scholarly journals The stellar atmosphere physical system II. An operative sequential algorithm to solve the stellar atmosphere problem

2019 ◽  
pp. 1-11
Author(s):  
Lucio Crivellari
Keyword(s):  
Radiative Transfer ◽  
Physical System ◽  
Stellar Atmosphere ◽  
Sequential Algorithm ◽  
Transfer Equations ◽  
Non Linear ◽  
Local Problems ◽  
Equilibrium Constraint ◽  
Non Local ◽  
Radiative Transfer Equations

In this paper, the second and the last of the series, we present a sequential algorithm to solve the stellar atmosphere problem that may serve as a paradigm for the solution of more general non-linear and non-local problems. The Iteration Factors (IF) Method is applied to achieve a solution of the radiative transfer equations, consistent with the radiative equilibrium constraint.

scholarly journals A Refined Four-Stream Radiative Transfer Model for Row-Planted Crops

2020 ◽  
Vol 12 (8) ◽  
pp. 1290 ◽  
Author(s):  
Xu Ma ◽  
Tiejun Wang ◽  
Lei Lu
Keyword(s):  
Radiative Transfer ◽  
Computer Simulations ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Growth Stages ◽  
Canopy Reflectance ◽  
Transfer Equations ◽  
Radiative Transfer Equations ◽  
Different Growth Stages

In modeling the canopy reflectance of row-planted crops, neglecting horizontal radiative transfer may lead to an inaccurate representation of vegetation energy balance and further cause uncertainty in the simulation of canopy reflectance at larger viewing zenith angles. To reduce this systematic deviation, here we refined the four-stream radiative transfer equations by considering horizontal radiation through the lateral “walls”, considered the radiative transfer between rows, then proposed a modified four-stream (MFS) radiative transfer model using single and multiple scattering. We validated the MFS model using both computer simulations and in situ measurements, and found that the MFS model can be used to simulate crop canopy reflectance at different growth stages with an accuracy comparable to the computer simulations (RMSE < 0.002 in the red band, RMSE < 0.019 in NIR band). Moreover, the MFS model can be successfully used to simulate the reflectance of continuous (RMSE = 0.012) and row crop canopies (RMSE < 0.023), and therefore addressed the large viewing zenith angle problems in the previous row model based on four-stream radiative transfer equations. Our results demonstrate that horizontal radiation is an important factor that needs to be considered in modeling the canopy reflectance of row-planted crops. Hence, the refined four-stream radiative transfer model is applicable to the real world.

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