Analysis for random error and correlation of HY-2B satellite andmodel wind speed data
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摘要: 当利用三配准（Triple Collocation，TC）方法进行误差分析时，系统间随机误差（简称误差）不相关是一个重要前提假设，而在实际应用中不同系统误差常存在相关性，基于最小二乘法扩展配准（Extended Collocation，EC）方法能够在误差相关性存在情况进行误差分析，但对于误差弱相关性情况不能够准确估计误差的标准差。为此本文提出利用3个误差独立系统对第四个系统进行误差估计的方法，同时考虑误差相关性和表征误差，在误差弱相关情况下能更精确估计系统误差的标准差。本文根据HY-2B卫星3个载荷风速观测数据集随机误差相互独立特点，利用扩展三配准（Extended Triple Collocation，ETC）方法计算得到散射计、辐射计和高度计3个载荷风速产品误差的标准差分别为0.600 m/s、0.742 m/s和0.533 m/s；再对ECMWF再分析数据集ERA5的风速产品误差及相关性进行估计，计算出ERA5再分析风速产品随机误差的标准差为0.810 m/s，HY-2B卫星散射计风速产品和ERA5再分析风速产品误差相关性为0.231，HY-2B卫星辐射计风速产品和ERA5再分析风速产品误差相关性为0.105。本文提出利用已知3个误差独立数据集对第四个数据集误差及相关性进行估计的方法，实现了在误差弱相关情况下对系统误差的标准差更为准确的估计，有助于在同化和融合中更好地使用这些数据。Abstract: Random errors between systems are not correlated is a necessary assumption for Triple Collocation (TC) analysis, but this assumption does not always hold in practice. The least squares-based Extended Collocation (EC) method can estimate random error in the presence of error correlation, but it cannot accurately estimate standard deviation (SD) of the random error as error correlation is weak. This paper proposes an error estimation method for the fourth system using three error-independent systems, which can estimate the SD of the system error more accurately in case of weak correlation by considering both error correlation and representative error. The SD of the errors of the scatterometer, radiometer and altimeter are 0.600 m/s, 0.742 m/s and 0.533 m/s respectively, as assumed that random errors of three HY-2B wind speed products are independent. The SD of error of ERA5 reanalysis wind speed is also estimated to be 0.810 m/s, the correlation coefficient of the errors of wind speed between HY-2B scatterometer and the ERA5 is 0.231, the correlation coefficient of the errors of wind speed between HY-2B radiometer and the ERA5 is 0.105. This paper proposes a method to estimate random errors and their correlation with the fourth dataset using three known error independent datasets, which achieves a more precise estimation for the SD of the random error in the case of weak correlation, and it helps to use these data better in assimilation and fusion.
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图 1 散射计、辐射计、高度计、ECMWF 4个数据集风速比较
Fig. 1 Comparison of wind speeds across four datasets of S/R/A/E
图 2 配准风速数据概率密度分布
Fig. 2 Probability density distribution of collocated wind speed data
图 3 HY-2B卫星风速与ECMWF风速差的概率密度分布
Fig. 3 Probability density distribution of wind speed bias between HY-2B satellite and ECMWF
图 4 HY-2B卫星3个风速产品相互差值概率密度分布
Fig. 4 Probability density distribution of wind speed bias between three products of HY-2B satellite
图 5 散射计、辐射计、高度计、ECMWF 4个数据集误差的标准差分布
Fig. 5 Error SD distributions of four dataset of S/R/A/E
表 1 不同误差相关性假设条件下误差及相关性（EC）
Tab. 1 Error and correlation under different assumption (EC)
$ Cov\left({\varepsilon }_{e}{\varepsilon }_{s}\right)\ne 0 $ $ Cov\left({\varepsilon }_{e}{\varepsilon }_{s}\right)\ne 0 $
$ Cov\left({\varepsilon }_{e}{\varepsilon }_{r}\right)\ne 0 $$ Cov\left({\varepsilon }_{e}{\varepsilon }_{s}\right)\ne 0 $
$ Cov\left({\varepsilon }_{e}{\varepsilon }_{a}\right)\ne 0 $$ {\sigma }_{{\varepsilon }_{e}} $ 0.769 0.769 0.769 $ {\sigma }_{{\varepsilon }_{s}} $ 0.600 0.600 0.600 $ {\sigma }_{{\varepsilon }_{r}} $ 0.721 0.721 0.721 $ {\sigma }_{{\varepsilon }_{a}} $ 0.565 0.565 0.565 $ {{\sigma }^{2}}_{t} $ 10.160 10.160 10.161 $ Cov\left({\varepsilon }_{e}{\varepsilon }_{s}\right) $ 0.079 0.113 0.046 $ Cov\left({\varepsilon }_{e}{\varepsilon }_{r}\right) $ 0.0 0.063 0.0 $ Cov\left({\varepsilon }_{e}{\varepsilon }_{a}\right) $ 0.0 0.0 −0.068 
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表 2 散射计、辐射计、高度计、ECMWF 4个数据集不同排列情况下的误差 （ETC）
Tab. 2 Error of different permutation of four datasets of E/S/R/A (ETC)
S/R/A(SR, RS,
SA, AS, RA, AR
6种排列情况)E/S/A(ES, SE,
EA, AE, SA, AS
6种排列情况)E/R/A(ER, RE,
EA, AE, RA, AR
6种排列情况)E/S/R(ES, SE,
ER, RE, SR, RS
6种排列情况)$ {\sigma }_{{\varepsilon }_{e}} $ 不计算 0.739 0.769 0.693 $ {\sigma }_{{\varepsilon }_{s}} $ 0.600 0.495 不计算 0.560 $ {\sigma }_{{\varepsilon }_{r}} $ 0.742 不计算 0.595 0.770 $ {\sigma }_{{\varepsilon }_{a}} $ 0.533 0.635 0.699 不计算 $ {{\sigma }^{2}}_{t} $ 10.550 10.206 10.7535 10.271
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表 3 3个数据集不同排列情况误差的协方差及表征误差
Tab. 3 Error covariance and representative error of different permutation for three datasets
ESA EAS ERA EAR ESR/ERS $ {\sigma }_{{\varepsilon }_{e}} $ 0.810 0.659 0.810 0.725 0.810
(known)C Cov(εeεs):
0.113Cov(εeεa):
−0.115Cov(εeεr):
0.063Cov(εeεa):
−0.068Cov(εeεs):
0.113D 不计算 不计算 不计算 不计算 Cov(εeεr):
0.063Y 3.04×107 3.04×107 5.93×108 5.93×108 3.61×107
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