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

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.

Keywords

space-time CoKriging / product-sum model / variogram / precipitation / interpolation

References

[1] HuD-g, ShuH, HuH-d, XuJ-hui. Spatiotemporal regression Kriging to predict precipitation using time-series MODIS data [J]. Cluster Computing, 2017, 20(1): 347-357

[2] JiapaerG, LiangS-l, YiQ-x, LiuJ-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

[3] YangY, QiuW-s, ZengW, XieH, XieS-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

[4] ShuHong. A unification of gaillangran’s spatio-temporal data models [J]. Geomatics and Information Science of Wuhan University, 2007, 32(8): 723-726(in Chinese)

[5] KyriakidisP, JournelA. Geostatistical space-time models: A review [J]. Mathematical Geology, 1999, 31(6): 651-684

[6] SubbaR T, TerdikG, SubbaR T, TerdikG. 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

[7] BahramiJ E, HosseiniS M, BahramiJ E, HosseiniS M. Predicting saltwater intrusion into aquifers in vicinity of deserts using spatio-temporal Kriging [J]. Environ Monit Assess, 2017, 189(2): 81

[8] RajaN B, AydinO, TurkogluN, CicekL. Space-time kriging of precipitation variability in Turkey for the period 1976–2010 [J]. Theoretical and Applied Climatology, 2016, 12912293-304

[9] GentonM G. Separable approximations of space-time covariance matrices [J]. Environmetrics, 2007, 18: 681-695

[10] MitchellM W, GumpertzM G G M L. Testing for separability of space-time covariances [J]. Environmetrics, 2005, 16: 819-831

[11] PorcuE P, Gregori, MateuJ. Nonseparable stationary anisotropic space-time covariance functions. Stochastic Environmental Research and Risk Assessment, 2006, 21(2): 113-122

[12] MastrantonioG G, JonaL, GelfandA E, MastrantonioG, LasinioG J, GelfandA E. Spatio-temporal circular models with non-separable covariance structure [J]. Test, 2015, 25(2): 331-350

[13] GneitingT. Nonseparable, stationary covariance functions for space-time data [J]. Journal of the American Statistical Association, 2002, 97: 590-600

[14] de IacoS, MyersD E, PosaD. On strict positive definiteness of product and product-sum covariance models [J]. Journal of Statistical Planning and Inference, 2011, 141(3): 1132-1140

[15] de CesareL, MyersD E, PosaD. Product-sum covariance for space-time modeling: An environmental application [J]. Environmetrics, 2001, 12(1): 11-23

[16] MyersD E. Space-time correlation models and contaminant plumes [J]. Environmetrics, 2002, 13(56): 535-553

[17] HeuvelinkG B M, GriffithD ASpace-time geostatistics for geography: A case study of radiation monitoring across parts of germany. geographical analysis [J], 2010, 42(2): 161-179

[18] PebesmaE. Spacetime: Spatio-temporal data in R [J]. Journal of Statistical Software, 2012, 51(7): 1-30

[19] XuJ, ShuH. Spatio-temporal kriging based on the product-sum model: Some computational aspects [J]. Earth Science Informatics, 2014, 8(3): 639-648

[20] GaoS-g, ZhuZ-l, LiuS-m, JinR, YangG-c, TanLei. 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

[21] KasmaeeS, RiskF 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

[22] KilibardaM, HenglT, HeuvelinkG, GraelerB, PebesmaE, TadicM P, BajatB. 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

[23] HenglT, HeuvelinkG, TadicM P, PebesmaE. Spatio-temporal prediction of daily temperatures using time-series of MODIS LST images [J]. Theoretical and Applied Climatology, 2011, 107(12): 265-277

[24] ChenF, ZhangM, WangS, QiuX, DuM. Environmental controls on stable isotopes of precipitation in Lanzhou, China: An enhanced network at city scale [J]. Sci Total Environ, 2017, 609: 1013-1022

[25] JesÚsR, CesarA M, EstebanA G, AlbaS V, FranciscoN S, IbaiR, JuanI 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

[26] WangYanApplied time series analysis [M], 20133Beijing, Renmin University of China Press(in Chinese)

[27] de IacoS, PalmaM, PosaD. Modeling and prediction of multivariate space-time random fields [J]. Computational Statistics & Data Analysis, 2005, 48(3): 525-547

[28] MateuJ, PorcuE, GregoriP. Recent advances to model anisotropic space-time data [J]. Statistical Methods and Applications, 2007, 17(2): 209-223

[29] CesareL D, MyersD E, PosaD. Estimating and modeling space-time correlation structures [J]. Statistics & Probability Letters, 2001, 51(1): 9-14

[30] MyersD E. Matrix formulation of Co-Kriging [J]. Mathematical Geology, 1982, 14(3): 249-257

[31] DenbyB, SchaapM, SegersA, BuiltjesP, HorÁlekJ. Comparison of two data assimilation methods for assessing PM10 exceedances on the European scale [J]. Atmospheric Environment, 2008, 42(30): 7122-7134

[32] KearnsM, RonD. Algorithmic stability and sanity-check bounds for leave-one-out cross-validation [J]. Neural Computation, 1999, 11(6): 1427-1453

[33] MehdizadehS, BehmaneshJ, KhaliliK. 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