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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with local surface tilt on the raw measurement data. The assump 
tion of a horizontal water surface can be achieved by either a con 
stant mean water level height over the entire area of investigation 
or by local horizontally oriented water surface elements at differ 
ent heights provided by the water surface points. The following 
cases are analyzed: 
1. horizontally oriented water surface elements and constant 
mean water level height (MO 
2. horizontally oriented water surface elements and different 
local heights (M2 ) 
3. tilted water surface elements and different local heights (M3) 
In the first case, the water surface is represented by a plane, whose 
height is extracted from the measurement data acquired under 
smooth water surface conditions. In the two other cases we gener 
ate a mesh including the original water surface points with linear 
interpolation methods. The water surface is represented by a tri 
angulation of the mesh points. To realize the refraction correction 
we estimate the direction vector between each water bottom point 
and the corresponding trajectory point. Subsequently, the direc 
tion vector is intersected with the water surface. Please note, that 
the laser pulse is treated as an infinitesimal small line here. In 
case of the meshed water surface the local height is derived by 
linear interpolation between the vertices of the intersected trian 
gle. Finally, the direction of the laser ray is corrected applying 
Snell’s law. Considering the reduced velocity of light in water 
results in the corrected water bottom point coordinates. To evalu 
ate the correction results we analyze the differences between the 
coordinates obtained from the different correction methods. 
Furthermore, we compare the refraction corrected data with the 
terrestrial reference data to assess the coordinate errors remain 
ing in the data after conventional refraction correction. The depth 
coordinates displacement is derived from the data on the pool 
bottom whereas planimetric coordinate displacements can be de 
termined from points on the pool wall. In order to reference 
ALS and TLS point clouds we perform a rough registration with 
three homologous points in both point clouds followed by an ICP- 
based fine registration. The registration accuracy is in the range 
of several centimeters. 
5. RESULTS AND DISCUSSION 
5.1 Numerical Simulation 
In order to simulate the wave pattern, like it is actual present in 
the measurement data, we analyze the measured water surface 
points. For this purpose, we aggregate 50 cm wide sections of the 
water surface point cloud to profiles. Afterwards, we derive wave 
parameters by fitting a spline function into each profile. The max 
imum amplitude and the wave length arise from the local minima 
and maxima, representing wave crests and troughs. Figure 4 (a) 
shows a typical profile with a maximal wave amplitude of abso 
lutely 0.96 m (max. wave crest height 0.50 m, min. wave trough 
height -0.46 m). The maximal wave length is 8.00 m. The ori 
gin of the waves is on the right side, whereby the water depth 
grows with increasing X-coordinates. The mean water level is 
visualized as a horizontal line. Using appropriate simulation pa 
rameters, the actual wave pattern is reproduced as close as possi 
ble. Figure 4 (b) shows the corresponding profile. The maximal 
height of the wave crests is 0.46 m and the minimal height of the 
x[m] 
(b) simulation 
Figure 4. Water surface profile in measurement data (a) and 
simulation (b). 
wave troughs is -0.31 m resulting in an amplitude of absolutely 
0.77 m. The maximal wave length is 10 m. 
The simulation is run for 1000 consecutive epochs, taking into 
consideration the refraction at the local wave-induced water sur 
face as well as the refraction at the horizontal or locally tilted wa 
ter surface. The point density of the locally tilted water surface 
defines the representation accuracy of the triangulation. Due to 
the inhomogeneous distribution of the water surface points in the 
measurement data we consider two cases with 1 point per square 
meter (p/m 2 ) as well as 10 p/m 2 . 
The resulting coordinate displacements are presented in figure 5 
and table 1. As the effect of wave patterns on refraction increases 
linearly with water depth, all results are presented in percentage 
of the water depth. The coordinate displacements consist of both 
a lateral component dXY (red curve in fig. 5, row 1-3 in table 
T) and a depth component dZ (blue curve in fig. 5, row 4-6 in 
table T). 
The root mean square error (RMSE) of the lateral coordinate dis 
placement at a flying height of 500 m is 1.40% (max. 3.12%)of 
the water depth for the horizontal water surface. The locally tilted 
water surface with a point density of 1 p/m 2 results in a RMSE 
of 1.02% (max. 2.45%). Assuming a water depth of 1.6 m, a 
RMSE of 1.6cm (max. 3.9 cm) has to be expected in areas with 
low point density. The RMSE is reduced to 0.23 % (max. 0.64 %) 
corresponding to 0.4 cm (max. 1.0 cm) if the tilted water surface 
is represented by 10 p/m 2 . In summary, the lateral coordinate dis 
placements decrease with increasing complexity of the water sur 
face. The same applies to the other two flying heights, whereby 
the coordinate errors in planimetry decrease with increasing laser 
beam footprint. 
In general, the depth component of the coordinate displacement is