THE NEAR-SURFACE LAYER OF THE OCEAN
where RD
D is the drop rate density,
RD
T
D
V N D
. Since the inversion
matrix A is supposed to be known, using singular value decomposition
Equation (7.17) can be inverted as follows
T
A U V
/ ,
(7.18)
1
0
T
RD
D
V
U I
ª
º
/
¬
¼
,
(7.19)
which provides an estimate of the drop size distribution in the rain. Once a
drop size distribution is derived, the rain rate is calculated by integrating
over all drop sizes.
The sound spectrum produced by different sizes of droplets has some
specific features (Figure 7-15), which makes a straightforward application of
the inversion technique unrealistic. Nystuen (2001) proposed a constrained
inversion technique to address this problem. It takes into account the
following spectral features of the rain-generated sound:
1) The sound of drizzle, which has a peak at 13–25-kHz (Figure 7-13),
is only detected when raindrops larger than 0.8-mm diameter are
present in the rain, because drops smaller than 0.8 mm do not
produce a detectable sound signal and cannot be measured
acoustically. This sets the lower size limit for small raindrops. The
upper size limit for small raindrops is set to 1.2 mm (see Table 7-1)
based on laboratory studies.
2) Medium drop splashes, which do not generate bubbles (Table 7-1),
are relatively quiet. Whenever the rain contains drops larger than 2.0
mm, the sound levels below 10 kHz are much increased. Thus, the
lower size limit for large raindrops is set at 2.0 mm. Table 7-1
therefore defines the medium drop size to be 1.2–2.0 mm diameter.
The small drops are so much louder than the medium drops from 13
to 30 kHz that the sound signature for the medium drops had to be
interpolated through this frequency range. The signal from the
medium drops is small, though it appears to be louder than expected
from laboratory studies. Presumably, this sound is from the impact
of the drop onto the water surface and thereby is a broadband signal.
3) Large drops sound loud underwater. The sound generated by any
individual large drop is, however, at the very narrow bands
associated with any bubbles that are generated plus a broadband
signal from the impact. According to laboratory results, larger drops
produce, on average, larger bubbles. The largest bubbles tend to be
loudest, producing a spectral peak in the mean spectrum at the
476
ĺ
ĺ
where RD
D is the drop rate density,
RD
T
D
V N D
. Since the inversion
matrix A is supposed to be known, using singular value decomposition
Equation (7.17) can be inverted as follows
T
A U V
/ ,
(7.18)
1
0
T
RD
D
V
U I
ª
º
/
¬
¼
,
(7.19)
which provides an estimate of the drop size distribution in the rain. Once a
drop size distribution is derived, the rain rate is calculated by integrating
over all drop sizes.
The sound spectrum produced by different sizes of droplets has some
specific features (Figure 7-15), which makes a straightforward application of
the inversion technique unrealistic. Nystuen (2001) proposed a constrained
inversion technique to address this problem. It takes into account the
following spectral features of the rain-generated sound:
1) The sound of drizzle, which has a peak at 13–25-kHz (Figure 7-13),
is only detected when raindrops larger than 0.8-mm diameter are
present in the rain, because drops smaller than 0.8 mm do not
produce a detectable sound signal and cannot be measured
acoustically. This sets the lower size limit for small raindrops. The
upper size limit for small raindrops is set to 1.2 mm (see Table 7-1)
based on laboratory studies.
2) Medium drop splashes, which do not generate bubbles (Table 7-1),
are relatively quiet. Whenever the rain contains drops larger than 2.0
mm, the sound levels below 10 kHz are much increased. Thus, the
lower size limit for large raindrops is set at 2.0 mm. Table 7-1
therefore defines the medium drop size to be 1.2–2.0 mm diameter.
The small drops are so much louder than the medium drops from 13
to 30 kHz that the sound signature for the medium drops had to be
interpolated through this frequency range. The signal from the
medium drops is small, though it appears to be louder than expected
from laboratory studies. Presumably, this sound is from the impact
of the drop onto the water surface and thereby is a broadband signal.
3) Large drops sound loud underwater. The sound generated by any
individual large drop is, however, at the very narrow bands
associated with any bubbles that are generated plus a broadband
signal from the impact. According to laboratory results, larger drops
produce, on average, larger bubbles. The largest bubbles tend to be
loudest, producing a spectral peak in the mean spectrum at the
476
ĺ
ĺ