Leaf angle distribution (LAD) is an important vegetation parameter quantifying the structure of the canopy. Together with leaf area index, LAD is often assumed to fully describe the structure of herbaceous plant canopies such as field crops. To this date, only a few papers have addressed the direct estimation of LAD from near-nadir imaging spectroscopy data. Using simulations with the PROSAIL vegetation reflectance model and measurements of six field crops, we propose and evaluate two methods of determining leaf mean tilt angle (MTA), the central moment of LAD, from reflectance data in blue, red and near infrared wavebands. First, we noted that when canopy reflectance in blue (479 nm) is plotted against that in red (663 nm), the PROSAIL-simulated canopies with different MTAs occupied different areas in the plot. Similarly, the six crop species in the measured dataset were separated in the red–blue reflectance plane. To retrieve MTA from spectral reflectance measurements, we created rotated coordinate axes in the red–blue plane and aligned one of the axes with the largest change in MTA. The new coordinate, which was highly and near-linearly correlated with MTA (R2 = 0.97), was subsequently used to estimate MTA from airborne imaging spectroscopy data. The second MTA retrieval algorithm was based on earlier findings of a high correlation (R2 = 0.78) between MTA and reflectance at 748 nm. Using a lookup table created with PROSAIL, we inverted MTA from measured crop reflectance at this far red edge wavelength. We evaluated the two MTA retrieval methods using photographically measured species-specific MTA. For the red–blue method, MTA was estimated with a root mean square difference (RMSD) of 18.7° between field measured and spectroscopically estimated values. Retrieval from crop reflectance at 748 nm provided a RMSD of 11.4°. To demonstrate the generality of our methods, analyze their limitations, and explain the differences between the two retrieval algorithms, we give an analytical interpretation of the observed correlations using the spectral invariants theory.
- Imaging spectroscopy
- Leaf inclination angle distribution
- Radiative transfer model
- Spectral invariant theory