一种遥感土壤湿度误差空间协方差的估算方法
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摘要
针对遥感反演土壤湿度空间相关的误差协方差难以估计的问题,提出了一种遥感反演数据误差空间协方差估算方法——3类数据集成分析误差协方差(triple collocation covariance,TC_Cov),将土壤湿度场的每个单元(像元)看作一个空间随机变量,用两个随机变量表示的土壤湿度值的时间序列作为样本进行空间协方差估计,由任何两个随机变量的协方差形成多个随机变量(随机场)的协方差矩阵。利用先进散射计(advanced scatterometer,ASCAT)和热带降雨测量卫星(tropical rainfall measuring mission, TRMM)的遥感土壤湿度数据以及ERA-Interim土壤湿度再分析数据作为TC_Cov方法的输入数据,分别估算了ERA-Interim、ASCAT和TRMM在澳大利亚Murrumbidgee流域的土壤湿度误差协方差矩阵,验证了估算方法的合理性和可行性。
We have designed an approach TC_Cov based on triple collocation covariance, which can be used to estimate spatially correlated error covariance of three soil moisture data sets retrieved from satellite data. In theory, we formalize each grid into one random variable and soil moisture time series of two grids into samples of two random variables, then the covariance of two random variables are estimated. An element of multivariate covariance matrix takes bivariate covariance. The experimental results are analyzed in a qualitative way. In the experimental region of Murrumbidgee catchment located in Australia, the error covariances of soil moisture data sets retrieved from ASCAT scatterometer, TRMM radiometer and ERA-Interim reanalysis data are estimated, and experimental results obey the Tobler's first law well and explain real soil moisture error covariance estimation effectively.
We have designed an approach TC_Cov based on triple collocation covariance, which can be used to estimate spatially correlated error covariance of three soil moisture data sets retrieved from satellite data. In theory, we formalize each grid into one random variable and soil moisture time series of two grids into samples of two random variables, then the covariance of two random variables are estimated. An element of multivariate covariance matrix takes bivariate covariance. The experimental results are analyzed in a qualitative way. In the experimental region of Murrumbidgee catchment located in Australia, the error covariances of soil moisture data sets retrieved from ASCAT scatterometer, TRMM radiometer and ERA-Interim reanalysis data are estimated, and experimental results obey the Tobler's first law well and explain real soil moisture error covariance estimation effectively.
引文
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[7]Xu Jianhui,Shu Hong.The Triple-CollocationBased Fusion of In-situ and Satellite Remote Sensing Data for Snow Depth Retrieval[J].Geomatics and Information Science of Wuhan University,2015,40(4):469-473(许剑辉,舒红.基于Triple-Collocation的地面观测与卫星遥感数据融合的雪深反演[J].武汉大学学报?信息科学版,2015,40(4):469-473)
[8]Wu Kai,Shu Hong,Nie Lei,et al.Error Analysis of Soil Moisture Based on Triple Collocation Method[J].Remote Sensing for Land and Resources,2018,30(3):68-75(吴凯,舒红,聂磊,等.基于Triple Collocation方法的土壤湿度误差分析[J].国土资源遥感,2018,30(3):68-75)
[9]Yilmaz M T,Crow W.Evaluation of Assumptions in Soil Moisture Triple Collocation Analysis[J].Journal of Hydrometeorology,2014,15(3):1 293-1 302
[10]Dorigo W A,Scipal K,Parinussa R M,et al.Error Characterization of Global Active and Passive Microwave Soil Moisture Data Sets[J].Hydrology and Earth System Sciences Discussions,2010,7(12):2 605-2 616
[11]Gruber A,Su C H,Crow W T,et al.Estimating Error Cross-Correlations in Soil Moisture Data Sets Using Extended Collocation Analysis[J].Journal of Geophysical Research Atmospheres,2016,121(3):1 208-1 219
[12]Maree S C.Correcting Non-positive Definite Correlation Matrices[D].Delft:Delft University of Technology,2012
[13]Naeimi V,Bartalis Z,Wagner W.ASCAT Soil Moisture:An Assessment of the Data Quality and Consistency with the ERS Scatterometer Heritage[J].Journal of Hydrometeorology,2009,10(2):555-563
[14]Wagner W,Hahn S,Kidd R,et al.The ASCATSoil Moisture Product:A Review of Its Specifications,Validation Results,and Emerging Applications[J].Meteorologische Zeitschrift,2013,22(1):5-33
[15]Balsamo G,Albergel C,Beljaars A,et al.ERA-Interim/Land:A Global Land Surface Reanalysis Data Set[J].Hydrology and Earth System Sciences,2015,19(1):389-407
[16]Albergel C,Dorigo W,Reichle R H,et al.Skill and Global Trend Analysis of Soil Moisture from Reanalysis and Microwave Remote Sensing[J].Journal of Hydrometeorology,2013,14(4):1 259-1 277
[17]Petropoulos G.Remote Sensing of Energy Fluxes and Soil Moisture Content[M].Abingdon:CRCPress Taylor and Francis Group,2013
[18]Jensen J B,H?yer S,Jensen M E.Soil Moisture Estimation Through ASCAT and AMSR-E Sensors:An Intercomparison and Validation Study Across Europe[J].Remote Sensing of Environment,2011,115(12):3 390-3 408
[19]Albergel C,Rüdiger C,Pellarin T,et al.From Near-Surface to Root-Zone Soil Moisture Using an Exponential Filter:An Assessment of the Method Based on In-situ Observations and Model Simulations[J].Hydrology and Earth System Sciences,2008,12(6):1 323-1 337
[20]Tobler W R.A Computer Movie Simulating Urban Growth in the Detroit Region[J].Economic Geography,1970,46(S1):234-240
[2]Hollingsworth A,L?nnberg P.The Statistical Structure of Short-Range Forecast Errors as Determined from Radiosonde Data.Part I:The Wind Field[J].Tellus Series A:Dynamic Meteorology and Oceanography,1986,38A(2):111-136
[3]Stoffelen A.Toward the True Near-Surface Wind Speed:Error Modeling and Calibration Using Triple Collocation[J].Journal of Geophysical Research Atmospheres,1998,103(C4):7 755-7 766
[4]Scipal K,Holmes T,Jeu R D,et al.A Possible Solution for the Problem of Estimating the Error Structure of Global Soil Moisture Data Sets[J].Geophysical Research Letters,2008,35(24):101-106
[5]Scipal K,Dorigo W,de Jeu R.Triple Collocation:A New Tool to Determine the Error Structure of Global Soil Moisture Products[C].Geoscience and Remote Sensing Symposium,Honolulu,USA,2010
[6]Leroux D J,Kerr Y H,Richaume P,et al.Estimating SMOS Error Structure Using Triple Collocation[C].IEEE International Geoscience and Remote Sensing Symposium,Vancouver,Canada,2011
[7]Xu Jianhui,Shu Hong.The Triple-CollocationBased Fusion of In-situ and Satellite Remote Sensing Data for Snow Depth Retrieval[J].Geomatics and Information Science of Wuhan University,2015,40(4):469-473(许剑辉,舒红.基于Triple-Collocation的地面观测与卫星遥感数据融合的雪深反演[J].武汉大学学报?信息科学版,2015,40(4):469-473)
[8]Wu Kai,Shu Hong,Nie Lei,et al.Error Analysis of Soil Moisture Based on Triple Collocation Method[J].Remote Sensing for Land and Resources,2018,30(3):68-75(吴凯,舒红,聂磊,等.基于Triple Collocation方法的土壤湿度误差分析[J].国土资源遥感,2018,30(3):68-75)
[9]Yilmaz M T,Crow W.Evaluation of Assumptions in Soil Moisture Triple Collocation Analysis[J].Journal of Hydrometeorology,2014,15(3):1 293-1 302
[10]Dorigo W A,Scipal K,Parinussa R M,et al.Error Characterization of Global Active and Passive Microwave Soil Moisture Data Sets[J].Hydrology and Earth System Sciences Discussions,2010,7(12):2 605-2 616
[11]Gruber A,Su C H,Crow W T,et al.Estimating Error Cross-Correlations in Soil Moisture Data Sets Using Extended Collocation Analysis[J].Journal of Geophysical Research Atmospheres,2016,121(3):1 208-1 219
[12]Maree S C.Correcting Non-positive Definite Correlation Matrices[D].Delft:Delft University of Technology,2012
[13]Naeimi V,Bartalis Z,Wagner W.ASCAT Soil Moisture:An Assessment of the Data Quality and Consistency with the ERS Scatterometer Heritage[J].Journal of Hydrometeorology,2009,10(2):555-563
[14]Wagner W,Hahn S,Kidd R,et al.The ASCATSoil Moisture Product:A Review of Its Specifications,Validation Results,and Emerging Applications[J].Meteorologische Zeitschrift,2013,22(1):5-33
[15]Balsamo G,Albergel C,Beljaars A,et al.ERA-Interim/Land:A Global Land Surface Reanalysis Data Set[J].Hydrology and Earth System Sciences,2015,19(1):389-407
[16]Albergel C,Dorigo W,Reichle R H,et al.Skill and Global Trend Analysis of Soil Moisture from Reanalysis and Microwave Remote Sensing[J].Journal of Hydrometeorology,2013,14(4):1 259-1 277
[17]Petropoulos G.Remote Sensing of Energy Fluxes and Soil Moisture Content[M].Abingdon:CRCPress Taylor and Francis Group,2013
[18]Jensen J B,H?yer S,Jensen M E.Soil Moisture Estimation Through ASCAT and AMSR-E Sensors:An Intercomparison and Validation Study Across Europe[J].Remote Sensing of Environment,2011,115(12):3 390-3 408
[19]Albergel C,Rüdiger C,Pellarin T,et al.From Near-Surface to Root-Zone Soil Moisture Using an Exponential Filter:An Assessment of the Method Based on In-situ Observations and Model Simulations[J].Hydrology and Earth System Sciences,2008,12(6):1 323-1 337
[20]Tobler W R.A Computer Movie Simulating Urban Growth in the Detroit Region[J].Economic Geography,1970,46(S1):234-240