be correct and excludes other uncertainties, such as confusing deep waters for
shallow dark benthos.
A more general approach to quantify uncertainty is to apply a noise-perturbed
repeated analysis to determine multiple model solutions in every pixel (Hedley
et al. 2009b, 2010). Figure 4.8 illustrates uncertainty propagation in a physicsbased inversion algorithm applied to CASI and QuickBird data of Heron Reef,
Australia. In this case environmental noise has been characterized as the covariance matrix of reflectance over a deep water area. For each pixel in the image the
model has been inverted 20 times, with the pixel reflectance perturbed by a random
noise term each time. Hence for every pixel there are 20 estimates of depth, 20 of
benthic composition etc., from this 90 % confidence intervals can be calculated
giving error bars on every parameter for every pixel.
Figure 4.8 illustrates the value of 19-band CASI data over 4-band QuickBird
data. Both datasets are capable of supporting bathymetric estimations (Fig. 4.8f),
although the uncertainty for QuickBird starts to increase below 5 m. However,
only the CASI data can support any level of benthic type mapping (Fig. 4.8b and
c). Uncertainty for sand is low and visual interpretation indicates the estimated
values are sensible (corresponds to Fig. 4.8d). While CASI estimated coral cover
is reasonable (Figs. 4.8b and 4.7c), QuickBird has extremely high uncertainty for
benthic type (Fig. 4.8b and c) and the mean estimations are clearly in error. Note
that uncertainty applies to all components of the system, CASI has high uncertainty for water column absorption where the water is shallow and benthos is
heterogeneous (left of Fig. 4.7d), but water properties over deep substrate that is
clearly identifiable as sand are more certain (right of Fig. 4.8d).
Therefore the limit of what can be achieved in a particular remote sensing
objective is a function of both environmental variation or ‘noise’ and sensor
configuration and sensor noise (Fig. 4.9). Mapping benthic type by QuickBird is a
‘sensor-limited’ scenario (Fig. 4.9b) because it’s possible to do better with the
same analysis with hyperspectral CASI data (Figs. 4.8b and c). If perfect hyperspectral data with zero sensor noise were available, environmental variations
would be the limiting factor (Fig. 4.9c). The key question is, how far along the
scale with current sensor technologies are we to the ‘environmentally limited’
scenario? That is, could a new sensor with more or narrower bands, and better
signal to noise characteristics, lead to better or more consistent results in reef
mapping than have been demonstrated to date? In fact, modeling experiments
(Hedley et al. 2012b) suggest we are very close to the environmental limit. So the
next significant developments in coral reef remote sensing will most likely not be
in sensor technology, but in techniques that minimize uncertainties by exploiting
multiple sources of data, image time series and spatial patterns.
One way to reduce uncertainties and increase accuracy is to constrain the
possibilities embodied in the analysis. For example, certain benthic types have
known depth ranges, and so the solution that they occur in combination with
certain depths is unlikely. Fearns et al. (2008) used a Bayesian analysis in this way
to improve a habitat map derived from HyMap data of Ningaloo Reef in Western
Australia. Statistical approaches to combine ancillary data such as sonar (Bejarano
4 Hyperspectral Applications
105
shallow dark benthos.
A more general approach to quantify uncertainty is to apply a noise-perturbed
repeated analysis to determine multiple model solutions in every pixel (Hedley
et al. 2009b, 2010). Figure 4.8 illustrates uncertainty propagation in a physicsbased inversion algorithm applied to CASI and QuickBird data of Heron Reef,
Australia. In this case environmental noise has been characterized as the covariance matrix of reflectance over a deep water area. For each pixel in the image the
model has been inverted 20 times, with the pixel reflectance perturbed by a random
noise term each time. Hence for every pixel there are 20 estimates of depth, 20 of
benthic composition etc., from this 90 % confidence intervals can be calculated
giving error bars on every parameter for every pixel.
Figure 4.8 illustrates the value of 19-band CASI data over 4-band QuickBird
data. Both datasets are capable of supporting bathymetric estimations (Fig. 4.8f),
although the uncertainty for QuickBird starts to increase below 5 m. However,
only the CASI data can support any level of benthic type mapping (Fig. 4.8b and
c). Uncertainty for sand is low and visual interpretation indicates the estimated
values are sensible (corresponds to Fig. 4.8d). While CASI estimated coral cover
is reasonable (Figs. 4.8b and 4.7c), QuickBird has extremely high uncertainty for
benthic type (Fig. 4.8b and c) and the mean estimations are clearly in error. Note
that uncertainty applies to all components of the system, CASI has high uncertainty for water column absorption where the water is shallow and benthos is
heterogeneous (left of Fig. 4.7d), but water properties over deep substrate that is
clearly identifiable as sand are more certain (right of Fig. 4.8d).
Therefore the limit of what can be achieved in a particular remote sensing
objective is a function of both environmental variation or ‘noise’ and sensor
configuration and sensor noise (Fig. 4.9). Mapping benthic type by QuickBird is a
‘sensor-limited’ scenario (Fig. 4.9b) because it’s possible to do better with the
same analysis with hyperspectral CASI data (Figs. 4.8b and c). If perfect hyperspectral data with zero sensor noise were available, environmental variations
would be the limiting factor (Fig. 4.9c). The key question is, how far along the
scale with current sensor technologies are we to the ‘environmentally limited’
scenario? That is, could a new sensor with more or narrower bands, and better
signal to noise characteristics, lead to better or more consistent results in reef
mapping than have been demonstrated to date? In fact, modeling experiments
(Hedley et al. 2012b) suggest we are very close to the environmental limit. So the
next significant developments in coral reef remote sensing will most likely not be
in sensor technology, but in techniques that minimize uncertainties by exploiting
multiple sources of data, image time series and spatial patterns.
One way to reduce uncertainties and increase accuracy is to constrain the
possibilities embodied in the analysis. For example, certain benthic types have
known depth ranges, and so the solution that they occur in combination with
certain depths is unlikely. Fearns et al. (2008) used a Bayesian analysis in this way
to improve a habitat map derived from HyMap data of Ningaloo Reef in Western
Australia. Statistical approaches to combine ancillary data such as sonar (Bejarano
4 Hyperspectral Applications
105