GSV-SRTS: A Heterogeneous Landscape Soil-Canopy Reflectance Model Over Sloping Terrain with an Extended GSV and Stochastic Radiative Transfer Theory

Li, Siqi; Hu, Guyue; Li, Shaoda; Yang, Ronghao; Tan, Junxiang; Liu, Chenghao; Bian, Jinhu

doi:10.5194/egusphere-2025-5173

Preprints

https://doi.org/10.5194/egusphere-2025-5173

Preprints

04 Jan 2026

| 04 Jan 2026

GSV-SRTS: A Heterogeneous Landscape Soil-Canopy Reflectance Model Over Sloping Terrain with an Extended GSV and Stochastic Radiative Transfer Theory

Siqi Li, Guyue Hu, Shaoda Li, Ronghao Yang, Junxiang Tan, Chenghao Liu, and Jinhu Bian

Abstract. Accurately modelling radiation interactions within canopy layers and soil backgrounds is crucial for biophysical variables retrieval across regional or global scales. However, terrain relief can introduce significant uncertainties into forward radiative transfer modeling. Despite the development of numerous canopy reflectance models for sloping terrain, the heterogeneous characteristics of soil-canopy objects have often been overlooked, leading to distortions in the bidirectional reflectance distribution in small-scale landscapes. In this study, we present a canopy reflectance model suitable for heterogeneous structures on sloping terrain. By extending the stochastic radiative transfer theory from flat terrain to sloping terrain and integrating the soil General Spectral Vector, the GSV-SRTS model was introduced. This enables accurate prediction of soil-canopy radiative transfer within subpixel 3-D heterogeneous mountain landscapes. The proposed GSV-SRTS model was evaluated against the Discrete Anisotropic Radiative Transfer (DART) model, compared with typical mountain canopy reflectance models, and validated against remote sensing observations at varying spatial resolutions. The results showed that the GSV-SRTS model achieves good accuracy in the comparisons with DART (R² = 0.9136 (0.9052) and root-mean-square errors (RMSE) = 0.0246 (0.0216) in the red (NIR (Near-Infrared)) band) and performs well in real mountainous areas, particularly with high spatial resolution remote sensing observations (R² = 0.9078 (0.9143) and RMSE = 0.0201 (0.0212)). Furthermore, the GSV-SRTS model effectively captures the impacts of canopy structure and terrain factors on bidirectional reflectance. This underscores the GSV-SRTS model as a reliable physical tool for simulating radiation regimes over sloping terrain, with the potential to enhance the accuracy of biophysical variable retrieval from remote sensing observations.

Received: 19 Oct 2025 – Discussion started: 04 Jan 2026

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Siqi Li, Guyue Hu, Shaoda Li, Ronghao Yang, Junxiang Tan, Chenghao Liu, and Jinhu Bian

Status: closed

RC1:
'Comment on egusphere-2025-5173', Anonymous Referee #1, 22 Feb 2026
This study presents the GSV-SRTS model, a novel canopy reflectance model designed for heterogeneous landscapes over sloping terrain by integrating an extended General Spectral Vector (GSV) with Stochastic Radiative Transfer (SRT) theory. The research objective is clear, and the integration of GSV for soil background characterization with SRT theory for canopy representation over sloping terrain represents a meaningful step forward. The experimental design is comprehensive, incorporating both theoretical comparisons with DART and practical validations using the remote sensing observations across different spatial scales. The writing is generally clear, and the study appears to fall within the scope of the journal. However, to further strengthen the manuscript and enhance its impact, several aspects regarding the mechanistic explanation of the model integration, the depth of discussion on certain findings, and the presentation clarity could be improved. The following specific comments and suggestions are provided to assist the authors in refining their work.
The GSV model is constructed based on the LUCAS global soil database, yet the study area is located in the mountainous region of the northeastern Tibetan Plateau. Please clarify whether this parameterization scheme requires localization adjustments for highly heterogeneous high-altitude areas and discuss the model's applicability in regions with non-European soil types.

Figure 9 shows that the model performs best with high-resolution imagery (Jilin-1). The attribution of this to the model's ability to resolve microscopic details is a reasonable explanation. It is suggested to further discuss: for medium-to-low resolution pixels (e.g., Sentinel-2, Landsat), does the homogenization of internal heterogeneity serve as the primary reason for the decrease in R²? Does this imply that the model is more suitable for scenes with high intra-pixel heterogeneity?

In the Introduction, when discussing the limitations of previous models, the phrasing could be more neutral. For instance, changing "these CR models overlooked the impact..." to "these models could be further enhanced by incorporating the impact..." would reflect a more constructive tone.

Some long sentences could be appropriately split to improve readability. For example, the long sentence in the Abstract spanning lines 10-12, "However, terrain relief...landscapes," contains multiple clauses and could be considered for segmentation.

The captions for Figures 3 and 4 already include clear descriptions for subpanels (a) and (b). It is recommended that all figure and table captions throughout the manuscript maintain this consistent style to ensure uniform formatting.

The overall formatting of the references is standard. It is advised to check if the author name format in individual entries (e.g., "Bruno Combal, H. I., and Craig Trotter: ...") conforms to the journal's specific requirements, ensuring consistency across all entries.

The titles for Sections 3.3 and 3.4 are currently identical. It is suggested to revise one of the titles based on their content; for example, changing the Section 3.3 title to "Assessment of the Canopy Structure Effects on Multi-angle CR Simulations" would make it more specific.

The current manuscript presents the GSV (soil background) and SRT (canopy transfer) as two relatively independent modules. It is suggested to add a paragraph at the beginning of the model framework section (Section 2.1) explaining the motivation for why and how these two components need to be coupled physically.

The article mentions the use of a local slope coordinate system but could elaborate more deeply on its necessity for solving the radiative transfer equation.

Equations (5) and (6) introduce a topographic modulation function to modify the scattering phase function. It is recommended to further explain the physical intention behind this operation.

The article addresses the effects of topography on the extinction coefficient (Equation 4) and the gap probability (via PCF) separately. It is suggested to briefly relate these two aspects in the Discussion section.
Citation: https://doi.org/10.5194/egusphere-2025-5173-RC1
- AC1: 'Reply on RC1', Siqi Li, 08 Mar 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2025-5173/egusphere-2025-5173-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-5173-AC1
CC1: 'Comment on egusphere-2025-5173', Yanli Zhang, 08 Apr 2026

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2025-5173/egusphere-2025-5173-CC1-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2025-5173-CC1
RC2:
'Comment on egusphere-2025-5173', Anonymous Referee #2, 08 Apr 2026
This study proposed a radiative transfer model over rugged terrains based on the theory of stochastic radiation transfer, named GSV-SRTS. The synthesis of GSV and SRT represents an advancement in modeling soil-canopy interactions in mountainous regions. The experimental framework is robust, including both rigorous comparisons with sophisticated DART simulations and multi-scale validation using actual satellite imagery. To further enhance the manuscript's clarity, impact, and readiness for publication, the following specific suggestions are offered concerning the depth of theoretical explanations, the interpretation of key results, and overall presentation. My suggestions and comments are as follows:
Major Comments:
The paper conceptualizes the 3D canopy structure as a spatial stochastic process, described by an indicator function and Poisson distribution. Could you specify in more detail how this stochasticity is specifically embedded into the solution process of the radiative transfer equations (Eq. 2, 3), rather than just as a parameter input？

The results show a distinct reflectance peak in the hotspot direction. What are the similarities and differences in the mechanisms of the hotspot effect simulated by the GSV-SRTS model under sloping terrain conditions compared to flat terrain? How does the model capture the influence of topography on the hotspot signature? Please add an explanation in the appropriate section.

The model simulations perform good correlationwith the high-resolution imagery. Does this mean the model's strength lies in resolving sub-pixel structural heterogeneity and soil spatial variability? For medium-to-low resolution pixels, where this heterogeneity is averaged, does using GSV-SRTS still offer an advantage over simpler homogeneous models? If so, what are the main advantages?

The authors have provided code and data. Regarding the model implementation, what are the key details and stability of the numerical method (e.g., discrete ordinate method, iterative scheme) used to solve the coupled SRT equations (e.g., Eq. 12)? This is important for other researchers to reproduce or modify the model.

Generally speaking, the global irradiance received by mountainous surfaces includes direct irradiance, diffuse irradiance, and reflected irradiance from the surrounding terrain. However, the proposed GSV-SRTS model seems to only consider the first two components and does not account for the surrounding-reflected radiationcontribution to the target pixel. This limitation needs to be pointed out in the conclusion.

Minors:
Terms such as "heterogeneous landscapes," "discontinuous canopies," and "patchy landscapes" are used in the paper. In the context of this study, could you more clearly define the spatial scales and structural characteristics these terms refer to, in order to avoid reader confusion?

The study area selected for this research features complex topographic conditions and high vegetation heterogeneity. How did the authors conduct field measurements to ensure the representativeness of the data obtained? Please supplement the explanation.

The paper clearly introduces the GSV and SRT modules, but could the beginning of the Methods section (Section 2.1) more explicitly elaborate on the core physical motivation and necessity for coupling the soil spectral vector (GSV) with the sloping terrain stochastic radiative transfer (SRT) theory? In other words, why is this coupling crucial for accurately simulating radiative transfer in heterogeneous mountainous landscapes?

In Section 3.1, the sentence "Finally, the remote sensing observations from different sensors were utilized for model evaluation to evaluate the suitability..." contains redundant phrasing and an unnecessary comma. Please change the sentenceand check the full text.

In Section 3.3, the construction "was set ranging from" is grammatically awkward, as the verb "set" typically takes a preposition like "to" for a fixed value. Additionally, starting a sentence with "And" is generally avoided in formal writing. Please check the full text for similar issues and make necessary revisions.

There is a minor tense inconsistency appears in Section 4.1: "The results showed that GSV-SRTS achieves the highest R² value..." The main verb "showed" is past tense, while "achieves" is present. For consistency in describing results, it is recommended to use the past tense.

In Section 4.4, the clause "which capture finer details in the microscale scenarios" is incorrectly linked to "the ability of the SRT theory and GSV model." The sentence structure is unclear.

There are issues with the citation format in several places, such as on page 2, line 41: sloping terrain (SLCT) (Verhoef and Bach, 2007) (Verhoef and Bach, 2012); lines51-52: Zeng et al. developed a RT model specifically designed for patchy landscapes based on SRT theory (Zeng et al., 2020).
Citation: https://doi.org/10.5194/egusphere-2025-5173-RC2
- AC2: 'Reply on RC2', Siqi Li, 13 Apr 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2025-5173/egusphere-2025-5173-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-5173-AC2

Status: closed

RC1:
'Comment on egusphere-2025-5173', Anonymous Referee #1, 22 Feb 2026
This study presents the GSV-SRTS model, a novel canopy reflectance model designed for heterogeneous landscapes over sloping terrain by integrating an extended General Spectral Vector (GSV) with Stochastic Radiative Transfer (SRT) theory. The research objective is clear, and the integration of GSV for soil background characterization with SRT theory for canopy representation over sloping terrain represents a meaningful step forward. The experimental design is comprehensive, incorporating both theoretical comparisons with DART and practical validations using the remote sensing observations across different spatial scales. The writing is generally clear, and the study appears to fall within the scope of the journal. However, to further strengthen the manuscript and enhance its impact, several aspects regarding the mechanistic explanation of the model integration, the depth of discussion on certain findings, and the presentation clarity could be improved. The following specific comments and suggestions are provided to assist the authors in refining their work.
The GSV model is constructed based on the LUCAS global soil database, yet the study area is located in the mountainous region of the northeastern Tibetan Plateau. Please clarify whether this parameterization scheme requires localization adjustments for highly heterogeneous high-altitude areas and discuss the model's applicability in regions with non-European soil types.

Figure 9 shows that the model performs best with high-resolution imagery (Jilin-1). The attribution of this to the model's ability to resolve microscopic details is a reasonable explanation. It is suggested to further discuss: for medium-to-low resolution pixels (e.g., Sentinel-2, Landsat), does the homogenization of internal heterogeneity serve as the primary reason for the decrease in R²? Does this imply that the model is more suitable for scenes with high intra-pixel heterogeneity?

In the Introduction, when discussing the limitations of previous models, the phrasing could be more neutral. For instance, changing "these CR models overlooked the impact..." to "these models could be further enhanced by incorporating the impact..." would reflect a more constructive tone.

Some long sentences could be appropriately split to improve readability. For example, the long sentence in the Abstract spanning lines 10-12, "However, terrain relief...landscapes," contains multiple clauses and could be considered for segmentation.

The captions for Figures 3 and 4 already include clear descriptions for subpanels (a) and (b). It is recommended that all figure and table captions throughout the manuscript maintain this consistent style to ensure uniform formatting.

The overall formatting of the references is standard. It is advised to check if the author name format in individual entries (e.g., "Bruno Combal, H. I., and Craig Trotter: ...") conforms to the journal's specific requirements, ensuring consistency across all entries.

The titles for Sections 3.3 and 3.4 are currently identical. It is suggested to revise one of the titles based on their content; for example, changing the Section 3.3 title to "Assessment of the Canopy Structure Effects on Multi-angle CR Simulations" would make it more specific.

The current manuscript presents the GSV (soil background) and SRT (canopy transfer) as two relatively independent modules. It is suggested to add a paragraph at the beginning of the model framework section (Section 2.1) explaining the motivation for why and how these two components need to be coupled physically.

The article mentions the use of a local slope coordinate system but could elaborate more deeply on its necessity for solving the radiative transfer equation.

Equations (5) and (6) introduce a topographic modulation function to modify the scattering phase function. It is recommended to further explain the physical intention behind this operation.

The article addresses the effects of topography on the extinction coefficient (Equation 4) and the gap probability (via PCF) separately. It is suggested to briefly relate these two aspects in the Discussion section.
Citation: https://doi.org/10.5194/egusphere-2025-5173-RC1
- AC1: 'Reply on RC1', Siqi Li, 08 Mar 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2025-5173/egusphere-2025-5173-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-5173-AC1
CC1: 'Comment on egusphere-2025-5173', Yanli Zhang, 08 Apr 2026

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2025-5173/egusphere-2025-5173-CC1-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2025-5173-CC1
RC2:
'Comment on egusphere-2025-5173', Anonymous Referee #2, 08 Apr 2026
This study proposed a radiative transfer model over rugged terrains based on the theory of stochastic radiation transfer, named GSV-SRTS. The synthesis of GSV and SRT represents an advancement in modeling soil-canopy interactions in mountainous regions. The experimental framework is robust, including both rigorous comparisons with sophisticated DART simulations and multi-scale validation using actual satellite imagery. To further enhance the manuscript's clarity, impact, and readiness for publication, the following specific suggestions are offered concerning the depth of theoretical explanations, the interpretation of key results, and overall presentation. My suggestions and comments are as follows:
Major Comments:
The paper conceptualizes the 3D canopy structure as a spatial stochastic process, described by an indicator function and Poisson distribution. Could you specify in more detail how this stochasticity is specifically embedded into the solution process of the radiative transfer equations (Eq. 2, 3), rather than just as a parameter input？

The results show a distinct reflectance peak in the hotspot direction. What are the similarities and differences in the mechanisms of the hotspot effect simulated by the GSV-SRTS model under sloping terrain conditions compared to flat terrain? How does the model capture the influence of topography on the hotspot signature? Please add an explanation in the appropriate section.

The model simulations perform good correlationwith the high-resolution imagery. Does this mean the model's strength lies in resolving sub-pixel structural heterogeneity and soil spatial variability? For medium-to-low resolution pixels, where this heterogeneity is averaged, does using GSV-SRTS still offer an advantage over simpler homogeneous models? If so, what are the main advantages?

The authors have provided code and data. Regarding the model implementation, what are the key details and stability of the numerical method (e.g., discrete ordinate method, iterative scheme) used to solve the coupled SRT equations (e.g., Eq. 12)? This is important for other researchers to reproduce or modify the model.

Generally speaking, the global irradiance received by mountainous surfaces includes direct irradiance, diffuse irradiance, and reflected irradiance from the surrounding terrain. However, the proposed GSV-SRTS model seems to only consider the first two components and does not account for the surrounding-reflected radiationcontribution to the target pixel. This limitation needs to be pointed out in the conclusion.

Minors:
Terms such as "heterogeneous landscapes," "discontinuous canopies," and "patchy landscapes" are used in the paper. In the context of this study, could you more clearly define the spatial scales and structural characteristics these terms refer to, in order to avoid reader confusion?

The study area selected for this research features complex topographic conditions and high vegetation heterogeneity. How did the authors conduct field measurements to ensure the representativeness of the data obtained? Please supplement the explanation.

The paper clearly introduces the GSV and SRT modules, but could the beginning of the Methods section (Section 2.1) more explicitly elaborate on the core physical motivation and necessity for coupling the soil spectral vector (GSV) with the sloping terrain stochastic radiative transfer (SRT) theory? In other words, why is this coupling crucial for accurately simulating radiative transfer in heterogeneous mountainous landscapes?

In Section 3.1, the sentence "Finally, the remote sensing observations from different sensors were utilized for model evaluation to evaluate the suitability..." contains redundant phrasing and an unnecessary comma. Please change the sentenceand check the full text.

In Section 3.3, the construction "was set ranging from" is grammatically awkward, as the verb "set" typically takes a preposition like "to" for a fixed value. Additionally, starting a sentence with "And" is generally avoided in formal writing. Please check the full text for similar issues and make necessary revisions.

There is a minor tense inconsistency appears in Section 4.1: "The results showed that GSV-SRTS achieves the highest R² value..." The main verb "showed" is past tense, while "achieves" is present. For consistency in describing results, it is recommended to use the past tense.

In Section 4.4, the clause "which capture finer details in the microscale scenarios" is incorrectly linked to "the ability of the SRT theory and GSV model." The sentence structure is unclear.

There are issues with the citation format in several places, such as on page 2, line 41: sloping terrain (SLCT) (Verhoef and Bach, 2007) (Verhoef and Bach, 2012); lines51-52: Zeng et al. developed a RT model specifically designed for patchy landscapes based on SRT theory (Zeng et al., 2020).
Citation: https://doi.org/10.5194/egusphere-2025-5173-RC2
- AC2: 'Reply on RC2', Siqi Li, 13 Apr 2026
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2025-5173/egusphere-2025-5173-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-5173-AC2

Siqi Li, Guyue Hu, Shaoda Li, Ronghao Yang, Junxiang Tan, Chenghao Liu, and Jinhu Bian

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Short summary

The GSV-SRTS model simulates radiative transfer for heterogeneous mountain forests, addressing slope-induced uncertainties in remote sensing. It extends stochastic theory to slopes and integrates soil spectral vectors. Validations with benchmark models and satellite data confirm its accuracy in red/NIR bands and its capability to capture canopy-terrain effects, offering a reliable tool for improved biophysical retrieval.


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