Hancock, S., Armston, J., Li, Z., Gaulton, R., Lewis, P., Disney, M., Danson, F.M., Strahler, A., Schaaf, C., Anderson, K. & Gaston, K.J. (2015) Waveform lidar over vegetation: An evaluation of inversion methods for estimating return energy. Remote Sensing of Environment 164, 208-224.
Full waveform lidar has a unique capability to characterise vegetation in more detail than any other practical method. The reflectance, calculated from the energy of lidar returns, is a key parameter for a wide range of applications and so it is vital to extract it accurately. Fifteen separate methods have been proposed to extract return energy (the amount of light backscattered from a target), ranging from simple to mathematically complex, but the relative accuracies have not yet been assessed. This paper uses a simulator to compare all methods over a wide range of targets and lidar system parameters. For hard targets the simplest methods (windowed sum, peak and quadratic) gave the most consistent estimates. They did not have high accuracies, but low standard deviations show that they could be calibrated to give accurate energy. This may be why some commercial lidar developers use them, where the primary interest is in surveying solid objects. However, simulations showed that these methods are not appropriate over vegetation. The widely used Gaussian fitting performed well over hard targets (0.24% root mean square error, RMSE), as did the sum and spline methods (0.30% RMSE). Over vegetation, for large footprint (15 m) systems, Gaussian fitting performed the best (12.2% RMSE) followed closely by the sum and spline (both 12.7% RMSE). For smaller footprints (33 cm and 1 cm) over vegetation, the relative accuracies were reversed (0.56% RMSE for the sum and spline and 1.37% for Gaussian fitting). Gaussian fitting required heavy smoothing (convolution with an 8 m Gaussian) whereas none was needed for the sum and spline. These simpler methods were also more robust to noise and far less computationally expensive than Gaussian fitting. Therefore it was concluded that the sum and spline were the most accurate for extracting return energy from waveform lidar over vegetation, except for large footprint (15 m), where Gaussian fitting was slightly more accurate. These results suggest that small footprint (≪ 15 m) lidar systems that use Gaussian fitting or proprietary algorithms may report inaccurate energies, and thus reflectances, over vegetation. In addition the effect of system pulse length, sampling interval and noise on accuracy for different targets was assessed, which has implications for sensor design.