The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-2, 2018
ISPRS TC II Mid-term Symposium “Towards Photogrammetry 2020”, 4-7 June 2018, Riva del Garda, Italy
This contribution has been peer-reviewed.
https://doi.org/10.5194/isprs-archives-XLII-2-961-2018 | ©Authors 2018. CC BY4.0 License.
961
NUMERICAL SIMULATION AND EXPERIMENTAL VALIDATION OF WAVE PATTERN
INDUCED COORDINATE ERRORS IN AIRBORNE LIDAR BATHYMETRY
K. Richter 1 * D. Mader 1 , R Westfeld 2 , H.-G. Maas 1
1 Institute of Photogrammetry and Remote Sensing, Technische Universität Dresden, Germany -
(katja.richterl, david.mader, hans-gerd.maas)@tu-dresden.de
2 Federal Maritime and Hydrographic Agency (BSH), Section Geodetic-hydrographic Techniques and Systems, Germany -
(patrick.westfeld@bsh.de)
Commission II, WG II/9
KEY WORDS: Airborne LiDAR bathymetry, multimedia photogrammetry, refraction, wave pattern, accuracy analysis
ABSTRACT:
Airborne LiDAR bathymetry (ALB) requires a refraction correction on the basis of Snell’s law at the air-water interface and a speed-
of-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.
1. INTRODUCTION
Geometric modeling in airborne LiDAR bathymetry is signifi
cantly more complex than in conventional laser scanning since
the laser pulse is passing two different media. Due to the differ
ent refraction indices the direction and velocity of the laser pulse
propagation is changing at the interface surface between the two
media. Additionally, the laser ray is subjected to influences such
as beam spreading due to dispersion at small sedimentary parti
cles and organic materials and the diffuse reflection at the water
bottom, both contribute to a different light path towards the sen
sor. Figure 1 shows the refraction of the incident laser pulse based
on the local wave-induced water surface. In order to achieve a
geometric accurate representation of the water bottom a run-time
correction and a refraction correction on the basis of Snell’s law
has to be applied on the raw laser data. The refraction correction
requires exact information on the local water surface inclination.
As this information is usually not available, existing correction
methods introduce certain simplifications.
The most common correction method assumes a horizontal and
planar water surface at which the laser beam is refracted (Fig. 1,
purple). Even small deviations from the planarity, already caused
by moderate sea swell, can lead to a significant lateral displace
ment d,XYh z and height displacement dZhz- More complex cor
rection methods try to consider the actual water surface geometry.
For this purpose, some system providers apply a local water sur
face tilt (Fig. 1, red), e.g. based on the intersection of the incident
laser ray with a triangular mesh of detected water surface points
* Corresponding author
in their bathymetry data processing methods (Ullrich and Pfen-
nigbauer, 2011). If such a linear local tilt has been considered in
data processing, the effects of wave patterns on coordinate accu
racy will be reduced and the coordinate displacements dXYtut
and dZtut will be smaller.
Beside the simplifications concerning the water surface geome
try, both correction approaches are limited by the fact that the
laser ray is considered to be an infinitesimal small line only. Ef
fects caused by a finite diameter laser pulse penetrating a curved
surface are neglected. In contrast, our simulation approach inves
tigates the effect of waves patterns on LiDAR bathymetry water
body bottom coordinates under strict consideration of refraction
effects (Westfeld et al., 2017). For this purpose, the refraction of
finite diameter laser pulses passing the air/water interface is mod
eled differentially in a strict manner. The developed models can
be used to correct each individual laser pulse. Therefore, the re
construction of the actual water surface, for instance from dense
laser scanner points, is required. If this information is not avail
able, the simulation results can also be used to derive wave pat
tern dependent correction terms which cover systematic errors.
In our previous simulation studies we examined the effect of wave
patterns on refraction and subsequently on coordinate accuracy
for typical ocean wave patterns (Westfeld et al., 2017) as well as
riverine wave patterns (Westfeld et al., 2016). It has been shown
that, depending on sea swell and laser footprint size, the effect on
lateral bottom point displacement dXY^z can amount to several
decimeters, in some cases even meters in the planimetry coordi
nates of underwater points. Furthermore, height displacements
dZhz in decimeter range have to be taken into account.
