An Introduction to the Physical Basis for Deriving River Information by Optical Remote Sensing - Fluvial Remote Sensing for Science and Management - page 63

bathymetric contour interval. The width of these contour
intervals, which can be defined as the sum of the smallest
detectable increase in depth and the smallest detectable
decrease in depth, depends on the radiometric resolution
of the imaging systemand the brightness contrast between
the bottom and the water column. If the reflectance of
the streambed and the optical properties of the water col-
umn are assumed constant, bathymetric precision (i.e.,
contour interval width) can be treated as a function of
sensor characteristics. A useful metric in this regard is the
noise-equivalent delta radiance

pure water implies that even small changes in depth
correspond to large changes in radiance. The strength
of absorption also dictates that at greater depths the
radiance signal will saturate, with additional increases in
depth producing very small changes in radiance that will
not be detectable by many imaging systems.
Legleiter and Roberts (2009) incorporated these con-
cepts into a forward image model that allows depth
retrieval accuracy and precision to be examined for a
particular river of interest and a given sensor configu-
ration. An application of the forward image model to a
gravel-bed river is shown in Figure 3.10, which indicates
considerable variation in bathymetric accuracy and preci-
sionwithin the channel. In essence, this approach involves
simulating an image from the streambed up by combining
information on bed topography, bottom reflectance, and
water column optical properties with numerical mod-
els describing radiative transfer in the water column and
atmosphere. The forward imagemodel can thus be used to
assess, a priori , the utility of image data for specific appli-
cations in river research and management. This study
demonstrated that the reliability of image-derived depth
estimates is strongly dependent on channel morphology
and thus varies spatially. Sensor spatial resolution was the
primary control on bathymetric accuracy, with depths
tending to be underestimated in pools (i.e., yellow tones
along the left side of Figure 3.10a), while mixed pix-
els along shallow channel margins also made near-bank
depth estimates unreliable. For example, the bright red
tones along the lower (south) end of the mid-channel bar
indicate that large under-predictions of depth occurred
where pixels along the water's edge included relatively
bright, sandy sediment. Similarly, bathymetric precision
was determined mainly by sensor radiometric resolution,
with broader bathymetric contour intervals also occur-
ring in deeper water (i.e., green tones along the left side
of Figure 3.10b). This type of analysis can temper one's
enthusiasm regarding the potential for remote sensing of
rivers, but carefully considering the limitations as well
as the capabilities associated with this technology will
ultimately lead to more effective use of remote sensing in
fluvial environments.
Another important point with regard to sensor char-
acteristics is that the three types of resolution discussed
above are not independent of one another, but rather
intimately connected. Essentially, remote sensing involves
collecting photons and sorting them into different 'bins'
based on where they came from (spatial resolution) and
the wavelength at which they travel (spectral resolution).
In order for the photons collected in one of these bins to

), which is most
simply defined as the change in radiance equivalent to
one digital number, or the inverse of the number of possi-
ble discrete values. For example, a 12-bit imaging system
would have a smaller

Δ L N ( λ

=
0.00024Wm − 2 sr − 1 (integrated over the sensor band pass)
than a less sensitive instrument that records 8-bit data and
thus enables only 2 8

Δ λ

) proportional to 1/2 12 L N (

= 256 possible values. In practice,

Δ ) also depends on instrumental and environmen-

tal signal-to-noise characteristics and a more inclusive
definition would account for these other factors as well
(e.g., Giardino et al., 2007). In any case, this approach can
be used to characterise the inherent uncertainty associ-
ated with image-derived depth estimates. Building upon
earlier work by Philpot (1989), Legleiter et al. (2004)
showed that the magnitude of this uncertainty increases
as depth increases, as bottom reflectance decreases, and
as scattering predominates over absorption. This study
demonstrated that relatively precise depth estimates, with
uncertainties of

L N ( λ

5 cm, could be achieved in shallow
water with highly sensitive instruments but that uncer-
tainties of

<

30 cm would be associated with deeper water
and less sensitive detectors.
Closely related to the precision of depth estimates
is the dynamic range of depth retrieval. Philpot (1989)
reasoned that the maximum detectable depth occurs
where the difference between the measured at-sensor
radiance and the radiance from a hypothetical infinitely
deep water body is equal to the radiance corresponding
to one digital number. The bottom contrast between the
water column and substrate also exerts an important
control in this context. For the conditions examined by
Legleiter et al. (2004), the maximum detectable depth
ranged from approximately 0.5m in strongly absorbing
near-infrared wavelengths for a sensor with a relatively
large

>

) to over 5m in less strongly absorbing green
wavelengths for a more sensitive detector with a smaller
Δ

Δ L N ( λ

). These results highlighted a tradeoff between
precision and dynamic range. Depth estimates are most
precise in the near-infrared, where strong absorption by

L N ( λ