Numerical Simulation and Experimental Validation of Wave Pattern Induced Coordinate Errors in Airborne Lidar Bathymetry

Abstract

Airborne LiDAR bathymetry (ALB) requires a refraction correction on the basis of Snell’s law at the air-water interface and a speedof- light correction to be applied on the raw laser data in order to achieve a geometric accurate representation of the water bottom. Strictly speaking, this requires exact knowledge about the local water surface inclination. If this information is not available, certain simplifications have to be introduced in correction methods. Common correction methods assume either a horizontal or a locally tilted planar water surface as well as an infinitesimally small thin laser ray, thus neglecting effects caused by the finite laser pulse diameter penetrating a curved surface. In our simulation approach, the refraction of finite diameter laser pulses passing the air/water interface is modeled differentially in a strict manner. The simulation tool is able to predict wave induced coordinate errors which have to be expected due to the neglections made in common refraction correction methods. Moreover, wave pattern dependent correction terms were be derived from systematic portions of the errors revealed by the simulations. The goal of this paper is to experimentally validate the coordinate errors predicted by the simulation tool. For that purpose, airborne laser bathymetry data of a 12 by 50 meter open air wave pool were processed, and the results were compared to reference data of the empty pool acquired by terrestrial laser scanning. The comparison showed that the effects predicted in the numerical simulation are confirmed by the experimental validation.

Refined Geometric Modeling of Laser Pulse Propagation in Airborne LiDAR Bathymetry

“…The deviation between actual laser pulse propagation and conventional geometric modeling may cause considerable coordinate errors at the water bottom. The impact of the introduced simplifications on the water bottom point coordinates have been investigated in previous studies (Westfeld et al 2017;Richter et al 2018). We developed a laser bathymetry simulation tool to simulate data acquisition for arbitrary wave conditions, recording constellations, and sensors.…”

“…The comparison of the reference bottom point coordinates resulting from simulation and the bottom point coordinates resulting from geometric modeling allows the prediction of coordinate errors which have to be expected due to the assumptions made in the geometric modeling approaches. Table 1 (column 2 and 3) provides an overview of the simulations performed in Westfeld et al (2017) and Richter et al (2018) and the geometric modeling conceptions studied. In Westfeld et al (2017), both large footprint systems and small footprint systems are considered, while Richter et al (2018) focus on small-footprint systems.…”

“…Table 1 (column 2 and 3) provides an overview of the simulations performed in Westfeld et al (2017) and Richter et al (2018) and the geometric modeling conceptions studied. In Westfeld et al (2017), both large footprint systems and small footprint systems are considered, while Richter et al (2018) focus on small-footprint systems. Westfeld et al (2017) have shown that, depending on the sea state, beam divergence, and water depth, the effect on lateral bottom point displacement can amount several decimeters, in some cases even meters, in the planimetry coordinates of underwater points.…”

“…The effect on the height coordinate is in the decimeter range. Even with more complex water surface models, the deviations between the true water surface and the representation by the triangular mesh lead to coordinate errors at the water bottom (Richter et al 2018).…”

Detection and Extraction of Water Bottom Topography From Laserbathymetry Data by Using Full-Waveform-Stacking Techniques

“…The coordinates of the water surface point are taken from the original processed data obtained from the provider. On the basis of the direction vector X1 as well as the local water surface normal, calculated from neighboring water surface points (Richter et al, 2018), the refraction correction according to the Snell's Law is applied. Consequently, the new propagation direction X2 of the laser beam can be determined.…”