e New data can be interpolated to a new grid
spacing and old data rejected.
e New and old data can be interpolated to a new
grid spacing and merged.
Half of the above listed updating strategies include
rejection of existing data from the data base and re-
placement with new sampled z-values. This may be a
critical action since the old data still contain informa-
tion on the terrain and can contribute to the data ba-
se. Of course, old data must be rejected if the eleva-
tion data base is updated in an area where any activi-
ty has changed the shape and the elevation of the ter-
rain. However, an updating often takes place because
new data of a higher quality or density are available
in a limited area without any changes of the terrain
surface.
The most general situation occurs when new and old
data are interpolated to a new grid and merged. This
involves 2 interpolations and a merging operation
between the interpolated data and can be desribed as
(1)
Zhase = À Zo,int + b- Zn,int
where z,4,, denotes z-values in the updated data ba-
se, Z, ;,, are old z-values and Z, int NEW values inter-
o,in
polated to the same grid point. The factors a and b re-
present the merging operation.
MERGING OLD AND NEW DATA
It could be claimed that the interpolation and mer-
ging should be looked at as a single operation. On the
other hand, it is obvious that the construction of a
new grid from old grid data and new sampled z-valu-
es situated at other positions includes a distance de-
pendent component which in this context is identified
as the interpolation procedure. The interpolation of
DEM data has been discussed extensively and in gre-
at detail by several authors. It should only be mentio-
ned that interpolation in triangular networks (TIN)
and least squares prediction seem to be the most po-
pular interpolation methods when a simple linear ap-
proach is not sufficient. So, the following discussion
will focus on the merging of old and new data, assu-
ming that the z-values have the same position.
In the area to be updated, the merging can be reali-
zed by applying a weight function to the old and new
data considering the individual accuracies of the da-
ta:
(2)
Zbase 7^ Wo: Zo t Wn: Zn
A satisfactory solution is the weighted mean value in-
troducing the variances of the two data sets.
dr zo lm
=~ 09 On
Zbase = 1 1 (3)
E + =e
c2 o2
This approach requires information on the quality of
528
the existing data base as well as the new data. It is
assumed that the variances include contributions
from the interpolation if such a procedure is applied.
The weight function works properly in the updating
area, and in the case of the new data being signifi-
cantly better than the existing data base, the new da-
ta will dominate the updated data base.
The result is probably a non-homogeneous data base
as regards point density, but the quality of the data
will also change suddenly when the border between
old and new data is crossed. This is illustrated in fi-
gure 2 by the change in standard deviation.
o
O1 pe
\
\
\
027 LU
a 2
p £m
d d
ER BE
OR DA
Figure 2.
In the updated elevation data base the variance is
most likely to change suddenly from one area to anot-
her.
It is recommended that an overlap is created which
can serve as a buffer zone between the existing data
base and the updated area. In the buffer zone, a smo-
oth transition between two areas with different vari-
ances can be established, while a change in grid spa-
cing, of course, has to be accepted as a discontinuity.
In case the old data in the updated area are comple-
tely replaced by new data, a "fidelity" measure can be
estimated in the buffer zone, and possible discrepan-
cies revealed. Small deviations can be eliminated by
an adjustment.
Similar to the interpolation, a distance dependent
weight function is introduced across the buffer zone
in order to ensure a smooth variance function in the
data base. A linear transition is obtained by
Zbuffer 2 Z1: (1- m + Zo: (C) (4)
where z, 2 zj4 and Z9 = Zpase from expression (3). The
distance from the outer border of the buffer zone is
denoted x, and b is the width of the zone. The corres-
ponding standard deviation function is illustrated in
figure 4. Obviously, the shape has become smoother,
