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Abstract
The canopy reflectance model is the physical basis of remote sensing inversion. In canopy reflectance modeling, the geometric optical (GO) approach is the most commonly used. However, it ignores the description of a multiple-scattering contribution, which causes an underestimation of the reflectance. Although researchers have tried to add a multiple-scattering contribution to the GO approach for forest modeling, different from forests, row crops have unique geometric characteristics. Therefore, the modeling approach originally applied to forests cannot be directly applied to row crops. In this study, we introduced the adding method and mathematical solution of integral radiative transfer equation into row modeling, and on the basis of improving the overlapping relationship of the gap probabilities involved in the single-scattering contribution, we derived multiple-scattering equations suitable for the GO approach. Based on these modifications, we established a row model that can accurately describe the single-scattering and multiple-scattering contributions in row crops. We validated the row model using computer simulations and in situ measurements and found that it can be used to simulate crop canopy reflectance at different growth stages. Moreover, the row model can be successfully used to simulate the distribution of reflectances (RMSEs < 0.0404). During computer validation, the row model also maintained high accuracy (RMSEs < 0.0062). Our results demonstrate that considering multiple scattering in GO-approach-based modeling can successfully address the underestimation of reflectance in the row crops.
Highlights
IntroductionThe canopy modeling of crops based on the row model can more accurately estimate the seasonal changes of biophysical canopy parameters in remote sensing [1]
In recent canopy modeling studies, row modeling has been extensively studied
There are two subproblems to be dealt with for the single- and multiple-scattering contributions: (1) How can we address the issue of ignoring the geometric characteristics of independent canopies in the establishment of multiple-scattering equations using the RT approach? (2) How can we establish a gap probability approach that considers the overlapping relationship between leaves and canopy closures and addresses computational deviations in the reflectance near the hotspot in a single-scattering contribution? we introduced the adding method and the mathematical solution of integral radiative transfer equation into row modeling
Summary
The canopy modeling of crops based on the row model can more accurately estimate the seasonal changes of biophysical canopy parameters in remote sensing [1]. The GO approach can describe the geometric characteristics of an individual canopy It is most suitable for heterogeneous canopy modeling [3]. The RT approach is based on volume scattering in the radiative transfer equation It is very suitable for describing the scattering issue in canopies [7]. The row crop is a heterogeneous canopy It has the typical geometric characteristics of an individual canopy, such as row structure (e.g., height, row width, between-row distance, etc.) [8,9,10,11]. Considering the advantages of accurately describing the row structure, the GO approach is widely used in the canopy modeling of row crops [9,10,12]
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