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. 
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Figure 1. Refraction based on the true local water surface (blue), a assumed horizontal water surface (purple) and a assumed locally 
titled water surface (red) resulting in a lateral displacement dXYhz and dXY t n t and a height displacement dZh z and dZ t n t . 
This contribution complements the numerical simulation by an 
experimental validation of wave pattern induced coordinate er 
rors for a real world scenario. The aim of the paper is to examine 
how the coordinate errors predicted in our simulation correspond 
to the errors derived from real measurement data acquired from 
a 12 by 50 meter open air wave pool. For this purpose, we apply 
the most simple refraction correction method assuming a hori 
zontal water surface as well as the more complex refraction cor 
rection method with local surface tilt on the raw measurement 
data. We compare the refraction corrected data with terrestrial 
reference data to assess the coordinate errors remaining in the 
data after conventional refraction correction. The depth coordi 
nates displacement is derived from the data on the pool bottom 
whereas planimetric coordinate displacements can be determined 
from points on the pool wall. In addition to the analysis of the 
measurement data we use our simulation to predict systematic 
coordinate errors with respect to both refraction correction meth 
ods mentioned above. For this purpose, we expand our modeling 
approach to the local water surface tilt based on our previous find 
ings referring to a horizontal water surface. By choosing suitable 
simulation parameters we can reproduce the wave pattern like it 
is actually present in the measurement data. 
The paper is structured in the following way: Section 2 briefly 
describes the experimental setup and the acquired reference and 
measurement data. The methods for numerical simulation and 
experimental validation are given in section 3 and 4. In section 
5, the results are presented and discussed whereas section 6 sum 
marizes the work and addresses future tasks. 
2. EXPERIMENTAL SETUP 
For the experimental investigations we chose an open air wave 
pool which has a total length of 50 m and a width of 12 m. With 
its wave generation possibilities as well as with its regular geom 
etry and good reflection properties, the pool seems well suited for 
a validation study. The bottom of the pool slopes from 0.3 m to a 
maximum water depth of 1.5 m (at horizontal water surface ). The 
wave machine produces regular waves with amplitudes of about 
0.5 m, which are characterized by braking crests and whitecaps 
especially in shallow water. The experimental setup offers con 
trolled examination conditions by reliably producing waves with 
known parameters, low water turbidity and a fixed precisely mea 
surable water bottom geometry. 
The reference data was collected by terrestrial laser scanning 
while the wave pool was empty. To achieve a dense represen 
tation of the water bottom geometry the pool was scanned with a 
Riegl LMS-Z420Ì from five different positions. Figure 2 shows 
the data acquisition as well as the resulting reference point cloud. 
The airborne survey campaign was carried out in the filled state 
under wavy as well as smooth water surface conditions (fig. 3). 
The LiDAR bathymetry data was acquired with a RIEGL VQ 
820G LiDAR system in different flying heights (500 m, 600 m, 
700 m) and flight directions (in direction of wave propagation and 
across). The laser beam divergence of 1 mrad results in a laser 
footprint with a diameter of approximately 0.5 m to 0.7 m at the 
water surface. Figure 3 shows a profile of the ALB point cloud 
under wavy conditions. 
3. NUMERICAL SIMULATION 
The numerical simulation of wave pattern induced effects on re 
fraction and thus on the planimetric and depth coordinates of wa 
ter bottom points requires water surface modeling, bottom surface 
modeling and ray path modeling. 
For the water surface modeling we used Tessendorf’s oceano 
graphic statistics based surface wave model for ocean waves 
(Tessendorf, 2001 ). The model treats each wave height as a ran 
dom variable of its planimetric position at a given time t. Based 
on Tessendorf’s model a height field is generated by means of 
Fast Fourier transform (FFT). The height field represents a realis 
tic ocean surface in the form of a dense regular grid. The charac-