/s10661-017-5795-8.

    Article  Google Scholar 

  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: https://doi.org/10.1007/00704-016-1788-8.

    Google Scholar 

  9. GENTON M G. Separable approximations of space-time covariance matrices [J]. Environmetrics, 2007, 18: 681–695. DOI: https://doi.org/10.1002/env.854.

    Article  MathSciNet  Google Scholar 

  10. MITCHELL M W, GUMPERTZ M G G M L. Testing for separability of space-time covariances [J]. Environmetrics, 2005, 16: 819–831. DOI: https://doi.org/10.1002/env.737.

    Article  MathSciNet  Google Scholar 

  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: https://doi.org/10.1007/s00477-006-0048-3.

    Article  MathSciNet  Google Scholar 

  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: https://doi.org/10.1007/s11749-015-0458-y.

    Article  MathSciNet  MATH  Google Scholar 

  13. GNEITING T. Nonseparable, stationary covariance functions for space-time data [J]. Journal of the American Statistical Association, 2002, 97: 590–600. DOI: https://doi.org/10.1198/016214502760047113.

    Article  MathSciNet  MATH  Google Scholar 

  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: https://doi.org/10.1016/j.jspi.2010.09.014.

    Article  MathSciNet  MATH  Google Scholar 

  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: https://doi.org/10.1002/1099-095x(200102)12:13.0.co;2-p.

    Article  Google Scholar 

  16. MYERS D E. Space-time correlation models and contaminant plumes [J]. Environmetrics, 2002, 13(5, 6): 535–553. DOI: https://doi.org/10.1002/env.536.

    Article  Google Scholar 

  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: https://doi.org/10.1111/j.1538-4632.2010.00788.x.

    Google Scholar 

  18. PEBESMA E. Spacetime: Spatio-temporal data in R [J]. Journal of Statistical Software, 2012, 51(7): 1–30. https://www.jstatsoft.org/article.

    Article  Google Scholar 

  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: https://doi.org/10.1007/s12145-014-0195-x.

    Article  MathSciNet  Google Scholar 

  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: https://doi.org/10.1016/j.jag.2014.03.003.

    Article  Google Scholar 

  21. KASMAEE S, RISK F M T. Reduction in Sechahun iron ore deposit by geological boundary modification using multiple indicator Kriging [J]. Journal of Central South University, 2014, 21: 2011–2017. DOI: https://doi.org/10.1007/s11771-014-2150-x.

    Article  Google Scholar 

  22. KILIBARDA M, HENGL T, HEUVELINK G, GRAELER B, PEBESMA E, TADIC M P, BAJAT B. Spatio-temporal interpolation of daily temperatures for global land areas at 1 km resolution [J]. Journal of Geophysical Research: Atmospheres, 2014, 119(5): 2294–2313. DOI: https://doi.org/10.1002/2013JD020803.

    Google Scholar 

  23. HENGL T, HEUVELINK G, TADIC M P, PEBESMA E. Spatio-temporal prediction of daily temperatures using time-series of MODIS LST images [J]. Theoretical and Applied Climatology, 2011, 107(1, 2): 265–277. DOI: https://doi.org/10.1007/s00704-011-0464-2.

    Google Scholar 

  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: https://doi.org/10.1016/j.scitotenv.2017.07.216.

    Article  Google Scholar 

  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: https://doi.org/10.5194/essd-9-993-2017.

    Article  Google Scholar 

  26. WANG Yan. Applied time series analysis [M]. 3rd ed. Beijing: Renmin University of China Press, 2013. (in Chinese)

    Google Scholar 

  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: https://doi.org/10.1016/j.csda.2004.02.011.

    Article  MathSciNet  MATH  Google Scholar 

  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: https://doi.org/10.1007/s10260-007-0056-6.

    Article  MathSciNet  MATH  Google Scholar 

  29. CESARE L D, MYERS D E, POSA D. Estimating and modeling space-time correlation structures [J]. Statistics & Probability Letters, 2001, 51(1): 9–14. https://www.sciencedirect.com/search/advanced?docId=10.1016/S0167-7152(00)00131-0.

    Article  MathSciNet  MATH  Google Scholar 

  30. MYERS D E. Matrix formulation of Co-Kriging [J]. Mathematical Geology, 1982, 14(3): 249–257. DOI: https://doi.org/10.1007/BF01032887.

    Article  MathSciNet  Google Scholar 

  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: https://doi.org/10.1016/j.atmosenv.2008.05.058.

    Article  Google Scholar 

  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: https://doi.org/10.1162/089976699300016304.

    Article  Google Scholar 

  33. MEHDIZADEH S, BEHMANESH J, KHALILI K. A comparison of monthly precipitation point estimates at 6 locations in Iran using integration of soft computing methods and GARCH time series model [J]. Journal of Hydrology, 2017, 554: 721–742. DOI: https://doi.org/10.1016/j.jhydrol.2017.09.056.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Collaborative Innovation Center of Geospatial Technology, Wuhan University, Wuhan, 430079, China

    Dan-gui Hu  (胡丹桂) & Hong Shu  (舒红)

  2. College of Computer Technology and Software Engineering, Wuhan Polytechnic, Wuhan, 430074, China

    Dan-gui Hu  (胡丹桂)

Authors
  1. Dan-gui Hu  (胡丹桂)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong Shu  (舒红)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hong Shu  (舒红).

Additional information

Foundation item: Project(17D02) supported by the Open Fund of State Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, China; Project supported by the State Key Laboratory of Satellite Navigation System and Equipment Technology, China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, Dg., Shu, H. Spatiotemporal interpolation of precipitation across Xinjiang, China using space-time CoKriging. J. Cent. South Univ. 26, 684–694 (2019). https://doi.org/10.1007/s11771-019-4039-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-019-4039-1

Key words

关键词

Search

Navigation