References

1. 1.
   Beckmann P. 1965. Shadowing of random rough surfaces. IEEE Transactions on Antennas and Propagation, 13(3): 384-388
2. 2.
   Blinn J F. 1977. Models of light reflection for computer synthesized pictures//Proceedings of the 4th Annual Conference on Computer Graphics and Interactive Techniques. San Jose: Association for Computing Machinery: 192-198
3. 3.
   Bourlier C, Saillard J and Berginc G. 2000. Effect of correlation between shadowing and shadowed points on the Wagner and Smith monostatic one-dimensional shadowing functions. IEEE Transactions on Antennas and Propagation, 48(3): 437-446
4. 4.
   Buhl D, Welch W J and Rea D G. 1968. Reradiation and thermal emission from illuminated craters on the lunar surface. Journal of Geophysical Research, 73(16): 5281-5295
5. 5.
   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
6. 6.
   Chen S Y, Xiao P F, Zhang X L, Liu H, Wang Y H, Sun L Y and Yin G F. 2024. Improved snow-covered forest bidirectional reflectance model incorporating canopy-intercepted snow and atmospheric effects. IEEE Transactions on Geoscience and Remote Sensing, 62: 4302117
7. 7.
   Chen Y, Hall A and Liou K N. 2006. Application of three-dimensional solar radiative transfer to mountains. Journal of Geophysical Research: Atmospheres, 111(D21): D21111
8. 8.
   Chen Y Y, Mu X H, McVicar T R, Wang Y Y, Guo Y H, Yan K, Lai Y K, Xie D H and Yan G J. 2025. Using an improved radiative transfer model to estimate leaf area index, fractional vegetation cover and leaf inclination angle from Himawari-8 geostationary satellite data. Remote Sensing of Environment, 318: 114595
9. 9.
   Cheng J, Wen J G, Xiao Q, Wu S B, Hao D L and Liu Q H. 2022. Extending the GOSAILT model to simulate sparse woodland bi-directional reflectance with soil reflectance anisotropy consideration. Remote Sensing, 14(4): 1001
10. 10.
    Chu Q, Yan G J, Qi J B, Mu X H, Li L Y, Tong Y Y, Zhou Y J, Liu Y N, Xie D H and Wild M. 2021. Quantitative analysis of terrain reflected solar radiation in snow-covered mountains: a case study in Southeastern Tibetan Plateau. Journal of Geophysical Research: Atmospheres, 126(11): e2020JD034294
11. 11.
    Combal B, Isaka H and Trotter C. 2000. Extending a turbid medium BRDF model to allow sloping terrain with a vertical plant stand. IEEE Transactions on Geoscience and Remote Sensing, 38(2): 798-810
12. 12.
    Despan D, Bedidi A, Cervelle B and Rudant J P. 1998. Bidirectional reflectance of gaussian random surfaces and its scaling properties. Mathematical Geology, 30(7): 873-888
13. 13.
    Di Girolamo L. 2003. Generalizing the definition of the bi-directional reflectance distribution function. Remote Sensing of Environment, 88(4): 479-482
14. 14.
    Dymond J R, Shepherd J D and Gillingham S. 2024. Directional reflectance of light from landscapes on a long transect in Australia-forest to desert. Science of Remote Sensing, 9: 100136
15. 15.
    Fan T Y, Wen J G, Jiao Z H, Bian Z J, Zhong S Y, Zhu W Z, Cao B, Li H, Du Y M, Xiao Q and Liu Q H. 2024. Modeling the topographic effect on directional anisotropies of land surface temperature from thermal remote sensing. Journal of Remote Sensing, 4: 0226
16. 16.
    Fan W L, Chen J M, Ju W M and Nesbitt N. 2014a. Hybrid geometric optical–radiative transfer model suitable for forests on slopes. IEEE Transactions on Geoscience and Remote Sensing, 52(9): 5579-5586
17. 17.
    Fan W L, Chen J M, Ju W M and Zhu G L. 2014b. GOST: a geometric-optical model for sloping terrains. IEEE Transactions on Geoscience and Remote Sensing, 52(9): 5469-5482
18. 18.
    Fan W L, Li J and Liu Q H. 2015. GOST2: the improvement of the canopy reflectance model GOST in separating the sunlit and shaded leaves. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 8(4): 1423-1431
19. 19.
    Gao B, Jia L and Menenti M. 2013. An improved bidirectional reflectance distribution function (BRDF) over rugged terrain based on moderate spatial resolution remote sensing data//2013 IEEE International Geoscience and Remote Sensing Symposium. Melbourne: IEEE: 2766-2769
20. 20.
    Gastellu-Etchegorry J P, Yin T G, Lauret N, Cajgfinger T, Gregoire T, Grau E, Feret J B, Lopes M, Guilleux J, Dedieu G, Malenovský Z, Cook B D, Morton D, Rubio J, Durrieu S, Cazanave G, Martin E and Ristorcelli T. 2015. Discrete anisotropic radiative transfer (DART 5) for modeling airborne and satellite spectroradiometer and LIDAR acquisitions of natural and urban landscapes. Remote Sensing, 7(2): 1667-1701
21. 21.
    Gemmell F. 1998. An investigation of terrain effects on the inversion of a forest reflectance model. Remote Sensing of Environment, 65(2): 155-169
22. 22.
    Geng J, Chen J M, Fan W L, Tu L L, Pang Y, Yuan G, Xu L C, Zhu C Y, Zhang T, Zhang C J, Ye Z R, Zhu Y C and Li Z X. 2022. Application of a hypergeometric model in simulating canopy gap fraction and BRF for forest plantations on sloping terrains. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 15: 2901-2913
23. 23.
    Geng J, Chen J M, Fan W L, Tu L L, Tian Q J, Yang R R, Yang Y J, Wang L, Lv C G and Wu S B. 2017. GOFP: a geometric-optical model for forest plantations. IEEE Transactions on Geoscience and Remote Sensing, 55(9): 5230-5241
24. 24.
    Goel N S. 1988. Models of vegetation canopy reflectance and their use in estimation of biophysical parameters from reflectance data. Remote Sensing Reviews, 4(1): 1-212
25. 25.
    Gu C Y, Clevers J G P W, Liu X, Tian X, Li Z Y and Li Z Y. 2018. Predicting forest height using the GOST, Landsat 7 ETM+, and airborne LiDAR for sloping terrains in the Greater Khingan Mountains of China. ISPRS Journal of Photogrammetry and Remote Sensing, 137: 97-111
26. 26.
    Han Y, Wen J G, Xiao Q, Bao Y F, Chen X, Liu Q and He M. 2023. Review of the land surface BRDF inversion methods based on remotely sensed satellite data. National Remote Sensing Bulletin, 27(9): 2024-2040
27. 27.
    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
28. 28.
    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
29. 29.
    Hapke B. 1984. Bidirectional reflectance spectroscopy: 3. Correction for macroscopic roughness. Icarus, 59(1): 41-59
30. 30.
    He M, Wen J G, Wu S B, Meng L, Lin X W, Han Y, You D Q, Tang Y and Liu Q H. 2024. A new forest leaf area index retrieval algorithm over slope surface. IEEE Transactions on Geoscience and Remote Sensing, 62: 4400718
31. 31.
    Heitz E, Hanika J, d’Eon E and Dachsbacher C. 2016. Multiple-scattering microfacet BSDFs with the smith model. ACM Transactions on Graphics, 35(4): 58
32. 32.
    Hu G Y and Li A N. 2022a. BOST: a canopy reflectance model suitable for both continuous and discontinuous canopies over sloping terrains. IEEE Transactions on Geoscience and Remote Sensing, 60: 4416119
33. 33.
    Hu G Y and Li A N. 2022b. SGOT: a simplified geometric-optical model for crown scene components modeling over rugged terrain. Remote Sensing, 14(8): 1821
34. 34.
    Hu G Y and Li A N. 2024. Investigating the surrounding topographic effects on target reflected radiance by extending the BOST model. IEEE Transactions on Geoscience and Remote Sensing, 62: 4412518
35. 35.
    Jin Y F, Schaaf C B, Gao F, Li X W, Strahler A H, Lucht W and Liang S L. 2003. Consistency of MODIS surface bidirectional reflectance distribution function and albedo retrievals: 1. Algorithm performance. Journal of Geophysical Research: Atmospheres, 108(D5): 4158
36. 36.
    Koenderink J J, Van Doorn A J, Dana K J and Nayar S. 1999. Bidirectional reflection distribution function of thoroughly pitted surfaces. International Journal of Computer Vision, 31(2): 129-144
37. 37.
    Koenderink J J, Van Doorn A J, Dana K J and Nayar S. 1999. Bidirectional reflection distribution function of thoroughly pitted surfaces. International Journal of Computer Vision, 31(2): 129-144
38. 38.
    Kuusk A. 2001. A two-layer canopy reflectance model. Journal of Quantitative Spectroscopy and Radiative Transfer, 71(1): 1-9
39. 39.
    Li A N, Bian J H, Miao G F, Wen J G, He T, Mu X H, Zhao W, Zhang Z J, Nan X, Lei G B, Jiao Z H, Cheng Z Q, Zeng H D, Xie D H, You D Q, Li L, Tian F, Jin H A, Jiang B and Ma Y C. 2025. Research progress of the stereoscopic observation and high spatial resolution products development of key global change parameters for mountain ecosystem. National Remote Sensing Bulletin, 29(6): 2015-2034
40. 40.
    Li D, Chen J M, Zhang X, Yan Y, Zhu J, Zheng H B, Zhou K, Yao X, Tian Y C, Zhu Y, Cheng T and Cao W X. 2020. Improved estimation of leaf chlorophyll content of row crops from canopy reflectance spectra through minimizing canopy structural effects and optimizing off-noon observation time. Remote Sensing of Environment, 248: 111985
41. 41.
    Li X, Sun Z Q, Lu S and Omasa K. 2023. PROSPECULAR: a model for simulating multi-angular spectral properties of leaves by coupling PROSPECT with a specular function. Remote Sensing of Environment, 297: 113754
42. 42.
    Li X W, Gao F, Chen L Z and Strahler A H. 1999. Derivation and validation of a new kernel for kernel-driven BRDF models//Proceedings of SPIE 3868, Remote Sensing for Earth Science, Ocean, and Sea Ice Applications. Florence: SPIE: 368-379
43. 43.
    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
44. 44.
    Li X Y, Shabanov N V, Chen L, Zhang Y G and Huang H G. 2022. Modeling solar-induced fluorescence of forest with heterogeneous distribution of damaged foliage by extending the stochastic radiative transfer theory. Remote Sensing of Environment, 271: 112892
45. 45.
    Lin X W, Wen J G, Wu S B, Hao D L, Xiao Q and Liu Q H. 2020. Advances in topographic correction methods for optical remote sensing imageries. Journal of Remote Sensing (in Chinese), 24(8): 958-974
46. 46.
    Liu H, Zhu J P and Wang K. 2015. Modified polarized geometrical attenuation model for bidirectional reflection distribution function based on random surface microfacet theory. Optics Express, 23(17): 22788-22799
47. 47.
    Liu Q H, Cao B, Zeng Y L, Li J, Du Y M, Wen J G, Fan W L, Zhao J and Yang L. 2016. Recent progresses on the remote sensing radiative transfer modeling over heterogeneous vegetation canopy. Journal of Remote Sensing (in Chinese), 20(5): 933-945
48. 48.
    Liu Q H, Yan G J, Jiao Z T, Xiao Q, Wen J G, Liang S L and Wang J D. 2019. Geometric-optical remote sensing modeling to quantitative remote sensing theory and methodology development: in memory of academician Li Xiaowen. Journal of Remote Sensing (in Chinese), 23(1): 1-10
49. 49.
    Ma Y C, He T, Aguilar C, Pimentel R, Liang S L, McVicar T R, Hao D L, Xiao X X and Liu X Y. 2024a. Evaluating topographic effects on kilometer-scale satellite downward shortwave radiation products: a case study in mid-latitude mountains. IEEE Transactions on Geoscience and Remote Sensing, 62: 5609816
50. 50.
    Ma Y C, He T, Liang S L, McVicar T R, Hao D L, Liu T and Jiang B. 2023. Estimation of fine spatial resolution all-sky surface net shortwave radiation over mountainous terrain from Landsat 8 and Sentinel-2 data. Remote Sensing of Environment, 285: 113364
51. 51.
    Ma Y C, He T, McVicar T R, Liang S L, Liu T, Peng W S, Song D X and Tian F. 2024b. Quantifying how topography impacts vegetation indices at various spatial and temporal scales. Remote Sensing of Environment, 312: 114311
52. 52.
    Martonchik J V, Bruegge C J and Strahler A H. 2000. A review of reflectance nomenclature used in remote sensing. Remote Sensing Reviews, 19(1/4): 9-20
53. 53.
    Mousivand A, Verhoef W, Menenti M and Gorte B. 2015. Modeling top of atmosphere radiance over heterogeneous non-Lambertian rugged terrain. Remote Sensing, 7(6): 8019-8044
54. 54.
    Nicodemus F E, Richmond J C, Hsia J J, Ginsberg I W and Limperis T. 1977. Geometrical Considerations and Nomenclature for Reflectance. National Bureau of Standards
55. 55.
    Poulin P and Fournier A. 1990. A model for anisotropic reflection. ACM SIGGRAPH Computer Graphics, 24(4): 273-282
56. 56.
    Proy C, Tanre D and Deschamps P. 1989. Evaluation of topographic effects in remotely sensed data. Remote Sensing of Environment, 30(1): 21-32
57. 57.
    Qin Z Q, Li X and Gu Y F. 2024. Hemisphere harmonics basis: a universal approach to remote sensing BRDF approximation. IEEE Transactions on Geoscience and Remote Sensing, 62: 1-16
58. 58.
    Roberts G. 2001. A review of the application of BRDF models to infer land cover parameters at regional and global scales. Progress in Physical Geography: Earth and Environment, 25(4): 483-511
59. 59.
    Ross V, Dion D and Potvin G. 2005. Detailed analytical approach to the Gaussian surface bidirectional reflectance distribution function specular component applied to the sea surface. Journal of the Optical Society of America A, 22(11): 2442-2453
60. 60.
    Sandmeier S and Itten K I. 1997. A physically-based model to correct atmospheric and illumination effects in optical satellite data of rugged terrain. IEEE Transactions on Geoscience and Remote Sensing, 35(3): 708-717
61. 61.
    Schaaf C B, Li X W and Strahler A H. 1994. Topographic effects on bidirectional and hemispherical reflectances calculated with a geometric-optical canopy model. IEEE Transactions on Geoscience and Remote Sensing, 32(6): 1186-1193
62. 62.
    Shi H Y, Jiang J Y, Jacquemoud S, Xiao Z Q and Ma M G. 2023. Estimating leaf mass per area with leaf radiative transfer model. Remote Sensing of Environment, 286: 113444
63. 63.
    Shi H Y and Xiao Z Q. 2021. The 4SAILT model: an improved 4SAIL canopy radiative transfer model for sloping terrain. IEEE Transactions on Geoscience and Remote Sensing, 59(7): 5515-5525
64. 64.
    Smith B. 1967. Geometrical shadowing of a random rough surface. IEEE Transactions on Antennas and Propagation, 15(5): 668-671
65. 65.
    Snyder W C. 2002. Definition and invariance properties of structured surface BRDF. IEEE Transactions on Geoscience and Remote Sensing, 40(5): 1032-1037
66. 66.
    Torrance K E and Sparrow E M. 1967. Theory for off-specular reflection from roughened surfaces. Journal of the Optical Society of America, 57(9): 1105-1114
67. 67.
    Verhoef W and Bach H. 2007. Coupled soil-leaf-canopy and atmosphere radiative transfer modeling to simulate hyperspectral multi-angular surface reflectance and TOA radiance data. Remote Sensing of Environment, 109(2): 166-182
68. 68.
    Verstraete M M, Pinty B and Dickinson R E. 1990. A physical model of the bidirectional reflectance of vegetation canopies: 1. Theory. Journal of Geophysical Research: Atmospheres, 95(D8): 11755-11765
69. 69.
    Wagner R J. 1967. Shadowing of randomly rough surfaces. The Journal of the Acoustical Society of America, 41(1): 138-147
70. 70.
    Wang K C, Zhou X J, Liu J M and Sparrow M. 2005. Estimating surface solar radiation over complex terrain using moderate-resolution satellite sensor data. International Journal of Remote Sensing, 26(1): 47-58
71. 71.
    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
72. 72.
    Wen J G, Liu Q, Liu Q H, Xiao Q and Li X W. 2009. Scale effect and scale correction of land-surface albedo in rugged terrain. International Journal of Remote Sensing, 30(20): 5397-5420
73. 73.
    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
74. 74.
    Wen J G, Liu Q H, Li Z Y, Li X, Liu S M, Xiao Q, Gao Z H, Ma M G, Che T, Liu L Y, Fang H L, Yan G J, Ge Y, Chen E X, Zhang Y, Ma L L, Wu X D and Chen X. 2023. A review of the development of remote sensing field experiments and product validation in China. National Remote Sensing Bulletin, 27(3): 573-583
75. 75.
    Wen J G, Liu Q H, Xiao Q, Liu Q and Li X W. 2008. Modeling the land surface reflectance for optical remote sensing data in rugged terrain. Science in China Series D: Earth Sciences, 51(8): 1169-1178
76. 76.
    Wen J G, Liu Q H, You D Q, Bian Z J, Wei K X, Zhao C C, Xiao Q, Du Y M, Yan G J, Fan W J and Wu Y R. 2025. Modeling of optical remote sensing mechanism: review and prospect. National Remote Sensing Bulletin, 29(6): 1331-1346
77. 77.
    Wen J G, Wu X D, Wang J P, Tang R Q, Ma D J, Zeng Q C, Gong B C and Xiao Q. 2022. Characterizing the effect of spatial heterogeneity and the deployment of sampled plots on the uncertainty of ground “truth” on a coarse grid scale: case study for Near-Infrared (NIR) surface reflectance. Journal of Geophysical Research: Atmospheres, 127(11): e2022JD036779
78. 78.
    Wu S B, Wen J G, Gastellu-Etchegorry J P, Liu Q H, You D Q, Xiao Q, Hao D L, Lin X W and Yin T G. 2019a. The definition of remotely sensed reflectance quantities suitable for rugged terrain. Remote Sensing of Environment, 225: 403-415
79. 79.
    Wu S B, Wen J G, Lin X W, Hao D L, You D Q, Xiao Q, Liu Q H and Yin T G. 2019b. 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
80. 80.
    Wu S B, Wen J G, Xiao Q, Liu Q H, Hao D L, Lin X W and You D Q. 2019c. 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
81. 81.
    Yan G J, Jiang H L, Yan K, Cheng S Y, Song W J, Tong Y Y, Liu Y N, Qi J B, Mu X H, Zhang W M, Xie D H and Zhou H M. 2021. Review of optical multi-angle quantitative remote sensing. National Remote Sensing Bulletin, 25(1): 83-108
82. 82.
    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
83. 83.
    Yang P Q, van der Tol C, Yin T G and Verhoef W. 2020. The SPART model: a soil-plant-atmosphere radiative transfer model for satellite measurements in the solar spectrum. Remote Sensing of Environment, 247: 111870
84. 84.
    Yang Y, Zhou Z F, Huang D H, Zhang F X M, Deng F F and Du S L. 2024. A comparative analysis of the applicability of typical land cover datasets in the karst strongly heterogeneous terrain in southern China. Geocarto International, 39(1): 2395318
85. 85.
    Yao C, Sun Z Q and Lu S. 2024. Evaluation of PROSPECT inversion approaches using multiangular spectral reflectance factor of leaves. IEEE Transactions on Geoscience and Remote Sensing, 62: 4402716
86. 86.
    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
87. 87.
    Yu W T, Li J, Liu Q H, Yin G F, Zeng Y L, Lin S R and Zhao J. 2020. A simulation-based analysis of topographic effects on LAI inversion over sloped terrain. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 13: 794-806
88. 88.
    Zhao C C, Wen J G, You D Q, Tang Y, Chen X and Liu Q. 2023. Remote sensing retrieval of high-spatial-resolution land surface albedo. National Remote Sensing Bulletin, 27(3): 724-737
89. 89.
    Zhao C C, Wen J G, You D Q, Tang Y, Han Y, Liu G K, Wei K X, Wang H J and Liu Q H. 2025. Modeling top-of-atmosphere anisotropic reflectance of discrete forests over sloped surface. IEEE Transactions on Geoscience and Remote Sensing, 63: 4407711
90. 90.
    Zhu W Z, You D Q, Wen J G, Tang Y, Gong B C and Han Y. 2023. Evaluation of linear kernel-driven BRDF models over snow-free rugged terrain. Remote Sensing, 15(3): 786