Figure 8: Left, focally analysed layer generated from
1:10,000 photogrammetry DSM using SD function and a
3x3 kernel; right, focally analysed layer generated from
LiDAR DSM using SD function and a 3x3 kernel
Figure 9: Estimated Manning's » map from a feature
layer created from Fourier transform of 1:10,000
photogrammetry DSM using Gaussian low pass filter
4.2 Filtering Using Image Processing Techniques
An analysis of a variety of low pass filters were implemented
and figure 6 Left and Right show the DTM layer and figures 7
Left and Right show the feature layer (DSM - DTM). This is
the result from using a Fourier transform Gaussian low pass
filter. Note how well the surface features have been stripped.
A focal analysis processing was also implemented and of
particular interest was the standard deviation focal analysis. It
would be expected that a large standard deviation from a group
of pixels (points) would indicate a rough surface and a low
standard deviation a smooth surface. This suggests another
potential measure of roughness which might relate to
Manning’s coefficient of roughness see figures 8 Left and
Right.
4.3 Values of Manning’s ‘n’ Coefficient of Roughness
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Values for Manning’s ‘n’ for the test site were obtained from a
consultant flood modeller: water surface areas n = 0.010, rural
landscape n = 0.035, urban landscape n = 0.100. This is a very
coarse level of differentiation and what is proposed in this
research is not just automation of the determination of
Manning’s ‘n’ but also providing it at a much higher level of
detail. This increase in level of detail will mean extra
information for the hydraulic engineers and potentially an
increase in accuracy.
Chow (1973) presents one of several equations available which
relates Manning's 7 to the theoretical roughness of the water
boundary (3). It is arguable which is the best; this one has been
chosen for illustrative purposes.
oF (R/k)'$ Oy
— | m —— 3
k) 21.9log(12.2R/k)
where: n= the coefficient of roughness
$- the slope angle of the sides of the water
boundary
R= the hydraulic radius of the cross section of the
water boundary (ft)
k= the height of the roughness (in feet)
Chow (1973) further states that experimental studies showed
that the variation in the term @(R/k) is very small in a wide
range of variation of R/k. So, as an approximation the term
@(R/k) is considered as a constant with an average value of
Q(R/k) — 0.0342 where the units are in the ‘foot-pound-second’
system. Therefore, equation (4) takes the form:
where: k= the height of the theoretical roughness in feet.
R |, 1/6
n=@ —k" (4)
k
Digital surface models from airborne remote sensing can
provide a good estimation of Æ for small areas of interest.
4.4 Manning’s ‘n’ from DSMs
Using the spatial modelling technique available in ERDAS
IMAGINE 8.3, ArcView and equation (5) with the Gaussian
filter feature layer, maps of Manning's ‘n’ were produced from
both photogrammetry with 1:10000 scale photographs (see
figure 9 and LIDAR data.
n = 0.0342 k!"S (5)
4.5 Manning’s ‘n’ using the Focal Analysis and Standard
Deviation Process
Considering the focal analysis of the DSM’s using the standard
deviation function with the kernel size of 25x25 (pixels) it was
found there was a need to introduce a multiplying factor to
scale the values. The scaling factor was produced by
standardisation against the rural landscape values. As can be
seen in figures 10 and 11 the values in the urban area are rather
high.
S. CONCLUSIONS
The determination of Manning’s ‘n’ is at present largely based
on subjective judgement and is therefore influenced by all the
‘personal’ variation in the judgement that can occur. This
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