Predicting Leaf BRDF from Phenotypic Traits

Overview

Leaves do not reflect light equally in all directions. Their anatomy, pigments and microscopic surface roughness determine how light is scattered, and therefore how it is distributed inside a canopy, yet most canopy models treat leaves as Lambertian reflectors. Measuring the directional reflectance of every leaf is impractical.

This study develops a framework that predicts leaf optical properties from traits that are easy to measure. It combines a custom-built Directional Spectrum Detection Instrument (DSDI), Cook–Torrance bidirectional reflectance distribution function (BRDF) fitting, phenotypic measurements and ensemble learning, and then uses canopy ray tracing to quantify how the predicted optical properties change light distribution in a canopy.

At a glance

• Plant material: maize, rice, cotton, and poplar leaves from upper and lower canopy positions.
• Directional spectra: 400–1000 nm, measured across a broad angular range with the DSDI.
• BRDF parameters: roughness $\sigma(\lambda)$, diffuse reflection coefficient $k(\lambda)$, and refractive index $n(\lambda)$.
• Predictive model: a stacking ensemble built from support vector, random forest, and gradient boosting regressors.
• Performance: BRDF fitting $R^2 > 0.95$; ensemble prediction $R^2 = 0.83$–$0.99$, depending on the parameter.

Measurement and modeling workflow

1. Measure directional reflectance

The DSDI uses a xenon light source, a fiber spectrometer, and mechanically controlled illumination and viewing angles. A Lambertian white reference is used to calibrate reflectance before leaf measurements.

Both adaxial and abaxial surfaces were measured, since the two differ in epidermal structure and optical response.

2. Fit the BRDF model

The Cook–Torrance formulation represents diffuse and specular reflection with three wavelength-dependent parameters:

Parameter	Physical interpretation	Related leaf properties
$\sigma(\lambda)$	Microfacet roughness	Epidermal texture and surface irregularity
$k(\lambda)$	Diffuse reflection coefficient	Internal scattering and the diffuse contribution to reflectance
$n(\lambda)$	Refractive index	Refraction and interface reflection, influenced by tissue composition

Adaptive grid search and least-squares optimization were used to fit these parameters to the measured directional spectra.

3. Predict optical parameters from traits

The input variables included leaf thickness, specific leaf weight, pigment measurements, microscopy-derived surface roughness, and wavelength. The stacking model combines:

• Support Vector Regression (SVR)
• Random Forest Regression (RFR)
• Gradient Boosting Regression Trees (GBRT)
• Linear regression as the meta-learner

The model links measured phenotypic traits directly to BRDF parameters, so that leaf optical properties can be estimated without directional spectral measurement.

4. Canopy-scale effects

Predicted BRDF parameters were introduced into a rice-canopy ray-tracing workflow based on fastTracer. The simulations show that changing roughness, diffuse reflection, or refractive behavior can alter the vertical and angular distribution of light inside a canopy.

Main findings

1. Directional leaf reflectance can be represented accurately with a physically based BRDF model.
2. Structural and biochemical leaf traits contain useful information for predicting BRDF parameters.
3. Differences in leaf optical properties substantially change the simulated light field inside a canopy, so leaf optics should be represented explicitly rather than assumed uniform.

Together these results connect leaf-scale phenotyping to radiative-transfer and canopy-photosynthesis models.

Scope and limitations

The model was built from 270 data entries covering four species, two canopy positions and both leaf surfaces, and applies within the measured trait and wavelength ranges (400–1000 nm); new species and conditions require new measurements to extend it. The canopy simulations quantify changes in light distribution; linking them to field yield is a subsequent step. Extending the dataset to more genotypes, environments, developmental stages and water status is the next step of this work.

Code and data availability

• BRDF fitting scripts and Roughness Calculator
• fastTracer canopy ray-tracing software
• The study data are available from the corresponding author upon reasonable request, as stated in the published article.

Citation

Deng, L., Yu, L. X., Mao, L., Wang, Y., Guo, X., Wang, M., Zhang, Y., Song, Q., & Zhu, X.-G. (2025). Leaf bidirectional reflectance distribution function (BRDF) prediction with phenotypic traits in four species: Development of a novel measuring and analyzing framework. Plant Phenomics, 7(4), 100135. https://doi.org/10.1016/j.plaphe.2025.100135