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Data from the directional polarimetric camera (DPC) instrument onboard Chinese Gaofen-5 satellite dedicated to aerosol monitoring have been available recently. By measuring the spectral, angular and polarization properties of the radiance at the top of atmosphere (TOA), a DPC provides the aerosol optical depths (AODs) as well as partial microphysical aerosol properties. In order to evaluate the capability and the retrieval uncertainty of DPC sensor systematically, the information content and a posteriori error analysis are applied to the synthetic data of DPC multi-angle observation in this paper, which inherits from the optimal estimate theoretical framework. The forward simulation is conducted by the unified linearized vector radiative transfer model (UNL-VRTM), and the Jacobians of four Stokes elements with respect to aerosol and surface model parameters can be obtained simultaneously. Firstly, the error influences of surface parameter on the TOA measurements are simulated. The results indicate that a 10% relative error of parameter k1 in the improved BRDF model results in about 4.65% error of the TOA reflectance, while the error of TOA polarized reflectance caused by the same error of parameter C in BPDF model is negligibly small. Secondly, the multi-angle dependence of total information content in DPC measurements is investigated. It is shown that the information content increases significantly with the number of viewing angles, especially for the measurements of the first 9 angles. The DPC multi-angle observation can provide extra 5 degrees of freedom for signal (DFS) for the retrieval of aerosol and surface parameters, in which the retrieval of aerosol parameters is more sensitive to observation geometries than the retrieval of surface parameters in most cases. In addition, the total aerosol DFS increases with the range extension of scattering angle under the same number of viewing angles. After that, the DFS of each retrieved aerosol and surface parameter are given. For the aerosols, the volume concentration, real-part refractive index and effective radius show a high DFS (greater than 0.8). For the surfaces, the mean DFS of each parameter is greater than 0.5, which indicates the well capability of DPC in the surface retrieval. Finally, the a posteriori error of each aerosol, surface parameter and corresponding vary with the number of viewing angles, and the observation error and aerosol model error are discussed. The a posteriori error decrease significantly with the number of viewing angles, and the influence of the aerosol model error on the a posteriori error is not remarkable. In general, the observation error is the main influence factor on the uncertainty of the inversion results.
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Keywords:
- directional polarimetric camera /
- optimal estimation inversion /
- information content analysis /
- a posteriori error
[1] IPCC 2014 Climate Change 2014: Synthesis Report (Geneva: IPCC Secretariat) pp2–8
[2] Diner D J, Chipman R A, Beaudry N, Cairns B, Food L D, Macenka S A, Cunningham T J, Seshadri S, Keller C 2005 Enabling Sensor and Platform Technologies for Spaceborne Remote Sensing (Bellingham: Spie-Int Soc Optical Engineering) pp88–96
[3] Hasekamp O P, Landgraf J 2007 Appl. Opt. 46 3332
Google Scholar
[4] Mishchenko M I, Geogdzhayev I V, Cairns B, Carlson B E, Chowdhary J, Lacis A A, Liu L, Rossow W B, Travis L D 2007 J. Quant. Spectrosc. Radiat. Transfer 106 325
Google Scholar
[5] Herman M, Deuzé J L, Marchand A, Roger B, Lallart P 2005 J. Geophys. Res. 110 D10S02
Google Scholar
[6] Tanré D, Bréon F M, Deuzé J L, Dubovik O, Ducos F, François P, Goloub P, Herman M, Lifermann A, Waquet F 2011 Atmos. Meas. Tech. 4 1383
Google Scholar
[7] Kokhanovsky A A, Breon F M 2012 IEEE Geosci. Remote Sens. Lett. 9 928
Google Scholar
[8] Waquet F, Cornet C, Deuzé J L, Dubovik O, Ducos F, Goloub P, Herman M, Lapyonok T, Labonnote L C, Riedi J, Thieuleux F, Vanbauce C 2013 Atmos. Meas. Tech. 6 991
Google Scholar
[9] Gu X F, Tong X D 2015 IEEE Geosci. Remote Sens. M 3 113
Google Scholar
[10] Li Z Q, Hou W Z, Hong J, Zheng F X, Luo D G, Wang J, Gu X F, Qiao Y L 2018 J. Quant. Spectrosc. Radiat. Transfer 218 21
Google Scholar
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Gu X F, Chen X F, Cheng T H, Li Z Q, Yu T, Xie D H, Xu H 2011 Acta Phys. Sin. 60 070702
Google Scholar
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Google Scholar
Xie D H, Gu X F, Cheng T H, Yu T, Li Z Q, Chen X F, Chen H, GUO J 2012 Acta Phys. Sin. 61 077801
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Xiang K S, Cheng T H, Gu X F, Guo H, Chen H, Wang Y, Wei X, Bao F W 2015 Acta Phys. Sin. 64 227801
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[20] Mishchenko M, Yatskiv Y, Videen G 2005 Photopolarimetry in Remote Sensing (Dordrecht: Springer Netherlands) pp65–106
[21] Rodgers C D 2000 Inverse Methods for Atmospheric Sounding: Theory and Practice (Singapore: World Scientific) pp13–99
[22] Wendisch M, Yang P 著(李正强, 李莉, 侯伟, 许华译)2014 大气辐射传输原理(北京: 高等教育出版社)第55—58页
Wendisch M, Yang P (translated by Li Z Q, Li L, Hou W Z, Xu H) 2014 Theory of Atmospheric Radiative Transfer (Beijing: Higher Education Press) pp55−58 (in Chinese)
[23] Deuzé J L, Bréon F M, Devaux C, Goloub P, Herman M, Lafrance B, Maignan F, Marchand A, Nadal F, Perry G, Tanré D 2001 J. Geophys. Res. 106 4913
Google Scholar
[24] Waquet F, Goloub P, Deuzé J L, Léon J F, Auriol F, Verwaerde C, Balois J Y, François P 2007 J. Geophys. Res. 112 D11214
Google Scholar
[25] Xu F, Dubovik O, Zhai P W, Diner D J, Kalashnikova O V, Seidel F C, Litvinnov P, Bovchaliuk A, Garay M J, Van Harten G, Davis A B 2016 Atmos. Meas. Tech. 9 2877
Google Scholar
[26] Zhang Y, Li Z Q, Qie L L, Zhang Y, Liu Z H, Chen X F, Hou W Z, Li K T, Li D H, Xu H 2016 Remote Sens. 8 417
Google Scholar
[27] Wang J, Xu X G, Ding S G, Zeng J, Spurr R, Liu X, Chance K, Mishchenko M 2014 J. Quant. Spectrosc. Radiat. Transfer 146 510
Google Scholar
[28] Spurr R J D 2006 J. Quant. Spectrosc. Radiat. Transfer 102 316
Google Scholar
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Google Scholar
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Google Scholar
[31] Hou W Z, Wang J, Xu X G, Reid J S, Han D 2016 J. Quant. Spectrosc. Radiat. Transfer 178 400
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[33] Chen X, Wang J, Liu Y, Xu X G, Cai Z N, Yang D, Yan C X, Feng L 2017 Remote Sens. Environ. 196 163
Google Scholar
[34] Maignan F, Bréon F M, Fédèle E, Bouvier M 2009 Remote Sens. Environ. 113 2642
Google Scholar
[35] Litvinov P, Hasekamp O, Cairns B 2011 Remote Sens. Environ. 115 781
Google Scholar
[36] Hou W Z, Li Z Q, Wang J, Xu X G, Goloub P, Qie L L 2018 J. Geophys. Res. 123 2215
Google Scholar
[37] Dubovik O, King M D 2000 J. Geophys. Res. 105 20673
Google Scholar
[38] Dubovik O, Holben B, Eck T F, Smirnov A, Kaufman Y J, King M D, Tanré D, Slutsker I 2002 J. Atmos. Sci. 59 590
Google Scholar
[39] Clark R N, Swayze G A, Wise R A, Livo K E, Hoefen T M, Kokaly R F, Sutley S J 2007 USGS Digital Spectral Library splib06a (Reston, VA: U. S. Geological Survey) Data Series 231
[40] Baldridge A M, Hook S J, Grove C I, Rivera G 2009 Remote Sens. Environ. 113 711
Google Scholar
[41] Litvinov P, Hasekamp O, Cairns B, Mishchenko M 2010 J. Quant. Spectrosc. Radiat. Transfer 111 529
Google Scholar
[42] Li Z Q, Xu H, Li K T, Li D H, Xie Y S, Li L, Zhang Y, Gu X F, Zhao W, Tian Q J, Deng R R, Su X L, Huang B, Qiao Y L, Cui W Y, Hu Y, Gong C L, Wang Y Q, Wang X F, Wang J P, Du W B, Pan Z Q, Li Z Z, Bu D 2018 Bull. Am. Meteorol. Soc. 99 739
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Google Scholar
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图 1 研究采用的DPC多角度观测几何
Figure 1. Multi-angle observation geometries adopted in the simulation, information content analysis and a posteriori error analysis. The solid circle, diamond, square and triangle with
$\phi $ = 0° represent the corresponding position of the Sun for Geometry1−4, respectively.
图 2 不同观测角度个数的观测示意图
Figure 2. Illustrationsof observation scenarios with different number of viewing angles.
图 3 四组观测在不同观测角度个数下的散射角分布
Figure 3. Distribution of the range of scattering angle corresponding to the geometries in Fig. 1.
图 4 不同观测几何下的地表反射率、表观反射率以及地表模型参数误差对表观反射率的影响 (a)–(e) 植被地表; (f)–(j) 裸土地表
Figure 4. Contribution of surface reflectance to TOA reflectance at 443, 490, 565, 670 and 865 nm, as well as the influence of BRDF parameter error to TOA reflectance for vegetation ((a)–(e)) and bare soil ((f)–(j)) surface. The horizontal axis of each case is arranged by scattering angle.
图 5 不同观测几何下植被地表偏振反射率和表观偏振反射率, 以及10%的参数不确定性对二者的影响
Figure 5. Contributionof polarized reflectance to TOA polarized reflectance for vegetation surface at 490, 670 and 865 nm, as well as the influence of BPDF parameter error to TOA polarized reflectance.
图 6 气溶胶和地表参数的总信息量随观测角度数量的变化情况 ((a)—(d)) 气溶胶参数; ((e)—(h))地表参数
Figure 6. The total DFS of aerosol((a)−(d)) and surface((e)−(h)) parameters as functions of number of viewing angles in terms of surface type(vegetation and bare soil) and aerosol type (fine-dominated and coarse-dominated) with AOD550 nm = 0.5. Quantities in each box-whisker include the median (dash in the box), the 25th and 75th percentiles (box), and the minimum and maximum (whiskers) for each number of viewing angles bin.
图 7 不同观测几何下气溶胶和地表各参数的信息量 (a)气溶胶; (b)地表
Figure 7. The DFS of aerosol and surface parameters under condition of 12 viewing angles (AOD550 nm = 0.5): (a) Aerosol; (b) surface. Each histogram and error bar are the mean value and standard deviation of different geometries.
图 8 多角度观测下气溶胶和地表参数的后验误差(灰色底柱为先验估计误差)
Figure 8. The posteriori error of retrieved aerosol parameters (a) and surface parameters (b). The histogram and error bars are the mean and standard deviation of different geometries (Geometry 1−4). Both (a) and (b) are calculated under condition of 12 viewing angles (AOD550 nm = 0.5). The gray histogram means the priori estimate error.
图 9 地表和气溶胶参数的后验误差随观测角度数量的变化情况
Figure 9. The posteriori error of retrieved aerosol and surface parameters as a function of number of viewing angles (AOD550 nm = 0.5). The curve and the error bar are the mean value and standard deviation of different aerosol and surface type, respectively.
图 10 地表和气溶胶参数的后验误差随观测误差的变化情况
Figure 10. The posteriori error of retrieved aerosol and surface parameters as a function of measurement error (AOD550 nm = 0.5). The solid line and the error bar are the mean value and standard deviation of different aerosol and surface type, respectively. The dash line denotes the contribution from polarized observation error.
图 11 地表和气溶胶参数的后验误差随气溶胶模型误差的变化情况
Figure 11. The a posteriori error of retrieved aerosol and surface parameters as a function of aerosol model error (AOD550 nm = 0.5). The curve and the error bar are the mean value and standard deviation of different aerosol and surface type, respectively.
表 1 DPC传感器的基本参数
Table 1. Basic characteristics of DPC sensor.
设备参数 值 观测角度个数 ≤12 波段/nm 443, 490(P), 565, 670(P), 763, 765, 865(P), 910 相应带宽/nm 20, 20, 20, 20, 10, 40, 40, 20 观测量 I, Q, U 辐射定标误差 ≤ 5% 偏振定标误差 ≤ 0.02 
DownLoad: CSV
表 2 状态向量和非状态向量的参数组成
Table 2. State vector and non-state vector elements for different scenarios.
符号 参数名称 情形1 情形2 x b x b V0f,V0c 气溶胶细、粗模态体积柱浓度/(μm3·μm-2) √ √ refff, reffc 气溶胶细、粗模态有效半径/(μm) √ √ vefff,veffc 气溶胶细、粗模态有效方差 √ √ mrf, mrc, 气溶胶细、粗模态复折射指数实部 √ √ mif,mic 气溶胶细、粗模态复折射指数虚部 √ √ fiso(${\lambda _1}$),…,
fiso(${\lambda _5}$)地表BRDF朗伯项参数 √ √ k1,k2 地表BRDF几何项和体积项参数 √ √ C 地表BPDF参数 √ √
DownLoad: CSV
表 3 气溶胶和地表模型参数及其先验估计误差
Table 3. A priori value of the aerosol and surface model parameters and corresponding errors adopted in the simulation.
气溶胶模型1 V0f/μm3·μm–2 V0c/μm3·μm–2 V0/μm3·μm–2 FMFV AOD(550 nm) 细粒子主导 0.0745(100%) 0.0186(100%) 0.093 0.8 0.5 粗粒子主导 0.0493(100%) 0.197(100%) 0.246 0.2 0.5 mr mi reff/μm veff 细模态 1.44(0.15, 0.025) 0.011(0.01, 50%) 0.21(80%, 15%) 0.25(80%, 15%) 粗模态 1.55(0.15, 0.04) 0.003(0.005, 50%) 1.90(80%, 35%) 0.41(80%, 35%) 地表模型2 fiso($\lambda $) k1 k2 C NDVI 裸土 0.0705(0.0215),
0.1006(0.0224),
0.1720(0.0466),
0.2427(0.0207),
0.3253(0.2119)0.547(80%) 0.158(80%) 6.9(80%) 0.03 植被 0.0325(0.0425),
0.0347(0.0495),
0.0737(0.0777),
0.0395(0.0917),
0.3809(0.0792)0.668(80%) 0.087(80%) 6.57(80%) 0.62 1气溶胶模型参数mr, mi, reff, veff括号内的值分别为该参数作为x和b时的误差;
2地表模型参数fiso($\lambda $)的值依次对应443, 490, 565, 670和865 nm.
DownLoad: CSV
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[1] IPCC 2014 Climate Change 2014: Synthesis Report (Geneva: IPCC Secretariat) pp2–8
[2] Diner D J, Chipman R A, Beaudry N, Cairns B, Food L D, Macenka S A, Cunningham T J, Seshadri S, Keller C 2005 Enabling Sensor and Platform Technologies for Spaceborne Remote Sensing (Bellingham: Spie-Int Soc Optical Engineering) pp88–96
[3] Hasekamp O P, Landgraf J 2007 Appl. Opt. 46 3332
Google Scholar
[4] Mishchenko M I, Geogdzhayev I V, Cairns B, Carlson B E, Chowdhary J, Lacis A A, Liu L, Rossow W B, Travis L D 2007 J. Quant. Spectrosc. Radiat. Transfer 106 325
Google Scholar
[5] Herman M, Deuzé J L, Marchand A, Roger B, Lallart P 2005 J. Geophys. Res. 110 D10S02
Google Scholar
[6] Tanré D, Bréon F M, Deuzé J L, Dubovik O, Ducos F, François P, Goloub P, Herman M, Lifermann A, Waquet F 2011 Atmos. Meas. Tech. 4 1383
Google Scholar
[7] Kokhanovsky A A, Breon F M 2012 IEEE Geosci. Remote Sens. Lett. 9 928
Google Scholar
[8] Waquet F, Cornet C, Deuzé J L, Dubovik O, Ducos F, Goloub P, Herman M, Lapyonok T, Labonnote L C, Riedi J, Thieuleux F, Vanbauce C 2013 Atmos. Meas. Tech. 6 991
Google Scholar
[9] Gu X F, Tong X D 2015 IEEE Geosci. Remote Sens. M 3 113
Google Scholar
[10] Li Z Q, Hou W Z, Hong J, Zheng F X, Luo D G, Wang J, Gu X F, Qiao Y L 2018 J. Quant. Spectrosc. Radiat. Transfer 218 21
Google Scholar
[11] 顾行发, 陈兴峰, 程天海, 李正强, 余涛, 谢东海, 许华 2011 60 070702
Google Scholar
Gu X F, Chen X F, Cheng T H, Li Z Q, Yu T, Xie D H, Xu H 2011 Acta Phys. Sin. 60 070702
Google Scholar
[12] 谢东海, 顾行发, 程天海, 余涛, 李正强, 陈兴峰, 陈好, 郭婧 2012 61 077801
Google Scholar
Xie D H, Gu X F, Cheng T H, Yu T, Li Z Q, Chen X F, Chen H, GUO J 2012 Acta Phys. Sin. 61 077801
Google Scholar
[13] Gu X F, Cheng T H, Xie D H, Li Z Q, Yu T, Chen H 2011 Atmos. Environ. 45 6607
Google Scholar
[14] 相坤生, 程天海, 顾行发, 郭红, 陈好, 王颖, 魏曦, 包方闻 2015 64 227801
Google Scholar
Xiang K S, Cheng T H, Gu X F, Guo H, Chen H, Wang Y, Wei X, Bao F W 2015 Acta Phys. Sin. 64 227801
Google Scholar
[15] Cheng T H, Gu X F, Xie D H, Li Z Q, Yu T, Chen X F 2011 Remote Sens. Environ. 115 1643
Google Scholar
[16] Dubovik O, Herman M, Holdak A, Lapyonok T, Tanré D, Deuzé J L, Ducos F, Sinyuk A, Lopatin A 2011 Atmos. Meas. Tech. 4 975
Google Scholar
[17] Wu L H, Hasekamp O, Van Diedenhoven B, Cairns B 2015 Atmos. Meas. Tech. 8 2625
Google Scholar
[18] Chen X, Yang D X, Cai Z N, Liu Y, Spurr R J D 2017 Remote Sens. 9 183
Google Scholar
[19] Hasekamp O P, Litvinov P, Butz A 2011 J. Geophy. Res. 116 D14204
Google Scholar
[20] Mishchenko M, Yatskiv Y, Videen G 2005 Photopolarimetry in Remote Sensing (Dordrecht: Springer Netherlands) pp65–106
[21] Rodgers C D 2000 Inverse Methods for Atmospheric Sounding: Theory and Practice (Singapore: World Scientific) pp13–99
[22] Wendisch M, Yang P 著(李正强, 李莉, 侯伟, 许华译)2014 大气辐射传输原理(北京: 高等教育出版社)第55—58页
Wendisch M, Yang P (translated by Li Z Q, Li L, Hou W Z, Xu H) 2014 Theory of Atmospheric Radiative Transfer (Beijing: Higher Education Press) pp55−58 (in Chinese)
[23] Deuzé J L, Bréon F M, Devaux C, Goloub P, Herman M, Lafrance B, Maignan F, Marchand A, Nadal F, Perry G, Tanré D 2001 J. Geophys. Res. 106 4913
Google Scholar
[24] Waquet F, Goloub P, Deuzé J L, Léon J F, Auriol F, Verwaerde C, Balois J Y, François P 2007 J. Geophys. Res. 112 D11214
Google Scholar
[25] Xu F, Dubovik O, Zhai P W, Diner D J, Kalashnikova O V, Seidel F C, Litvinnov P, Bovchaliuk A, Garay M J, Van Harten G, Davis A B 2016 Atmos. Meas. Tech. 9 2877
Google Scholar
[26] Zhang Y, Li Z Q, Qie L L, Zhang Y, Liu Z H, Chen X F, Hou W Z, Li K T, Li D H, Xu H 2016 Remote Sens. 8 417
Google Scholar
[27] Wang J, Xu X G, Ding S G, Zeng J, Spurr R, Liu X, Chance K, Mishchenko M 2014 J. Quant. Spectrosc. Radiat. Transfer 146 510
Google Scholar
[28] Spurr R J D 2006 J. Quant. Spectrosc. Radiat. Transfer 102 316
Google Scholar
[29] Xu X G, Wang J 2015 J. Geophys. Res. 120 7059
Google Scholar
[30] Xu X G, Wang J, Zeng J, Spurr R, Liu X, Dubovik O, Li L, Li Z Q, Mishchenko M I, Siniuk A, Holben B N 2015 J. Geophys. Res. 120 7079
Google Scholar
[31] Hou W Z, Wang J, Xu X G, Reid J S, Han D 2016 J. Quant. Spectrosc. Radiat. Transfer 178 400
Google Scholar
[32] Hou W Z, Wang J, Xu X G, Reid J S 2017 J. Quant. Spectrosc. Radiat. Transfer 192 14
Google Scholar
[33] Chen X, Wang J, Liu Y, Xu X G, Cai Z N, Yang D, Yan C X, Feng L 2017 Remote Sens. Environ. 196 163
Google Scholar
[34] Maignan F, Bréon F M, Fédèle E, Bouvier M 2009 Remote Sens. Environ. 113 2642
Google Scholar
[35] Litvinov P, Hasekamp O, Cairns B 2011 Remote Sens. Environ. 115 781
Google Scholar
[36] Hou W Z, Li Z Q, Wang J, Xu X G, Goloub P, Qie L L 2018 J. Geophys. Res. 123 2215
Google Scholar
[37] Dubovik O, King M D 2000 J. Geophys. Res. 105 20673
Google Scholar
[38] Dubovik O, Holben B, Eck T F, Smirnov A, Kaufman Y J, King M D, Tanré D, Slutsker I 2002 J. Atmos. Sci. 59 590
Google Scholar
[39] Clark R N, Swayze G A, Wise R A, Livo K E, Hoefen T M, Kokaly R F, Sutley S J 2007 USGS Digital Spectral Library splib06a (Reston, VA: U. S. Geological Survey) Data Series 231
[40] Baldridge A M, Hook S J, Grove C I, Rivera G 2009 Remote Sens. Environ. 113 711
Google Scholar
[41] Litvinov P, Hasekamp O, Cairns B, Mishchenko M 2010 J. Quant. Spectrosc. Radiat. Transfer 111 529
Google Scholar
[42] Li Z Q, Xu H, Li K T, Li D H, Xie Y S, Li L, Zhang Y, Gu X F, Zhao W, Tian Q J, Deng R R, Su X L, Huang B, Qiao Y L, Cui W Y, Hu Y, Gong C L, Wang Y Q, Wang X F, Wang J P, Du W B, Pan Z Q, Li Z Z, Bu D 2018 Bull. Am. Meteorol. Soc. 99 739
Google Scholar
[43] Waquet F, Cairns B, Knobelspiesse K, Chowdhary J, Travis L D, Schmid B, Mishchenko M I 2009 J. Geophys. Res. 114 D01206
Google Scholar
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