EFFECTS OF CLUMPING ON MODELLING LIDAR WAVEFORMS IN FOREST CANOPIES K. Calders a , P. Lewis b , M. Disney b , J. Verbesselt a , J. Armston c,d , M. Herold a a Laboratory of Geo-Information Science and Remote Sensing; Wageningen University; Droevendaalsesteeg 3, Wageningen 6708 PB, The Netherlands b Department of Geography; University College London; Gower Street, London, WC1E 6BT, UK c Remote Sensing Centre; Department of Science, Information Technology, Innovation and the Arts; Ecosciences Precinct, 41 Boggo Road, Dutton Park QLD, Australia, 4102 d Joint Remote Sensing Research Program; School of Geography, Planning and Environmental Management; University of Queensland; Brisbane, Australia, 4072 ABSTRACT Empirical relations are frequently used to derive leaf area in- dex (LAI). Such relations often make assumptions that make it hard to link the derived LAI to realistic trees and forest canopies. In previous work we developed a set of analyti- cal expressions to describe LiDAR waveforms with only a limited number of assumptions based on radiative transfer. These expressions were a function of crown macro-structure and LAI. The expressions were successfully tested when ap- plied on crown archetypes, but showed significant error when applied to more realistic crowns. In this study, we analyse the effect of clumping on inferring LAI from realistic trees. De- spite the potential of the expressions to detect subtle changes in LAI, absolute inferred LAI values can be significantly off. However, the strong correlation between true and inferred LAI (R 2 > 0.97) for the two test cases in this study, allows for calibration of the inferred LAI values. Index Terms— LiDAR waveforms, radiative transfer, canopy structure, LAI, clumping 1. INTRODUCTION Leaf area index (LAI) is an important structural parameter in forest ecosystems. LAI closely relates to several biologi- cal and physical processes such as respiration, transpiration, photosynthesis, carbon and nutrient cycle and rainfall inter- ception. LiDAR (light detection and ranging) is an active remote sensing technique that can measure something approximating the retroreflectance as a time or distance resolved signal. Li- DAR is therefore an excellent technique to assess forest struc- ture and the three-dimensional distribution of plant canopies [1, 2]. Large footprint LiDAR has the potential to infer forest structural information related to the physical characteristics of the trees. This is in contrast with the more commonly used empirical relations, which often make assumptions that make it hard to relate the inferred structural parameters to realistic forest canopies. Two types of LiDAR systems are commonly used: discrete return LiDAR and waveform LiDAR. Discrete return LiDAR measures only a limited number of pulses re- turning from a particular object. Waveform LiDAR digitises the whole of the return signal and it can therefore provide ad- ditional information about the structure of vegetation. 2. MODELLING LIDAR WAVEFORMS Modelling LiDAR waveforms is important to understand the effects of forest structure on deriving biophysical parameters. Previous studies on complex modelling approaches for Li- DAR waveforms mainly focused on understanding some of the influences on the LiDAR waveform. [3] presented a 3D model for simulating LiDAR waveforms over forest stands. Their results demonstrated that LiDAR waveforms contain information of both horizontal and vertical structure of for- est canopies. [4] introduced a time-dependent stochastic ra- diative transfer theory, which allowed for a more realistic de- scription of clumping and gaps. [5] used a hybrid geometric optical and radiative transfer model (GORT) to understand LiDAR waveforms with respect to canopy structure and vali- dated their results using SLICER data. In [6] we looked at single tree LiDAR waveforms in an ef- fort to understand the information content of such LiDAR sig- nals. The relation between canopy structure and LiDAR was studied and quantified in the nadir direction. We returned to a limited number of assumptions based on radiative transfer. These assumptions included crown archetypes, constant leaf area density throughout the crown and first order scattering. We developed a new set of analytical expressions to describe