References

1. 1.
   Bell J B. 1978. Solutions of ill-posed problems. by A. N. Tikhonov, V. Y. Arsenin. Mathematics of Computation, 32(144): 1320-1322
2. 2.
   Chen J M and Leblanc S G. 1997. A four-scale bidirectional reflectance model based on canopy architecture. IEEE Transactions on Geoscience and Remote Sensing, 35(5): 1316-1337
3. 3.
   Chen J M, Menges C H and Leblanc S G. 2005. Global mapping of foliage clumping index using multi-angular satellite data. Remote Sensing of Environment, 97(4): 447-457
4. 4.
   Chen X, Cui H J and Yang H. 2007. The application of Bootstrap method in linear BRDF models inversion. Journal of Remote Sensing, 11(6): 845-851
5. 5.
   Chou K C, Willsky A S and Benveniste A. 1994. Multiscale recursive estimation, data fusion, and regularization. IEEE Transactions on Automatic Control, 39(3): 464-478
6. 6.
   Cui S C, Yang S Z, Qiao Y L, Zhao Q, Wang J C and Wang Z. 2012. Adaptive regularized filtering for BRDF model inversion and land surface albedo retrieval based on spectrum cutoff technique. Optik, 123(3): 250-256
7. 7.
   Fan W, Chen J M, Ju W, and Nesbitt N. 2014. Hybrid geometric optical-radiative transfer model suitable for forests on slopes. IEEE Transactions on Geoscience and Remote Sensing, 52(9): 5579-5586
8. 8.
   Gao F, Jin Y F, Schaaf C B and Strahler A H. 2002. Bidirectional NDVI and atmospherically resistant BRDF inversion for vegetation canopy. IEEE Transactions on Geoscience and Remote Sensing, 40(6): 1269-1278
9. 9.
   Gao F, Li X W, Xia Z G, Zhu Q J and Straher A H. 1998. Multi angle remote sensing inversion based on knowledge staged uncertainty. Science in China (Series D), 28(4): 346-350
10. 10.
    Gao F, Schaaf C B, Strahler A H and Lucht W. 2001. Using a multikernel least-variance approach to retrieve and evaluate albedo from limited bidirectional measurements. Remote Sensing of Environment, 76(1): 57-66
11. 11.
    Garguet-Duport B, Girel J, Chassery J M and Pautou G. 1996. The use of multiresolution analysis and wavelets transform for merging SPOT panchromatic and multispectral image data. Photogrammetric Engineering and Remote Sensing, 62(9): 1057-1066
12. 12.
    Gastellu-Etchegorry J P, Demarez V, Pinel V and Zagolski F. 1996. Modeling radiative transfer in heterogeneous 3-D vegetation canopies. Remote Sensing of Environment, 58(2): 131-156
13. 13.
    Goel N S, Rozehnal I and Thompson R L. 1991. A computer graphics based model for scattering from objects of arbitrary shapes in the optical region. Remote Sensing of Environment, 36(2): 73-104
14. 14.
    Govaerts Y M and Verstraete M M. 1998. Raytran: a Monte Carlo ray-tracing model to compute light scattering in three-dimensional heterogeneous media. IEEE Transactions on Geoscience and Remote Sensing, 36(2): 493-505
15. 15.
    Guan Y W, Zhou Y R, He B B, Liu X Z, Zhang H G and Feng S L. 2020. Improving land cover change detection and classification with BRDF correction and spatial feature extraction using Landsat Time Series: a case of urbanization in Tianjin, China. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 13: 4166-4177
16. 16.
    Hansen P C. 1998. Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. Philadelphia: SIAM.
17. 17.
    Hao D L, Wen J G, Xiao Q, Wu S B, Lin X W, You D Q and Tang Y. 2018. Modeling anisotropic reflectance over composite sloping terrain. IEEE Transactions on Geoscience and Remote Sensing, 56(7): 3903-3923
18. 18.
    Hao D L, Wen J G, Xiao Q, You D Q and Tang Y. 2020. An improved topography-coupled kernel-driven model for land surface anisotropic reflectance. IEEE Transactions on Geoscience and Remote Sensing, 58(4): 2833-2847
19. 19.
    Hasegawa K, Matsuyama H, Tsuzuki H and Sweda T. 2010. Improving the estimation of leaf area index by using remotely sensed NDVI with BRDF signatures. Remote Sensing of Environment, 114(3): 514-519
20. 20.
    Huang H G, Qin W H and Liu Q H. 2013. RAPID: a radiosity applicable to porous IndiviDual objects for directional reflectance over complex vegetated scenes. Remote Sensing of Environment, 132: 221-237
21. 21.
    Huemmrich K F. 2001. The GeoSail model: a simple addition to the SAIL model to describe discontinuous canopy reflectance. Remote Sensing of Environment, 75(3): 423-431
22. 22.
    Jackson D D. 1979. The use of a priori data to resolve non-uniqueness in linear inversion. Geophysical Journal International, 57(1): 137-157
23. 23.
    Jonsson P and Eklundh L. 2002. Seasonality extraction by function fitting to time-series of satellite sensor data. IEEE Transactions on Geoscience and Remote Sensing, 40(8): 1824-1832
24. 24.
    Lacaze R. 2006.POLDER-2 BRDF Database-User Document.
25. 25.
    Lacaze R. 2008. POLDER-3 / PARASOL BRDF Databases User Manual.
26. 26.
    León-Tavares J, Swinnen E, Smets B and Roujean J L. 2017. Angular normalisation of PROBA-V 300m NDVI//Proceedings of the 9th International Workshop on the Analysis of Multitemporal Remote Sensing Images. Brugge: IEEE: 1-5
27. 27.
    Li X W, Gao F, Wang J D and Strahler A. 2001a. A priori knowledge accumulation and its application to linear BRDF model inversion. Journal of Geophysical Research: Atmospheres, 106(D11): 11925-11935
28. 28.
    Li X W, Gao F, Wang J D and Zhu Q J. 1997. Uncertainty and sensitivity matrix of parameters in inversion of physical BRDF model. Journal of Remote Sensing, 1(1): 5-14
29. 29.
    Li X W, Gao F, Wang J F, Straher A H, Lucht W and Schaaf C. 2000. Estimation of the parameter error propagation in inversion based BRDF observations at single sun position. Science in China (Series E), 30(S1): 6-11
30. 30.
    Li X W, Gao F, Yang H, Wang J D, Strahler A and Schaaf C. 2001b. Bi-directional NDVI and atmosphere-coupled BRDF inversion//Proceedings of the Scanning the Present and Resolving the Future. Proceedings. IEEE 2001 International Geoscience and Remote Sensing Symposium. Sydney: IEEE: 2391-2393
31. 31.
    Li X W and Strahler A H. 1985. Geometric-optical modeling of a conifer forest canopy. IEEE Transactions on Geoscience and Remote Sensing, GE-23(5): 705-721
32. 32.
    Li X W and Strahler A H. 1992. Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: effect of crown shape and mutual shadowing. IEEE Transactions on Geoscience and Remote Sensing, 30(2): 276-292
33. 33.
    Li X W, Wang J D, Hu B X and Alan H S. 1998. On utilization of a priori knowledge in inversion of remote sensing models. Science in China Series D: Earth Sciences, 41(6): 580-585
34. 34.
    Li X W, Strahler A H and Woodcock C E. 1995. A hybrid geometric optical-radiative transfer approach for modeling albedo and directional reflectance of discontinuous canopies. IEEE Transactions on geoscience and remote sensing, 33(2), 466-480
35. 35.
    Liu S H, Liu Q, Liu Q H, Wen J G and Li X W. 2010. The angular and spectral kernel model for BRDF and albedo retrieval. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 3(3): 241-256
36. 36.
    Lucht W, Schaaf C B and Strahler A H. 2000. An algorithm for the retrieval of albedo from space using semiempirical BRDF models. IEEE Transactions on Geoscience and Remote Sensing, 38(2): 977-998
37. 37.
    Minnaert M. 1941. The reciprocity principle in lunar photometry. Astrophysical Journal, 93(3): 403-410
38. 38.
    Muller J P, López G, Watson G, Shane N, Kennedy T and Lewis P. 2012. The ESA GlobAlbedo Project for mapping the Earth’s land surface albedo for 15 Years from European Sensors. IEEE Geoscience and Remote Sensing Symposium.
39. 39.
    Ni W G, Li X W, Woodcock C E, Caetano M R and Strahler A H. 1999. An analytical hybrid GORT model for bidirectional reflectance over discontinuous plant canopies. IEEE Transactions on Geoscience and Remote Sensing, 37(2): 987-999
40. 40.
    Nicodemus F E, Richmond J C, Hsia J J, Ginsberg I W and Limperis T. 1977. Geometrical Considerations and Nomenclature for Reflectance. Washington: National Bureau of Standards
41. 41.
    North P R J. 1996. Three-dimensional forest light interaction model using a Monte Carlo method. IEEE Transactions on Geoscience and Remote Sensing, 34(4): 946-956
42. 42.
    Pocewicz A, Vierling L A, Lentile L B and Smith R. 2007. View angle effects on relationships between MISR vegetation indices and leaf area index in a recently burned ponderosa pine forest. Remote Sensing of Environment, 107(1/2): 322-333
43. 43.
    Privette J L, Eck T F and Deering D W. 1997. Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS-like data. Journal of Geophysical Research: Atmospheres, 102(D24): 29529-29542
44. 44.
    Qi J B, Xie D H, Yin T G, Yan G J, Gastellu-Etchegorry J P, Li L Y, Zhang W M, Mu X H and Norford L K. 2019. LESS: LargE-scale remote sensing data and image simulation framework over heterogeneous 3D scenes. Remote Sensing of Environment, 221: 695-706
45. 45.
    Qin J, Yan G J, Liu S M, Liang S L, Zhang H, Wang J D and Li X W. 2006. Application of ensemble Kalman filter to geophysical parameters retrieval in remote sensing: a case study of kernel-driven BRDF model inversion. Science in China Series D, 49(6): 632-640
46. 46.
    Qin W H and Gerstl S A W. 2000. 3-D scene modeling of semidesert vegetation cover and its radiation regime. Remote Sensing of Environment, 74(1): 145-162
47. 47.
    Quaife T and Lewis P. 2010. Temporal constraints on linear BRDF model parameters. IEEE Transactions on Geoscience and Remote Sensing, 48(5): 2445-2450
48. 48.
    Rahman H, Verstraete M M and Pinty B. 1993. Coupled surface-atmosphere reflectance (CSAR) model: 1. Model description and inversion on synthetic data. Journal of Geophysical Research: Atmospheres, 98(D11): 20779-20789
49. 49.
    Roujean J L, Leroy M and Deschamps P Y. 1992. A bidirectional reflectance model of the earth’s surface for the correction of remote sensing data. Journal of Geophysical Research: Atmospheres, 97(D18): 20455-20468
50. 50.
    Sahoo S, Russo T A, Elliott J and Foster I. 2017. Machine learning algorithms for modeling groundwater level changes in agricultural regions of the U.S. Water Resources Research, 53(5): 3878-3895
51. 51.
    Salomonson V V. 1968. Anisotropy in Reflected Solar Radiation. Fort Collins: Department of Atmospheric Science Colorado State University
52. 52.
    Samain O, Geiger B and Roujean J L. 2006. Spectral normalization and fusion of optical sensors for the retrieval of BRDF and albedo: application to VEGETATION, MODIS, and MERIS data sets. IEEE Transactions on Geoscience and Remote Sensing, 44(11): 3166-3179
53. 53.
    Samain O, Roujean J L and Geiger B. 2008. Use of a Kalman filter for the retrieval of surface BRDF coefficients with a time-evolving model based on the ECOCLIMAP land cover classification. Remote Sensing of Environment, 112(4): 1337-1346
54. 54.
    Schaaf C, Martonchik J, Pinty B, Govaerts Y, Gao F, Lattanzio A, Liu J C, Strahler A and Taberner M. 2008. Retrieval of surface albedo from satellite sensors//Liang S L, ed. Advances in Land Remote Sensing. Dordrecht: Springer: 219-243
55. 55.
    Schaaf C B, Gao F, Strahler A H, Lucht W, Li X W, Tsang T, Strugnell N C, Zhang X Y, Jin Y F, Muller J P, Lewis P, Barnsley M, Hobson P, Disney M, Roberts G, Dunderdale M, Doll C, d'Entremont R P, Hu B X, Liang S L, Privette J L and Roy D. 2002. First operational BRDF, albedo nadir reflectance products from MODIS. Remote Sensing of Environment, 83(1/2): 135-184
56. 56.
    Schowengerdt R A. 1980. Reconstruction of multispatial, multispectral image data using spatial frequency content. Photogrammetric Engineering and Remote Sensing, 46(10): 1325-1334
57. 57.
    Shi W Z, Zhang M, Zhang R, Chen S X and Zhan Z. 2020. Change detection based on artificial intelligence: state-of-the-art and challenges. Remote Sensing, 12(10): 1688
58. 58.
    Staylor W F and Suttles J T. 1986. Reflection and emission models for deserts derived from nimbus-7 ERB scanner measurements. Journal of Climate and Applied Meteorology, 25(2): 196-202
59. 59.
    Strahler A H, Lucht W, Schaaf C B, Tsang T, Gao F, Li X, Muller J P, Lewis P and Barnsley M J. 1999. MODIS BRDF/Albedo product: algorithm theoretical basis document version 5.0.
60. 60.
    Strugnell N C and Lucht W. 2001. An algorithm to infer continental-scale albedo from AVHRR data, land cover class, and field observations of typical BRDFs. Journal of Climate, 14(7): 1360-1376
61. 61.
    Suits G H. 1971. The calculation of the directional reflectance of a vegetative canopy. Remote Sensing of Environment, 2: 117-125
62. 62.
    Susaki J, Hara K, Kajiwara K and Honda Y. 2004. Robust estimation of BRDF model parameters. Remote Sensing of Environment, 89(1): 63-71
63. 63.
    Tarantola A. 1987. Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Amsterdam: Elsevier
64. 64.
    van Leeuwen W J D and Roujean J L. 2002. Land surface albedo from the synergistic use of polar (EPS) and geo-stationary (MSG) observing systems: an assessment of physical uncertainties. Remote Sensing of Environment, 81(2/3): 273-289
65. 65.
    Verhoef W. 1984. Light scattering by leaf layers with application to canopy reflectance modeling: the SAIL model. Remote Sensing of Environment, 16(2): 125-141
66. 66.
    Walthall C L, Norman J M, Welles J M, Campbell G and Blad B L. 1985. Simple equation to approximate the bidirectional reflectance from vegetative canopies and bare soil surfaces. Applied Optics, 24(3): 383-387
67. 67.
    Wang L Z, Yan J N, Mu L and Huang L. 2020. Knowledge discovery from remote sensing images: a review. WIREs Data Mining and Knowledge Discovery, 10(5): e1371
68. 68.
    Wang Y F, Li X W, Nashed Z, Zhao F, Yang H, Guan Y N and Zhang H. 2007. Regularized kernel-based BRDF model inversion method for ill-posed land surface parameter retrieval. Remote Sensing of Environment, 111(1): 36-50
69. 69.
    Wanner W, Li X and Strahler A H. 1995. On the derivation of kernels for kernel-driven models of bidirectional reflectance. Journal of Geophysical Research: Atmospheres, 100(D10): 21077-21089
70. 70.
    Wei S S and Fang H L. 2016. Estimation of canopy clumping index from MISR and MODIS sensors using the normalized difference hotspot and darkspot (NDHD) method: the influence of BRDF models and solar zenith angle. Remote Sensing of Environment, 187: 476-491
71. 71.
    Wen J G, Dou B C, You D Q, Tang Y, Xiao Q, Liu Q and Liu Q H. 2017. Forward a small-timescale BRDF/albedo by multisensor combined BRDF inversion model. IEEE Transactions on Geoscience and Remote Sensing, 55(2): 683-697
72. 72.
    Wen J G, Liu Q, Xiao Q, Liu Q H, You D Q, Hao D L, Wu S B and Lin X W. 2018. Characterizing land surface anisotropic reflectance over rugged terrain: a review of concepts and recent developments. Remote Sensing, 10(3): 370
73. 73.
    Wolanin A, Mateo-García G, Camps-Valls G, Gómez-Chova L, Meroni M, Duveiller G, You L Z and Guanter L. 2020. Estimating and understanding crop yields with explainable deep learning in the Indian Wheat Belt. Environmental Research Letters, 15(2): 024019
74. 74.
    Wu S B, Wen J G, Lin X W, Hao D L, You D Q, Xiao Q, Liu Q H and Yin T G. 2019a. Modeling discrete forest anisotropic reflectance over a sloped surface with an extended GOMS and SAIL model. IEEE Transactions on Geoscience and Remote Sensing, 57(2): 944-957
75. 75.
    Wu S B, Wen J G, Xiao Q, Liu Q H, Hao D L, Lin X W and You D Q. 2019b. Derivation of kernel functions for kernel-driven reflectance model over sloping terrain. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 12(2): 396-409
76. 76.
    Xiao Z Q, Liang S L, Wang J D, Jiang B and Li X J. 2011. Real-time retrieval of Leaf Area Index from MODIS time series data. Remote Sensing of Environment, 115(1): 97-106
77. 77.
    Yan K, Li H L, Song W J, Tong Y Y, Hao D L, Zeng Y L, Mu X H, Yan G J, Fang Y, Myneni R B and Schaaf C. 2022. Extending a linear kernel-driven BRDF model to realistically simulate reflectance anisotropy over rugged terrain. IEEE Transactions on Geoscience and Remote Sensing, 60: 4401816
78. 78.
    Yang H, Xu W L, Zhao H R, Chen X and Wang J D. 2005. Information flow and controlling in regularization inversion of quantitative remote sensing. Science in China Series D: Earth Sciences, 48(1): 74-83
79. 79.
    Yin G F, Li A N, Zhao W, Jin H A, Bian J H and Wu S B. 2017. Modeling canopy reflectance over sloping terrain based on path length correction. IEEE Transactions on Geoscience and Remote Sensing, 55(8): 4597-4609
80. 80.
    Zeng Y L, Li J, Liu Q H, Huete A R, Xu B D, Yin G F, Zhao J, Yang L, Fan W L, Wu S B and Yan K. 2016. An iterative BRDF/NDVI inversion algorithm based on a posteriori variance estimation of observation errors. IEEE Transactions on Geoscience and Remote Sensing, 54(11): 6481-6496
81. 81.
    Zhang X Y, Friedl M A, Schaaf C B, Strahler A H, Strahler J C F, Gao F, Reed B C and Huete A. 2003. Monitoring vegetation phenology using MODIS. Remote Sensing of Environment, 84(3): 471-475
82. 82.
    Zhao H R, Tang Z S and Li X W. 2007. A regularization parameter choice method on linear quantitative remote sensing inversion. Geomatics and Information Science of Wuhan University, 32(6): 531-535
83. 83.
    Zhao X, Liu S H, Tang Y M, Yu K and Li X W. 2006. Studying on multi-stage robust estimation of BRDF model parameters. Journal of Remote Sensing, 10(6): 901-909
84. 84.
    Zobitz J M, Quaife T and Nichols N K. 2020. Efficient hyper-parameter determination for regularised linear BRDF parameter retrieval. International Journal of Remote Sensing, 41(4): 1437-1457