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  2.  Empty  wave  pool  (a)  and  intensity  coded  reference
point  cloud  (b)  acquired  by  terrestrial  laser  scanning.

v  .»o-v-*v-  a

V.'CUtôK'MMi

(b)
Figure  3.  Swimming  pool  with  artificial  waves  generated  by  a
wave  machine  (a)  and  ALB  point  cloud  (b)  with  water  surface
points  in  blue  and  water  bottom  points  in  grey.

teristics  of  the  height  held  can  be  influenced  by  parameters  of  the
Fourier  grid  (width,  height,  mesh  size)  as  well  as  wind  conditions
(wind  speed,  wind  direction).  In  order  to  achieve  comparability
to  the  experimental  validation,  we  aim  at  reproducing  the  wave
pattern  like  it  is  actually  present  in  the  measurement  data.  For
this  purpose,  we  analyzed  the  wave  pattern  represented  by  the
measured  water  surface  points  to  derive  its  amplitude  and  wavelength. ­
  The  wave  amplitude  refers  to  the  vertical  distance  from
mean  level  to  crest  and  the  wave  length  specifies  the  horizontal
distance  from  crest  to  crest.  Subsequently,  we  choose  suitable
simulation  parameters  to  obtain  a  water  surface  model  with  similar ­
  properties.
The  bottom  surface  modeling  is  focused  on  the  plane  characteristic ­
  of  the  actual  pool  bottom.  We  deliberately  omit  the  slope
down,  since  the  predicted  measurement  errors  will  be  specified
in  percent  of  the  water  depth.  Therefore,  the  simulated  water  bottom ­
  is  generated  as  a  horizontal  plane  surface.
The  ray  path  modeling  is  realized  by  dividing  the  incident  laser
pulse  into  a  large  number  of  subbeams  representing  a  finite  footprint ­
  at  the  water  surface.  The  intensity  distribution  within  the
incident  laser  pulse  follows  a  Gaussian  intensity  profile.  The  refraction ­
  effects  at  the  air/water  interface  are  modeled  by  Snell’s
law  for  every  individual  subbeam.  Our  simulations  are  limited  to
identical  forward  and  backward  laser  pulse  paths  here.  Effects  of
diffuse  reflections  at  the  water  bottom  with  fractions  of  the  diffusely ­
  reflected  signal  accidentally  being  projected  towards  the
receiver  aperture  are  neglected.  The  final  ground  reflections  are
represented  by  the  intensity-weighted  centroid  of  all  individual
subbeams.
In  order  to  quantify  the  total  effect  of  waves,  the  simulations  compare ­
  laser  pulse  paths  resulting  from  the  refraction  at  the  local
wave-induced  water  surface  (fig.  1,  blue)  to  paths  resulting  from
the  refraction  at  the  horizontal  (fig.  1,  purple)  or  local  tilted  (fig.
1,  red)  water  surface  assumed  in  conventional  correction  methods. ­
  The  assumption  of  a  horizontal  water  surface  is  realized
by  local  horizontally  oriented  water  surface  elements  at  different ­
  heights  provided  by  the  water  surface  pulse  echoes.  For  the
locally  titled  water  surface  we  perform  a  Delaunay  triangulation
for  all  water  surface  points.  The  water  surface  point  density  is
adapted  to  the  distribution  actual  present  in  the  data  set.  The  incidence ­
  angle  a t n t  required  by  Snell’s  law  is  calculated  with  respect
to  the  surface  normal  of  the  triangle  intersected  by  the  incoming
laser  ray.

4.  EXPERIMENTAL  VALIDATION
The  experimental  validation  is  based  on  the  LiDAR  bathymetry
data  as  well  as  the  terrestrial  laser  scanner  data,  which  serve  as
reference  for  the  following  tests.  The  bathymetry  data,  acquired
in  the  airborne  survey  campaign,  is  provided  as  uncorrected  3D
point  cloud,  i.  e.  no  refraction  correction  and  run  time  correction ­
  was  applied  on  the  raw  data  set.  An  accurate  time  stamp  is
available  for  each  3D  point  in  addition  to  the  classification  in  water ­
  surface  and  water  bottom  points.  Furthermore,  information  on
the  sensors  trajectory  and  manufacturer  specifications  regarding
the  refractive  indices  of  air  and  water  are  accessible.
Based  on  these  information  we  apply  a  runtime  correction  and  the
simple  refraction  correction  method  assuming  a  horizontal  water
surface  as  well  as  the  more  complex  refraction  correction  method