基于西南地区台站降雨资料空间插值方法的比较
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摘要
以西南地区1996～2000年93个气象台站观测的月均降雨量为基础,对各月降雨量进行空间自相关性,变异特征等空间分析后,采用反距离加权法(IDW)和以不同变异函数模型(指数模型、球面模型、高斯模型)为基础的普通克里金(O-Kriging)两种方法进行空间插值,通过交叉验证结果对两种方法进行分析比对。结果表明:(1)西南地区月均降雨量存在明显的空间集聚现象,并具有显著的空间自相关性和变异特征,可对该研究区域降雨量进行空间插值研究。(2)在O-Kriging插值时,变异函数选用指数模型的效果最好,球面模型次之,高斯模型最差。(3)两种方法对月均降雨量及其极大值和极小值插值时,O-Kriging的插值误差均小于IDW,插值误差整体上与降雨量呈正相关关系。在剔除各月降雨量极大值较为集中的两个站点后进行插值,插值结果的误差均明显降低。(4)对研究区域整体来说,O-Kriging的插值效果优于IDW,但就单个站点来看,结果并非如此。在降雨量的空间插值中,由于研究区域和时间尺度的不同,并不存在绝对的最优方法,应根据实际应用效果选择最适方法。
Based on monthly precipitation observations collected at 93 meteorological stations in Southwest China from 1996 to 2000, this study investigates the spatial interpolation results with the Inverse Distance Weighting(IDW) and O-Kriging interpolation methods. Firstly, we analyze the spatial autocorrelation and spatial variability character of monthly average precipitation data. Secondly, the IDW and O-Kriging based on three semi-variograms(exponential, spherical and, Gaussian model) are used to spatially interpolate monthly precipitation. Finally, the interpolation results are compared and discussed using the cross-validation method. The conclusions are:(1) Monthly precipitation distribution in Southwest China shows a spatial aggregation feature with high spatial autocorrelation and variation, which favors for the spatial interpolation.(2) Compared to the three semi-variograms used in the O-Kriging interpolation method, the best performance is from the exponential model, while the worst is from the Gaussian model.(3) When the O-Kriging and IDW are used in spatial interpolation of monthly average and maximum and minimum precipitation, the former one perform better than the latter one. The errors between interpolated data and observations overall increase with monthly precipitation magnitude, and the errors from both interpolation methods are obviously reduced after removing the maximum monthly precipitation points.(4) For the study area as a whole, the interpolation effect of the O-Kriging is better than that of IDW, however, this is not true at single sites. There is no absolute optimal method in the spatial interpolation of precipitation for every study area and on all time scales. The optimal interpolation method depends on the actual demands and applications.
Based on monthly precipitation observations collected at 93 meteorological stations in Southwest China from 1996 to 2000, this study investigates the spatial interpolation results with the Inverse Distance Weighting(IDW) and O-Kriging interpolation methods. Firstly, we analyze the spatial autocorrelation and spatial variability character of monthly average precipitation data. Secondly, the IDW and O-Kriging based on three semi-variograms(exponential, spherical and, Gaussian model) are used to spatially interpolate monthly precipitation. Finally, the interpolation results are compared and discussed using the cross-validation method. The conclusions are:(1) Monthly precipitation distribution in Southwest China shows a spatial aggregation feature with high spatial autocorrelation and variation, which favors for the spatial interpolation.(2) Compared to the three semi-variograms used in the O-Kriging interpolation method, the best performance is from the exponential model, while the worst is from the Gaussian model.(3) When the O-Kriging and IDW are used in spatial interpolation of monthly average and maximum and minimum precipitation, the former one perform better than the latter one. The errors between interpolated data and observations overall increase with monthly precipitation magnitude, and the errors from both interpolation methods are obviously reduced after removing the maximum monthly precipitation points.(4) For the study area as a whole, the interpolation effect of the O-Kriging is better than that of IDW, however, this is not true at single sites. There is no absolute optimal method in the spatial interpolation of precipitation for every study area and on all time scales. The optimal interpolation method depends on the actual demands and applications.
引文
Abzalov M.2016.Introduction to geostatistics[M]//Abzalov M.Applied Mining Geology.Cham:Springer International Publishing,doi:10.1007/978-3-319-39264-6_17..
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蔡福,于慧波,矫玲玲,等.2006.降水要素空间插值精度的比较--以东北地区为例[J].资源科学,28(6):73-79.Cai Fu,Yu Huibo,Jiao Lingling,et al.2006.Comparison of precision of spatial interpolation of precipitation factors:A case study in northeastern China[J].Resources Science(in Chinese),28(6):73-79,doi:10.3321/j.issn:1007-7588.2006.06.011.
de Amorim Borges P,Franke J,da Anuncia??o Y M T,et al.2016.Comparison of spatial interpolation methods for the estimation of precipitation distribution in Distrito Federal,Brazil[J].Theor.Appl.Climatol.,123(1-2):335-348,doi:10.1007/s00704-014-1359-9.
段平,盛业华,李佳,等.2014.自适应的IDW插值方法及其在气温场中的应用[J].地理研究,33(8):1417-1426.Duan Ping,Sheng Yehua,Li Jia,et al.2014.Adaptive IDW interpolation method and its application in the temperature field[J].Geographical Research(in Chinese),33(8):1417-1426,doi:10.11821/dlyj201408003.
冯锦明,赵天保,张英娟.2004.基于台站降水资料对不同空间内插方法的比较[J].气候与环境研究,9(2):261-277.Feng Jinming,Zhao Tianbao,Zhang Yingjuan.2004.Intercomparison of spatial interpolation based on observed precipitation data[J].Climatic and Environmental Research(in Chinese),9(2):261-277,doi:10.3878/j.issn.1006-9585.2004.02.04.
封志明,杨艳昭,丁晓强,等.2004.气象要素空间插值方法优化[J].地理研究,23(3):357-364.Feng Zhiming,Yang Yanzhao,Ding Xiaoqiang,et al.2004.Optimization of the spatial interpolation methods for climate resources[J].Geographical Research(in Chinese),23(3):357-364,doi:10.3321/j.issn:1000-0585.2004.03.009.
高涛,谢立安.2014.近50年来中国极端降水趋势与物理成因研究综述[J].地球科学进展,29(5):577-589.Gao Tao,Xie Li’an.2014.Study on progress of the trends and physical causes of extreme precipitation in China during the last 50 years[J].Advances in Earth Science(in Chinese),29(5):577-589,doi:10.11867/j.issn.1001-8166.2014.05.0577.
何红艳,郭志华,肖文发.2005.降水空间插值技术的研究进展[J].生态学杂志,24(10):1187-1191.He Hongyan,Guo Zhihua,Xiao Wenfa.2005.Review on spatial interpolation techniques of rainfall[J].Chinese Journal of Ecology(in Chinese),24(10):1187-1191,doi:10.13292/j.1000-4890.2005.0125.
IPCC.2013.Climate Change 2013:The Physical Science Basis:Working Group I Contribution to the IPCC Fifth Assessment Report of the Intergovernmental Panel on Climate Change[M].Cambridge:Cambridge University Press.
靳国栋,刘衍聪,牛文杰.2003.距离加权反比插值法和克里金插值法的比较[J].长春工业大学学报,24(3):53-57.Jin Guodong,Liu Yancong,Niu Wenjie.2003.Comparison between inverse distance weighting method and Kriging[J].Journal of Changchun University of Technology(in Chinese),24(3):53-57,doi:10.3969/j.issn.1674-1374-B.2003.03.017.
孔峰,史培军,方建,等.2017.全球变化背景下极端降水时空格局变化及其影响因素研究进展和展望[J].灾害学,32(2):165-174.Kong Feng,Shi Peijun,Fang Jian,et al.2017.Advances and prospects of spatiotemporal pattern variation of extreme precipitation and its affecting factors under the background of global climate change[J].Journal of Catastrophology(in Chinese),32(2):165-174,doi:10.3969/j.issn.1000-811X.2017.02.029.
孔云峰,仝文.2008.降雨量地面观测数据空间探索与插值方法探讨[J].地理研究,27(5):127-138.Kong Yunfeng,Tong wen.2008.Spatial exploration and interpolation of the surface precipitation data[J].Geographical Research(in Chinese),27(5):127-138.Li J,Heap A D.2014.Spatial interpolation methods applied in the environmental sciences:A review[J].Environmental Modelling&Software,53(3):173-189,doi:10.1016/j.envsoft.2013.12.008.
林忠辉,莫兴国,李宏轩,等.2002.中国陆地区域气象要素的空间插值[J].地理学报,57(1):47-56.Lin Zhonghui,Mo Xingguo,Li Hongxuan,et al.2002.Comparison of three spatial interpolation methods for climate variables in China[J].Acta Geographica Sinica(in Chinese),57(1):47-56,doi:10.11821/xb200201006.
刘爱利,王培法,丁园圆.2012.地统计学概论[M].北京:科学出版社,144-160.Liu Aili,Wang Peifa,Ding Yuanyuan.2012.Introduction to Geostatistics(in Chinese)[M].Beijing:Science Press,144-160.
卢燕宇,吴必文,田红,等.2011.基于Kriging插值的1961~2005年淮河流域降水时空演变特征分析[J].长江流域资源与环境,20(5):567-573.Lu Yanyu,Wu Biwen,Tian Hong,et al.2011.Spatial and temporal variability characteristics of precipitation in Huai River Basin during 1961-2005[J].Resources and Environment in the Yangtze Basin(in Chinese),20(5):567-573.
Ord J K,Getis A.2001.Testing for local spatial autocorrelation in the presence of global autocorrelation[J].Journal of Regional Science,41(3):411-432,doi:10.1111/0022-4146.00224.
乔方利,Zhang S Q.2002.现代海洋/大气资料同化方法的统一性及其应用进展[J].海洋科学进展,20(4):79-93.Qiao Fangli,Zhang Shaoqing.2002.The unification and application reviews of modern oceanic/atmospheric data assimilation algorithms[J].Advances in Marine Science(in Chinese),20(4):79-93,doi:10.3969/j.issn.1671-6647.2002.04.013.
秦伟良,刘悦.2010.空间插值法在降水分布中的应用[J].南京信息工程大学学报(自然科学版),2(2):162-165.Qin Weiliang,Liu Yue.2010.Application of spatial interpolation in rainfall distribution analysis[J].Journal of Nanjing University of Information Science and Technology(Natural Science Edition)(in Chinese),2(2):162-165,doi:10.3969/j.issn.1674-7070.2010.02.013.
Sokal R R,Thomson J D.1987.Applications of spatial autocorrelation in ecology[M]//Legendre P,Legendre L.Develoments in Numerical Ecology.Berlin,Heidelberg:Springer,431-466,doi:10.1007/978-3-642-70880-0_12.
Wang A H,Fu J J.2013.Changes in daily climate extremes of observed temperature and precipitation in China[J].Atmospheric and Oceanic Science Letters,6(5):312-319,doi:10.3878/j.issn.1674-2834.12.0106.
Worthington R.2000.Reviewed Work:Interpolation of spatial data:Some theory for Kriging by Michael L.Stein[J].Technometrics,42(4):436-437.
吴昌广,林德生,周志翔,等.2010.三峡库区降水量的空间插值方法及时空分布[J].长江流域资源与环境,19(7):752-758.Wu Changguang,Lin Desheng,Zhou Zhixiang,et al.2010.Spatial interpolation methods and temporal-spatial distribution of precipitation in the Three Gorges Reservoir area[J].Resources and Environment in the Yangtze Basin(in Chinese),19(7):752-758.
邬伦,吴小娟,肖晨超,等.2010.五种常用降水量插值方法误差时空分布特征研究--以深圳市为例[J].地理与地理信息科学,26(3):19-24.Wu Lun,Wu Xiaojuan,Xiao Chenchao,et al.2010.On temporal and spatial error distributions of five precipitation interpolation models:Acase of Shenzhen[J].Geography and Geo-Information Science(in Chinese),26(3):19-24.
叶小岭,沈云培,熊雄.2016.一种基于改进克里金法的地面气温质量控制算法[J].气候与环境研究,21(5):614-620.Ye Xiaoling,Shen Yunpei,Xiong Xiong.2016.A quality control algorithm for surface temperature observations based on improved Kriging method[J].Climatic and Environmental Research(in Chinese),21(5):614-620,doi:10.3878/j.issn.1006-9585.2016.15264.
曾红伟,李丽娟,张永萱,等.2011.大样本降水空间插值研究--以2009年中国年降水为例[J].地理科学进展,30(7):811-818.Zeng Hongwei,Li Lijuan,Zhang Yongxuan,et al.2011.Study on spatial interpolation of precipitation with large scale samples:A case study on2009’s precipitation of China[J].Progress in Geography(in Chinese),30(7):811-818,doi:10.11820/dlkxjz.2011.07.005.
Zhao T B,Yatagai A.2014.Evaluation of TRMM 3B42 product using a new gauge-based analysis of daily precipitation over China[J].International Journal of Climatology,34(8):2749-2762,doi:10.1002/joc.3872.
中国气象局.2006.中国气象地理区划手册[M].北京:气象出版社,1.China Meteorological Administration.2006.Handbook of Meteorological and Geographical Regionalization of China(in Chinese)[M].Beijing:China Meteorological Press,1.
朱会义,贾绍凤.2004.降雨信息空间插值的不确定性分析[J].地理科学进展,23(2):34-42.Zhu Huiyi,Jia Shaofeng.2004.Uncertainty in the spatial interpolation of rainfall data[J].Progress in Geography(in Chinese),23(2):34-42,doi:10.11820/dlkxjz.2004.02.005.
Bartier P M,Keller C P.1996.Multivariate interpolation to incorporate thematic surface data using inverse distance weighting(IDW)[J].Computers&Geosciences,22(7):795-799,doi:10.1016/0098-3004(96)00021-0.
蔡福,于慧波,矫玲玲,等.2006.降水要素空间插值精度的比较--以东北地区为例[J].资源科学,28(6):73-79.Cai Fu,Yu Huibo,Jiao Lingling,et al.2006.Comparison of precision of spatial interpolation of precipitation factors:A case study in northeastern China[J].Resources Science(in Chinese),28(6):73-79,doi:10.3321/j.issn:1007-7588.2006.06.011.
de Amorim Borges P,Franke J,da Anuncia??o Y M T,et al.2016.Comparison of spatial interpolation methods for the estimation of precipitation distribution in Distrito Federal,Brazil[J].Theor.Appl.Climatol.,123(1-2):335-348,doi:10.1007/s00704-014-1359-9.
段平,盛业华,李佳,等.2014.自适应的IDW插值方法及其在气温场中的应用[J].地理研究,33(8):1417-1426.Duan Ping,Sheng Yehua,Li Jia,et al.2014.Adaptive IDW interpolation method and its application in the temperature field[J].Geographical Research(in Chinese),33(8):1417-1426,doi:10.11821/dlyj201408003.
冯锦明,赵天保,张英娟.2004.基于台站降水资料对不同空间内插方法的比较[J].气候与环境研究,9(2):261-277.Feng Jinming,Zhao Tianbao,Zhang Yingjuan.2004.Intercomparison of spatial interpolation based on observed precipitation data[J].Climatic and Environmental Research(in Chinese),9(2):261-277,doi:10.3878/j.issn.1006-9585.2004.02.04.
封志明,杨艳昭,丁晓强,等.2004.气象要素空间插值方法优化[J].地理研究,23(3):357-364.Feng Zhiming,Yang Yanzhao,Ding Xiaoqiang,et al.2004.Optimization of the spatial interpolation methods for climate resources[J].Geographical Research(in Chinese),23(3):357-364,doi:10.3321/j.issn:1000-0585.2004.03.009.
高涛,谢立安.2014.近50年来中国极端降水趋势与物理成因研究综述[J].地球科学进展,29(5):577-589.Gao Tao,Xie Li’an.2014.Study on progress of the trends and physical causes of extreme precipitation in China during the last 50 years[J].Advances in Earth Science(in Chinese),29(5):577-589,doi:10.11867/j.issn.1001-8166.2014.05.0577.
何红艳,郭志华,肖文发.2005.降水空间插值技术的研究进展[J].生态学杂志,24(10):1187-1191.He Hongyan,Guo Zhihua,Xiao Wenfa.2005.Review on spatial interpolation techniques of rainfall[J].Chinese Journal of Ecology(in Chinese),24(10):1187-1191,doi:10.13292/j.1000-4890.2005.0125.
IPCC.2013.Climate Change 2013:The Physical Science Basis:Working Group I Contribution to the IPCC Fifth Assessment Report of the Intergovernmental Panel on Climate Change[M].Cambridge:Cambridge University Press.
靳国栋,刘衍聪,牛文杰.2003.距离加权反比插值法和克里金插值法的比较[J].长春工业大学学报,24(3):53-57.Jin Guodong,Liu Yancong,Niu Wenjie.2003.Comparison between inverse distance weighting method and Kriging[J].Journal of Changchun University of Technology(in Chinese),24(3):53-57,doi:10.3969/j.issn.1674-1374-B.2003.03.017.
孔峰,史培军,方建,等.2017.全球变化背景下极端降水时空格局变化及其影响因素研究进展和展望[J].灾害学,32(2):165-174.Kong Feng,Shi Peijun,Fang Jian,et al.2017.Advances and prospects of spatiotemporal pattern variation of extreme precipitation and its affecting factors under the background of global climate change[J].Journal of Catastrophology(in Chinese),32(2):165-174,doi:10.3969/j.issn.1000-811X.2017.02.029.
孔云峰,仝文.2008.降雨量地面观测数据空间探索与插值方法探讨[J].地理研究,27(5):127-138.Kong Yunfeng,Tong wen.2008.Spatial exploration and interpolation of the surface precipitation data[J].Geographical Research(in Chinese),27(5):127-138.Li J,Heap A D.2014.Spatial interpolation methods applied in the environmental sciences:A review[J].Environmental Modelling&Software,53(3):173-189,doi:10.1016/j.envsoft.2013.12.008.
林忠辉,莫兴国,李宏轩,等.2002.中国陆地区域气象要素的空间插值[J].地理学报,57(1):47-56.Lin Zhonghui,Mo Xingguo,Li Hongxuan,et al.2002.Comparison of three spatial interpolation methods for climate variables in China[J].Acta Geographica Sinica(in Chinese),57(1):47-56,doi:10.11821/xb200201006.
刘爱利,王培法,丁园圆.2012.地统计学概论[M].北京:科学出版社,144-160.Liu Aili,Wang Peifa,Ding Yuanyuan.2012.Introduction to Geostatistics(in Chinese)[M].Beijing:Science Press,144-160.
卢燕宇,吴必文,田红,等.2011.基于Kriging插值的1961~2005年淮河流域降水时空演变特征分析[J].长江流域资源与环境,20(5):567-573.Lu Yanyu,Wu Biwen,Tian Hong,et al.2011.Spatial and temporal variability characteristics of precipitation in Huai River Basin during 1961-2005[J].Resources and Environment in the Yangtze Basin(in Chinese),20(5):567-573.
Ord J K,Getis A.2001.Testing for local spatial autocorrelation in the presence of global autocorrelation[J].Journal of Regional Science,41(3):411-432,doi:10.1111/0022-4146.00224.
乔方利,Zhang S Q.2002.现代海洋/大气资料同化方法的统一性及其应用进展[J].海洋科学进展,20(4):79-93.Qiao Fangli,Zhang Shaoqing.2002.The unification and application reviews of modern oceanic/atmospheric data assimilation algorithms[J].Advances in Marine Science(in Chinese),20(4):79-93,doi:10.3969/j.issn.1671-6647.2002.04.013.
秦伟良,刘悦.2010.空间插值法在降水分布中的应用[J].南京信息工程大学学报(自然科学版),2(2):162-165.Qin Weiliang,Liu Yue.2010.Application of spatial interpolation in rainfall distribution analysis[J].Journal of Nanjing University of Information Science and Technology(Natural Science Edition)(in Chinese),2(2):162-165,doi:10.3969/j.issn.1674-7070.2010.02.013.
Sokal R R,Thomson J D.1987.Applications of spatial autocorrelation in ecology[M]//Legendre P,Legendre L.Develoments in Numerical Ecology.Berlin,Heidelberg:Springer,431-466,doi:10.1007/978-3-642-70880-0_12.
Wang A H,Fu J J.2013.Changes in daily climate extremes of observed temperature and precipitation in China[J].Atmospheric and Oceanic Science Letters,6(5):312-319,doi:10.3878/j.issn.1674-2834.12.0106.
Worthington R.2000.Reviewed Work:Interpolation of spatial data:Some theory for Kriging by Michael L.Stein[J].Technometrics,42(4):436-437.
吴昌广,林德生,周志翔,等.2010.三峡库区降水量的空间插值方法及时空分布[J].长江流域资源与环境,19(7):752-758.Wu Changguang,Lin Desheng,Zhou Zhixiang,et al.2010.Spatial interpolation methods and temporal-spatial distribution of precipitation in the Three Gorges Reservoir area[J].Resources and Environment in the Yangtze Basin(in Chinese),19(7):752-758.
邬伦,吴小娟,肖晨超,等.2010.五种常用降水量插值方法误差时空分布特征研究--以深圳市为例[J].地理与地理信息科学,26(3):19-24.Wu Lun,Wu Xiaojuan,Xiao Chenchao,et al.2010.On temporal and spatial error distributions of five precipitation interpolation models:Acase of Shenzhen[J].Geography and Geo-Information Science(in Chinese),26(3):19-24.
叶小岭,沈云培,熊雄.2016.一种基于改进克里金法的地面气温质量控制算法[J].气候与环境研究,21(5):614-620.Ye Xiaoling,Shen Yunpei,Xiong Xiong.2016.A quality control algorithm for surface temperature observations based on improved Kriging method[J].Climatic and Environmental Research(in Chinese),21(5):614-620,doi:10.3878/j.issn.1006-9585.2016.15264.
曾红伟,李丽娟,张永萱,等.2011.大样本降水空间插值研究--以2009年中国年降水为例[J].地理科学进展,30(7):811-818.Zeng Hongwei,Li Lijuan,Zhang Yongxuan,et al.2011.Study on spatial interpolation of precipitation with large scale samples:A case study on2009’s precipitation of China[J].Progress in Geography(in Chinese),30(7):811-818,doi:10.11820/dlkxjz.2011.07.005.
Zhao T B,Yatagai A.2014.Evaluation of TRMM 3B42 product using a new gauge-based analysis of daily precipitation over China[J].International Journal of Climatology,34(8):2749-2762,doi:10.1002/joc.3872.
中国气象局.2006.中国气象地理区划手册[M].北京:气象出版社,1.China Meteorological Administration.2006.Handbook of Meteorological and Geographical Regionalization of China(in Chinese)[M].Beijing:China Meteorological Press,1.
朱会义,贾绍凤.2004.降雨信息空间插值的不确定性分析[J].地理科学进展,23(2):34-42.Zhu Huiyi,Jia Shaofeng.2004.Uncertainty in the spatial interpolation of rainfall data[J].Progress in Geography(in Chinese),23(2):34-42,doi:10.11820/dlkxjz.2004.02.005.
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