Modeling Forest Bidirectional Reflectance Distribution Function(BRDF)over Rugged Terrain

The anisotropic scattering property of land surface is characterized by bidirectional reflectance distribution(BRDF),which is essential for the retrieval of surface biophysical and biochemical variables from remote sensing observations.Surface albedo calculated by the integration of surface BRDF in the incident and viewing geometries,is crucial for surface energy budget and global climate change.Currently,remote sensing community provides a suit of BRDF/albedo products covering a variety of spatial and temporal resolutions.These products are highly accurate over horizontal terrain and plays key roles in climate change and land surface ecosystem models.However,such applications are still challenging over rugged terrain due to the remote sensing albedo products with low accuracy and large uncertainty,which are attributed to the following four key aspects.Firstly,an appropriate understanding of surface BRDF and its derivative variables is still lacking.Current physical canopy reflectance models adopt different BRDF definitions for rugged terrain.Secondly,a physical and simple BRDF model accounting for topographic effects is still lacking for sloping terrain,which leads to inaccurate canopy reflectance simulations,especially for shaded slopes receive only diffuse irradiance.Thirdly,the liner semi-empirical,kernel-driven BRDF models are most widely used for the operational retrieval of surface BRDF/albedo from remote sensing observations.However,topographic effects are neglected in current kernel-driven BRDF models,leading to considerable errors in BRDF/albedo products over rugged terrain.Fourthly,to evaluate the accuracy and uncertainty of remote sensing products,in situ observations are usually collected as direct or indirect ground reference truth.However,it is hotly debated that whether the radiometer should be installed horizontally or parallel to slope to collect downward and upward irradiances.In this study,we try to solve the four aforementioned challenges,which include proposing the physical definitions of BRDF and its derivative variables for rugged terrain,developing a physical BRDF model for discrete forest for sloping terrain,proposing a linear semi-empirical,kernel-driven BRDF model for sloping terrain,and exploring in situ albedo measurement technology for sloping terrain.(1)The physical definitions of remotely sensed reflectance quantities suitable for rugged terrain were proposed.Firstly,we defined the effective projection area along the illumination and viewing geometries,quantified the multiple scattering among slopes.Thus,we defined a physical radiance reflected by target surface that fulfills with the energy budget conversation.Secondly,the heterogeneous incident irradiance was normalized by a virtual horizontal reference plane,for example,placed on the highest points on the target terrain.Then,the relationships among BRDFs across multiple spatial scales were proposed by the radiosity and geometric optical theories.Finally,the BRDF and its derivative variables were defined for rugged terrain.These definitions are suitable for randomly heterogeneous surface as they account for the topographic effects.To advance the development of physical BRDF models and their operational usage,we simplified the calculation of multiple scatterings among different slopes.(2)A discrete forest anisotropic reflectance over a sloped surface with an extended GOMS and SAIL(GOSAILT)model was proposed.The tree gravidity effect that growing upward rather than perpendicularly to local slope,was adopted to modify the areal proportion calculations of four scene components.The SAIL radiative transfer model and discrete canopy gap model for sloping terrain were coupled to characterize the spectral properties of scene components.The proposed model is suitable for the reflectance simulations of sunlit and shaded sloping surfaces.Compared with DART simulations and WIDAS observations,GOSAILT performances much better than the other canopy reflectance models which neglect the geotropic nature of vegetation and diffuse irradiance.(3)A semi-empirical kernel driven model for sloping terrain(KDST)was developed.The geometric optical kernels suitable for direct and diffuse illuminations were derived from the physical GOSAILT model.The volumetric scattering kernels suitable for direct and diffuse illuminations were derived from the physical Ross radiative transfer over sloping terrain.Similar to the RTLSR model for horizontal terrain with only three kernel parameters retrieved by the least square method,the proposed KDST model has a good capability in reflectance characterization for sloping terrain.It is promising for remote sensing BRDF/albedo retrieval over rugged terrain.(4)The effects of radiometer orientations on in situ albedo measurements over sloping terrain were explored.We characterized the downward and upward irradiances received by the horizontal and slope-parallel radiometers and calculated the corresponding albedo.Then,we investigated the factors that control these albedo patterns and their daily variations,as well as the conversion between horizontal and slope-parallel radiometers measured albedo.Finally,the albedo measured by radiometer with different orientations was used to analyze their effects on the upward irradiances.The proposed albedo characterizations over sloping terrain are potential for the collection of albedo ground truth over rugged terrain because they do not imply additional assumptions on the target surface.To advance the quantitative land surface remote sensing over rugged terrain,we extended and updated the physical definitions of remotely sensed reflectance quantities,developed a physical discrete canopy reflectance model,proposed a semi-empirical kernel-driven reflectance model,and explored in situ measurement strategy over rugged terrain.These efforts are helpful for the reflectance product standardization and validations,and retrieval of surface biophysical parameters over rugged terrain.