2004
2)
ics of
avelet
tique,
main.
avelet
htting
2 was
> was
pace-
ponds
scale,
9)
ith a
this
was
nded
nt to
| was
International Archives of the Photogrammetry, Remote Sensin
F(w)
60
50
40
PLA E,
) ; | d. n VET: T.
% 0.005 0.01 0.015 0.02 0.025 [Hz]
Fig. 6. Fourier spectrum (Path = 415, Row = 319, Jiparana)
F(w)
16
14 |
ty
0 ! pn : Y f A o ie ^ - €
0 0.005 0.01 0.015 0.02 0.025 [Hz]
Fig. 7. Fourier spectrum (Path=419, Row=3 15, Porto Velho)
scale
0 250
40 Wb, a)
50
60
70
80
0 20 40 60 80 100 120 140 160 180
Length [pixel]
Fig. 8. Space-frequency plane
(Path=415, Row=319, Jiparana)
0 60
W(b,a)
60
70
80
0. 20 40 60 80 100 120 140 160 180 200 220
Length [pixel]
Fig. 9. Space-frequency plane
(Path=414, Row=306, Manaus)
g and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
891
Furthermore, we calculated the averages of every Fourier
spectrum, wavelet's scale and level. Thus, we analyzed the
meandering of the river shapes, and obtained the average of
the spatial frequencies as follows.
Ez (4)
where j=a wavelet’s level or scale
w^ — average of spectral intensity
N = number of the level or scale
Finally, to compare these characteristics with the existing
discharge data, we derived each regression equation between
the Fourier power spectrum and the discharge, the wavelet's
scale and the discharge, the level and the discharge, and the
amplitude of the one-dimensional signal and the discharge.
Next, we obtained the macro scaled river characteristics from
the drainage map with 1:2,500,000 (Fig. 10). Namely, we.
analyzed the orders of drainage patterns with the Horton's rule,
and we calculated the numbers and the lengths of the branches
for each order. Moreover, we obtained the river slopes from
DEM. On the other hand, we estimated the river lengths and
the drainage area with the Hack's rule. Then, we supposed the
invisible rivers in the original images as an order of zero, and
estimated the river length, the drainage area, and the discharge
of the order of zero with the relationships from the order of
one to five (Figs. 11 to 13). Finally, we compared these results
with the micro scaled characteristics derived from the SAR
images.
3. RESULTS
We could obtain a good correlation between the discharge of
the Amazon River branches and the characteristics of the river
shapes. The derived regression equations are as follows.
Qui47x1050725 (R* 0.737)
Qz495x10 FT 4-612 (R^ 2 0.683) (5)
Q-149x10*CWT -9690 (R*>=0.819)
Q-3.65x10 DWT —9210 — (R? 20,817)
Q = discharge (m/s)
0 = amplitude of the one-dimensional signal (degree)
FT = Fourier power spectrum
CWT = continuous wavelet spectrum
DWT = discrete wavelet spectrum
where
Furthermore, the river characteristics of an order of zero
derived from a macro scaled drainage map were very similar
to the narrow open-water channels with less resolution derived
from SAR. Then, we showed the average of the numbers and -
the lengths of the branches for each order from the Madeira
river basin (Table 1), and the estimated numbers, lengths,
