New method to determine the optimal canopy shape for shade fraction estimation


A study published in remote sensing designed a reflectance simulator to determine the optimal canopy shape for calculating shade fraction based on reflectance measured by satellite sensors. This is the first time that the optimal canopy shape has been determined for estimating shade fraction, and this study will improve the future accuracy of the global gross ground estimate (GPP).

Study: Shade modeling with voxel-based trees for Sentinel-2 reflectance simulation in tropical rainforest. Image Credit: GoncharukMaks/

Importance of the ghost fraction in estimating global terrestrial gross primary production

Tropical forests cover 45% of global forests and 34% of global gross primary productivity. However, it is difficult to estimate gross primary productivity using remote sensing due to the complex three-dimensional (3D) structure of forests and cloud contamination.

Geostationary satellites such as GOES and HIMAWARI have made it possible to capture cloud-free images. However, uncertainties remain due to complex forest structures.

Shade fraction is an important factor in determining leaf surface conductance, as it influences the net rate of photosynthesis and ultimately the GPP and light use efficiency (LUE) of the forest. .

Several studies have highlighted the importance of integrating the shade fraction induced by forest structure in LUE models. Yet limited efforts have made it difficult to use on a larger scale.

Methods for estimating the ghost fraction

Virtual forests estimate shadow fraction without 3D data. Estimation of daytime shadows is another advantage of using virtual forests. A virtual forest is often used to derive an equation that relates the physical quantity of a forest to the reflectance measured by a satellite sensor.

The shape of the canopy is an important factor in determining shade fraction. Cones and ellipsoids are used to illustrate the canopy morphologies of coniferous and deciduous forests.

However, the canopy shapes of tropical rainforests with different tree species are unknown. Therefore, the optimal canopy shape for virtual woods needs to be determined to estimate the shade fraction.

The reflectance measured in the two-way reflectance distribution function is significantly affected by the shade fraction produced by the forest surface. Therefore, it is expected that the virtual forest with the lowest reflectance simulation error would be able to predict the shadow fraction of the real forest.

Determining the optimal canopy shape for shade estimation

The purpose of this study was to create a reflectance simulator and determine the optimal canopy shape for calculating shade fraction using the satellite sensor reflectance as a constraint.

The target is evergreen tropical forest, representing 58% of tropical forests. Initially, the impacts of canopy shape on reflectance simulation were examined using virtual forests with varying canopy shapes. This result was validated using Tukey’s significant difference test.

The optimal canopy shape was found by comparing Sentinel-2’s atmospheric reflectance to those simulated from virtual forests. Finally, the performance of the optimal canopy shape on shade fraction estimation was examined.

An unmanned aerial vehicle (UAV) was used to acquire parameters other than canopy shape and validate the estimated shade fraction.

Important Study Findings

The half-ellipsoid gave the best results, with the lowest root mean square error (0.0385) for the reflectance simulation. This canopy shape provided the most accurate estimates of shade fraction.

The half-ellipsoid showed lower reflectance than the ellipsoid, suggesting the impact of shadows created by the rounded lower part of the canopy. The reflectance of inverted half-ellipsoids and flat-topped cylinders was similar.

The influence of the shape of the canopy was insignificant when the zenith angle of the sun was 10oh, but it increased as this angle increased. In addition, there were notable variations in canopy shapes at Sun zenith angles greater than 20°.

For future estimates to be more accurate, it will be essential to reduce the uncertainty induced by phenology, simulation models and the development of virtual forests.

Limitations of the proposed study

Applying this study to forests with noticeable phenological fluctuations will be difficult due to the possibility that forest phenology may alter the shade fraction and the estimate of the simulated reflectance.

There are uncertainties in the design of virtual forests. The virtual forest was created using allometric equations and canopy development was assumed to be orthotropic. However, canopy shyness plays an important role in canopy closure. There could therefore be variations between virtual and real forest landscapes.

Future work

The proposed method can be applied to the boreal forest. However, boreal forests are sensitive to climate change and have asymmetrical canopy shapes. Therefore, it is crucial to improve the accuracy of Canopy Shadow and Reflectance Simulators (CSRS) by taking into account the asymmetric shape of the canopy, which will be more sensitive to real forests and contribute to the accurate estimation of shadow fraction.


Fujiwara, T., & Takeuchi, W. (2022). Shade modeling with voxel-based trees for Sentinel-2 reflectance simulation in tropical rainforest. remote sensing.

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