International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B8, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
second momentum of area of the wave's three-dimensional
surface peak. Based on the mathematical equations below Egl
2. THE EXPLANATION OF METHODE AND
ALGORITHMS
As mentioned in the previous section, there are various
approaches to achieve the velocity and direction of surface
water waves in order to be used in the process of finding and
extracting properties and features of ocean surface waters. In
this paper concentration is on achieving the direction of surface
currents in coastal areas, and unlike the most of other common
works it is based on a geometrical method applied on the water
surface digital elevation model.
Surface DEM can be obtained by exerting interpolation or
Delaunay algorithms on a set of elevation points acquired from
a surface 1 51 P109] "This model has a variable extent depending
on vastness of points taken through radar scan in a single epoch
or several epochs got from techniques applied to discrete or gap
data !!!l, This model is a continuous surface of water surface
shape at the time of scan and displays the topography of water
which includes the wave peaks and lows.
There are 3 dimensional peaks and lows of small and large wave
length resulted from tide or surface winds or any other external
source of force. The surface winds produce waves with short
wave lengths which have different shapes depending on the
depth of water. So their shapes are different in the coastal or
near coastal areas in comparison with far shore waters.
The waters in the coastal and near coastal zones are much likely
to have an oriented wave shape and also with significant
elevation difference between waves peaks and lows. In the
presence of surface winds this shape deviates toward the wind
direction.
It is possible to construe information of external forces from
deformed shape of water wave. One of the information is
direction of external force applied to water surface. The
behavior analysis of this elevation model depends on the spatial
resolution of data attained from radar altimetry satellite.
Currently because of achieving high accuracy in satellite orbital
coordinates (with basic measurement accuracy in the range 2 cm
to 4 cm) [12][13] it is possible to have accuracy a few
centimetres over elevation coordinates which can help monitor
even not very strong surface currents.
Figure 1. a) A typically normal wave peak shape (Right) b) A
typically deformed wave peak shape by any external forces
In this paper it is assumed that the surface model of water is
available in the coastal areas. This surface model has peaks and
lows which can be described in detail. In the figl a wave peak is
displayed in both normal and deformed by external forces
shapes. Wave's peaks shapes in deep waters like oceans are
mainly symmetric figl-a but in low depth and coastal waters are
deformed and have an attitude in line with the wind's direction
fig1-b.
The method offered in this article takes profit of this behavior
and exerts mathematical analysis on it in order to find out
currents and consequently wind’s direction. The analysis is
related to the vector connecting points between the first and
the surface relative extremes can be found.
IT om fae ar Dice
;j "— LESQY,M IR
: s
By defining a local Cartesian coordinate system in the
neighborhood of the maximum point it would be easier to
perform computations on coordinates of points in a way which
its Z axis approximately and without much need of precision be
in line with gravity direction regardless of its direction and also
with an arbitrary X-Y plane orientation.
B
^.
: E.
-—X
Figure 2. A wave peak and its neighbour low points in a 2-D
view and the arbitrary local Cartesian coordinate
system
Having extremes location and performing the algorithm below
Eq2, it is possible to determine the maximum points limit range
to be used in the analysis Fig3.
A M em pex = #,
Hm=1/2{hb+ ih
Q)
Where H = Height
Hmin=Height of points of low in the neighbourhood of
a peak point.
By applying this algorithm, here comes a spatial shape like a
pork-pie hat.
A threshold is needed to specify the plane which is considered
as the removal border of its floor edges. These edges are
problematic in the procedure of locating the second surface
momentum in respective of first order point.
In this work by using normal distribution as a model for normal
shape of peak and its neighbourhood threshold plane, which is
perpendicular to Z axis of local coordinate system is located in
where, the volume between threshold plane and upper surface is
the 67% of its total volume. This is the amount of volume
between the cz. After exertion of these reductions on the
elevation surface, it results in a typical shape like below (Fig3).
Figures 3-a and 3-c display first order of surface momentum
point of resulted surface in a cross section of a plane
perpendicular to the X-Y plane. The first surface momentum of
a normal wave and an inclined one resulted of the impact of
surface winds are shown in the figures 3-b and 3-d respectively.
JE uri
Internation:
The second r
but indicate t
of momentun
obvious that
coincident wl
inclined and
second order
wave's peak i
the X-Y plar
coordinate Sj
coordinate sy
compute the
the coordinat
WI
Air
Figure 3. a)
surface
perpendicul
between su
point of res
of a plane
order of
normal way
X-Y plan
momentum
Cross se
