Investigating assumptions of crown archetypes for modelling LiDAR returns

• We present analytical expressions to describe LiDAR waveforms from crown archetypes.
• We show parameter retrieval degrades as crowns depart from archetype assumptions.
• Clumping has a significant influence on the waveform inversion of realistic crowns.
• Inferred parameters can be deceptive due to real crown departure from archetypes.

LiDAR has the potential to derive canopy structural information such as tree height and leaf area index (LAI), via models of the LiDAR signal. Such models often make assumptions regarding crown shape to simplify parameter retrieval and crown archetypes are typically assumed to contain a turbid medium to account for within-crown scattering. However, these assumptions may make it difficult to relate derived structural parameters to measurable canopy properties. Here, we test the impact of crown archetype assumptions by developing a new set of analytical expressions for modelling LiDAR signals. The expressions for three crown archetypes (cuboids, cones and spheroids) are derived from the radiative transfer solution for single order scattering in the optical case and are a function of crown macro-structure (height and crown extent) and LAI. We test these expressions against waveforms simulated using a highly-detailed 3D radiative transfer model, for LAI ranging from one to six. This allows us to control all aspects of the crown structure and LiDAR characteristics. The analytical expressions are fitted to both the original and the cumulative simulated LiDAR waveforms and the CV(RMSE) of model fit over archetype trees ranges from 0.3% to 21.2%. The absolute prediction error (APE) for LAI is 7.1% for cuboid archetypes, 18.6% for conical archetypes and 4.5% for spheroid archetypes. We then test the analytical expressions against more realistic 3D representations of broadleaved deciduous (birch) and evergreen needle-leaved (Sitka spruce) tree crowns. The analytical expressions perform more poorly (APE values up to 260.9%, typically ranging from 39.4% to 78.6%) than for the archetype shapes and ignoring clumping and lower branches has a significant influence on the performance of waveform inversion of realistic trees. The poor performance is important as it suggests that the assumption of crown archetypes can result in significant errors in retrieved crown parameters due to these assumptions not being met in real trees. Seemingly reasonable inferred values may arise due to coupling between parameters. Our results suggest care is needed in inferring biophysical properties based on crown archetypes. Relationships between the derived parameters and their physical counterparts need further elucidation.